Eindhoven University of Technology
MASTER
A machine learning approach for data-driven maintenance with the absence of run-to-failure
data
Koks, J.J.C.
Award date:
2021
Link to publication
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Department of Industrial Engineering and Innovation Sciences — Information Systems group
A machine learning approach for data-driven maintenance with the
absence of run-to-failure data
J. Koks (1395769)
Master of Science in Operations Management and Logistics
07 July 2021
Supervisors:
Dr. Y. (Yingqian) Zhang – TU/e First supervisor
Dr. H. (Rik) Eshuis – TU/e Second supervisor
Supervisors from company are known but hided
Abstract
This thesis proposes a way to apply data-driven maintenance, which is set up without run-to-failure
data. A choice was made to implement a predictive data-driven maintenance policy based on the
degradation trajectory. The most appropriate method is to work with a data-driven degradation
model based on a health indicator. Because the degradation of a specific part indicated by the
health indicator behaves as a linear line, we can set an arbitrary failure point. Because the
degradation is constant, substitution can be applied when run-to-failure data is gathered. The main
focus is on the predictability of the process. After comparing different machine learning algorithms
and finding the best settings in the data preprocessing, the Random Forest algorithm turned out
to be the best in terms of accuracy. Data-driven maintenance can reduce maintenance time,
material costs, and maintenance planning time, and maintenance costs. While on the other hand
can increase the equipment uptime and availability
ii
Executive Summary
Problem statement and research goal
This report results from a master thesis project at a healthcare company located in Europe, in
collaboration with the Eindhoven University of Technology. The project focuses on applying datadriven maintenance for a specific machine (deliberately unnamed), named machine Y, which
fabricates a specific product (deliberately unnamed). The company currently uses a time-based
maintenance policy for its maintenance activities at the specific machine. In this specific machine
there is a specific component, namely component X. Component X is an essential component
within this machine. There is no documentation on how many products component X can
manufacture before replacing them. When the first machine was purchased, a life span was
determined based on average production. The determination was already several years ago, and
internal aspects are changed over time. As a result, knowledge lacks what constitutes an
appropriate life span for component X.
Data-driven maintenance can reduce maintenance time, material costs, and maintenance
planning time, and maintenance costs. While on the other hand, it can increase the equipment
uptime and availability. The problem statement summarizes the research goal and its relevance:
Conducting maintenance activities is not optimized for effectivity and frequency and does not use
historic planned maintenance and event data to replace the component X in machine Y.
An improvement on the current situation (i.e., time-based policy) could be a different maintenance
policy like condition-based maintenance based on the data available. Condition-based
maintenance will decrease the number of maintenance moments that will lead to a higher
production capacity and lower maintenance costs. On top of that, the findings can be applied to
other similar production lines within the factories of the healthcare company. To improve the
current situation the main question was constructed, which helps to investigate possibilities of
using data to optimize the maintenance policy for component X. The main research question is:
How can the data currently measured within machine Y help implement a more data-driven
maintenance policy for component X?
iii
Performed activities in the project
For this project, we will use the CRISP-DM methodology. In contrary to other methodologies,
CRISP-DM focuses on data-related improvements or designs. Based on the steps of the CRISPDM methodology, the important findings per phase is described:
Business understanding + Data understanding: Based on the current time-based preventive
maintenance policy, component X are replaced before the actual failure of component X occurred.
Therefore, a characteristic of the absence of run-to-failure data characterizes the project.
Additionally, there is no direct measurement on the equipment (e.g., sensors that used
temperature, vibrations) but an indirect relationship that reflects the degradation of component X.
This indirect relationship is known but deliberately not noted for the public version of the Thesis.
Data preparation: All the datasets are integrated. All string variables are removed. Data is
reduced to a lower granularity to perform different tests. Based on different sliding time windows,
time-domain features are created. Lastly, odd maintenance moments were corrected. Different
time domain features are compared to find the most fitting health indicator for predicting the
degradation of component X. Evaluation of the health indicator is done based on monotonicity,
trendability, and correlation with the Remaining Useful Lifetime (RUL). The best performance
health indicator was removed due to company sensitive information when using hourly data (i.e.,
granularity) and using a sliding time window of one hour to create time-domain features. For
solving the problem of the absence of run-to-failure data, an arbitrary lower bound is set. Because
the degradation of component X indicated by the health indicator behaves more or less as a linear
relationship, we can substitute this arbitrary lower bound when run-to-failure data is gathered.
Because the degradation is constant, substitution can be applied, and the main focus is on the
predictability of the condition of component X.
Modeling: A comparison is made with simpler time series based solely on one parameter to
investigate if there is explainable behavior in the dataset. We compare that method with more
complex machine learning predictive models. For our implementation, we selected a Simple Linear
Regression, XGBoost, Random Forest, 1D-CNN, and LSTM for predicting the RUL of the
Component X and performed multiple experiments.
Evaluation: An in-depth comparison is made for each machine learning model compared to a
simple linear regression. The best performing algorithm is Random Forest, which has a Root Mean
iv
Squared Error (RMSE) of roughly 18 active production hours (RMSE in products known but
anomalized). For achieving those results, a data granularity of hourly data is used, and a hourly
sliding time window.
Deployment: The domain experts have indicated that they would like to get hold of the code of
the prediction model to make a prediction one to several times a week as to how long a specific
machine can produce. They can then schedule a time for the maintenance engineer to replace
Component X. When planning the maintenance, a safety margin equal to the average RMSE
should be included.
Results
At the beginning of this research project, the goal of the research project and the research
questions were defined. The main research question is:
How can the maintenance be more data-driven to optimize the current maintenance policy for
machine Y?
Based on the needs of the company, the knowledge of the process, and the gathered data of the
machine Y, a choice was made to implement predictive data-driven maintenance based on
degradation. However, the characteristics that made this project challenging are the absence of
run-to-failure data and indirect equipment measurement. The most appropriate method is to work
with a data-driven degradation model based on a health indicator. The health indicator was
evaluated based on trendability, monotonicity, and correlation with the RUL. The correlation
between the degradation of the health indicator and the degradation based on the RUL confirms
that the indirect measurement can serve as a health indicator for the component X. For solving
the problem of the absence of run-to-failure data, there using a relative arbitrary lower bound.
Because the degradation of component X indicated by the health indicator behaves as a linear
line, we can substitute this arbitrary lower bound when run-to-failure data is gathered. Because
the degradation is constant, substitution can be applied, and the main focus is on the predictability
of the process. After comparing different predictive models and finding the best settings in the data
preprocessing, the Random Forest algorithm became the best in terms of accuracy. An RMSE of
(RMSE in products known but anomalized), which means that a prediction can be made with an
error of roughly 18 active production hours. A note to implement the data-driven maintenance
policy, run-to-failure data must be collected to ultimately find the true point of failure to establish
the lower bound.
v
Preface
This thesis serves as the conclusion of my Master Operational Management & Logistics, which I
have been following for 2,5-3 years. I would also like to thank the company for allowing me to
apply the knowledge I have gained in the field.
First, I would like to thank my mentor, Dr. Yingqian Zhang, for her guidance throughout the project.
The joint meetings with other students on Wednesday morning always supported showing
intermediate results and receiving feedback. Also, fellow students' projects were a nice touch,
which made you think about possible methods I could apply in my project. Secondly, I would like
to thank Ya Song for the individual moments to help me with different questions regarding
predictive maintenance. I would also like to thank Dr. Rik Eshuis for his feedback on my draft
version of my Thesis.
Secondly, I would like to thank my supervisors from the company, individuals and
acknowledgments have been removed due to company sensitive information
Finally, I would like to thank my family, girlfriend, friends, and fellow students. Who supported me
and provided sufficient distraction during my internship period in social isolation.
Eindhoven, July 2021
Jelle Koks
vi
Contents
Abstract ..........................................................................................................................................................ii
Executive Summary ....................................................................................................................................... iii
Problem statement and research goal ...................................................................................................... iii
Performed activities in the project............................................................................................................ iv
Results ........................................................................................................................................................v
Preface........................................................................................................................................................... vi
List of Acronyms ............................................................................................................................................. x
List of Figures................................................................................................................................................. xi
List of Tables ................................................................................................................................................. xii
List of Equations ........................................................................................................................................... xii
Part I – Introduction & Problem Description................................................................................................. 1
1.
Introduction ........................................................................................................................................... 1
1.1
Context: Company ......................................................................................................................... 2
1.1.1
Production line and product produce .................................................................................. 2
1.1.2
A deeper understanding of Machine Y .................................................................................. 3
1.1.3
Data availability ..................................................................................................................... 5
1.2
Problem description ...................................................................................................................... 7
1.2.1
Problem formulation ............................................................................................................. 7
1.2.2
Research Questions and research method per question ...................................................... 8
1.2.3
Scope ................................................................................................................................... 10
1.2.4
Research design ................................................................................................................... 11
Part II – A literature overview ..................................................................................................................... 13
2.
Literature Review ................................................................................................................................ 13
2.1
Maintenance................................................................................................................................ 13
2.1.1
Maintenance strategies ....................................................................................................... 13
2.1.2
Different condition-based maintenance strategies as predictive maintenance ................. 15
2.1.3
Answering sub research question Q-1 ................................................................................ 19
2.2
Process of data-driven strategy................................................................................................... 19
2.2.1
Process of prognostics ......................................................................................................... 19
2.2.2
Impact of missing labels ...................................................................................................... 21
2.2.3
Answering sub research question Q-3 ................................................................................ 23
2.3
Predictive models used in data-driven maintenance .................................................................. 24
vii
2.3.1
Statistical approaches.......................................................................................................... 24
2.3.2
Machine learning approaches (AI approaches) ................................................................... 25
2.3.3
(Deep) Transfer Learning ..................................................................................................... 27
2.3.4
Quality measures ................................................................................................................. 28
2.3.5
Answering sub research question Q-4 ................................................................................ 28
2.4
Conclusion of literature review ............................................................................................... 29
2.4.1
GAP in literature .................................................................................................................. 29
Part III – Data exploration, understanding, preparation ............................................................................. 30
3.
Data exploration .................................................................................................................................. 30
3.1
4.
Descriptive statistics .................................................................................................................... 30
3.1.1
Product dataset ................................................................................................................... 30
3.1.2
Process dataset.................................................................................................................... 32
3.2
Production and incidents per period........................................................................................... 34
3.3
Failure rate during lifetime of Component X .............................................................................. 35
3.4
Seeking trends in data ................................................................................................................. 35
3.5
Analyzing maintenance moments ............................................................................................... 38
Data preparation ................................................................................................................................. 39
4.1
Data integration .......................................................................................................................... 39
4.2
Data cleaning ............................................................................................................................... 39
4.2.1
Handling outliers and missing data ..................................................................................... 40
4.2.2
Adjusting maintenance moments ....................................................................................... 40
4.2.3
Selection of applicable production periods......................................................................... 40
4.3
Data transformation .................................................................................................................... 41
4.4
Feature selection ......................................................................................................................... 42
4.5
Data reduction ............................................................................................................................. 42
4.6
Conclusion data exploration........................................................................................................ 42
Part IV – Modeling ....................................................................................................................................... 43
5.
6.
Experimental setup ............................................................................................................................. 43
5.1
Heal indication construction ....................................................................................................... 43
5.2
Health stage division ................................................................................................................... 46
5.3
RUL prediction ............................................................................................................................. 47
Modeling.............................................................................................................................................. 50
6.1
Linear Regression ........................................................................................................................ 50
viii
6.2
Decision Tree ............................................................................................................................... 50
6.2.1
Gradient boosted regression tree (XGBoost) ...................................................................... 51
6.2.2
Random Forest .................................................................................................................... 52
6.3
Convolutional neural network..................................................................................................... 53
6.4
Long-short-term-memory ........................................................................................................... 55
Part V – Results............................................................................................................................................ 59
7.
8.
9.
Results ................................................................................................................................................. 59
7.1
Comparison of different predictions prediction models for RUL ................................................ 59
7.2
Impact of the determination of the lower bounds ..................................................................... 65
7.3
Impact of data granularity and sliding time window .................................................................. 66
7.4
Impact of filtering the data on production cell-level .................................................................. 67
7.5
Impact of adding process data as features ................................................................................. 67
7.6
Conclusion of experiments .......................................................................................................... 67
Conclusion ........................................................................................................................................... 68
8.1
Conclusion ................................................................................................................................... 68
8.2
Recommendations....................................................................................................................... 70
Future opportunities and implementation ......................................................................................... 71
9.1
Implementation on the work floor .............................................................................................. 71
9.2
Experiment with run-to-failure data ........................................................................................... 72
9.3
Created capacity and saved costs ............................................................................................... 74
References ................................................................................................................................................... 75
Appendix A: ................................................................................................................................................. 79
Appendix B: ................................................................................................................................................. 80
Appendix C: ................................................................................................................................................. 81
Appendix D: ................................................................................................................................................. 82
Appendix E:.................................................................................................................................................. 83
ix
List of Acronyms
ANN
Artificial Neural Network
ARMA
Auto-Regressive Moving-Average
CBM
Condition based maintenance
CNN
Convolutional Neural Network
CRISP-DM
Cross-Industry Standard Process for Data Mining
DT
Decision Tree
DBM
Detection based maintenance
GB
Gradient Boosting
HI
Health Indicator
HS
Health stage
LR
Linear Regression
LSTM
Long Short Term Memory
MAPE
Mean Absolute Percentage Error
PdM
Predictive Maintenance
RF
Random Forest
RMSE
Root Mean Squared Error
RUL
Remaining Useful Lifetime
SVR
Support Vector Regression
XGBoost
eXtreme Gradient Boosting
x
List of Figures
Figure 1.1 Product Z ...................................................................................................................................... 2
Figure 1.2 Production line of the Product Z .................................................................................................. 2
Figure 1.3 Pocket within EDM-unit ............................................................................................................... 3
Figure 1.4 Clamping jaws in pocket ............................................................................................................... 3
Figure 1.5 Electrical contact .......................................................................................................................... 3
Figure 1.6 New contact spring ....................................................................................................................... 4
Figure 1.7 Worn-out contact spring .............................................................................................................. 4
Figure 1.8 parameters Product Z ................................................................................................................... 6
Figure 1.9 Structure of sub-research questions ............................................................................................ 8
Figure 1.10 CRISP-DM methodology ........................................................................................................... 11
Figure 2.1 Categorization of maintenance policies (Avontuur, 2017) ........................................................ 14
Figure 2.2 Different condition-based maintenance strategies ................................................................... 16
Figure 2.3 General approach of prognostics, Abid et al. (2018) ................................................................. 20
Figure 3.1 Boxplot of each parameter for each machine ............................................................................ 31
Figure 3.2 Boxplot of height difference per diameter for each pocket within VT16-machine ................... 31
Figure 3.3 Zoomed in boxplot of height difference per diameter for each pocket within VT16-machine . 32
Figure 3.4 Failure rate during lifetime of Component X ............................................................................. 35
Figure 3.5 Example abnormal behavior....................................................................................................... 38
Figure 5.1 Experiment setup of RUL prediction .......................................................................................... 47
Figure 5.2 Trajectories of train and test set with a cut-off point ................................................................ 48
Figure 6.1 Graphical display of Random Forest........................................................................................... 52
Figure 6.2 General structure of convolution neural network as described in Chen et al. (2020) ............... 53
Figure 6.3 Structure of long short-term memory network as described in Chen et al. (2020) ................... 55
Figure 6.4 Time window processing ............................................................................................................ 58
Figure 7.1 Linear regression of Health index and Remaining useful lifetime.............................................. 60
Figure 7.2 Predicted RUL-values versus the real RUL values performed by XGBoost................................. 61
Figure 7.3 Predicted RUL-values versus the real RUL values performed by Random Forest ...................... 62
Figure 7.4 Predicted RUL-values versus the real RUL values performed by CNN ....................................... 63
Figure 7.5 Predicted RUL-values versus the real RUL values performed by LSTM...................................... 64
Figure 9.1 Process of implementing prediction model ............................................................................... 71
Figure 9.2 Replacements of Component X or production cell after last batched maintenance moment .. 72
Figure 9.3 health indicator trajectory run-to-failure data........................................................................... 73
xi
List of Tables
Table 1.1 Standard maintenance moments for Machine Y ........................................................................... 5
Table 3.1 Descriptive statics product dataset ............................................................................................. 30
Table 3.2 Descriptive statics process dataset.............................................................................................. 33
Table 3.3 Production per period for each machine..................................................................................... 34
Table 3.4 Results of Mann Kendall trend test for product dataset ............................................................. 37
Table 3.5 Reviewed maintenance moments ............................................................................................... 38
Table 4.1 Review of production periods ..................................................................................................... 41
Table 4.2 Time-domain features ................................................................................................................. 42
Table 5.1 Testing monotonicity and trendability on potential HI's ............................................................. 45
Table 5.2 impact of granularity and sliding time window ........................................................................... 45
Table 7.1 Comparison of different data granularity and sliding window on performance Random Forest 66
List of Equations
Equation 2.1 RMSE formula ........................................................................................................................ 28
Equation 2.2 MAPE formula ........................................................................................................................ 28
Equation 3.1 Sign formula of Mann Kendall trend test ............................................................................... 36
Equation 3.2 S statistic formula of Mann Kendall trend test ..................................................................... 36
Equation 3.3 Variation formula of Mann Kendall trend test....................................................................... 36
Equation 3.4 Normalized test static of Mann Kendall trend test ................................................................ 36
Equation 5.1 Formula for Monotonicity ...................................................................................................... 43
Equation 5.2 Formula for Trendability ........................................................................................................ 44
Equation 6.1 Simple linear regression ......................................................................................................... 50
Equation 6.2 Convolutional operation for each feature map ..................................................................... 53
Equation 6.3 Pooling function for CNN ....................................................................................................... 54
Equation 6.4 Min-max normalization formula ............................................................................................ 54
Equation 6.5 Forget gate ............................................................................................................................. 56
Equation 6.6 learned information as input for input gate .......................................................................... 56
Equation 6.7 input gate ............................................................................................................................... 56
Equation 6.8 Update of the current gate .................................................................................................... 56
Equation 6.9 Output gate ............................................................................................................................ 57
Equation 6.10 Output of hidden layer......................................................................................................... 57
Equation 6.11 Standardization of data........................................................................................................ 57
xii
Part I – Introduction & Problem Description
1. Introduction
This report results from a master thesis project at a healthcare company located in Europe, in
collaboration with the Eindhoven University of Technology. The project focuses on applying datadriven maintenance for Machine Y to produce Product Z. The company currently uses a timebased maintenance policy for its maintenance activities at Machine Y (i.e., replacing component
X). Component X is an essential component within Machine Y. There is no documentation on how
many products Component X can manufacture before replacing them. When the first machine was
purchased, a life span was determined based on average production. The determination was
already several years ago, and internal aspects are changed over time. As a result, knowledge
lacks what constitutes an appropriate life span for Component X.
Lately, industrial consultants at the company have gained interest in Industry 4.0. Industry 4.0 is
what experts have called “The fourth industrial revolution,” the digital revolution. New technologies
from Industry 4.0 integrate people, machines, and products, enabling faster and more targeted
exchange of information (Rauch et al., 2020). Industry 4.0 is strongly associated with the
integration between physical and digital systems of production environments. This digital
revolution enables a collection of a large amount of data measured by different equipment (i.e.,
sensors) located in various places.
These big amounts of data contain information about the processes in production. Analyzing
the data can bring out valuable information regarding system dynamics. By applying analytics, it
is possible to find interpretive results for strategic decision making, providing advantages such as
cost reduction, machine fault reduction, repair stop reduction, spare parts inventory reduction,
spare part life increasing, increased production, improvement in operator safety, repair
verification, overall profit, among others (Peres et al., 2018; Sezer et al., 2018; Biswal and
Sabareesh, 2015).
Data-driven maintenance can support current maintenance policies. This Master Thesis project
aims to improve the current maintenance policy into a data-driven maintenance policy. The initial
goal was to implement an accurate prognostics model that predicts when the specific part (i.e.
component X) of the machine can be replaced before faulty products are manufactured with all its
consequences.
1
The project helped to optimize the life span of the replaceable machine part (i.e. Component X).
In this situation, an operator can be involved on a preventive basis to replace worn-out equipment
based on the current condition. (i.e., data-driven predictive maintenance).
1.1
Context: Company
This section presents some background information about the company manufacturing site in
Anomalized, where the thesis project was executed. The company is a leading manufacturer of
healthcare technology. This thesis project has been executed at the Product Z production site in
Anomalized.
1.1.1
Production line and product produce
This thesis focuses on the production of the Product Z, see
Figure 1.1. Within the production line, only one unique product
is produced. Thus, there are no changeovers for the
machines. The Product Z line consists of several machines
that are positioned behind each other. A simplified
representation of the process is shown in Figure 1.2. A deeper
description of the process is given in Appendix A.
Figure 1.1 Product Z
To be able to perform data-driven maintenance, there should be data available. Data is available
in the case for machine Y. Machine Y consists of several parts, but we focus on the part that has
to be replaced regularly and is in direct contact with the operation of the machine, namely
component X. Machine Y is maintained regularly (i.e., preventively every two weeks). Machine Y
contains a certain part of the equipment that wears out relatively quickly. This part of the equipment
is called component X. See subsection 1.1.2 for a detailed description of the function of component
X.
Figure 1.2 Production line of the Product Z
Because machine Y performs the most complex tasks in the production line, data has already
been gathered before this project started to monitor the situation accurately. To see the data
availability, see subsection 1.1.3.
2
1.1.2 A deeper understanding of Machine Y
To fully understand the function of machine Y, the importance of the component X, and the
associated collected data, a deeper understanding of the process within the machine is required.
This information is gathered by visiting the production line and talking to domain experts to explain
the process.
Machine Y consists of four identical machines, which behave all in
the same way. Each machine consists of 30 production cells. Figure
1.3 shows a production cell. A production cell has several functions
within the Machine Y. Those functions are transporting and centering
the Product Z, clamping the Product Z during transport, and lastly,
conducting the operation (anomalized)
Construction-wise, a production cell is built up in different parts.
Each part has a function in it. Below the parts are named:
1. Clamping jaws/fixing fingers: One production cell has three
Figure 1.3 Production cell within
Machine Y
clamping jaws: L1, L2, and L3. See Figure 1.4. The clamping
jaws fixate Product Z with a clamping force, making the same
position remain during transport and the process.
2. Component X: Product Z are mounted on the clamp fingers for
conducting the operation (anomalized). Figure 1.5 shows the
contact between Component X and the Product Z.
As said in the previous section, Component X is equipment the thesis
Figure 1.4 Clamping jaws in production
cell
is focused on. If a component X not replaced timely, the Machine Y
cannot conduct the operation. Which means faulty products. There
is a risk that a component X will break, leading to an unexpected
interruption during production. Because Machine Y is highly
automated and records a significant amount of event data, this is the
part of the process where data-driven maintenance can potentially
be applied.
Figure 1.5 Electrical contact
3
The reason why Component X was chosen is the following. It is the product that has to be replaced
the most frequently, and it is the only parameter for which an indirect measurement is measured.
Section 1.1.3 elaborates on the indirect relationship between the measured parameter and the
condition of component X
Figure 1.6 and Figure 1.7 show the difference between a new Component X and a worn-out
Component X. Figure 1.6 shows a new Component X. Comparison between a new and a wornout Component X is removed due to company sensitive information
Figure 1.6 New Component X
Figure 1.7 Worn-out Component X
To give an insight into which relevant parameters provide meaningful insights into the condition of
Component X, the available data from the Machine Y is described in the following subsection.
4
1.1.3 Data availability
Different sources of data were available, which were used to make the maintenance more datadriven based. In total, there were three datasets used for this project. Firstly, a document keeps
track of when maintenance was performed on top of the planned maintenance moments. The
second dataset consists of event log data which is logged within Machine Y. Furthermore, the third
dataset keeps quality measure about Product Z. To better understand the key parameters from
each dataset, each dataset is treated individually.
The first dataset keeps a record of when maintenance is carried out, i.e., a logbook. Normally
every two weeks, when Component X are replaced. To plan maintenance moments evenly over
time, a set moment for each machine within Machine Y, set every two weeks, see Table 1.1.
Table 1.1 Standard maintenance moments for Machine Y
Machine:
VT16
VT26
VT36
VT46
Week:
Even weeks
Odd weeks
Odd weeks
Even weeks
Moment
Saturday 11:00 AM
Saturday 11:00 AM
Wednesday 11:00 AM
Wednesday 11:00 AM
Incidentally, the relevant part is also replaced. Unplanned maintenance is recorded in this logbook.
Because the logbook is tracked manually, this provides some margin of error in the indicated time
when maintenance is performed and the actual time. Also, the engineers in question mentioned
that Saturday 11:00 is a target time they prefer to stick to, but it is not always done. Planned
maintenance is not recorded in the logbook. A margin of error is considered while performing
analysis and predictions in the later stage of this Thesis.
The second source contains log data regarding the parameters of the machine, i.e., multivariate
time series. Different parameters can be distinguished, such as relative position based on a
calibration, parameters regarding count values based on occurrences of behavior within a
specified timeframe, and subsequent steps regarding the operation of the process. A more
detailed overview of each parameter is given in Appendix B.
Log data is recorded per product within each production cell in Machine Y. Data gathering
is done automatically. Because the data gathering is gathered automatically, there is no margin of
error when recording the data. However, there are empty values in this dataset and outliers, which
should be discussed with the domain experts.
5
Lastly, the third source contains log data of the end product, i.e.,
multivariate time series. Company sensitive information is shown in
Figure 1.8 and detailed description is removed.
Hence, there are three different track parameters on top of the
assignment of each machine and each production cell. Each 40-60
seconds, an end product is measured. The measurements are
automatically logged. The delay from production to final measurement
Figure 1.8 parameters Product Z
is negligible. As the second dataset, the empty values and outlies are handled closely with the
domain experts.
A major observation is that due to the timely maintenance policy, there is no run-to-failure data
available. The failure data which is available so far is individual per production cell. The absence
of run-to-failure data will be one of the challenges to finding a suitable method. As mentioned
previously, a relationship is found between the degradation of the measured parameters and the
condition of the Component X. A more thorough exploration is made in section 3. In the following
section, an in-depth problem description is given to break down the problem into several subquestions and structure the project.
6
1.2
Problem description
This section defines the problem that forms the stimulant for this research project. The company
is investigating how data and analytics as part of Industry 4.0 (i.e., smart industries) can make the
maintenance policy more data-driven. First, the problem is introduced and defined. Subsequently,
the sub-problems and associated research questions are formulated.
1.2.1 Problem formulation
The company currently uses planned maintenance manuals that describe all the required planned
maintenance activities for each machine, and this is handled through a time-based maintenance
policy. There is, for example, no documentation of how many products Component X can
manufacture. When the first machine was purchased, a life span was determined to average
production. This determination was already several years ago, and some things have changed
regarding the supplier of component X, the material of product Z, and other influencing factors. As
a result, knowledge is lacking as to what constitutes an appropriate life cycle for component X and
whether it is use-based or condition-based.
The company has decided to do more with big data with the smart industry. Data-driven
maintenance can reduce maintenance time, material costs, and maintenance planning time. While
on the other hand can increase the equipment uptime and availability. The problem statement
summarizes the goal of the research and its relevance: Conducting maintenance activities is not
optimized for effectivity and frequency and does not use historic planned maintenance and event
data to replace the Component X in Machine Y.
The company’s goal for this project is to investigate whether data-driven maintenance can be
applied to the Machine Y. An improvement on the current situation (i.e., time-based policy) could
be a different maintenance policy like condition-based maintenance based on the data available.
Condition-based maintenance will decrease the number of maintenance moments that will lead to
a higher production capacity and lower maintenance costs. On top of that, the findings can be
applied to other similar production lines.
7
1.2.2 Research Questions and research method per question
The main question was constructed to structure the project answer to this question provides
necessary insights. The research question of this project is formulated as follows: How can the
data currently measured within Machine Y unit help implement a more data-driven maintenance
policy for Component X?
Several sub-questions were drafted to give more structure to the research to answer this rather
broad research question. These sub-questions are divided into groups, as shown in Figure 1.9.
Q-1, Q-3, and Q-4 help to find meaningful insights applicable to the case's current situation. Q-2
describes the current situation and desired outputs with all its characteristics. Q-5 helps to
structure the experimental setup, and Q-6 supports the comparison to a baseline and results found
in the domain of data-driven maintenance.
Figure 1.9 Structure of sub-research questions
Q-1: Which maintenance policies are there, and what are the characteristics of each policy?
This sub-question was created to have the spectrum of maintenance coherent. It serves as an
introduction, and the first goal of the literature review to know the characteristics of all possible
maintenance policies. A literature review is used as a research method to answer this subquestion. It supports the description of the current situation and the desired output in the second
sub-question. A detailed answer to this sub-question is given in section 2.
Q-2: What are the characteristics of the current situation?
To answer this question, the findings of the literature review are used. Also, the production factory
was visited to get an overview of the production line. On top of that, unstructured interviews were
conducted with domain experts. It can conclude that the lack of run-to-failure data is the biggest
bottleneck for figuring out an effective maintenance policy. On top of that, there is no direct
8
measurement on the equipment (e.g., temperature, vibrations) but an indirect relationship that
reflects the Component X’s degradation. Those two aspects were considered while finding an
applicable policy. The current maintenance policy is a preventive maintenance policy conducted
every two weeks.
Q-3: Based on the available data, what type of data-driven strategy is best and realizable for the
situation of Component X?
Based on the conducted literature review and assessing the current situation due to a factory visit
and unstructured interview, two constraints can be identified. Firstly, no run-to-failure data is
available. Secondly, the sensor data is not measured directly on the maintained equipment. The
most appropriate method is to work with a data-driven degradation model based on a Health
Indicator (HI). An indirect relationship has been found between product related parameters and
the condition of component X. Those product related parameters are used as a health indicator.
The health indicator was evaluated on trendability, monotonicity, and correlation with the RUL. For
solving the problem of the absence of run-to-failure data, there using an arbitrary lower bound.
Because the degradation of the Component X indicated by the health indicator behaves as a linear
line, we can substitute this arbitrary lower bound when sufficient run-to-failure data is gathered.
The model must be a prognostic prediction model to predict a failing point.
Q-4: Which predictions models can be applied for data-driven maintenance?
Based on the literature review, several predictive models can be applied from the machine learning
domain for creating a degradation-based model. A comparison is made with simpler time series
based solely on one parameter to investigate if there is explainable behavior in the dataset. We
compare that method with more complex machine learning predictive models. All the used models
are explained in detail in section 2.3. This choice was made because this predictive model is often
used during RUL predications. A baseline: linear regression was chosen for the reason that it is
the easiest choice to implement. The decision tree methods (Random Forest and XGBoost) were
chosen because of their ability to retrace the important parameters. Furthermore, the more
complex neural networks were chosen to see if more complex models perform better. We selected
a Simple Linear Regression, XGBoost, Random Forest, 1D-CNN, and LSTM for predicting the
Remaining Useful Lifetime (RUL) of Component X for our implementation.
9
Q-5: How can we optimize each predictive model that in terms of accuracy?
To ensure that each predictive model performs to its fullest potential, Section 6 provides a
narrative describing how each predictive model operates. Subsequently, the input data is
supposed to be set up to lend itself to its respective model. Five different experiments have been
conducted to find the best input data and settings for each prediction model to find a performing
predictive model. Finding the optimal dataset (e.g., granularity, feature selection) is found in
sections 6 and 7. If applicable, for each model, hyperparameter optimization based on a grid
search is performed, which can be read in section 6.
Q-6: What is the performance of the best-performing prediction mode based on accuracy?
An in-depth comparison is made for each machine learning model compared to intuitive time
series methods. In section 7, this comparison is made. However, the best performing predictive
model is Random Forest, which has an RMSE of roughly 18 active production hours (RMSE in
products known but anomalized). For achieving those results, a data granularity of hourly data is
used, and a sliding time window is based on a window of an hour.
1.2.3 Scope
Several decisions have been made to adjust the magnitude of this research project. An overview
of these decisions is given in this section.
1.2.3.1
Restrictions on data collection
As previously indicated in a previous section, there are no direct sensors associated with the
condition of the maintained equipment of Machine Y. As a result, less accurate results are
obtained compared when there would be sensor data directly on the piece of equipment. This
drawback has been discussed with the stakeholders. However, there is no option to collect
additional data with additional sensors.
1.2.3.2
Implementation of predictive model
In order to maximize the applicability of this research, the choice is made to work with limited
company data instead of simulation data to make a predictive model. Using company data will
cause the accuracy of the predictive model to perform less than if it were done with more usable
simulation data.
A prototype in the form of a proof-of-concept has been delivered. This solution is based
on historical data for the year XXXX. Ensuring that the solution is implemented in real-time in the
working environment with possible visualization is not part of the project definition.
10
1.2.4 Research design
This project aims to deliver a proof of concept
for data-driven maintenance based on the
current data available within the production
process of the Product Z in Drachten. For this
project,
we
will
use
the
CRISP-DM
methodology, also shown in Figure 1.10.
CRISP-DM is a Cross-Industry Standard
Process for Data Mining widely used by
industry members (Olson & Delen, 2008). In
contrary to other methodologies, CRISP-DM
focuses on data-related improvements or
designs. Briefly, each phase of the CRISP-DM
model is described with each core task and
relevant sub-question. The CRISP-DM model
is used as the structure of the thesis continued
from this moment forward.
Figure 1.10 CRISP-DM methodology
In the business understanding phase business, the current situation of the process is described
with the context and desired goals for this data-driven maintenance. This phase is mainly
described in section 1.
The data understanding phase is closely related to the business understanding phase. It
was necessary to understand which data is available and what it means. Also, data exploration is
done. Through new information from the data understanding, the perception of the business
understanding can be changed and vice versa. It was important that the understanding of the data
if verified with domain experts. The data understanding phase is described in sections 1 and 3. Q2 can be answered after the business understanding and data understanding phase.
In parallel, during the business understanding phase and data understanding phase, a
literature review is conducted. During this literature review, research questions Q-1, Q-3, and Q4 are answered. The summary of the literature review is shown in section 2.
The three different datasets are integrated during the data preparation phase, missing
values and outliers were handled. Nominal data is converted to numerical data. Moreover, all
parameters which were not relevant were removed—the most useful parameters were chosen as
input to the modeling phase. The data preparation stage is described in section 4.
11
Subsequently, in section 8, the modeling phase is described within different experiments.
Different predictive models and settings in those predictive models are compared with a traditional
regression method. The modeling phase is described in sections 6 and 7. During this section, subquestion Q-5 is answered.
Next, the evaluation phase follows. The results of different predictive models are compared
to different situations. The evaluation phase is shown in section 7. The last sub-question, Q-6, is
answered in that section.
The last phase is the deployment of the predictive model. However, this thesis project ends
when the proof-of-concept is delivered. Making the predictions workable in a real-time application
is out of the scope described in section 3.4
12
Part II – A literature overview
2. Literature Review
To explore different maintenance policies with their characteristics, a literature review was
conducted. The goal was to find out the most applicable one for the company’s needs. Also,
several predictive models are discussed, which can be applied within the maintenance strategies
considering the absence of run-to-failure data. During this literature review, several sub-questions
are addressed, which are listed in this section.
2.1
Maintenance
During this section, Q-1 stands central. To answer the question of Which maintenance strategies
are there and what are the characteristics of each policy? An in-depth analysis is made of which
maintenance strategies are there and which is the most applicable for the current situation and
the desired situation.
Maintenance may be defined as actions necessary for retaining or restoring a piece of equipment,
machine, or system to the specified operable condition to achieve its maximum useful life. More
specifically, maintenance includes repairing broken equipment, preserving equipment conditions,
and preventing failure, which ultimately reduces production losses and down lime and reduces
environmental and associated safety hazards (Adebimpe et al., 2015). In the past, maintenance
was seen as a necessary evil to keep a company's core business. Nowadays, the role of
maintenance has changed to be a strategically important part of the company’s business. New
requirements are set up regarding quality, automation, performance, environment, safety, and
agility, according to Duffuaa & Raouf (2015). Because of the new maintenance role, new
maintenance strategies and maintenance models were established to gain competitive
advantages.
2.1.1 Maintenance strategies
Maintenance can roughly be divided into Corrective Maintenance (CM) and Preventive
Maintenance (PM).
Corrective Maintenance: Under a breakdown corrective maintenance policy, a part is not
replaced until it has failed (Arts 2014). The corrective maintenance policy is the most expensive
because the failed equipment can damage other parts of the machine or products. When repair is
conducted, the whole production must be stopped, which will lead to downtime in production.
13
Costs involved can be high machine downtime, low production availability, and other equipment
costs. Corrective maintenance is an attractive option for components that do not wear, such as
electronics. Mobley (2013) has shown that corrective maintenance is about three times more
expensive than the same task conducted in a preventive mode.
Preventive Maintenance: or planned maintenance, the aim is to replace parts before failure
occurs (Arts 2014). The goal of preventive maintenance is to reduce the frequency of failure rate
of an item. It improves product performance and reduces or even minimizes machine downtime
and failure costs (Shagluf et al., 2014). The general principle for preventive maintenance is that
the risk of component failure can increase over time (Peng, 2014). Based on the work of Avontuur
(2017), different preventive maintenance policies can be indicated, as shown in Figure 2.1.
Figure 2.1 Categorization of maintenance policies (Avontuur, 2017)
Avontuur (2016) categorized Preventive Maintenance is divided between the categories Timebased Maintenance, Usage-based Maintenance, Detection-based maintenance, and Conditionbased maintenance. Each preventive maintenance policy is briefly discussed.
-
Time-based maintenance: maintenance actions are performed after an amount of time. The
parameter “time” can either be a reference to the time a component has been in use (i.e.,
time in production) or calendar time (i.e., real-time)
-
Usage-based maintenance: It is almost similar to the previous policy, but instead of time, a
parameter that expresses the real usage of a product is used
-
Detection-based maintenance: Under Detection Based Maintenance (DBM), manual
inspections through human senses (visually inspect, hear, smell or touch) is performed to
detect whether a maintenance action is required (Waeyenbergh, 2006). This maintenance
policy can be continuous or with fixed periods.
14
-
Condition-based maintenance (CBM): is a decision-making policy based on a real-time
diagnosis of impending failures and prognosis of future equipment health. To predict the
moment of failure to make a timely decision on when to perform the appropriate preventive
maintenance actions using a modeling approach (Veldman et al., 2011). Predefined control
level thresholds set on measured parameters define when preventive maintenance should
be performed to avoid costly downtime (Zhu, Peng, & van Houtum, 2014). This can be
continuous or with fixed periods.
Condition-based maintenance (CBM) is the most desirable for the case of the company. Data is
automatically logged in a database related to producing a Product Z and measuring the final
product itself. Predictive maintenance can be scaled as predictive condition-based maintenance
based on the system's condition and its components. The condition of a system is quantified by
obtaining data from various sensors in the system periodically or even continually. CBM attempts
to avoid unnecessary maintenance tasks by taking maintenance actions only when there is
evidence of abnormal behaviors of a physical asset. It is a proactive process that requires
developing a predictive model that can trigger an alarm for corresponding maintenance (Peng et
al., 2009). In the next subsection, different condition-based maintenance strategies are discussed
to implement fault prognostics (i.e., predictive maintenance).
2.1.2 Different condition-based maintenance strategies as predictive maintenance
Condition-based maintenance can be divided into two different sorts of strategies. Diagnostics
and prognostics are two important aspects of a predictive maintenance program. Diagnostics
deals with fault detection, isolation, and identification when an abnormality occurs. Prognostics
deals with fault and degradation prediction before they occur. Prognostic algorithms for predictive
maintenance have only recently been introduced into technical literature and have received much
attention in maintenance research and development (Peng et al., 2009).
The prognosis part is important for the thesis because the company benefits from a situation
where machine malfunctions are predicted. Additionally, no failure data is currently available when
the data is filtered on its respective machine. The absence of run-to-failure data leads to the fact
that diagnostics cannot be applied. Also, a diagnostics algorithm has little added value. If a
Component X breaks, a production cell within this Machine Y can no longer produce. Machine Y
itself already does the detection of a non-functional production cell.
15
In diagnostics detects the presence of an incipient failure or point of transition from the normal
state to a degraded state. Anomaly detection can be done statistically (e.g., detect outliers based
on a simple threshold or dynamic threshold). Recently, statistical processes are machine learning
algorithms are also used for diagnostic purposes. Jimenez et al. (2020) divide unsupervised
anomaly detection algorithms into different main groups: Nearest-neighbor-based techniques,
clustering-based, statistical algorithms, subspace techniques, unsupervised neural networks, and
real-time and time-series analysis-based algorithms. However, for the company, diagnostics are
not interesting due to the absence of failure data because of the preventive maintenance policy.
For now, the focus is laid on prognosis.
Prognosis is a relatively new area and has become a significant function of a maintenance system
(Yang et al., 2009). From a human perspective, it seems that machines fail abruptly. Nevertheless,
machines usually go through a measurable sign of failure before occurring (Lee et al., 2006). For
that reason, the prognosis can use this measurable sign for predicting the appearance and the
amount of time is left before failure.
As shown in Figure 2.2, prognostic approaches can be classified into three basic groups;
model-based prognostic, data-driven prognostics, and experience-based prognostic (Luo et al.,
2008; Yang et al., 2008; Muller et al. 2008).
Figure 2.2 Different condition-based maintenance strategies
Because the prognostic methods of condition-based maintenance best fit the desired situation,
the model-based policy, the experience-based policy, and the data-driven strategy are succinctly
explained in the following subsections. A combination of two or more of these strategies is also
possible.
16
2.1.2.1
Model-based approach
Based on the work of Peng et al. (2009), physical model-based approaches usually employ
mathematical models that are directly tied to physical processes that have direct or indirect effects
on the health of related components. Domain experts usually develop physical models, and large
sets of data validate the parameters in the model. Physical model-based approaches used for
prognostics require specific mechanistic knowledge (i.e., first principles) and theories relevant to
the monitored systems.
The main advantage of the model-based approach is the ability to incorporate a physical
understanding of the system monitored. Moreover, if the understanding of the system degradation
improves, the model can be adapted to increase accuracy. Peng et al. (2009) stated that it is
usually tough to build a mathematical model for a physical system with prior principles in realworld applications. So, the uses of physical model-based methodologies are limited. Especially
when there is no deep understanding about the mechanics of the process is known or are nonlinear, as is the case of the company.
2.1.2.2
Experience-based approach
An experience-based prognosis is an approach that does not depend on equipment’s historical
data or the output from a mechanical model-based system. The approach solely depends on
expert judgment (Yang et al., 2009). This method is the least used approach of all three
approaches. The prognosis researchers are more focused on the existence of a numerical
condition of data. Two widely known examples of the knowledge-based approach are expert
systems (ES) and fuzzy logic.
Peng et al. (2009) stated that expert systems are suitable for human specialists' problems. ES can
be considered a computer system programmed to exhibit expert knowledge in solving a domain
problem. Usually, rules are expressed in the form: IF condition, THEN consequence. The condition
portion of a rule is usually some fact, while the consequence portion can be outcomes that affect
the outside world. However, it is difficult to obtain domain knowledge and convert it to rules.
Fuzzy logic provides a very human-like and intuitive way of representing and reasoning
with incomplete and inaccurate information by using linguistic variables.
17
However, for the case within the company, no domain knowledge is known. Maintenance is done
based on a preventive policy. Therefore, the behavior of the process is unknown after producing
for too long with the same Component X. An experience-based approach seems unusable with
the current knowledge.
2.1.2.3
Data-driven approach
The data-driven prognostic methodology is based on statistical and learning techniques originating
from pattern recognition theory for system degradation behavior (Peng, 2009). Data-driven models
are usually developed from collected input/output data. These models can process various data
types and exploit the nuances in the data that rule-based systems cannot discover.
Dragomir et al. (2009) classify data-driven methods into two categories: statistical approaches and
AI approaches. Statistical approaches include multivariate statistical methods, linear and
quadratic discriminant, partial least squares (PLS), and signal analysis. Artificial intelligence (AI)
techniques include neural networks, decision trees, and graphical models.
Based on the current knowledge of the process, this method seems the most convenient.
Data-driven maintenance tries to make connections based on data where no domain knowledge
is required.
2.1.2.4
Hybrid approach
Peng et al. (2010) stated that in real-world prognostic processes, the trends of all characteristic
parameters are diversified and difficult to predict by using a single prediction method. Thus, a
combination prediction method is adopted for prognostics. Using a well-designed condition-based
combination prediction method that combines two or more prognostic approaches for data
extraction, data analysis, and modeling may have the following advantages:
(1) the demerit of individual theory will be offset, and the merits of all prediction methods could
be utilized,
(2) the complexity of the computation may be reduced, and
(3) the prediction precision could be improved.
There must be sufficient knowledge within the department to apply at least two methods to have
a hybrid prognostic model. Sufficient knowledge is not known for the case at the company because
maintenance is always done preventively. The engineers do not know what happens after the twoweek cycle. Also, there are no distributions available that can be linked to the wear of Component
X. No run-to-failure data is available. Although there are arguments to apply a hybrid approach,
this turns out to be impossible with the current information available.
18
2.1.3 Answering sub research question Q-1
The sub-question that was central to this chapter was as follows: Which maintenance policies are
there, and what are the characteristics of each policy? To give a brief recap, the current situation
within the company is a time-based maintenance policy. Every two weeks, Component X are
replaced (i.e., real-time). A usage-based policy or a condition-based policy can replace the timebased maintenance. The reason for this is that data is automatically logged during production.
Some measurements are also taken on the final product.
The next sub-question will be Q-3. Based on the available data, what type of data-driven
strategy is best and realizable for the situation of Component X? Here, the specifications within
the company are specifically considered and what type of method is best to work out. This subquestion is described in the next sub-question, section 2.2.
2.2
Process of data-driven strategy
Firstly, the characteristics are mentioned in the current situation. Subsequently, a suitable type of
data-driven strategy will be examined based on the literature. During this section, Q-3 stands
central. As shown in section 2.1.3, a condition-based maintenance policy is possible with the data
currently gathered in the process of the company. Condition-based maintenance can again be
subdivided into diagnostics and prognostics. Because there is no failure data available at the
machine level, a prognostic method is chosen. The most appropriate method to work out is the
data-driven maintenance policies, and this could be a statistical approach or more AI approach.
2.2.1 Process of prognostics
Prognostics can predict a fault before it occurs and estimates the remaining useful life (RUL) of
equipment. It is generally performed with three key steps (Xu et al. 2019). This general approach
is used in multiple papers (Xu et al., 2019, Abid et al., 2018, Saidi et al. 2017; Javed et al. 2015;
Zhang et al. 2016):
(1) Health Indicator (HI) construction: HI’s are built to represent the health status of equipment.
(2) Health Stage (HS) division: the lifetime of equipment is divided into several HSs based on the
built HIs.
(3) RUL prediction: the RUL is estimated through the assessment of degradation trends in the
unhealthy stage
19
Abid et al. (2018) and Lei et al. (2018) also taking data acquisition in the form of data-monitoring
into account as a preliminary step. The process of making an RUL prediction can be described as
a series of steps depicted in Figure 2.3.
Figure 2.3 General approach of prognostics, Abid et al. (2018)
This method is chosen because it is the standard approach for prognostics. Health prognostics
are the main tasks in condition-based maintenance, which aims to predict the RUL of machinery
based on historical and ongoing degradation trends observed from condition monitoring
information (Abid et al., 2018). Because in our data also a degradation trend can be traced, it is
logical to use the same method.
2.2.1.1
Health indicator (HI) construction
Abid et al. (2018) describe Health Indicator (HI) construction as the main step for achieving
prognosis. It represents the evolution over time of the performance of the system. HIs can be
classified into two categories: physical health indicators and virtual health indicators. Physical
health indicators are based on a single feature, such as using the raw data gathered from sensors.
In contrast, virtual health indicators are based on a fusion of multiple features that can better
represent the system's health. The most relevant HI evaluation criteria are monotonicity and
trendability (Saidi et al., 2017; Javed et al., 2015; Zhang et al., 2016).
Monotonicity: The monotonicity evaluates the negative or positive trend of the HI, with the
assumption that the system cannot self-heal.
Trendability: Trendability is related to time and represents the correlation between the
degradation trend and the operating time of a component
When selecting a fitting health indicator (e.g., physics or virtual), the monotonicity and trendability
need to be considered. If the health indicator is not monotonic and has no trendability, the fitting
health indicator is not fitting.
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2.2.1.2
Health stage (HS) division
When a degradation occurred, the HI presents an increasing or decreasing trend. The degradation
can be detected by dividing the HI into two or multiple stages using a threshold according to the
degradation trend. Using a threshold is widely used in the literature for this task (Abid et al., 2018).
The goal of this division using a threshold is to:
(1) identify the stages where the degradation process is active
(2) separate the degradation process or evolution over time according to its dynamics
However, in the case of the company maintenance has been carried out preventively. Therefore,
making health placements can be described as difficult. While analyzing the data, it will be
necessary to focus on the deterioration of the process. To establish one or more thresholds that
describe the condition of the Component X. Health stage division allows improving the reliability
of degradation detection and the RUL estimation. (Abid et al. 2018).
2.2.1.3
RUL prediction
The RUL of machinery is defined as the length from the current time to the end of the useful life.
The RUL can be addressed as a time unit or production unit. Still, two issues related to RUL
prediction are unanswered. Firstly, how to predict the RUL based on the condition monitoring
information, and secondly, how to measure the prediction accuracy of different approaches. Those
two things are answered in the next chapter. On top of that, the impact of missing labels since
preventive maintenance is now in place is discussed.
2.2.2 Impact of missing labels
Like the situation of the company, Zschech et al. (2019) attempt to develop a prognostic model
with missing labels. Zschech et al. (2019) stated that for the case of critical machines, the aim is
to avoid failures and faults through strictly short maintenance intervals. As a result, no thresholds
and tolerance limits are known or observed that provide labels to mark necessary intervention
points. In addition, sensors, which can describe physical health conditions directly (e.g., crack
size, state of wear), are rarely used. Moreover, due to the pressure to use plants efficiently, it is
often impossible to carry out test runs beyond safe conditions.
Consequently, possible data observations might be truncated before the actual end of life, and
thus, interesting events to describe fault patterns are not recorded. Overall, such circumstances
can be characterized by the absence of a prospective target variable to build the prognosis.
21
Henceforth, this problem called missing labels can be seen as a major hurdle in developing
adequate prognostic models (Gouriveau et al., 2013). In the case of Zschech et al. (2019), no
direct labels were provided due to missing CBM thresholds and non-traceable results from quality
control. However, no mention was made about the absence of run-to-failure data.
On the other hand, Kim et al. (2021) described a method by calculating the HI with the MAE of the
input and output data using an autoencoder. An autoencoder is a neural network that has a
bottleneck as a hidden layer and focuses on the essentials of the input data. The input data is also
the output data. Kim et al. (2021) use the difference between the input data and the output data
of the autoencoder to determine whether the data are normal. The reason behind this is that the
autoencoder learns the relationship between the input variables. As the autoencoder learns the
training data, if the test data are similar to the input data, the reconstruction error (i.e., HI) between
the input and the output will be small. On the contrary, when data that differs from the training data
are used as the test data, the reconstruction error between the input and output will be large.
However, the problem of determining a sensible HS (i.e., lower bound) stays.
Normally, if there is historical run-to-failure data, the initial threshold can be set using failure
data. However, when there is no historical run-to-failure data, the initial threshold is assumed
arbitrarily. To determine a threshold, Kim et al. (2021) suggest two methods. First, let an expert
provide a threshold, or secondly, determine it based on the HI calculated from the training data.
Kim et al. (2021) proposed to use a gaussian distribution-based value because z-normalization
was applied to the preprocessing method. Lastly, Kim et al. (2021) stated that the threshold could
be updated when run-to-failure data accumulates. This way of determining a failure point can be
useful for the case of the company. However, the main drawback of this approach is that the lower
bound is based on the standard deviation. There is no data to measure the quality of this prediction
because there is no run-to-failure data. However, it can be looked at to train the autoencoder on
relatively short production periods versus long ones. If no meaningful health indicator can be
determined based on monotonicity and trendability. The health indicator examined by the
autoencoder can be used. However, during the study, establishing a lower limit as a health stage
division will be investigated, as Kim et al. (2021) proposed. The idea that if data is standardized,
a lower bound can be established on whether the deviation from the mean can serve as a more
relative lower limit.
22
Malhotra et al. (2016) use a similar method with an LSTM encoder-decoder (LSTM-ED). You et
al. (2013) also made a solution where large failed historical samples were available. The results
were ineffective when failed historical samples were limited, but the performance improved fast
when failed historical samples are increasingly available.
2.2.3 Answering sub research question Q-3
To answer sub-question Q-3: Based on the available data, what type of data-driven strategy is
best and realizable for the situation of Component X The general approach of prognostics
suggested by Abid et al. (2018). The approach consists of four steps, namely: monitoring data,
health indicator (HI) construction, degradation detection using health stage (HS) divisions, and
lastly, an RUL estimation. For a HI, we have to find a which is monotonicity and trendability.
However, because the company uses a preventive maintenance policy, run-to-failure data
are absent. Kim et al. (2021) suggest an autoencoder calculate a HI and use a Gaussian
distributed value as a threshold to come up with an initial threshold for the health stages.
In the next section, various prediction algorithms are discussed and methods to measure the
prediction accuracy of different approaches. During this process, sub-question Q-4 stands central:
Which prediction models can be applied for data-driven maintenance?
23
2.3
Predictive models used in data-driven maintenance
This section answers Q-4: which prediction models can be applied for data-driven maintenance?
During this section, we distinguish two sorts of prognostics data-driven algorithms (i.e., predictive
maintenance). We will firstly discuss statistical data-driven approaches and subsequently machine
learning approaches.
To find the most applicable algorithms for our data-driven maintenance policy, we used different
(systematic) literature reviews and surveys (Lei et al. 2018; Jimenez et al. 2020; Adhikari et al.
2018; Ramezani et al. 2019; Mathew et al. 2017). Because we want to give an RUL based on a
threshold found by conducting a threshold during HS, we only take regression-based models are
considered (i.e., no classification models were used). On top of that, anomaly detection algorithms
are widely used within predictive maintenance. However, the common goal for those algorithms
is fault detection.
2.3.1 Statistical approaches
Jimenez et al. (2020) stated that statistical models aim to analyze random variables' behavior
based on recorded data. For predictive maintenance, statistical models are used to determine the
current degradation and the expected remaining life of the technical systems. Predicting the
expected remaining life is performed by comparing the current behavior of measured random
variables against known behaviors represented by a series of data. Normalization and data
cleaning are common preliminary tasks performed on data series to obtain the distribution function
before the trend analysis. Cleaning prevents outliers, constants, binary, or any other variable that
is not useful for degradation analysis.
Linear Regression: This is the most basic type of algorithm used for predictive analysis.
Regression estimates are used to explain the relationship between a dependent variable and one
or multiple independent variables (i.e., multiple linear regression such as Luo et al. (2015)). In this
situation, the RUL is considered to be a dependent variable. Also, Mathew et al. (2017) include a
simple linear regression in their work. This linear regression can also serve as a baseline to
measure the quality of more complex algorithms.
ARMA: Stands for autoregressive-moving-average models is primarily a system identify
techniques, generated by using only normal operating data to identify the behavior of complex
systems. The root mean square of residual errors is then used to indicate the machine degradation
through a degradation index. Those residual errors are the different output between the
24
identification model and the behavior of the system. If it exceeds a certain threshold, this indicates
a faulty system. Pham et al. (2012) use such an algorithm on top of a proportional hazard model
and support vector machine to develop a remaining useful lifetime estimation for a low methane
compressor. However, this method seems hard to work out with the absence of run-to-failure data.
Liao et al. (2020) also use an ARMA model. However, run-to-failure data was available.
Bayesian models: The bayesian model is a statistical model where you use probability to
represent all uncertainty within the model, uncertainty regarding the output, and the uncertainty
regarding the input data (i.e., parameters) to the model. Finding these prior probabilities poses the
main problem for Bayesian theorem application. Bayesian models can be applied for predictive
maintenance purposes when data, including anticipated failures with their related symptoms and
life expectancy, is available (Jiminez et al., 2020). However, due to the absence of run-to-failure
data, it is impossible to determine such probabilities to an event.
Statistical models offer potential solutions for diagnostic as prognostics tasks. However, the main
drawbacks of statistical models concern the need for enough previous data to build a reliable
model and uncertainty models. For predictive maintenance systems, statistical models are often
implemented in multi-model approaches. Containing historical data makes statistical models
harder to implement except for the linear regression and other (simple) regression analyses.
2.3.2 Machine learning approaches (AI approaches)
Machine learning is a branch of artificial intelligence that uses specialized learning algorithms to
build models from data. These models can deal with and capture complex relationships among
data, difficult to obtain using physics-based, statistical, or stochastic models (Jiminez et al., 2020).
The results of such approaches are hard to be explained because of the lack of transparency.
Many of these techniques are named “black boxes”. One key point of machine learning models is
their learning process and depends on the system's application, goal, and available data. The
following methods were considered based on the goal of using the algorithms as prognostics.
Decision Tree: In decision tree algorithms, a tree is constructed to serve as a predictive model.
The branches of this tree illustrate the outcome of the decision taken. The observations about an
item can be converted to conclusions with the help of this decision tree, as stated in Mathew et al.
(2017). The work of Patil et al. (2018) also underly the use of decision tree algorithms to retrace
the feature importance for the predictive algorithms.
25
Random Forest (RF): Random forest is an ensemble learning method. It operates by constructing
multiple decision trees when training the algorithm, and the output is the mean prediction of each
of the individual trees. In the research Mathew et al. (2017) conducted while predicting the RUL
of a turbofan engine, the Random Forest Algorithm performed the best compared to various other
machine learning algorithms. Bey-Temsamani et al. (2009) also used it for their similarity model.
Gradient Boosting (GB): This is a forward learning ensemble method. Based on the idea that
good predictive results can be obtained through increasingly refined approximations. Gradient
boosting builds regression trees subsequentially, based on all the dataset features in a fully
distributed way. In the work of Matthew et al. (2017), the gradient boosting algorithm performed
the second to best when predicting the RUL of a turbofan engine.
Support Vector Machine/Regression (SVR): The numeric variables in the data in different
columns form an n-dimensional space. A hyperplane is a line that splits the input variable space.
With the support vector machine, a hyper plan is selected to best separate the points in the input
variable space by their class, normally done using a kernel. Using a support vector regression, it
will converge to RUL prediction. Benkedjouh et al. (2013) use such an SVR method with a
Gaussian kernel to predict the RUL of bearings.
Artificial Neural Network (ANN): ANNs mimic human brains' working process, which connects
many nodes in a complex layer structure. They are the most commonly used AI techniques in the
field of machinery RUL prediction (Lei et al.,2018)
Long Short Term Memory (LSTM): Long Short-Term Memory (LSTM) network is an architect
specializing in discovering the underlying patterns embedded in time-series, is proposed to track
the system degradation, and consequently, predict the RUL. Zhang et al. (2018) use such a
method to predict the RUL of a plane's engine.
Convolution Neural Network: Convolutional neural networks are distinguished from other neural
networks by their superior performance with image, speech, or audio signal inputs. However, it is
also widely used as prognostics of an RUL prediction, as proposed by Li et al. (2018)
Each of those machine learning approaches can be used in an RUL estimation for the company.
When looking at (systematic) literature reviews and surveys (Lei et al., 2018; Jimenez et al., 2020;
Adhikari et al., 2018; Ramezani et al., 2019; Mathew et al., 2017) within the prognostic aspect of
26
data-driven maintenance no to little mention is paid to decision tree methods. The choice is made
to focus on those methods. A benefit of tree methods is that it is relatively easy to determine which
parameters were important in the prediction. Also, more complex methods will be worked out in
the form of CNN and LSTM since these outperform the regular ANN.
2.3.3 (Deep) Transfer Learning
In real-life scenarios, the absence of run-to-failure data is applicable. In the last few years, (deep)
transfer learning or (deep) domain adaptation is also used for a Remaining Useful Lifetime (RUL)
estimation. RUL relates to the amount of time lift before a piece of equipment is considered not to
perform its intended function. Da Costa et al. (2019) delineates a situation where processes that
require prognostics prediction models that can leverage real-time data collected consciously over
different locations. Although they perform similar processes, the system logs different multivariate
sensor data due to equipment version updates, sensor malfunction, and timing. In such cases, Da
Costa et al. (2019) suggest that high dimensional temporal data has to be directly used to
determine the health state of the systems and models to adapt to incoming changes in the data.
The work performed by da Costa et al. (2019) proposes an LSTM network to address the problem
of learning temporal dependencies from time-series sensor data that can be transferred across
relation RUL prediction tasks. The learning is based on a source domain with sufficient run-tofailure annotated data, the target domain containing only sensor data. Da Costa et al. (2019)
developed a Domain Adversarial Neural Network (DANN) approach to learning domain invariant
features that can be used to predict the RUL of the target domain.
This option could be interesting for the case of the company due to the handling of the absence
of run-to-failure data. However, the most important principle of transfer learning is to have a source
domain with sufficient run-to-failure data. The learned behavior can then be subsumed with some
transformations by (deep) transfer learning to be applied to the target domain. In the situation of
the company, there are no similar machines or processes with somewhat partially the same
parameters, which leaves the possibility of implementing (deep) transfer learning.
27
2.3.4 Quality measures
General quality measures stated in various papers, including the papers of Malhotra et al. (2016),
Kim et al. (2021), Abid et al. (2018), Zschech et al. (2019), uses the Root Mean Squared Error
(RMSE) and Mean Absolute Percentage Error (MAPE) as a quality measure for their RUL
prediction. RMSE is shown in Equation 2.1, and MAPE is shown in Equation 2.2.
Equation 2.1 RMSE formula
𝑛
1
2
𝑅𝑀𝑆𝐸 = √ ∑(𝑟 𝑙 (𝑡) − 𝑟∗𝑙 (𝑡))
𝑛
𝑡=1
Equation 2.2 MAPE formula
𝑛
100%
𝑟 𝑙 (𝑡) − 𝑟∗𝑙 (𝑡)
𝑀𝐴𝑃𝐸 =
|
∑|
𝑛
𝑟 𝑙 (𝑡)
𝑡=1
Where n is the number of observations, t is the time index, 𝑟 𝑙 (𝑡) represents the true RUL, and
𝑟∗𝑙 (𝑡) represents the predicted RUL. Because we want to predict the remaining useful lifetime in
products or time units, we used such methods and not the accuracy.
2.3.5 Answering sub research question Q-4
To answer the sub-research question Q-4: Which prediction models can be applied for data-driven
maintenance? We decided to start with simple machine learning methods such as a decision tree
regression. On top of that, we want to apply a more complex neural network that specifically uses
time-series, namely a Long-Term Short Memory (LSTM) network. We use a statistical regression
approach to compare these methods, namely a linear regression. Such a wide variety of methods
is to see which predictive algorithm comes up with the best predictions for the RUL estimation.
28
2.4
Conclusion of literature review
To conclude the systematic literature review, various maintenance policies are identified. Different
methods and algorithms are applicable for diagnostics and prognostics of machine failure
depending on the available information. For the case of the company, the most fitting maintenance
approach is data-driven maintenance since much data is gathered and measured within the
production process of Product Z. Limited knowledge is known about the internal process and the
degradation of the equipment during the production of the product. Various algorithms are
applicable for an RUL estimation. However, the choice is made for two simple machine learning
algorithms (Decision Tree, Random Forest), two complexes machine learning algorithms (LSTM,
CNN), and a statistical approach to compare the machine learning algorithms, namely a simple
linear regression.
2.4.1 GAP in literature
Xu et al. (2019) attempt to provide a brief overview of the PdM system, emphasizing the current
developments of data-driven fault diagnostics and prognostics methods. Xu et al. (2019) described
future trends in the field where data-driven fault diagnostics and prognostics are still developing.
The suggestion is made for future trends in this field, namely:
•
developing accurate hybrid methods combining data-driven and model-based diagnostics
and prognostics approaches.
•
Improving the efficiency of diagnostics and prognostics methods.
•
Predicting the machinery RUL with limited labeled data.
•
Managing the uncertainties properly in the scheduling process of maintenance tasks.
For our case, we have limited labeled data or, more precisely, no labeled data. Little research has
been done presented in the literature on predictive maintenance with no labeled data. This offers
relevance to the academic field of this topic; this is also confirmed by the number of search results
when specifically searched for during the systematic literature review. During this literature review,
only the papers of Kim et al. (2021), Zschech et al. (2019), Malhortra et al. (2016), and You et al.
(2013) mentioned the absence of labeled data. Where Kim et al. (2021), Malhortra et al. (2016),
and You et al. (2013) also mentioned the absence or redundancy of run-to-failure data. None of
those papers used decision tree methods to predict the RUL.
29
Part III – Data exploration, understanding, preparation
3. Data exploration
A deeper understanding of the data is obtained during this phase. The available datasets are
explored in order to understand what data is available as well as its quality. This data exploration
is guided by the problem formulation and the literature review. The focus lies on what data suitable
for our chosen data-driven maintenance strategy. Firstly, general statics are shown to get an idea
of how the distribution looks. Subsequently, the amount of production and incidental maintenance
moments are analyzed to see deviating production cycles. After that, a trend analysis is performed
to analyze parameters that show a constant trend that is necessary for a predictive degradation
model, as was shown in the previous section. Furthermore, the maintenance moments are
analyzed.
3.1
Descriptive statistics
For both numerical datasets, descriptive statics are given to seek outliers and see how different
machines within Machine Y behave compared to each other. On a deeper level, a comparison is
made between each production cell in Machine Y. All the data for the year XXXX is used.
3.1.1 Product dataset
First, the general descriptive statistics are derived from the processed dataset. In Table 3.1, all
the parameters are shown. The product dataset consists of 601,956 data rows. The dataset
consists of five parameters. ROD_11, ROD_12, and ROD_13 indicates removed due to company
sensitive information. And OTAFP indicates the production cell.
Table 3.1 Descriptive statics product dataset
count
missing
mean
std
min
25%
50%
75%
max
ROD_11
601956.00
0.00
6.85
2.12
0.69
5.43
6.61
7.99
105.34
ROD_12
601956.00
0.00
7.30
2.24
1.01
5.81
7.03
8.47
105.09
ROD_13
601956.00
0.00
7.35
2.21
0.80
5.87
7.10
8.54
110.24
OTAFP
601956.00
0.00
15.46
8.66
1.00
8.00
15.00
23.00
30.00
What can be seen is that when we take the first quantile and third quantile into account, that for
all the three parameters (i.e., ROD_11, ROD_12, and ROD_13) are within a range of 5.43 and
8.43. However, what can be seen at the max values is the extremely high numbers compared to
the first and third quantiles. We needed to see if these particular outliers are equally distributed
across all machines within Machine Y (i.e., VT16,VT26,VT36,VT46) or one of those machines is
causing those outliers. It is also important to look at the production cell level. Should the cause be
30
specific to a machine and production cell therein, the cause should be investigated. The same can
be said about the min-value numbers.
When looked at the machine level, Figure 3.1, it can be concluded that the outliers are evenly
distributed across each machine within the Machine Y. Even if the different parameters measured
on Product Z are looked at, this is also evenly distributed.
Figure 3.1 Boxplot of each parameter for each machine
Subsequently, the production cell within these machines are examined. For visibility, this is done
per parameter and each machine. An example is shown in Figure 3.2. To see all parameters with
the respective Machine Y, refer to Appendix C.
Figure 3.2 Boxplot of parameters for production cell within VT16-machine
31
The differences based on the first and third quantities for each production cell distribution differ
but are fairly minimal. Also, the differences in outliers are not specifically attributable to a certain
production cell within a machine, even when looking at Appendix C.
When zooming in on the first and third quartiles per machine, it appears that the
parameters shown minimal differences between different production cells. See Figure 3.3. Based
on the behavior per production cell, it is particularly striking that there are no outliers below the
lowest quartile on some production cell (e.g., cell 1 and cell 6). The median also often differs per
different production cells, as does the distribution of the quantiles. These differences are minimal,
but it can be interesting to make analyses at a production cell level during the modeling phase.
Figure 3.3 Zoomed in boxplot of parameters for production cell within VT16-machine
3.1.2 Process dataset
Secondly, a similar analysis is made for the product dataset. However, this dataset has more data
rows and columns, respectively 22,000,000+ rows and 35 columns. The columns REMARK,
OBEWF, OCTPP, ORACT, and OTFAP are binary or categorical parameters. Therefore, quantiles
of those parameters are meaningless. On the contrary, the descriptive statics of the other
parameters gives meaningful insights. OL1PR, OL2PR, and OL3PR give negative numbers when
the minimal value is given in Table 5.2. It makes sense because those parameters indicate the
position of Product Z within the production cell based on a reference point. For comparison, OVKZ
also gives a negative number as the minimum value. Having discussed this with the domain
expert, this may not be possible, indicating corrupted data.
After discussing all the descriptive statics with the domain expert, a product can only be
produced if removed due to company sensitive information indicated by the parameter OTVKT. A
missing value for this parameter is a corrupted data point; this is the case for 2,666,070 data
points. Those data points would be removed in the data preparation phase. In Table 3.2, all
32
parameters are shown, which are measured when the Machine Y is fabricating.
Table 3.2 Descriptive statics process dataset
count
missing
mean
std
min
25%
50%
75%
max
count
missing
mean
std
min
25%
50%
75%
max
count
missing
mean
std
min
25%
50%
75%
max
REMARK
0
22246927
OL2PR
17153164
5093763
-0.0453
35.19797
-1870.6
-18.8
0
18.8
1710.8
OTVKT
19580857
2666070
1304.731
155.3285
0
1191
1291
1396
3721
OBEWF
329132
21917795
19.06832
7.568774
0
19
24
24
30
OL3PR
17547304
4699623
1.183271
36.78888
-1983.4
-18.8
0
18.8
1739
OVNKT
19367536
2879391
311.2378
34.61268
0
279
303
343
2000
OCTEN
19627563
2619364
21600.26
3962.155
0
19248
21344
23776
104736
OPRPX
19649003
2597924
14320.05
1519.914
0
12565
15184.16
15286.14
17121.76
OVNKZ
19549684
2697243
165.6038
18.72718
-81.8
153
165
178.3
1413.8
OCTEO
19611740
2635187
19819.13
2570.739
0
18544
19872
21264
70016
OPRPY
19649287
2597640
16491.61
977.1917
0
15535.29
16286.65
17589.03
18983.24
OVSP1
19561000
2685927
4129.676
637.0317
0
3638.7
3965.3
4203
6033.6
OCTOK
19627323
2619604
61385.99
7441.904
0
57696
61600
65568
144768
OPTEW
8544604
13702323
2671.496
762.0827
-1
2071
2674
3307
4550
OVSP3
17731528
4515399
20.76635
0.768799
0
20.4
20.6
21
28.2
OCTOV
12548883
9698044
104.0141
21.87353
0
96
96
112
3552
ORACT
57250
22189677
0.985659
0.118892
0
1
1
1
1
OVSP4
17341812
4905115
10.48372
0.483952
0
10.2
10.4
10.7
29.5
OCTPG
158787
22088140
14.35211
855.5327
0
0
0
0
117376
OSTV1
19584413
2662514
1017.452
121.4371
0
932
1003
1088
2017
OVSP5
16624150
5622777
7.355334
0.374405
0
7.1
7.3
7.5
12.1
OCTPP
91285
22155642
0
0
0
0
0
0
0
OSTV3
19186064
3060863
131.5311
22.86511
0
116
127
142
2004
OVTV1
19580374
2666553
998.7494
124.7466
0
910
987
1073
1987
OCTSC
19602719
2644208
5252.139
2777.877
0
3456
4512
6528
71920
OSTV4
19209996
3036931
109.8519
20.44288
0
95
107
122
852
OVTV3
19083104
3163823
118.1898
22.6554
0
103
114
128
1861
OCTU3
4788930
17457997
96.18299
116.1308
0
16
48
128
1168
OSTV5
19338658
2908269
106.2063
30.33349
0
85
101
122
938
OVTV4
19110594
3136333
96.01248
20.24725
0
82
92
108
837
For each parameter within this dataset, histograms and boxplots are made. Those boxplots are
shown per machine and, on a deeper level, per production cell. On top of that, histograms are
made for the categorical parameters to see the distribution per category. All the outliers per
respective machine or production cell are discussed with the domain experts. All corrupt behavior
is removed in the data preparation phase, removing all the behavior for each parameter which is
more than three standard deviations from the mean.
Next, the production for each machine is shown in the following subsection. The production, in
combination with the number of incidents of the Component X or production cell, gives a clear
picture of which maintenance period obtained irregular behavior. When the data is prepared, this
is considered only to take clean data periods into account.
33
OL1PR
17629655
4617272
2.902294
38.39188
-1974
-18.8
0
18.8
1720.2
OTAFP
19683300
2563627
15.49777
8.653749
0
8
15
23
30
OVTV5
19277183
2969744
92.55479
30.27356
0
71
88
109
656
3.2
Production and incidents per period
The number of products produced for each machine within Machine Y is shown in Table 3.3. In
this table, the production numbers per period (i.e. every two weeks) for each specific machine
are indicated to indicate if the production is evenly distributed over the year. The incidental
maintenance moments are given between brackets.
Table 3.3 Production per period for each machine
Because the VT46 was not introduced within the organization until the end of XXXX, this creates
extensive gaps in the data. There are also gaps in the production of the VT46 due to
malfunctions in the recording of data. There are also some fluctuations for each production
period. During the data preparation phase, periods with low manufactured products or a high
number of incidental maintenance moments are considered. Those moments could cause
unpredictable behavior and are unable to represent reality.
34
3.3
Failure rate during lifetime of Component X
A logical consequence of the aging of the Component X would be that more products would fail in
the production process. After all, the Component X are replaced so that the process can perform
optimally. However, this is not the case. In Figure 3.4, the production hour compared to the last
maintenance moment shows no increase in failed products. Also, the number of product failures
due to the Component X is neglectable, about 4,000 products based on 22,000,000 products.
Figure 3.4 Failure rate during lifetime of Component X
3.4
Seeking trends in data
A Mann-Kendall Trend test is used to determine whether or not a trend exists in time series data
(Kamal and Pachauri, 2018). It is a non-parametric test, meaning there is no underlying
assumption made about the normality of the data. The null hypothesis, H0, states that there is no
monotonic trend, and this is tested against one of three possible alternative hypotheses, HA: (i)
there is a monotonic upward trend, (ii) there is a monotonic downward trend, or (iii) there is either
a monotonic upward trend or a monotonic downward trend. It is a robust test for trend detection.
Kemal and Pachauri (2018) stated the following assumptions underlie the MK test:
-
In the absence of a trend, the data are independently and identically distributed (iid).
-
The measurements represent the true states of the observables at the times of
measurements.
-
The methods used for sample collection, instrumental measurements, and data
handling are unbiased.
35
Following the approach of Kamal and Pachauri (2018), the first step in the Mann-Kendall test for
a time series x1 , x2 , … , xn of length n is to compute the indicator function sgn(xi − xj ) such that,
see Equation 3.1:
Equation 3.1 Sign formula of Mann Kendall trend test
1,
𝑠𝑔𝑛(𝑥𝑖 − 𝑥𝑗 ) = { 0,
−1,
𝑥𝑖 − 𝑥𝑗 > 0
𝑥𝑖 − 𝑥𝑗 < 0
𝑥𝑖 − 𝑥𝑗 ≥ 0
Which tells whether the difference between the measurements at time 𝑖 and 𝑗 are positive,
negative, or zero. Next, the mean and variance of the above quantities, the mean 𝐸[𝑆], is given
by Equation 3.2. S is the statistic calculated by the Mann-Kendall trend test:
Equation 3.2 S statistic formula of Mann Kendall trend test
𝑛−1
𝐸[𝑆] = ∑
𝑖=0
𝑛
∑ 𝑠𝑔𝑛(𝑥𝑖 − 𝑥𝑗 ),
𝑗=𝑖+1
Furthermore, the variance 𝑉𝐴𝑅(𝑆) is given by Equation 5.3:
Equation 3.3 Variation formula of Mann Kendall trend test
𝑝
1
𝑉𝐴𝑅(𝑆) =
(𝑛(𝑛 − 1)(2𝑛 + 5) − ∑ 𝑞𝑘 (𝑞𝑘 − 1)(𝑞𝑘 − 1)(2𝑞𝑘 + 5)),
18
𝑘=1
Where 𝑝 is the total number of tie groups in the data, 𝑞𝑘 The number of data points in the 𝑘-th tie
group, and 𝑛 the number of data points within the time series.
Using the 𝐸[𝑆] and the 𝑉𝐴𝑅(𝑆) the Mann-Kendell statistic is computed, using the following
transformation, which ensures that the test statistic 𝑍𝑀𝐾 (normalized test statistic) is distributed
approximately normally, following Equation 3.4:
Equation 3.4 Normalized test static of Mann Kendall trend test
𝐸[𝑆] − 1
𝑍𝑀𝐾
√𝑉𝐴𝑅(𝑆)
= 0,
𝐸[𝑆] − 1
,
{√𝑉𝐴𝑅(𝑆)
,
𝐸[𝑆] > 0
𝐸[𝑆] = 0
𝐸[𝑆] < 0
At a significant level 𝛼 (0.05) of the test, the computation is made whether or not to accept the
alternative hypothesis 𝐻𝑎 for each variant 𝐻𝑎 Separately: The trend is decreasing if Z is negative
and the computed probability is greater than the level of significance. The trend is increasing if the
Z is positive and the computed probability is greater than the level of significance. If the computed
probability is less than the level of significance, there is no trend. This process is done for all
36
parameters within the process dataset and the production dataset for each production period.
However, only a continual trend was found for the product dataset. Parameters that have a trend
are used to re-evaluate the correctness of the planned maintenance moments in the next
paragraph.
In Table 3.4, only the parameters shown a constant trend for the time-series data, which is only
the product dataset that measures removed due to company sensitive information. Looking at
which production cycles deviate from the other cycles helps us exclude these production cycles
in the data preparation phase, which will improve the quality of the predictive model.
Table 3.4 Results of Mann Kendall trend test for product dataset
VT16
VT26
VT36
VT46
Period
Samples
Trend
Sig
Samples
Trend
Sig
Samples
Trend
Sig
Samples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
9069
9875
8939
8363
8573
4515
10133
7172
11167
7846
11537
9863
9201
2503
4245
7318
13038
11324
8304
9688
9097
7520
7292
3913
2996
down
down
down
down
down
down
down
down
down
down
down
down
down
down
No
up
down
down
down
down
down
down
down
down
down
***
***
***
***
***
***
***
***
***
***
***
***
***
***
No
***
***
***
***
***
***
***
***
***
***
9236
10081
9944
11505
7967
7795
5645
8846
8324
8155
7794
10717
10473
7068
down
down
down
down
down
down
up
down
down
down
up
down
down
down
***
***
**
***
***
***
***
***
***
***
*
***
***
***
6479
13622
9509
11638
7663
8676
9062
1461
1329
2868
down
down
down
down
down
down
down
down
down
down
***
***
***
***
***
***
***
***
***
***
8609
8411
8191
8454
6619
8123
4662
8697
7907
8482
8872
3067
7565
8854
74
7424
6346
4457
8039
7132
7921
4410
3605
4129
5538
down
down
down
down
down
down
down
down
down
down
up
down
down
down
No
down
down
down
down
No
down
No
down
down
down
***
***
***
***
***
***
*
***
***
***
***
***
***
***
No
***
***
***
***
No
3
No
No
***
144
No
No
No
8087
down
***
***
10116
down
***
***
3288
down
*
***
4961
down
***
*** p < 0.001, ** p < 0.01, * p < 0.05
Trend
Sig
What strikes one when looking at Table 3.4 are the deviating production cycles. For VT16: period
15 & 16, for VT26: 7, 11 & 15, for VT36: 11, 15, 20 & 22 (to a lesser extent period 7) and for VT46:
period 20 & 21 (to a lesser extent period 24). These periods are not included in the data
preparation phase. It also appears that ROD_11, ROD_12, ROD_13 have a constant downward
trend. This downward trend offers the possibility to use this as a degradation parameter to
establish a lower bound for a predictive maintenance policy. Because these parameters have the
same behavior most of the time, they are also used in the following subsection to check the
maintenance moments for the correctness
37
3.5
Analyzing maintenance moments
Since the previous subsection parameters were found to show a stable trend over the lifetime of
the Component X, these parameters are used to evaluate the maintenance periods. There are
four machines with individual production cycles. An example of a sequence of data that indicates
abnormal behavior is given in Figure 3.5. Abnormal behavior are: jumps in the data are not linked
to a maintenance moment (red dotted) or a maintenance moment with no the data (green dotted).
Figure 3.5 Example abnormal behavior
All the possible irregular behavior is recorded in Table 3.5. In that case, the maintenance moments
have deviated from the two-week cycle. All these abnormal maintenance moments are discussed
with domain experts, and during the data preparation phase, the maintenance periods were
adjusted.
Table 3.5 Reviewed maintenance moments
Timestamp
removed due to
company sensitive
information
Machine
VT16
VT16
VT16
VT16
VT16
VT16
VT16
VT26
VT26
VT26
VT36
VT36
VT36
VT36
VT36
VT36
VT36
VT36
VT36
VT36
VT36
Action
Remove
Remove
Remove
Add
Add
Add
Add
Remove
Remove
Add
Remove
Remove
Remove
Remove
Remove
Add
Add
Add
Add
Add
Add
Confirmed
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
38
4. Data preparation
Validation of the data is important so that a good analysis will be made. Using incorrect data can
affect the quality of your model severely. The data has to be prepared so it is correct, and it can
be used for the analysis and as input for the model. With the data preparation step, it is necessary
to take the following steps: data integration, data cleaning, data transformation, feature selection,
and data reduction. This sequence is also used as the structure of this section,
4.1
Data integration
For the analysis to see whether data-driven maintenance can be applied to Machine Y, historical
data (i.e., full production year XXXX) is used, obtained as CSV files from an ORACLE database;
this applies to both the product and process dataset.
We can classify the data sources under the following headings: Logbook, which keeps track of the
incidental maintenance moments (entered manually). The process dataset logs various
parameters related to the production of the product, and finally, the product dataset, which
measures different parameters regarding the product. Both the product and process datasets are
automatically maintained in the ORACLE database. Based on the timestamp, the data can be
linked to each other, as it is tracked automatically in real-time with minimal delay.
However, the data can be grouped at several layers, namely at the machine level or at the
production cell level. We grouped the data based on the respective machine. Because the process
data is kept per product, and the product data is based on a production sample. It was decided to
use different degrees of granularity, the data grouped through the mean of this interval. The data
is split into daily, 8-hourly, hourly, and quarter data on the machine level.
4.2
Data cleaning
Data cleaning is necessary to correct corrupt or inaccurate data. Tasks fill in the missing values,
identify the outliers, correct inconsistent data, and resolve redundancy caused by data integration.
Data cleaning for the current situation can be divided into three tasks, namely
•
Handling of outliers and missing values
•
Adjusting maintenance moments
•
Selection of applicable production periods
The actions that have been carried out are briefly dealt with in the following sub-sections. This
is in response to the behavior in the data exploration stage.
39
4.2.1 Handling outliers and missing data
First, we focus on the process dataset concerning the missing data. In Table 5.2, descriptive
statics of the process dataset is shown. After discussing this with the domain experts, it turned out
that a data entry must at least have a value for the parameter OTVKT. Otherwise, the product
cannot be manufactured. A data entry must also be linked to a table position and a machine, which
is indicated with OTAFP and WORKCELL, respectively. All data entries with no value filled in for
these parameters are deleted, indicating a corrupt datapoint. The number of data points from the
processed dataset is the original 22,246,927 datapoints. When the requirements above are taken
into consideration, the number of data points is 18,495,610.
Since we are using historical data from 2020, we have a period before the first maintenance
point and a period after the last maintenance point, which cannot be linked to a whole production
cycle. These data points are also not considered. When this is considered, we are left with
18,214,165 data points for the process dataset. This number is used to create a target variable for
each cycle based on these production numbers. Before using the variables, outliers are removed.
For the product dataset, there are no missing data for one of the parameters. All data entries are
interconnected to a specific machine and production cell. Therefore, only actions have been taken
concerning the outliers. All data points that are more than three standard deviations from the mean
are removed concerning the specific parameter (i.e., all three parameters). Also, the points that
cannot be linked to a production cycle are removed, just like in the dataset. If all steps are followed,
the total number of data entries is reduced from 601,956 to 582,832 data points.
4.2.2 Adjusting maintenance moments
For each machine, the data points of the process dataset are examined. The constant trend found
in the data for these parameters in subsection 3.4 shows several moments where the trend
continues, suggesting that there has been no maintenance and moments where there should have
been maintained, not showing the expected behavior. The adjusted moments are shown in Table
3.5
4.2.3 Selection of applicable production periods
To ensure that the prediction model is as accurate as possible, only realistic production cycles will
be considered. After consultation with the domain experts, cycles with limited production (i.e.
removed due to company sensitive information), cycles with relatively high numbers of incidental
maintenance moments (i.e. removed due to company sensitive information), and cycles that show
40
no or opposite trends are not included. After entering the new maintenance moments, the same
analysis was performed as in the data exploration stage. This results in the following periods as
input for the model, see Table 4.1. Prod. Indicates the limit of removed due to company sensitive
information products is reached. Inc. indicates incidental maintenance moments which could not
exceed removed due to company sensitive information. The trend indicates the downwards trend
for the parameters in the product dataset. In the last column, the determination is made on whether
the period is used as input for the prediction model
Table 4.1 Review of production periods
Period
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Prod.
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
4.3
VT16
Inc. Trend
Y
Y
Y
Y
Y
Y
N
Y
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Used
Y
Y
Y
N
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
Prod.
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
N
Y
VT26
Inc. Trend
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
Y
N
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Used
Y
Y
Y
Y
Y
N
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
N
Y
Prod.
N
N
N
N
N
Y
Y
N
N
N
Y
Y
N
N
N
N
N
Y
N
N
Y
Y
Y
Y
Y
Y
VT36
Inc. Trend
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
N
Y
Y
N
Y
Y
Y
Y
Y
Y
Used
N
N
N
N
N
Y
Y
N
N
N
Y
Y
N
Y
N
N
N
Y
N
N
Y
N
N
Y
Y
Y
Prod.
N
N
Y
Y
Y
Y
VT46
Inc. Trend
Y
N
Y
Y
Y
Y
N
N
N
N
Y
Y
Used
N
N
N
N
Y
Y
Data transformation
Data has to be converted to the right format. In the data, the column WORKCELL is used to
indicate which machine is used to manufacture the product in question—indicated as a string,
which is converted to a binary value while using one-hot encoding. Subsequently, the timestamps
are changed from string to DateTime. Lastly, a different name is used for the table position (i.e., a
production cell within a machine) for the process and the product dataset to a general name to
link the datasets.
Data is grouped on different granularities to extract variation from the data. These time
buckets were also used to create different features stated in the next subsection.
41
4.4
Feature selection
For selecting fitting input parameters from both the product dataset and the process, the dataset
can be accessed. This is because the product dataset had a degrading trend in all three measured
parameters, which would correlate with the wear of Component X. In the experiments, Yang et al.
(2007) conducted their classification model performance improved for fault diagnosis with timedomain features. Yang et al. (2007) had a different goal in mind, namely fault detection. Their
project focuses on prognostic maintenance. It was decided to apply the time-domain features they
had used for this case, intending to obtain a more accurate prediction model. The input for the
time-domain features is based on different time granularities (i.e., daily, 8-hourly, hourly, quarter)
based on the average value of the parameters of the product dataset, see Table 4.2.
Table 4.2 Time-domain features
Feature
Equation
1
Feature
Equation
Variance
𝑛 (𝑥(𝑡)
𝑥𝑣𝑎𝑟 = 𝛴𝑡=1
− 𝑥̅ )2
1
Mean
𝑛
𝑥̅ = 𝛴𝑡=1
𝑥(𝑡)
Square mean root
𝑛 |𝑥(𝑡)|1/2 2
𝑥𝑟 = ( 𝛴𝑡=1
)
Root mean square
𝑛
𝑥𝑟𝑚𝑠 = ( 𝛴𝑡=1
𝑥(𝑡)2 )1/2
Max value
Peak-peak value
Skewness
𝑥𝑚𝑎𝑥 = 𝑚𝑎𝑥(𝑥(𝑡))
𝑥̂ = max( |𝑥(𝑡)|)
Min value
𝑥𝑚𝑖𝑛 = 𝑚𝑖𝑛(𝑥(𝑡))
𝑛 (𝑥(𝑡)
𝑥𝑠𝑘𝑒 = 𝛴𝑡=1
− 𝑥̅ )3
Kurtosis
𝑛 (𝑥(𝑡)
𝑥𝑘𝑢𝑟 = 𝛴𝑡=1
− 𝑥̅ )4
S-factor
I-factor
𝑆 = 𝑥𝑟𝑚𝑠 /𝑥̅
𝐼 = 𝑥̂/𝑥̅
C-factor
L-factor
𝐶 = 𝑥̂/𝑥𝑟𝑚𝑠
𝐼 = 𝑥̂/𝑥𝑟
4.5
𝑛
1
𝑛
1
𝑛
𝑛
1
𝑛
1
𝑛
Data reduction
As mentioned before, all data entries that could not be linked to a production period (i.e., the period
between two planned maintenance moments) were removed. Also, several cycles were not
included because of limited production, due to numerous incidents, or no proven trend. See Table
6.1. Finally, the following parameters have been removed from the process dataset: E.REMARK,
the parameter is removed it has only empty values.
4.6
Conclusion data exploration
The goal of this section was to prepare the data for the modeling phase. A more in-depth overview
is given about the available data. Data exploration helps to answer the sub-question: Q-2: What
are the characteristics of the current situation? The maintenance moments are revised. Timedomain features are added. The parameters in the product dataset show a trend and are
potentially useable to use as a health indicator. The maintenance moments are revised. In
Appendix D a snapshot of the different granularities is shown. For making different granularities,
raw data consists of 582,832 rows and 25 columns (i.e., features).
42
Part IV – Modeling
5. Experimental setup
As noted in section 2, prognostics can be divided into three phases (i.e., four if data monitoring is
included). Those three prognostics steps: Health indication (HI), Health stage (HS) division, and
RUL prediction. The section is structured based on those three key steps.
5.1
Heal indication construction
For selecting a fitting HI for the case of the company, we first evaluate which kind of HI fits best
for the situation. Abid et al. (2018) describe HI’s classified in two categories: physics health
indicators and virtual health indicators. Physical HI’s are based on a single feature such as using
raw data gathered from sensors, residuals-based feature, time domain, or time-frequency feature
extracted from data measured by monitoring sensors. In the case of complex degradation, it is
hard to find one feature sensitive to those degradations. To tackle this problem, features can be
combined in order to exploit their complementarity. However, during the data exploration, no form
of degradation was found except for the parameters in the product dataset. Because the
degradation in those parameters was gradual, we make use of physical HI. To evaluate possible
health indicators, monotonicity and trendability are considered, as suggested by Abid et al. (2018).
Nguyen et al. (2021) also mentioned that monotonicity and trendability are the only factors that
can evaluate a HI when no run-to-failure data is available.
Monotonicity is used to evaluate the negative or positive trend of the health indicator. Monotonicity
can be measured by the absolute difference between HI's negative and positive derivatives, as
indicated in Equation 5.1.
Equation 5.1 Formula for Monotonicity
𝑑
𝑑
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 ( > 0) 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 ( < 0)
𝑑𝑥
𝑑𝑥
𝑀= |
−
| , 𝑀 ∈ [0; 1]
𝑛−1
𝑛−1
𝑑
Where 𝑑𝑥 represents the derivative of the HI, 𝑛 represents the number of variations, 𝑀 represents
higher monotonicity of degradation when it approaches 1.
43
Trendability is related to time and represents the correlation between the degradation trend and
the operating time of the Component X. Trendability is calculated with Equation 5.2:
Equation 5.2 Formula for Trendability
𝑅=
𝑛
𝑛
𝑛
𝑛(𝛴𝑖=1
𝑥𝑖 𝑡𝑖 ) − 𝑛(𝛴𝑖=1
𝑥𝑖 )𝑛(𝛴𝑖=1
𝑡𝑖 )
𝑛
√[𝑛𝛴𝑖=1
𝑥𝑖2
−
2
𝑛
𝑛
𝑥𝑖 ) ] [𝑛𝛴𝑖=1
𝑡𝑖2
(𝛴𝑖=1
2
𝑛
− (𝛴𝑖=1
𝑡𝑖 ) ]
, 𝑅 ∈ [−1; 1]
𝑅 ∈ [−1; 1] represents the correlation coefficient between indicator x and the time index t. When
𝑅 approaches, 1 HI has a strong positive linear correlation with time.
In subsection 3.4, the raw parameters regarding the parameters of the product dataset (i.e.,
ROD_11, ROD_12, and ROD_13) were monotonic and had a trend. When the results were
discussed with domain experts from the company, a potential reason was given why there is a
possible correlation between parameters of the product dataset and the condition of the
Component X. Due to the position of Product Z in the production cell, removed due to company
sensitive information regarding the indirect relationship This explains the difference between a
new Component X and a worn-out Component X. We will test this hypothesis in the next
subsection by calculating the correlation of the HI to the RUL.
However, to find the best single parameter to use as a health indicator, we want to quantify the
results. We also took the time-domain features based on the parameters of the product dataset
into consideration. In Table 4.2, results are shown for monotonicity and trendability for various
options as a HI. The results are averaged based on each production cycle, as shown in Table 5.1.
In Table 5.1, we can see the effect of monotonicity and trendability when changing the data
granularity. Different time-domain features are calculated based on various rolling windows. It can
be seen that a higher data granularity (e.g., daily) results in a higher score based on monotonicity
and trendability. During production, differences in measured data are quite large (i.e., much
variation), and when the data is averaged, it creates less noise, and it will degrade more stepwise.
Based on the evaluation criteria, the mean (i.e., based on sliding window) outperforms other timedomain features in monotonicity and trendability. AVG_ROD is used as a baseline. This parameter
holds the average values of the parameters of the product dataset, while the mean takes a sliding
window based on this parameter.
44
Table 5.1 Testing monotonicity and trendability on potential HI's
Raw
Mon
Trend
0.005 -0.245
-
Avg. ROD
Mean
Var
Max
Min
SMR
RMS
Peak-peak
Skewness
Kurtosis
S-factor
C-factor
I-factor
L-factor
Daily
Mon
Trend
0.428 -0.771
0.534 -0.829
0.283
0.208
0.167 -0.140
0.382 -0.762
0.514 -0.827
0.449 -0.800
0.257
0.534
0.178
0.047
0.169
0.116
0.248
0.567
0.424
0.743
0.418
0.753
0.419
0.754
8 Hourly
Mon
Trend
0.161 -0.686
0.205 -0.773
0.109
0.197
0.116 -0.243
0.175 -0.674
0.224 -0.774
0.200 -0.737
0.138
0.301
0.097 -0.022
0.083
0.041
0.114
0.438
0.160
0.575
0.155
0.590
0.165
0.592
Hourly
Mon
Trend
0.028 -0.614
0.035 -0.642
0.033
0.136
0.044 -0.272
0.049 -0.539
0.038 -0.631
0.031 -0.590
0.050
0.090
0.029 -0.020
0.037
0.007
0.033
0.226
0.055
0.317
0.055
0.331
0.055
0.334
Quarter
Mon
Trend
0.016 -0.484
0.017 -0.527
0.016 0.084
0.035 -0.265
0.035 -0.461
0.017 -0.512
0.020 -0.474
0.040 0.051
0.020 -0.016
0.015 -0.002
0.169 0.129
0.039 0.218
0.042 0.226
0.039 0.229
Based on the values found for monotonicity and trendability, a deeper analysis was conducted to
see the impact when data granularity is adjusted based on different sliding windows. The results
for this analysis are shown in Table 5.2. When a higher-level granularity is taken, the better the
monotonicity scores. When a lower-level granularity is taken, the monotonicity will decrease due
to variation in the data because many data points are considered. Also, when taken a wider sliding
window, the trendability has increased for lower granularity data.
To conclude the analysis, the mean of a sliding time window is fitted due to the high trendability
over time. However, the monotonicity is scoring low at lower-level granularity, and this can cause
inaccuracy during a prediction or the RUL. To test the suitability chosen HI, a correlation is
conducted to the RUL in the next subsection.
Table 5.2 impact of granularity and sliding time window
Mean
Daily
Granularity
8-hourly
Hourly
Quarter
Raw data
Daily
Mon: 0.534
Trend: -0.829
Mon: 0.402
Trend: -0.817
Mon: 0.243
Trend: -0.839
Mon: 0.151
Trend: -0.847
Mon: 0.093
Trend: -0.854
Sliding time window
8-Hourly
Hourly
Mon: 0.486
Mon: 0.421
Trend: -0.802
Trend: -0.759
Mon: 0.205
Mon: 0.165
Trend: -0.773
Trend: -0.668
Mon: 0.095
Mon: 0.035
Trend: -0.797
Trend: -0.642
Mon: 0.056
Mon: 0.020
Trend: -0.804
Trend: -0.645
Mon: 0.054
Mon: 0.029
Trend: -0.810
Trend: -0.659
Quarter
Mon: 0.425
Trend: -0.763
Mon: 0.152
Trend: -0.671
Mon: 0.034
Trend: -0.605
Mon: 0.017
Trend: -0.527
Mon: 0.021
Trend: -0.522
45
5.2
Health stage division
In the previous subsection, we chose the best HI to the condition of the Component X (i.e., system
health). When a degradation occurred, the HI presents a decreasing trend. The next step in the
process to predict the RUL is the HS division. Normally, when determining different HS divisions,
the degradation can be detected by dividing the HI into two or multiple stages using a threshold
according to the degradation trend. Dividing the health stage using a threshold is widely used in
the literature for this task (Abid et al., 2018).
Abid et al. (2018) offer solutions for determining an initial threshold when no-fault history is known.
Abid et al. (2018) assume an arbitrary threshold. This arbitrary initial threshold can be provided by
an expert or determined based on the HI calculated from the training data.
After contact with domain experts of the operational process at the company, no initial
threshold for a parameter can be set based on expert knowledge. Therefore, the only option
available is to determine a somewhat arbitrary initial threshold. Abid et al. (2018) use a gaussian
distributed-based value because z-normalization was applied in their preprocessing method.
However, there are more options, namely:
•
A static lower bound (i.e., arbitrary number)
•
A relative lower bound (i.e., based on a degraded percentage based on the first few
measurements of a cycle)
•
Lower-bound based on statistics (i.e., same method as Abid et al. (2018)
When results are generated in section 7, the three methods to determine a lower bound are
compared. To analyze which lower bound fits best with the data in terms of accuracy. Still, a
correlation has been calculated between the RUL and the HI. The results were 0.945, 0.35, and
0.948, respectively, to the static, relative, and statistics way of determining a lower bound. The
options were calculated based on hourly data and using a rolling window of one day to reduce the
variation for each datapoint. The high correlation between the RUL and HI confirms that the
average values of the product parameters can predict the condition of the Component X.
To conclude, this method can be used even if run-to-failure data do not exist, and it is expected
that the threshold can be updated when run-to-failure data accumulates, as mentioned by Abid et
al. (2018). An HI in an unsupervised manner can capture the degradation in a system. The HI
decreases as the system degrades. The lower bound can be replaced when run-to-failure data
becomes available.
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5.3
RUL prediction
As stated, we use degradation modeling based on a data-driven approach. In the literature review
(see section 2), various potential prediction models were discussed and are implemented. To
ensure satisfactory results, an experimental setup has been drafted. For graphical representation,
see Figure 5.1.
Figure 5.1 Experiment setup of RUL prediction
At first, the preprocessing set will be reviewed to guarantee that only valuable and useful
information is used for the prediction model. Data is integrated, cleaned, transformed, and
removed in this preprocessing step according to section 4. After that, the data is split into training
to determine the best parameters and a test set to predict the RUL. This split is done based on a
70%-30% split based on a full production cycle. A production cycle is a period on a specific
machine between preventive maintenance moments. The feature selection is done by a
comparison between the importance of each feature. After the RUL prediction, the accuracy
results will be described. The split based on the train and test set is shown in Figure 7.2 on the
next page.
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In Figure 5.2, the different trajectories are shown based on the health indicator. A relative lower
bound is used for this graph based on 15% degradation based on the first 10 hours of data. The
health indicator is the average result of the parameters from the product dataset. Based on the
test set, a random point in time is selected to estimate the RUL. This method is chosen to take
any real-life application into account. Where at some point, you want to see how many more
products can be produced until Component X needs to be replaced.
Figure 5.2 Trajectories of train and test set with a cut-off point
To determine the effectiveness of the different prediction models, an evaluation must be made
using suitable and meaningful metrics. Based on the literature review conducted in section 2, the
Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) are widely used
in the literature for RUL evaluation depending on the real RUL. For the evaluation, the failure point
is set based on the lower bound. A comparison is made based on the real RUL is compared to
the predicted RUL.
During the process so far, different choices and options are discussed without knowing the effect
on the accuracy of the RUL prediction. Therefore, we want to evaluate different variations which
could be based on the current data. Various experiments are prepared, namely:
•
Determine the best RUL prediction models for the case of the company
•
The determination of lower bounds on the RUL prediction
•
The granularity of the data versus the sliding time window on the RUL prediction
•
Filtering the data on machine level versus production cell level on the RUL prediction
•
Impact of stationary process data on RUL prediction
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To determine the best prediction models, two different decision tree methods are implemented
and two different complexes neural networks, namely: CNN and LSTM. As a baseline, we
compare those results versus a simple linear regression based on the HI.
To see the best determination of lower bounds, three options are compared to the bestperforming prediction models. The three options are a static lower bound, a relative lower bound,
and a more statistical-based lower bound based on a gaussian distribution after standardizing the
data.
Based on the best prediction models for the prediction, RUL with the best functioning lower
bound of different settings within the data preprocessing is compared based on data granularity
and a sliding time window. The different data granularities and sliding time windows can be seen
in Table 5.2.
Second last, another adjustment is made within the data preprocessing. The data is filtered
at a position level within the machine (i.e., production cell) rather than at the machine-level. In
order to compare the accuracy based on the same analysis. However, it has been stated from the
company that maintenance of all production cells is preferably changed simultaneously per
machine because of efficiency and the associated costs.
Lastly, the influence of adding additional features is evaluated. All the variables based on
the process data were not considered due to their stationary behavior. Additionally, when finding
trends in the data understanding phase, no trends were found when performing the Mann-Kendall
Trend test is.
Before we perform all the tests, all used prediction models are briefly discussed in the next section.
Where needed, the method by which the data is standardized or normalized is explained. Lastly,
hyperparameter optimization is addressed to achieve the optimal results for each specific
prediction model.
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6. Modeling
In this section, all the models are briefly explained, which are applied to the RUL prediction of
Component X. First, the general concept of each prediction model is described. Following this, we
discuss specific tunings within the respective prediction model. We also mentioned that
standardization or normalization is applicable for the prediction model. Lastly, we mentioned how
parameter optimization had been done for its respective prediction model.
6.1
Linear Regression
Simple linear regression is a statistical model, widely used in ML regression tasks, based on the
idea that the relationship between two variables can be explained by Equation 6.1:
Equation 6.1 Simple linear regression
𝑦𝑖 = 𝛼 + 𝛽𝑥𝑖 + 𝜀𝑖
Where 𝜀𝑖 Is the error term, 𝛼 and 𝛽 are parameters of the regression, 𝛽 represents the variation
of the dependent variable compared to the independent variable. α represents the value of our
dependent variable when the independent one is equal to zero (i.e., intercept). Using simple linear
regression, we want to find the parameters 𝛼 and 𝛽 that minimize the error term squared; this
procedure is called Ordinary Least Squared error (OLS).
For the company, we use simple linear regression as a baseline to compare the more complex
machine learning algorithms. The RUL is the dependent variable, while the HI is the independent
variable. We train a linear regression function based on the training data, as shown in the previous
section. For finding the optimal parameters for the linear regression, we used an Ordinary Least
Square method (OLS). After that, we use new data (test data) to validate the found linear function
and know the performance based on the RMSE and MAPE.
6.2
Decision Tree
Patil et al. (2018) described a decision tree as the principle of simple decision-making rules worked
out in a flow chart form to get the desired output. In decision tree regression, various subsets of
the existing dataset are created to form decision nodes and leaf nodes. Decision nodes represent
features, and leaf nodes represent a decision. However, because we focus on the regression of
the decision tree, the target is in the form of a numerical value (i.e., RUL value). The input is the
feature set, while the output is the formation of a decision tree with a decision called a root node
representing the topmost decision node of the tree corresponding to the best predictor. We use
two decision tree methods for our method: Gradient Boosted Regression Tree and Random
Forest.
50
6.2.1 Gradient boosted regression tree (XGBoost)
Gradient boosted regression tree (e.g., XGBoost) is an iteratively accumulative decision tree
algorithm. The prediction model can accumulate the results of multiple decision trees as the final
prediction output by establishing a group of weak learners
Gradient boosted regression trees are also ensemble learners like Random Forest, which use
decision trees as base learners, but they differ in the following manners according to Singh et al.
(2019):
(1) Random Forest is an ensemble of low bias and high variance deep decision trees whereas,
boosted trees use high bias and low variance shallow trees as base learners
(2) In Random Forest, base decision trees grow in parallel, whereas in gradient boosted trees,
it is done sequentially. Since boosting is a directed search where a new tree learns the
gradient of the residuals at each iteration, between the target values and the currently
predicted values. Gradient boosted trees use gradient descent based on learned
gradients.
For optimizing the results found for the XGBoost, a python module for gradient boosted regression
tree learning. A grid search strategy is used for the eta and max depth. The eta is the step size
shrinkage used in the update to prevent overfitting, while the max depth means the max depth of
a tree (i.e., amount of decision nodes). There is also made use of an early stopping round to find
the optimal number of boosting rounds. The number of boosted rounds correspondent to the
number of boosting rounds or trees to build. Using early stopping rounds if the performance has
not improved for n rounds, the training is stopped, and the best number of boosting rounds is
stored. We use a window of 10 rounds. On top of that, we used 10-fold cross validation to average
the performance of the training data to eliminate coincidences. No data normalization or
standardization is needed for the gradient boosted regression tree to work.
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6.2.2 Random Forest
Random forest is a supervised learning algorithm that uses ensemble methods (bagging) to solve
both regression and classification problems. Random Forest Regression is the assembly of
various Decision Tree regressors, combined using ensemble and predictions of each tree, which
are averaged to find the best predictions for the RUL. We focus on the regression models because
we want to predict the RUL of Component X. A graphical of a Random Forest is shown in Figure
6.1.
Figure 6.1 Graphical display of Random Forest
Generally, Random Forest (Regression) is used for noisy datasets as they increase the model's
bias and prevent overfitting (Patil et al., 2018). Patil et al. (2018) also stated that small variation in
the dataset does not make the model unstable due to the ensemble of the tress. The randomized
sampling of features that more noisy features contribute minimally to the prediction of the RUL.
The fundamental concept behind random forest regression is the large number of uncorrelated
models operating as a committee that will outperform any individual constituent models (i.e., single
decision tree).
Same as for optimizing the results of the XGBoost algorithm, for the Random Forest, we also
made use of a grid search for the hyperparameter optimization. However, this is done with the
number of estimators (i.e., the number of trees that have been built before taking the maximum
voting of predictions) and the max features. Max features define how many features should be
considered when looking for the best split. Similar to the XGBoost method, we used 10-fold cross
validation to average the training data results. Subsequently, no standardization or normalization
is needed for the Random Forest to work.
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6.3
Convolutional neural network
Convolution is mainly known for technology in computer vision, such as image recognition or
object detection. Chen et al. (2020) describe the general structure based on Figure 6.2. This
Figure show two significant characteristics (i.e., spatial weight sharing and local receptive field).
Those characteristics are realized by alternately stacking the convolution layer and pooling layer.
The network convolves multiple kernels or filters with input data in convolution layers to generate
features maps, from which pooling layers are applied to aggregate features and significant
abstract features afterward (Chen et al., 2020).
Figure 6.2 General structure of convolution neural network as described in Chen et al. (2020)
Generally, CNN is employed using two-dimension format data. However, for our application, the
input data is one-dimensional. We want to see the relationship between the health indicator and
the degradation of Component X. The one-dimensional data is represented as 𝑥 = [𝑥1 , 𝑥2 , … 𝑥𝑁 )
Where 𝑁 denotes the length of each sample. The convolutional operation in each feature map can
be expressed as Equation 6.2
Equation 6.2 Convolutional operation for each feature map
𝑎 = 𝑔(𝑤 𝑇 ⋅ 𝑥𝑖:𝑖+𝐾𝐿 −1 + 𝑏),
𝑖 = 1,2,3, … , 𝑁 − 𝐾𝐿 + 1
53
Where 𝑤 is the filter with the length being 𝐾𝐿 ; the symbols 𝑏 and 𝜎 denote bias and the activation
function, respectively. The activation function is selected as a rectified linear unit (ReLU). The
output 𝑎 can be seen as learned features concerning input sample 𝑥.
Pooling is another operation of CNN. Convolution layers are used to generate features.
Because of those convolution layers, the input signal is considered local stationery in this
research, indicating that the extracted features useful in one local and short-time window can also
be valuable in other window regions. Pooling is used to summarize the outputs of adjacent groups
of units in the same feature map. It remarkably reduces feature dimension and over-fitting. The
features generated by the convolution network are described as 𝑎 = [𝑎1 , 𝑎2 , … , 𝑎𝑚 ]. Then, the
pooling function is defined as Equation 6.3
Equation 6.3 Pooling function for CNN
𝐹 = {max {𝑎𝑖:𝑖+𝑃𝐿 −1 }|𝑖 = 𝑠𝑙 − 𝑠 + 1,
𝑙 = 1,2,3, … }
Where 𝑃𝐿 moreover, 𝑠 denote window size and stride of pooling, respectively. In our case, CNN
extracts local spatial features with a sliding window way and cannot encode time-series
information.
Chen et al. (2020) indicate that deep neural networks (DNNs) are hard to train, which can be
solved by normalization. Normalization ensures a stable distribution of activation values and
further reduces the internal covariate shift generated by the change of network parameters.
Subsequently, it allows a higher learning rate to be deployed and acts as a regularizer.
Normalization is done on the training dataset based on a min-max scaler, which is done with
Equation 6.4.
Equation 6.4 Min-max normalization formula
𝑥𝑛𝑜𝑟𝑚 =
𝑥 − 𝑥𝑚𝑖𝑛
𝑥𝑚𝑎𝑥 − 𝑥𝑚𝑖𝑛
Batch normalization helps over-fitting to a certain degree (Chan et al. 2020). On top of that, the
performance of a CNN network can be optimized when using different layers. We use a relatively
simple CNN network because of the simple linear degradation in the data. Subsequently, the
number of epochs, learning rate, batch size can be changed. Because optimizing a CNN is more
an art than a profession, the best adjustments are made using a trial and error method. On top of
that, we used the Adam optimizer, which provides an optimization algorithm that can handle
sparse gradients on noisy problems to minimize the RMSE of the CNN network.
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6.4
Long-short-term-memory
Long short-term memory network is one of the advanced structures in recurrent neural networks
(RNN), which is often used to deal with time-series tasks (Chen et al., 2020). LSTM networks have
memory capability and enable the collected information stream to continue to flow inside the
network, compared to feed-forward neural networks. LSTM networks can link the previous
information to the present time, enabling sequence data to the prediction model to use historical
status information to decide the current state of the equipment. LSTM networks contain four core
elements: cell state, forget gate, input gate, and output gate. Those four components are shown
in Figure 6.3.
Figure 6.3 Structure of long short-term memory network as described in Chen et al. (2020)
The three other gates update the information of the cell state (i.e., forget gate, input gate, an output
gate, which makes LSTM remove or add information automatically.
The forget gate determines what information the LSTM is intended to remove from the previous
cell state 𝐶𝑡−1.
55
The mathematical expression is shown in Equation 6.5:
Equation 6.5 Forget gate
𝑓𝑡 = 𝜎(𝑊𝑓 ⋅ [ℎ𝑡−1 , 𝑥𝑡 ] + 𝑏𝑓 )
ℎ𝑡−1 and 𝑥𝑡 represent the hidden state at time 𝑡 − 1 and input feature at time 𝑡, respectively. 𝑊𝑓
and 𝑏𝑓 Are weight parameters and bias term of forget gate layer. 𝜎 is the sigmoid function. The
output of this gate is 𝑓𝑡 whose value ranges from 0 to 1. 0 indicates that the behavior is fully
dropped out, while 1 indicates that the information of the cell state is totally retained (Chen et al.
2020).
The input gate decides what new learned information the LSTM is going to add to the
current state 𝐶𝑡 . The mathematical expression of the learned information is shown in Equation
6.6:
Equation 6.6 learned information as input for input gate
𝐶̃𝑡 = tanh (𝑤𝑐 ⋅ [ℎ𝑡−1 , 𝑥𝑡 ] + 𝑏𝑐 )
The input gate is calculated by mapping the previous hidden state and current input features in a
non-linear way. Subsequently, the input gate selects partially significant information from (Chen
et al. 2020). The input gate is expressed as the following mathematical expression, see Equation
6.7.
Equation 6.7 input gate
𝑖𝑡 = 𝜎(𝑊𝑖 ⋅ [ℎ𝑡−1 , 𝑥𝑡 ] + 𝑏𝑖 )
If the two equations are combined (i.e., equation X and equation Y), the current cell state 𝐶𝑡 is
computed as the following term, see Equation 6.8:
Equation 6.8 Update of the current gate
𝐶𝑡 = 𝑓𝑡 ⊙ 𝐶𝑡−1 + 𝑖𝑡 ⊙ 𝐶̃𝑡
The current cell is thus composed of two terms, 𝑓𝑡 ⊙ 𝐶𝑡−1 and 𝑖𝑡 ⊙ 𝐶̃𝑡 . 𝑓𝑡 ⊙ 𝐶𝑡−1 represents the
filtered information after being discarded. 𝑖𝑡 ⊙ 𝐶̃𝑡 means the newly generated feature information
which is being added.
56
The output gate determines which part of the cell state the LSTM is going to output. The final
output of the hidden layer ℎ𝑡 is calculated as follows, see Equation 6.9 and Equation 6.10:
Equation 6.9 Output gate
𝑜𝑡 = 𝜎(𝑤𝑜 ⋅ [ℎ𝑡−1 , 𝑥𝑡 ] + 𝑏𝑜
Equation 6.10 Output of hidden layer
ℎ𝑡 = 𝑜𝑡 ⊙ tanh(𝐶𝑡 )
Based on all the equations, the non-linear gates regulate the incoming and outcoming information
of the LSTM network adaptively. Moreover, the hidden state ℎ𝑡 contains all historical state
information from time 0 till the current time (i.e., time t). The time-series information is helpful to
construct accurate health indictor (Chen et al. 2020).
Standardization of the data is needed to perform the LSTM network, during the following formula,
see Equation 6.11:
Equation 6.11 Standardization of data
𝑥𝑠𝑐𝑎𝑙𝑒 =
𝑥 − 𝑥𝑚𝑒𝑎𝑛
𝜎
Batch normalization helps over-fitting to a certain degree (Chan et al. 2020). Same as with the
CNN network, the performance of an LSTM network can be optimized when using different layers,
here we also use a simple LSTM model for the same reason mentioned at the CNN network. The
CNN network uses a trial and error method to see fitting epochs, learning rate, and batch size.
The Adam optimizer is also applied to minimize the RMSE of the LSTM network
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A characteristic of an LSTM network is that it can use time window processing, shown in Figure
6.4. The window size will be a sequence of times series data with length n. Based on the window
length, the LSTM network takes the datapoints for each feature (i.e., parameter) of n-1 timesteps
back in time. Taken sequence data into account offers a possibility that the prediction model can
include fluctuations in this sliding time window. The sliding time window moves up with the knumber of timesteps, also called a shift. The sliding window principle is also used in the 1D-CNN
network but not for the XGBoost and Random Forest. For our prediction model, we use a shift of
1-step and a time window of 25 timesteps for hourly data.
s
Figure 6.4 Time window processing
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Part V – Results
7. Results
In this subsection, two sub-questions are answered., namely Q-5: How can we optimize each
predictive model in terms of accuracy? And Q-6: What is the performance of the best-performing
prediction mode based on accuracy? Different prediction models were examined in the previous
section with optional normalization or standardization of the data and hyperparameter
optimalisation. This answers Q-5 partly. This section examines the best settings of the data in
terms of lower bounds, data granularity and sliding window, inclining features, and the way data
is filtered to see which prediction model performs optimally. When we know the best settings, we
also have enough information to answer sub-question Q-6.
First, we test the different prediction models against each other to choose the best prediction
model. Then, different settings of the lower bounds are considered. Subsequently, different
settings between the data granularity and sliding window are compared. Next, the data is filtered
on the production cell level to see if it affects the accuracy of the prediction model. Furthermore,
process data is added to the model to see if any useful features improve the prediction model's
performance.
7.1
Comparison of different predictions prediction models for RUL
For comparing the different machine learning algorithms, the choice is made to use a data
granularity of an hour to get relatively quick answers in terms of computational power for each
prediction model. We use a sliding window based on a time window of a day. This because Table
5.2 has the highest monotonicity and trendability for a granularity of hourly data. For the
implementation, we use a relatively lower bound, as it is the simplest and fairly easy to implement
and, at first glance, the best to use.
Linear Regression: The easiest prediction model to implement as a simple linear regression. The
data was diverged based on a 70%-30% ratio as a train and test set based on whole production
cycles. We take an evenly distributed sample for this split over all the machines to get balanced
input data evenly distributed over the approved production periods. When we train a linear
regression based on the HI (i.e., average values of product dataset) on the training set, a global
formula is discovered with an intercept of -306,473 products and a coefficient of 54,920 for each
unit (anomalized) gained. The linear regression is also graphically shown in Figure 7.1
59
To evaluate its results, an RMSE of roughly 28 production hours (RMSE in products known but
anomalized) realized when calculating the MAPE. A result of 85.66% is realized. The difference
between the MAPE and RMSE is that MAPE will penalize more in smaller predictions if inaccurate.
Before we can say anything meaningful about the results of the linear regression, the results of
the other prediction models will first be discussed
Figure 7.1 Linear regression of Health index and Remaining useful lifetime
XGBoost: Same as for the Linear Regression, we used the same split for the train and test set.
We only make one prediction per production cycle; this also applies to the other prediction models.
We used a lower bound of 15% degradation than the health indicator (HI) based on the first 10
data points (i.e., first 10 production hours in a production cycle). A constraint is added that a
machine must be active for 24 production hours to gather enough input data. Now there is a
timeline between the first 24 production hours and the time the lower bound is reached. A random
moment is taken between those points and based on that current moment. We see if we can
predict how many more products there can be manufactured before the lower bound will be
reached.
When generating results, hyperparameter optimization regarding the eta and max depth of the
trees is discussed in the previous section—the optimal depth and eta where five layers and an eta
of 0.1, respectively. After running the XGBoost prediction model, an RMSE of 25 production hours
(RMSE in products known but anomalized) was found for 13 test periods; this result improved
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compared to the linear regression. In terms of MAPE, 122.23% is realized, which is higher than
with the linear regression. The reason for this can be seen in Figure 7.2. What can be observed
is the relative true RUL value of periods 9, 10, 11, 12, and 13. This fluctuation will lead to a higher
MAPE compared to the average values of the linear regression.
Figure 7.2 Predicted RUL-values versus the real RUL values performed by XGBoost
For now, it is too early to say anything about prediction performance. First, we will work out the
other decision tree algorithm together with the two neural networks.
Random Forest: To get a fair comparison, the same data split is considered for the Random
Forest algorithm for the XGBoost algorithm. However, for the Random Forest algorithm, other
hyperparameters must be optimized. For the Random Forest algorithm, we use a grid search to
evaluate the number of evaluators (i.e., number of trees to build the forest) and the number of
parameters used per tree (e.g., auto, sqrt, or log2). When the grid search is performed, the optimal
number of estimators for the training dataset is 250, while the maximum number of features is
determined based on the square of the total input parameters. After the hyperparameter
optimization, an RMSE of 22 production hours is reached (RMSE in products known but
anomalized), while a MAPE of 78.84% is realized. The result of the prediction model is also shown
in Figure 7.3
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What can be observed based on this graph is that the predictions are closer to the true RUL for
most of the datapoints compared to the graph created by the XGBoost algorithm, hence the better
results. However, there is still a gap between the prediction for the test dataset's 10th and 11th
production cycles.
Figure 7.3 Predicted RUL-values versus the real RUL values performed by Random Forest
CNN: For the 1D convolution neural network, we use the same split as before. Also, the CNN
network is unique and has interchangeable parameters. Because CNN is a more complex
method and an optimal outcome is difficult to achieve, trial and error are used for the structure
of the network and the number of epochs and learning rate. The performance, however, is less
than with the other prediction models. For the convolution neural network used, we used 50
epochs to get a result with a stepwise learning rate to get optimal results. When running the
CNN, we made use of an extra validation set. When the CNN network is trained, the history
shown after each epoch is closely followed to see if the prediction model trains.
When we look at the results, they perform worse than the XGBoost, Random Forest, or even
the simple Linear Regression. An RMSE of 63 production hours is realized (RMSE in products
known but anomalized), and a MAPE of 424.13% is achieved, which distressing. When looking
at the training feed, the prediction model improves over time. However, the model overfits. Much
time was spent on getting the CNN better, but this is the best result that could be found for it.
This overfitting is probably because the degradation linear happens that the CNN network tries
to find more complex connections that are not there. CNN networks take the history of an n62
number of time points. With this, it tries to analyze behavior based on the transformation of a
parameter over this period, possibly coupled with other parameters. This makes the prediction
model think that based on the training data, there is a complex connection between the data,
which there is not. A decision tree algorithm (i.e., Random Forest) is better to apply in our
situation. A graphical result of the CNN network is shown in Figure 7.4.
Figure 7.4 Predicted RUL-values versus the real RUL values performed by CNN
LSTM: Like all the other prediction models, we use the same train and test split to get a fair
comparison. Same as for CNN, the LSTM network is more complex than decision tree methods.
For this LSTM network, we also used different settings for the hyperparameters, such as the
number of epochs, the learning rate that is also stepwise, and the batch size when running the
LSTM network. Same as before, we used an extra validation set based on the training set to see
if the prediction model works. Because the degradation behaves more or less linearly, the decision
is made to implement a relatively simple LSTM.
Taking a look at the LSTM network's performance, the model performs similarly to the CNN
network. Same as with the CNN network, the LSTM looks at n-number of time points back in time
to analyze trends within that interval. However, LSTM is specialized in time series data. However,
because there are no returning and constant patterns in the data, the performance of the LSTM
model is worse when a comparison is made to the decision tree algorithms. The same reason for
overfitting is the same as with the CNN network. The LSTM network tries to find patterns in the
window it was given, which there are not. When looking at the RMSE and MAPE, 55 production
63
hours (RMSE in products known but anomalized) and 450.65% are realized, respectively. The
results of the LSTM network are graphically shown in Figure 7.5.
Figure 7.5 Predicted RUL-values versus the real RUL values performed by LSTM
Conclusion: When comparing all the prediction models, the best-found results based on the
RMSE and MAPE have been found when predicting the RUL with the Random Forest algorithm.
For further experiments, we will use the RF algorithm to compare different settings in the
preprocess data. However, it can be interesting to see which parameters took account in the
prediction of the RUL. The main parameters used were the number of products produced till a
certain point, the cycle number (based on the specific machine). On a lower level, the importance
of the minimum value of ROD 11 of the previous day, minimum value of ROD 13 of the previous
day, the SMR of the AVG_ROD, the minimum of the AVG_ROD and the SMR of ROD 13. For a
full analysis of how important each parameter was for predicting the RUL, see Appendix E for a
graphical review with a legend.
After talking to the domain experts, on average, when a machine is fully functioning, 2000 products
per hour can be fabricated. When we look at the best prediction, an RMSE of around 22 production
hours (RMSE in products known but anomalized). Based on Figure 9.3, it is observed that in most
cases, an overprediction is made. With a margin of safety one production day, it can be predicted
when a certain lower limit is reached on the HI.
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7.2
Impact of the determination of the lower bounds
The second experiment is based on the determination of various lower bounds. As discussed,
three options are compared based on the Random Forest. We compare a static lower bound, a
relative lower bound and a statistical lower bound based on the standard deviation for the training
dataset. We select a lower bound from which roughly equal amounts of data will be available for
all options. For the experiment performed in section 9.1, we used 5571 hours of data. A specific
bound will be selected for the static and statistical lower bound with roughly the same amount.
First, the static way was implemented. A lower bound was determined based on the HI. If
AVG_ROD would decrease below 6.7units, we used that as our failure point. 5292 hourly data
points were used from the four machines. After running a prediction based on the Random Forest
algorithm, an RMSE of 25 production hours was realized (RMSE in products known but
anomalized). However, the MAPE was relatively high with 62847%; the reason behind this
extraordinary number is that one of the test production cycles had a real RUL of 0, so it is better
to look at the fair comparison for a fair comparison RMSE. When looking at the important
parameters, the HI itself was determined as the most important feature.
Secondly, the statistic way was implemented. First, the HI was standardized, as shown in Equation
8.11. A similar split in the number of hourly data points used a lower bound was set on -0.5 for the
data. When setting this lower bound 5313 hourly data points were used from the four machines.
When running the Random Forest algorithm, the performance is significantly lower than in
comparison with the static lower bound or a relative lower bound. An RMSE of 40 produciton hours
(RMSE in products known but anomalized) is realized with a MAPE of 26,344%. The reason for
this extraordinarily high number is the same as for the static way. One of the test periods real RUL
was 0.
Lastly, the relative way of determining the lower bound is briefly repeated. When comparing the
different prediction models based on the experiment in the previous subsection, the relative lower
bound has already been implemented. It resulted in an RMSE of 22 production hours (RMSE in
products known but anomalized ) is reached while a MAPE of 78.84% is realized; this is the best
performing method of selecting a lower bound for the case of the company.
65
7.3
Impact of data granularity and sliding time window
The third experiment is based on finding the most suitable settings concerning the data granularity
and sliding time window. This optimization is done based on the preprocessing step before a
prediction is made with the Random Forest algorithm. We compare the same settings for the data
granularity and sliding time window used to calculate the monotonicity and trendability. The results
are expressed in terms of RMSE. MAPE can get extraordinarily high when the RUL comes around
0. Finding the optimal data granularity and using a sliding time window to create the features can
improve the accuracy. If the data granularity is high, the Random Forest can easily detect the
current health of Component X due to its high monotonicity and trendability. However, the
intermediate steps at which the RUL is projected will also be substantial. The trick is to predict a
level where the Random Forest algorithm can easily deduce the condition of Component X but
can predict as accurately as possible. The results are shown in Table 7.1.
Table 7.1 Comparison of different data granularity and sliding window on performance Random Forest
Granularity
Performance
Random Forest
Daily
8-hourly
Hourly
Quarter
Raw data
Daily
RMSE: 33 hours
RMSE: 45 hours
RMSE: 25 hours
RMSE: 40 hours
RMSE: 31 hours
Sliding time window
8-Hourly
Hourly
RMSE: 20 hours
RMSE: 13 hours
RMSE: 30 hours
RMSE: 25 hours
RMSE: 42 hours
RMSE: 18 hours
RMSE: 31 hours
RMSE: 25 hours
RMSE: 21 hours
RMSE: 23 hours
Quarter
RMSE: 32 hours
RMSE: 26 hours
RMSE: 31 hours
RMSE: 31 hours
RMSE: 33 hours
What can be observed from Table 7.1 is an improvement in the RMSE when compared to the
results of the first experiment, which can be found in section 7.1. Looking vertically at Table 9.1, it
appears that a sliding window produces the best results. When the data has a granularity of one
day, exceptionally good results are obtained (i.e., sliding window based on hourly data). This has
to do with the fact that the prediction model focuses on the production so far when looking at the
most important features during making a prediction—a note for the results. Purely based on the
train and test dataset split and the timing of choosing at what point during the test set a prediction
is made, the result can also be influenced. This is demonstrated for a granularity of one hour and
a sliding window of one day. The prediction was done again compared to the first experiment,
where the same settings were included. Now the prediction model scores slightly worse based on
the RMSE.
As a conclusion from this experiment, the sliding window of one hour with a data granularity
of one hour provides the best results. When a day's granularity is taken, it is purely based on the
production up to a certain point in time, making it unreliable.
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7.4
Impact of filtering the data on production cell-level
We test if each cell's prediction within the machines is better predictable for the second to last
experiment. To test this concept, instead of filtering the data based on each machine, we split the
data based on each production cell within the machine (i.e., different granularity). The test is
relatively simple. Instead of giving one prediction for the machine, we get 30 individual predictions.
Also, when calculating the time-domain features, this is done based on the production cell level.
We made 30 individual predictions at the production cell level; the average of these 30 predictions
was an RMSE of 24 production hours (RMSE in products known but anomalized). This was done
on a granularity of hourly data and a sliding time window of one hour for creating the HI and timedomain features. When this is compared to a realized RMSE of 18 production hours (RMSE in
products known but anomalized) the RUL of individual production cell is less accurate than at the
machine level. A note is that the result may be influenced by the randomness of selecting the
train/test split and the time from which the RUL is predicted.
7.5
Impact of adding process data as features
For the last experiment, we test if the accuracy of the Random Forest algorithm would increase if
we extend it with process parameters. As stated in section 5.4, no trend was found for one of the
process parameters when performing the Mann Kendall trend test. For testing the influence of
process data as features, we use a granularity of hourly data combined with a sliding time window
of one hour when creating the time domain features and HI.
When a prediction is made, including the process parameters, see appendix B. on top of the other
(time-domain) features used. An RMSE is realized of 31 production hours (RMSE in products
known but anomalized), indicating that the Random Forest algorithm performs worse when
including the process parameters.
7.6
Conclusion of experiments
To conclude, the Random Forest algorithm performs the best in terms of accuracy based on the
RMSE and MAPE. The best choice of the lower bound is made based on the relative lower bound
based on the first 10 hours of production data. Using a granularity based on hourly data and
creating the time-domain features, the Random Forest algorithm will perform optimal. Other
experiments based on the impact of filtering the data on production cell-level and adding process
data as features were unsuccessful. The best RMSE found was 18 production hours (RMSE in
products known but anomalized). When the machine normally produces XXXX products per hour,
we can predict reaching a lower limit within 18 hours of accuracy.
67
8. Conclusion
8.1
Conclusion
At the beginning of this research project, the goal and the research questions were defined. The
main research question is:
How can the data currently measured within Machine Y help implement a more data-driven
maintenance policy for Component X?
To answer the main research question is captured in the CRISP-DM methodology. This
methodology was used to help to structure this data-driven maintenance project. The goal of the
research project is:
Deliver a proof of concept for data-driven maintenance based on the current data available
within the production process of Machine Y.
It can be concluded that the goal of the research project has been achieved. A remaining useful
lifetime condition is possible based on an indirect measurement based on parameters of the
product. However, there were some assumptions made to get the question answered. In order to
partially walk through the process, all the sub-questions will be answered first, and then the main
question will be answered.
Q-1: Which maintenance strategies are there, and what are the characteristics of each policy?
Various maintenance policies are described and analyzed. The policy the company used before
was a time-based preventive maintenance policy. Every two weeks, unrelated to the number of
products produced, the Component X were preventively replaced. Based on the needs of the
company, the knowledge of the process, and the gathered data of Machine Y. A choice was made
to implement a prognostic data-driven maintenance policy.
Q-2: What are the characteristics of the current situation?
It can conclude that the lack of run-to-failure data is the biggest drawback for figuring out an
effective maintenance policy. On top of that, there is no direct measurement on the equipment
(e.g., temperature, vibrations) but an indirect relationship that reflects the Component X’s
degradation. Those two aspects were considered while finding an applicable policy. The current
maintenance policy is a preventive maintenance policy conducted every two weeks.
68
Q-3: Based on the available data, what type of data-driven strategy is best and realizable for the
situation of Component X?
Based on the current situation described in Q-2. The most fitting method is to work with a datadriven degradation model based on a health indicator. We test the indirect measurements, which
are the parameters of the product and the condition of Component X. This is used as a health
indicator. The health indicator was evaluated based on trendability, monotonicity, and correlation
with the RUL. For solving the problem of the absence of run-to-failure data, there using a relative
arbitrary lower bound. Because the degradation of the Component X indicated by the health
indicator behaves as a linear line, we can substitute this arbitrary lower bound when run-to-failure
data is gathered.
Q-4: Which predictions models can be applied for data-driven maintenance?
Based on the researched literature, several predictive prediction models can be applied from the
machine learning domain for creating a degradation-based model. A comparison is made with
simpler time series based solely on one parameter to investigate if there is explainable behavior
in the dataset. We compare that method with more complex machine learning predictive models.
The following predictive models are used: a Simple Linear Regression, XGBoost, Random Forest,
1D-CNN, and LSTM for predicting the Remaining Useful Lifetime (RUL) of the Component X.
Q-5: How can we optimize each predictive model that in terms of accuracy?
To ensure that each prediction model performs to its fullest potential, in the first place, a deep
analysis is made on how each prediction model works. Subsequently, the input data is supposed
to be set up so that it lends itself to its respective prediction model. This is done to optimize the
data preprocessing, i.e., data granularity, feature selection, and a sliding time window. If
applicable, for each model, hyperparameter optimization based on a grid search is performed.
Q-6: What is the performance of the best-performing prediction mode based on accuracy?
An in-depth comparison is made for each machine learning model compared to a simple linear
regression. The best performing prediction model is Random Forest which has an RMSE of
roughly 18 production hours (RMSE in products known but anomalized). For achieving those
results, a data granularity of hourly data is used, and a sliding time window is based on a window
of an hour.
69
Main-Question: How can the maintenance be more data-driven to optimize the current
maintenance policy for Machine Y?
Based on the needs of the company, the knowledge of the process, and the gathered data of
Machine Y, a choice was made to implement prognostic data-driven maintenance based on
degradation. However, the characteristics that made this project challenging are the absence of
run-to-failure data and indirect equipment measurement. The most fitting method is to work with
a data-driven degradation model based on a health indicator. The health indicator was evaluated
based on trendability, monotonicity, and correlation with the RUL. The correlation between the
degradation of the health indicator and the degradation based on the RUL confirms that the
indirect measurement can serve as a health indicator for Component X. For solving the problem
with the absence of run-to-failure data, there using a relative arbitrary lower bound. Because the
degradation of Component X indicated by the health indicator behaves as a linear line, we can
substitute this arbitrary lower bound when run-to-failure data is gathered. Because the degradation
is constant, substitution can be applied, and the main focus is on the predictability of the process.
After comparing different prediction models and finding the best settings in the data preprocessing,
the Random Forest algorithm became the best in terms of accuracy. An RMSE of 36.193 of
roughly 18 active production hours (RMSE in products known but anomalized). To ultimately
implement the policy of data-driven maintenance, run-to-failure data must be collected to
ultimately find the true point of failure to establish the lower bound based on failure data.
8.2
Recommendations
Different recommendations can be given based on the outcomes of the project. First of all, it is
important to generate run-to-failure data to extend the life of Component X. If Component X remain
operational for longer in Machine Y, this means fewer maintenance moments and fewer
maintenance costs. After all, the predictability of Component X has been proven through this
project.
Second, it might be interesting to focus more specifically on traditional time series based
on the health indicator alone. This might improve the predictability of the Component X’s life.
Lastly, adding direct sensors to the process (e.g., vibrations, temperature) can improve
predictability. A predictive maintenance project is easier to implement with direct measurements
on the replaceable equipment.
70
9. Future opportunities and implementation
Since the scope of the assignment was to establish a more data-driven method for the Machine
Y, and there is insufficient time to implement it, there are several aspects described for future
implementation and cost savings for the data-driven maintenance policy. First, the way of
implementing the data-driven maintenance policy is described. Next, the savings of the solution
are given based on additional capacity and costs. Furthermore, a final experiment is done on runto-failure data to see if the degradation does indeed behave downwards that was assumed until
now.
9.1
Implementation on the work floor
Normally, at the end of a CRISP-DM cycle, development is the last step in the process. When the
decision was made to begin this case study, the result was estimated to establish a working proofof-concept for the Machine Y. This is delivered. The role fulfilled during this case study can be
compared to the role of a data analyst, which is to create a suitable prediction model, the next
steps of implementing (real-time) data-driven maintenance is shown in Figure 8.1
Figure 9.1 Process of implementing prediction model
It was decided based on the accuracy of the results not to implement the solution in real-time. The
domain experts have indicated that they would like to get hold of the code of the prediction model
to make a prediction one to several times a week as to how long a specific machine can produce.
They can then schedule a time for the maintenance engineer to replace the Component X. This
should include a safety margin equal to the average RMSE.
71
9.2
Experiment with run-to-failure data
After talking to the engineers at the company regarding Machine Y, the absence of run-to-failure
data was discussed. After making clear that a final lower bound can only be made once failure
data has been collected, it was decided to let several machines produce up to the failure point.
Agreed with the maintenance personnel that a Component X will be replaced when the
Component X is not functional.
First, the replacements of Component X are shown in Figure 8.2. Observable from this graph is
that the renewal of the Component X or production cells takes place gradually. This indicates that
not every Component X in the production cell has the same lifespan, provided that there are
corresponding products manufactured for each production cell.
REPLACEMENTS OF COMPONENT X
VT16
VT26
VT36
6
4
2
0
1
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
Figure 9.2 Replacements of Component X or production cell after last batched maintenance moment
It is more interesting to see how the health index behaves on which the lower bound is based.
When a health indicator is compiled per individual production cell, no structural downward trend
can be found. This was also the case when looking for trends in section 4. In section 4, it was then
decided to work with data so that a consistent parameter from which a health indicator could be
compiled could be found. All the production cells regarding VT16 and VT26 which were not
replaced are used to see if the health indicator will depredate over time. The reason why VT36 is
not included is since every production cell in it has been renewed. This is shown in Figure 8.3 on
the next page.
72
The behavior that can be observed from Figure 8.3 does not meet expectations. There is no
monotonic trend. A reason for that may be that several Component X’s or production cells have
been replaced and are not documented. Several staggered patterns in Figure 8.3 may indicate
this.
Figure 9.3 health indicator trajectory run-to-failure data
For now, we should not draw too many conclusions based on two health indicators on possibly
incorrect data. It is recommended that the company conduct more trials to see if the health
indicator remains consistent.
A final observation during the evaluation was the number of products produced compared to the
number of maintenance moments. As discussed earlier, the maintenance moments are not errorfree. Removed due to company sensitive information regarding the found results
73
9.3
Created capacity and saved costs
Removed due to company sensitive information regarding the found results
74
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Appendix A:
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Appendix B:
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Appendix C:
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Appendix D:
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Appendix E:
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