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journal homepage: www.elsevier.com/locate/ijrefrig
Important sensors for chiller fault detection and diagnosis
(FDD) from the perspective of feature selection and machine
learning
H. Han a,*, B. Gu a, T. Wang a, Z.R. Li b
a
Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, 800 Dongchuan Road, Minhang District,
Shanghai 200240, PR China
b
Institute of HVAC & G, School of Mechanical Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, PR China
article info
abstract
Article history:
The benefits of applying automated fault detection and diagnosis (AFDD) to chillers include
Received 7 June 2010
less expensive repairs, timely maintenance, and shorter downtimes. This study employs
Received in revised form
feature selection (FS) techniques, such as mutual-information-based filter and genetic-
23 July 2010
algorithm-based wrapper, to help search for the important sensors in data driven chiller
Accepted 17 August 2010
FDD applications, so as to improve FDD performance while saving initial sensor cost. The
Available online 21 August 2010
‘one-against-one’ multi-class support vector machine (SVM) is adopted as a FDD tool. The
results show that the eight features/sensors, centered around the core refrigeration cycle
Keywords:
and selected by the GA-SVM wrapper from the original 64 features, outperform the other
Sensor
three feature subsets by the GA-LDA (linear discriminant analysis) wrapper, with an overall
Chiller
classification correct rate (CR) as high as 99.53% for the 4000 test samples randomly
Compression system
covering the normal and seven typical faulty modes. The CRs for the four cases with FS are
Detection
all higher than that without FS (97.45%) and the test time is much less, about 28e36%. The
Genetic
FDD performance for normal or each of the faulty modes is also evaluated in details in
Fault
terms of hit rate (HR) and false alarm rate (FAR).
ª 2010 Elsevier Ltd and IIR. All rights reserved.
Capteurs importants pour la détection et le diagnostic
d’anomalies des refroidisseurs du point de vue des choix des
caractéristiques et des connaissances du système
Mots clés : Capteur ; Refroidisseur ; Système à compression ; Détection ; Génétique ; Anomalie
1.
Introduction
Automated fault detection and diagnosis (AFDD) along with
prognostics is the cornerstone for automated condition-based
maintenance, whose wide-spread adoption will help cut down
much of the waste caused by poorly maintained, degraded
and/or improperly controlled equipment. Although there is
a wealth of literature related to AFDD for critical processes,
* Corresponding author. Tel./fax: þ86 21 3420 6260.
E-mail address: [email protected] (H. Han).
0140-7007/$ e see front matter ª 2010 Elsevier Ltd and IIR. All rights reserved.
doi:10.1016/j.ijrefrig.2010.08.011
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 5 8 6 e5 9 9
Nomenclature
b
bias or threshold for the discriminant function
c
target class vector
C
penalty constant (also called slack penalty)
ConfMat confusion matrix
CR
correct rate
FAR
false alarm rate
FN
number of false negative samples
FP
number of false positive samples
FWC
flow rate of condenser water
HR
hit rate
mean of the jth variable/feature
Mj
MCR
misclassification rate
p
matrix of the posterior probabilities for the
classifier
PO_feed pressure of oil feed
training set of two class
Sa
possible values’ set for X
Sx
possible values’ set for Y
Sy
such as nuclear, aircraft engines or production-related
processes, such as those that exist within chemical process
plants, relatively little exists for application to chillers or other
vapor compression equipment, especially those from the
viewpoint of important sensors.
Commonly recognized categorization of FDD methodology
is that based on model, quantitatively or qualitatively, and
that based on process history (or data driven), as Katipamula
and Brambley (2005a,b) stated. Bendapudi and Braun (2002)
provide a detailed list of available quantitative models, especially dynamic models for vapor compression equipment.
Qualitative physics-based and rule-based systems belong to
the qualitative model-based category, such as expert systems
(Kaler, 1990; Grimmelius et al., 1995; Kaldorf and Gruber,
2002), rules derived from first principles (Gordon et al., 1995;
Brambley et al., 1998), bond graphs (Ghiaus, 1999) and casebased reasoning (Dexter and Pakanen, 2001), etc. The data
driven methodology (Tassou and Grace, 2005; Liang and Du,
2007; Han et al., 2010) is based solely/mainly on process
history and contains models of black box or gray box, where
pattern recognition techniques are often employed to develop
the relationship between inputs and outputs, and into which
the machine learning methodology to be presented in this
study falls, thanks to the data-rich nature of chillers and the
dedicated experiments by Comstock and Braun (1999a,b).
TCO
TEO
TN
TP
TRC
TR_dis
TWCO
TWI
VE
w
X
b
X
Y
Z
587
temperature of condense water out by RTD
temperature of evaporator water out
number of true negative samples
number of true positive samples
saturated refrigerant temperature in condenser
refrigerant discharge temperature
temperature of condense water out by thermistor
temperature of city water in
position of the electronic valve installed in the
evaporator water loop
weight vector for SVM
discrete random variable
normalized sample matrix
discrete random variable
observed sample matrix
Greek symbols
Lagrange multiplier
ai
g
width of Gaussian kernel function
standard deviation of the jth variable/feature
sj
Feature selection (FS) is frequently used as a preprocessing
step to machine learning. It is a process of choosing a subset of
original features so that the feature space is optimally reduced
according to a certain evaluation criterion. FS has been
a fertile field of research and development since 1970’s and
proven to be effective in removing irrelevant and redundant
features, increasing efficiency in learning tasks, improving
learning performance like predictive accuracy, and enhancing
comprehensibility of learned results (Blum and Langley, 1997;
Dash and Liu, 1997; Kohavi and John, 1997). Making use of FS
technique, together with machine learning knowledge, this
study aims to search preliminarily for relatively important
sensors/features for chiller AFDD.
As a novel machine learning method, support vector
machine (SVM) (Cristianini and Taylor, 2000) is a powerful
tool for solving the practical problems always characterized
by nonlinearity, high dimension, local minima and/or small
sample. It was first suggested by Vapnik in the 1960s and
has recently become an area of intense interests and
research. Besides the advantages just mentioned, the main
reasons for considering SVM as an AFDD tool, are: 1) the
purpose of this study is concentrated on the important
sensors or features in chiller AFDD, not AFDD itself; 2) SVM
proved to be the most suitable technique for chiller application in Choi et al. (2005) and also in our study (Han et al.,
Fig. 1 e Illustration of Feature Selection (FS).
588
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 5 8 6 e5 9 9
Table 1 e ConfMat for the two-class case.
Diagnosed Fault (Predicted Class)
Happening Fault
(True Class)
Yes
No
Yes
No
TP
FP
FN
TN
sensors and their influence on the AFDD performance; the
conclusions are drawn in Section 6. Appendix A and B
includes further information about the experiments and the
features/sensors.
2.
Fig. 2 e Feature selection (FS) by Genetic Algorithm (GA).
2010) for a vapor-compression refrigeration system with
4.0 kW cooling capacity.
Experimental data for normal and seven faulty modes
(each with four severity levels) from ASHRAE project 1043-RP
(Comstock and Braun, 1999b) were utilized for the implementation and validation of FS and AFDD strategy for chiller
applications. The remainder of this paper is organized as
follows: Section 2 explains the FS methods used, mutual
information (MI) based filter and genetic algorithm (GA) based
wrapper; Section 3 briefly introduces the SVM theory, depicts
the structure of the multi-class SVM with FS and elaborates
the evaluation guidelines for the SVM classifiers; Section 4
describes the experimental data, the data preprocessing and
the performing scheme of the AFDD strategy on the data;
followed by the results of FS, SVM training and test in Section
5, along with the detailed discussions about the important
Methods of feature selection (FS) adopted
There are two critical parts in the process of FS (Fig. 1):
searching methods by which new feature subsets are generated, and evaluation methods by which feature subsets are
evaluated for decision making.
Based on whether the classifier to be used is employed as the
evaluation method, FS algorithms fall into two broad categories,
the filter model or the wrapper model (Das, 2001; Kohavi and
John, 1997). MI-based filter where MI performs evaluation with
sequential forward searching and GA-based wrapper where GA
acts as a searching method, were adopted in this study.
2.1.
MI-based filter
For a quick idea about the number of features selected and the
trend of the performance in classification, MI-based filter type
FS is first employed for the chiller data concerned. A brief
introduction is given below.
The MI (Zhu, 2000; Peng et al., 2005) of two random variables is a quantity that measures the mutual dependence of
the two variables by measuring the information they share.
For two discrete random variables X and Y with possible
values’ set Sx and Sy respectively, MI is defined as:
IðX; YÞ ¼ X X
x˛Sx y˛Sy
pðx; yÞlogb
pðx; yÞ
pðxÞpðyÞ
Fig. 3 e Structure of FS D SVM model. Note: Data preprocessing will be introduced in Section 4.2.
(1)
589
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Table 2 e Definition and Calculation of HR, FAR, CR and MCR.
Evaluation
Guidelines
Definition
Calculation
Individual
HR
Performance
FAR
For a given class, it is defined as the fraction of the ‘predicted and
happened’ (TP) samples among all the actually happened samples.
For a given class, it is defined as the fraction of the ‘predicted but
not happened’ (FP) samples among all the actually not-happened samples.
HR ¼ True Positive Rate
¼ Recall ¼ TP/(TP þ FN) ¼ TP/row1
FAR ¼ False Positive Rate
¼ FP/(FP þ TN) ¼ FP/row2
Overall
CR
Performance
MCR
the fraction of the correctly classified samples among
the total, for all classes under investigation
not-correctly-classified-sample fraction for all classes
CR ¼(TP þ TN)/Total
¼ Main Diagonal/Total
MCR ¼ 1CR
where p(x) is the probability of x, p(x,y) is the joint probability
of x and y, b is the base of the logarithm with the most
common values, 2, employed.
It measures how much knowing one of the two variables
reduces our uncertainty about the other. For example, if X
and Y are independent, then knowing X does not give any
information about Y and vice versa, so their mutual information is zero. Otherwise, their mutual information would be
a positive number. The larger the mutual information, the
greater the dependency on each other is. If one of the variables is the target class and the other is a feature, then the
mutual information may give us an idea about how much
important the feature is in classifying the samples, or how
much relevant the feature is to the target class. That is the
basic principle of MI-based FS. For experimental data matrix
such as those in our study, rounding should first be done to
extract possible values before any calculation of the probability and MI begins.
MI-based minimal-redundancyemaximal-relevance (mR
MR) FS (Peng et al., 2005) is implemented in this study, which
aims to search for those features that are both minimally
redundant among themselves and maximally relevant to the
target classes. Incremental search methods can be used in
practice to find the near-optimal features. Suppose Sm-1 is the
feature set with m-1 features. The task is to select the mth
feature from the remaining set. The respective incremental
algorithm optimizes the following condition:
6
max 4I xj ; c
xj ˛XSm1
,
3
!
X 1
7
I xj ; xi þ 0:01 5
m 1 x ˛S
i
GA-based wrapper
GA is a time-consuming methodology itself. The original
purpose of wrapping it with a simple classifier, linear discriminant analysis (LDA) (Krzanowski, 1988) by the ‘classify’ function of Matlab, is to save computational time while keeping
classification information as much as possible. The selected
feature subset may not be the optimal one for the machine
learning method to be adopted in AFDD, but we have the
opportunity to practice try-and-error process and find the near
optimal subset accordingly, thanks to the shortened time
period for each selection. It is a reasonable attempt in a sense.
In fact, the advantage of SVM in chiller AFDD application is
further confirmed by comparing the classification performance
of different AFDD strategies, LDA or SVM.
GA (Goldberg, 1989) is a way of solving problems by
mimicking the same processes Mother Nature uses. They use
the same combination of selection, recombination (or crossover) and mutation to evolve a solution to a problem. In
searching for an optimal or near optimal feature subset for
chiller AFDD application, the population is a collection of
possible feature subsets and the fitness is measured by a function of classifier performance. Fig. 2 depicts the FS process by
GA. For GA-LDA wrapper, fitness function employed in this
study is a linear combination of the misclassification rate (MCR)
and the posteriori probability of the classifier (Eq. (3)). For GASVM wrapper, more direct expression, 100 MCR þ 1, is used.
(2)
Steam
m1
where c is the target class vector that stores the class labels for
the samples concerned; 0.01 is added just for the non-zero
requirement of the denominator.
City Water
Table 3 e ConfMat for the three-class case.
Diagnosed Fault (Predicted Class)
class 1
Happening
Fault
(True Class)
class 1
class 2
class 3
a11 (TN)
a21 (FN)
a31 (TN)
a
class 2
class 3
a12 (FP)
a22 (TP)
a32 (FP)
a13 (TN)
a23 (FN)
a33 (TN)
Bold has been used for emphasis
a Those in () are for class 2, as an example.
Steam HX
Condenser Water
to City Water HX
Evaporator
Water Loop
Chilled Water to
Hot Water HX
bypass
Hot Water Loop
2
2.2.
Condenser Water to
Evaporator Water HX
Chiller
Evaporator
Condenser Water Loop
Condenser
Fig. 4 e Simplified experimental layout to emphasize water
flow circuits.
590
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 5 8 6 e5 9 9
Table 4 e Seven faulty modes under investigation.
1
2
3
4
5
6
7
8
Normal or faulty modes
Abbreviations
Normal
Refrigerant leak/undercharge
Condenser fouling
Reduced condenser water flow
Non-condensables in refrigerant
Reduced evaporator water flow
Refrigerant overcharge
Excess oil
Normal
RefLeak
ConFoul
ReduCF
NonCon
ReduEF
RefOver
ExcsOil
Fitness ¼ 100 MCR þ 1 meanðmaxðp;½ ; 2ÞÞ
two classes may not be desirable, slack variables (also called
a margin error) are employed to allow for training errors.
Let Sa ¼ fðx1 ; y1 Þ; ðx2 ; y2 Þ; /; ðxN ; yN Þg be a training set for
two classes, where xi ˛Rn denotes the input vectors, yi ˛f1; 1g
stands for their class label, and N is the sample number. The
discriminant function with kernel K(x,xi) is:
)
(
N
X
ai yi Kðx; xi Þ þ b
(4)
f ðxÞ ¼ sgn
i¼1
where, sgn(u) is the sign function, if u > 0 then sgn(u) ¼ 1, if u<¼0
then sgn(u) ¼ 1; x is the sample to be recognized; b is called the
bias or threshold; the Lagrange multiplier ai is the solution of the
following quadratic programming (QP) problem:
(3)
where p is a matrix of the posterior probabilities that the jth
training group was the source of the ith sample observation,
i.e., Pr( group jjobs i).
maximize
a
Subject to :
N
X
ai i¼1
N
X
N X
N
1X
yi yj ai aj xTi xj
2 i¼1 j¼1
yi ai ¼ 0;
0 ai C;
(5)
ci
i¼1
3.
Machine learning d support vector
machine (SVM)
This section includes a brief introduction to basic two-class
SVM, multi-class SVM, SVM with FS and the evaluation
guidelines for the SVM classifiers.
3.1.
SVM
The basic SVM classifier deals with linearly separable twoclass cases d in which the data are separated by an optimal
separating surface that is defined by the support vectors. In
order to solve nonlinear problems, kernel functions such as
polynomial, sigmoid, Gaussian radial basis function (RBF),
etc., that map input space implicitly into high-dimensional
feature space where the problems may be solved linearly, are
introduced. For noisy data, when complete separation of the
where, C > 0 is a penalty constant (also called slack penalty) for
those samples misclassified by the optimal separating plane,
which sets the relative importance of maximizing the margin
and minimizing the amount of slack, and will be determined
via grid search and k-fold cross validation (presented in detail
in our study (Han et al., 2010), including the detailed SVM
training process).
Only a small portion of ai (for i ¼ 1,2,.,N) are not zero, and
the corresponding samples are those on the margin, i.e. the
SVs, which further confirms that only the SVs play a part in
defining the optimal separating hyperplane. The bias b can be
obtained from:
b ¼ yi wT xi
(6)
where xi is any support vector (although in practice it is safer
to average over all support vectors (Burges, 1998)), and w is the
weight vector as follows:
Table 5 e List of features/variables obtained from experiments.
1
TEI
9
TSI
2
TWEI
10
TSO
3
TEO
11
TBI
4
TWEO
12
TBO
5
TCI
13
Cond Tons
6
TWCI
14
Cooling Tons
17
Evap Tons
18
Shared
Evap Tons
26
TEA
34
Tsh_suc
19
Building
Tons
27
TCA
35
TR_dis
20
Evap Energy
Balance
28
TRE
36
Tsh_dis
21
kW
42
Tolerance%
43
Unit
Status
51
VSS
59
TWO
25
FEW
33
T_suc
41
Heat
Balance (%)
49
TWCD
57
VW
50
TWED
58
TWI
22
COP
7
TCO
15
Shared
Cond Tons
23
kW/Ton
8
TWCO
16
Cond Energy
Balance
24
FWC
29
PRE
37
P_lift
30
TRC
38
Amps
31
PRC
39
RLA%
44
Active Fault
45
TO_sump
46
TO_feed
47
PO_feed
32
TRC_sub
40
Heat
Balance (kW)
48
PO_net
52
VSL
60
THI
53
VH
61
THO
54
VM
62
FWW
55
VC
63
FWH
56
VE
64
FWB
Note: further information of the features is available in Appendix A.
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 5 8 6 e5 9 9
591
open literature (Hsu and Lin, 2002; Platt et al., 2000; Rifkin and
Klautau, 2004; Liu et al., 2006). Among them, the ‘one against
one’ algorithm (Chang and Lin, 2001; Hsu and Lin, 2002), which
constructs one two-class SVM between each pair of classes, is
the most easy to be understood and has a slightly better
performance than ‘one against others’ algorithm for the
chiller data to be used in this study, though the latter proved
to be better in Han et al. (2010), probably because of the
different distribution of the samples. Therefore, the ‘one
against one’ multi-class algorithm is chosen for this study.
The detailed structure of SVM classifier with FS is demonstrated in Fig. 3.
3.2.
Evaluation of SVM classifier
Table 1 is a confusion matrix (ConfMat) for the two-class case,
where TP (true positive) denotes the number of samples
happened and diagnosed, TN (true negative) that of samples
not happened and not diagnosed, FP (false positive) that of
samples not happened but diagnosed, and FN (false negative)
that of samples happened but not diagnosed. TP and TN are
correct classifications, and FP and FN are incorrect ones.
Hence, good results correspond to large numbers down the
main diagonal and small, ideally zero, off-diagonal elements.
There are literatures (Fawcett, 2004; Yélamos et al., 2007)
that analyze ConfMat from different viewpoints. To make it
simple and easy to understand for FDD use, correct rate (CR) or
misclassification rate (MCR) is adopted for the overall performance of the classifier, and hit rate (HR) and false alarm rate
(FAR) are used to evaluate the performance of the classifier for
individual class. Their definition and calculations are given in
Table 2. The wording of accuracy is avoided so as to minimize
misunderstanding.
For multi-class problems to which FDD belongs, ConfMat
for the three-class case, labeled as 1, 2 and 3, respectively, is
shown in Table 3, where CR, HR and FAR for class 2 are easy to
be obtained and so do those for class 1 and 3.
Fig. 5 e Performing scheme of AFDD with feature selection
(FS).
4.
Experimental data and AFDD framework
4.1.
Experimental data
The experimental data used come from ASHRAE project 1043
(Comstock and Braun, 1999a,b). The full name of the research
w¼
N
X
ai yi xi
(7)
i¼1
Gaussian RBF is selected as kernel function in our model for
its excellent performance (Lin and Lin, 2003):
Kðx; xi Þ ¼ exp gx xi 2
(8)
where, g > 0 is a parameter that controls the width of Gaussian.
The greater the width, the more flexible the classifier is. It is
determined together with slack penalty C in practice.
Two-class classification is useful but not suitable for fault
diagnosis (FD) in its original form for FD is always a problem of
multi-class classification or pattern recognition. A bunch of
algorithms for multi-class applications have been proposed in
Fig. 6 e Cross validation results for MI-based feature
selection (FS).
592
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 5 8 6 e5 9 9
Table 6 e Features selected by each selection scheme.
Num. of Features
Feature No. Selected
1e9
Case1
Case2
Case3
Case4
Case5
All features
GA-LDA
GA-LDA
GA-LDA
GA-SVM
64
13
10
8
8
10e19
e
6,
6,
4,
3,
9
8
8
7
20e29
30e39
40e49
50e59
60w
e
e
17, 19
18
e
e
23, 24, 29
e
24, 27, 28
24
e
31, 34, 38
30
e
30, 35
e
45, 47
45, 47
47
47
e
55, 56
56
56
56, 58
e
60
60, 63
e
e
Note: Features No. 3 (TEO) and 4 (TWEO) are the same features obtained by different sensors, RTD and thermistor, respectively. So do No. 7 and 8.
project is “Fault Detection and Diagnostic (FDD) Requirements
and Evaluation Tools for Chillers” referred to as ASHRAE 1043RP in this study, where a 90-ton centrifugal chiller was
installed indoor with a nearly constant ambient temperature
of 72 F (22.2 C). Both the evaporator and condenser are flooded-type, 2-pass shell-and-tube heat exchangers, with water
flowing in the tubes as the secondary-coolant. Fig. 4 depicts the
important equipment contained within the chiller test facility
and emphasizes the five water flow circuits d evaporator
water circuit, condenser water circuit, hot water circuit, city
water supply and steam supply. The abbreviation ‘HX’ in the
figure stands for ‘heat exchanger’.
Seven faults (Table 4), chosen based on the results of chiller
fault survey, were artificially introduced and investigated in
laboratory with each fault four levels of severity. They were
sequenced in descending order according to the normalized
happening frequency (Comstock and Braun, 1999a). Sixty-four
features (Table 5) were obtained at 10-s intervals, with 16 of
them calculated in real time by VisSim program (see Appendix
A). To investigate all seven faults, four sets of normal data
(Normal, Normal R1, Normal CF and Normal NC) were chosen
according to the recommendation of Comstock and Braun
(1999b).
4.2.
Data preprocessing
4.2.1.
Steady state detection
Before the FDD process begins, steady state detection is needed
to filter out data indicative of transient operation, such as those
during chiller start-up and shut down time periods or when the
driving conditions change abruptly. There are many classic
steady state filters measuring the change rate of a variable with
respect to time. Among them, the method of computing
geometrically weighted averages and variances (Glass et al.,
1995) is implemented because it has the advantage that the
computations are recursive, requiring a minimum of memory,
and it is sensitive in reacting promptly whenever the current
data depart from their steady-state values.
Three variables, i.e., temperatures of evaporator water in
(TWEI), evaporator water out (TWEO) and condenser water in
(TWCI), were selected as the state characteristics for they are
deterministic for the performance of a chiller with constant
water flow rates. Only if the weighted deviation of each of
these three variables (or features) falls below a pre-determined threshold, could the chiller be considered as under
steady state. In this study, the threshold is set at 0.2 C, the
time increment between measurements is 10 s and the time
window is 80 s.
4.2.2.
Data normalization
For a data set of N observations and n process variables, the
observed sample matrix Z ðZ˛RNn Þ is constructed and
b.
normalized by Eq. (9) to obtain data matrix X
8
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
:
Mj ¼ N1
N
P
zi; j
i¼1
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
N 2
P
1
sj ¼ N1
zi; j Mj
(9)
i¼1
bi; j ¼
x
zi; j Mj
sj
where Mj and sj are the mean and the standard deviation,
respectively, of the jth variable; zi,j is an element of matrix Z,
b
bi;j is an element of matrix X.
and x
4.3.
Performing scheme of chiller AFDD strategy
In practice, the chiller AFDD strategy combined with FS
previously presented is performed according to the scheme
Table 7 e SVM model and AFDD performance.
Correct Rate (CR) %
Select
Case1
Case2
Case3
Case4
Case5
e
88.02
85.60
87.15
e
Train
99.34
98.94
99.25
98.15
99.48
Note: ‘Select’ means feature selection.
Bold has been used for emphasis
Test
97.45
99.20
99.18
98.02
99.53
CPU Time Consumed (s)
Select
e
65.99
72.72
86.83
Train
11,559
2104
1460
1200
about 8 days
100.00%
18.20%
12.63%
10.38%
SVM Parameters
Test
3.1512
1.1388
1.0764
1.0608
0.9048
100.00%
36.14%
34.16%
33.66%
28.71%
C
4
2
24
23
23
23
g
24
21
22
22
22
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 5 8 6 e5 9 9
593
Table 8 e ConfMat for Case 1 and Case 5.
Case1: All Features
Normal
RefLeak
ConFoul
ReduCF
NonCon
ReduEF
RefOver
ExcsOil
0
B
B
B
B
B
B
B
B
B
B
@
Results and discussion
Data for each test run passed through the steady state
detector (SSD, Section 4.2.1), first. 12 000 samples were then
randomly selected from the historical data pool where the
steady state data for the normal and seven faulty modes (each
with four severity levels) were stored. The selected data set
was split randomly, afterwards, into 8000 and 4000 samples
for training and testing, respectively. Before any further
application began, the training set and test set were normalized independently by Eq. (9). After that, FS was conducted on
the training data and the selected features were transferred to
the test data to kick out those not selected; SVM was then
trained and tested for chiller AFDD and evaluation was made
accordingly, as Fig. 5 shows. Both training and test sets are
composed of a data matrix with rows for samples and
columns for features, and a target class vector where the class
labels for the samples are stored. Hence, before any FS, the
training set contains an 8000 64 data matrix and an
8000 1target class vector. The results are given below. So
does the corresponding discussion.
All the programs were run on a notebook with a CPU of
Intel Core2 P7370 (2.00 GHz), a memory of 2.00 GB and an
operating system of Windows Vista Home Basic. Libsvm 2.89
(Chang and Lin, 2001) was installed as a toolbox for Matlab
7.8 with Genetic Algorithm and Direct Search Toolbox.
5.1.
0
1
479
4
0
0
0
0
0
0
62 424
0
0
0
0
6
1 C
C
2
0
492
0
0
0
0
0 C
C
1
0
0
532
0
0
0
0 C
C
3
0
0
0
514
0
0
0 C
C
0
0
0
0
0
475
0
0 C
C
8
1
0
0
0
0
487 11 A
2
1
0
0
0
0
0
495
shown in Fig. 5. Detailed explanation is given in the first
paragraph of Section 5.
5.
Case5: GA-SVM Wrapper 8 features
B
B
B
B
B
B
B
B
B
B
@
5.2.
1
483
0
0
0
0
0
0
0
0
490
1
0
0
0
1
1 C
C
2
0
491
1
0
0
0
0 C
C
0
0
0
533
0
0
0
0 C
C
0
0
0
1
516
0
0
0 C
C
0
0
0
1
0
474
0
0 C
C
0
4
0
0
0
0
503
0 A
4
1
1
1
0
0
0
491
GA-based wrapper
In practice, GA-LDA wrapper was first employed to select 13,
10 and 8 features, respectively. The selected feature subsets
were then used to train SVM model. After that, validation was
performed on the trained model using the test set. The results
are given below in Tables 6e8 and Figs. 7e9. Also in the tables
and figures are those of GA-SVM wrapper for 8 features and no
FS (64 features).
5.2.1.
Features/sensors selected for each case
The FS results are shown in Table 6. Features No. 47 (PO_feed)
and 56 (VE) distinct themselves from other features for they
appeared in each scheme. PO_feed is the pressure of oil feed
and VE is the position of the electronic valve installed in the
evaporator water loop. The next important features are No. 7
(TCO) or 8 (TWCO) and 24 (FWC) for they were selected by
three schemes. TCO and TWCO are both the temperature of
condense water out, by different types of sensors (RTD and
thermistor, respectively). FWC is the flow rate of condenser
water. All these four features are there in Case 5 where GASVM wrapper is adopted for selection of 8 features. That is
a possible sign for Case 5 to perform the best.
Further study on the characteristics of PO_feed, VE (Fig. 7)
and FWC indicates that each of them almost distinctively
pointed to one of the fault: PO_feed / ConFoul, VE / ReduEF
MI-based mRMR feature selection (FS)
Based on the mechanism introduced in Section 2.1, MI-based
mRMR filter was implemented on the training data. In order to
have a quick idea about the trend the AFDD performance
varies with the number of features, 10-fold cross validation
was implemented with the MATLAB built-in ‘crossval’ function. The results were shown in Fig. 6. It can be seen from the
figure that when the number of features increases beyond
certain value (say, 21), the performance will no further be
improved, and there are several turning points (6, 8, 13, 17,
etc.) where the trend has been shifted or changed sharply. We
chose and focused on 13, 8 and 10 in-between them for further
investigation.
Fig. 7 e Characteristics of features No. 47 and 56.
594
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 5 8 6 e5 9 9
Fig. 8 e Hit rate (HR) for each class.
and FWC / ReduCF. As an example, Fig. 7 depicts the entire
sample points in the training set (after normalization), twodimensionally, with PO_feed as X axis and VE as Y axis. The
light blue samples represent the fault of reduced evaporator
flow (ReduEF) and their Y values (VE) are obviously independent from those of the other samples, so do the X values
(PO_feed) of the yellow points (ConFoul), which means that VE
and PO_feed are good indicators for ReduEF and ConFoul,
respectively. This is reasonable based on our knowledge about
refrigeration and the system. TCO or TWCO is not that
distinctive, but when it is combined with other features, such
as those left in Case 5, a comparatively satisfying AFDD
performance may be obtained.
Also in Case 5 are features numbered 3 (TEO, temperature
of evaporator water out), 30 (TRC, saturated refrigerant
temperature in condenser), 35 (TR_dis, refrigerant discharge
temperature) and 58 (TWI, temperature of city water in). The
positions of the five sensors other than those in the refrigerant
cycle (TRC, TR_dis and PO_feed) are shown in Appendix B,
among which two were found in the evaporator water loop
(TEO and VE) and the other three were directly related to the
condenser water loop (TCO, FWC and TWI).
5.2.2.
Overall performance of the AFDD strategy
Table 7 shows the main AFDD results by SVM model, including
the correct rate (CR) of FS (LDA classifier with 10-fold cross
validation), SVM training (10-fold cross validation) and testing,
the corresponding CPU time consumption and the optimal (or
near optimal) parameters for SVM. The CRs of LDA classifiers
(‘Select’) are all about or more than ten percent less than those
of SVM, which provides another proof for the better performance of SVM model in chiller AFDD. The training and test
CRs are always comparable except for Case 1 where the test
CR falls somewhat drastically, nearly two percent less (97.45
vs. 99.34), probably because of the noise or redundancy existed in the full feature set. Case 5 performs the best with the
test CR as high as 99.53%, Case 2 comes the second with
99.20% and Case 3 the third with 99.18%. The pairwise probability (Chang and Lin, 2001) prediction for the ‘one-againstone’ multi-class SVM model was opened during training and
Fig. 9 e False Alarm Rate (FAR) for each class.
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 5 8 6 e5 9 9
testing for each case. That helps improve the performance
slightly and reduce the test time consumption sharply. For
example, without the pairwise probability prediction, the test
CR for Case 5 was 99.475% and the test time for 4000 test
samples was 2.0904 s, compared to 99.53% and 0.9048 s,
respectively. This reduction in time, together with the high
CR, makes its future promising for online AFDD application.
The CPU time consumed by GA-LDA wrapper for FS is about
1.0e1.5 min (65e87 s). Even plus SVM training time, it is still
much less than that of GA-SVM wrapper, about 1.86& of the
latter. The much longer time for Case 5could be attributed to the
combination of GA and SVM, where each of the eight individuals for each generation needs undergo the time-consuming
process of grid search and 10-fold cross validation for SVM
training. That is, in a sense, the price to pay for performance
bettering. In fact, we found another subset of features accidentally, during an interrupted GA-SVM selection after running
two days (8 generations), that behaves just like Case 2 (13
features) with a test CR of 99.2% (8 features). The features are
No. 1 (TEI), 6 (TWCI), 21 (kW), 26 (TEA), 32 (TEC_sub), 45
(TO_sump), 48 (PO_net) and 58 (TWI), with the SVM parameters
C ¼ 8 and g ¼ 2. The interesting thing is that this subset is mainly
about the inlet sensors for water, refrigerant, power or even oil.
This does not necessarily mean that the sensors at inlet are not
that important compared with those at outlet, in consideration
of the random process in GA algorithm and the interrupted
running, but it does includes some information about the
combination of sensors in chiller AFDD, which accordingly
leave some space and certain direction for future investigation.
It can also be noticed from the table that the less the
features in the subset, the less the time consumed by training
and testing (except for GA-SVM wrapper training). For Case 4
and 5, where the number of features is the same, the testing
time for Case 5 is less while the CR is higher, maybe because
subset 4 includes more noise or redundancy.
Also in Table 7 are the near optimal parameters obtained
for SVM model via grid search and 10-fold cross validation.
Hsu et al. (2004) found that trying exponentially growing
sequences of C and g is a practical method to identify good
parameters, for example, with 2 as base. In our study, the
search ranges were considered from log2C ¼ 1 w 4 and
log2g ¼ 4 w 2, both with grid space 1. Searches may also be
conducted on the neighborhood of the parameters listed in
the table. The training time will increase, accordingly.
5.2.3.
Individual performance for each class
The performance for individual class is shown in Figs. 8 and 9.
To make it clear, part of the figure was magnified. There is
a sharp drop of HR for RefLeak Fault in Case 1, which indicts
that many RefLeak samples were reported as others. This is
confirmed from Table 8 for 62 out of 493 RefLeak samples were
alarmed in Normal, which constitutes the major reason why
the FAR for Normal in Case 1 is surprisingly high (Fig. 9). With
all features (64), it is exceptionally difficult for RefLeak to be
discerned from Normal. Generally speaking, Case 5 behaves
the best for each class with higher (if not the highest, say, for
ExcsOil) HR and lower (if not the lowest, say, for Normal and
ReduCF) FAR. The middle parts of all lines in both figures are
near optimal, which means that the four faults, ConFoul,
ReduCF, NonCon and ReduEF, are easy to be detected and
595
diagnosed, even with the slightest severity level (level 1).
CR ¼ 100% reveals that all the samples of the class are
correctly predicted by the AFDD model, that is, as long as it
happens, it could be exactly identified, e.g. ReduEF for Case 1,
ReduCF and ReduEF for Case 2, and Normal and ReduCF for
Case 5. FAR ¼ 0% suggests that all the samples reported in the
class truly happened, that is, as long as it is reported, it
happens, e.g. NonCon and ReduEF for all cases. For all the SVM
AFDD strategies presented in this study, if a sample is identified as NonCon or ReduRF, it is definitely right. The two
faults, RefLeak and RefOver, are the most difficult to be hit.
The three faults, Normal, RefLeak and ExcsOil, are the easiest
to be falsely alarmed. Though most of the FARs for Case 4 are
higher than those for Case 5 (both with 8 features), the former
performs better than the latter for ReduCF probably due to the
inclusion of features No. 18 (Shared Evap Tons), 27 (TCA) and
28 (TRE) (the other five features are the same for the two cases
as in Table 6).
Table 8 lists the confusion matrices of Case 1 and Case 5 for
comparison. As previously stated in Section 3.3, good results
correspond to large numbers down the main diagonal and
small, ideally zero, off-diagonal elements. It can be known at
a glance that the performance of Case 5 is better than that of
Case 1. The most distinct difference focuses on the first and
last columns, where there are many non-zero off-diagonal
elements for Case 1, especially for RefLeak and RefOver faults.
If all features are used, level 1 RefLeak is easy to be misdiagnosed as Normal and level 1 RefOver is easy to be
confused with ExcsOil. All faults have sample(s) reported as
Normal, except for ReduEF whose HR is 100% (no non-zeros
off-diagonal elements in the row) and FAR is 0% (no non-zeros
off-diagonal elements in the column). When features are
reduced to eight as those in Case 5, the diagnose performance
for RefLeak and RefOver will be greatly improved with the HR
enhanced from 86% to 99.39% and from 96.0% to 99.21%,
respectively, and the FAR lowered from 0.17% to 0.14% and
from 0.17% to 0.03%, respectively. Naturally, there is the price
to pay d a slight drop for ReduEF’s HR to 99.79%.
6.
Conclusions
This study researches on the important sensors for chiller
AFDD application, based on FS techniques and machine
learning methodology. MI-based filter has been adopted for
a preliminary idea about how the number of features affects
the AFDD performance. GA-based wrapper has then been
investigated in a detailed manner with GA-LDA wrapper for
13, 10 and 8 features and GA-SVM wrapper for 8 features.
‘One-against-one’ multi-class SVM has been employed as an
AFDD strategy after or within FS. The results showed that the
features/sensors could be successfully reduced to one-third of
the original number, from 64 to 8, while achieving a much
better AFDD performance d higher CR, HR, lower FAR and
much less computational time. Details are as follows:
1) For the four cases with FS, the test CRs are all higher than
that for no FS, and the test time is cut down about 63e72%.
2) Features No. 47 (PO_feed) and 56 (VE) distinct themselves
from other features for they appeared in each selection
596
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 5 8 6 e5 9 9
scheme. Detailed study on their characteristics shows that
they are fairly indicative to certain fault: PO_feed /
ConFoul, VE / ReduEF. FWC is also an indicator that
directly points to ReduCF. See Appendix A for detailed
information about the features.
3) Among all five cases, GA-SVM wrapper (Case 5) performs
the best with eight features/sensors including five
temperatures (TEO, TCO, TRC, TR_dis, and TWI), one pressure (PO_feed), one flow rate (FWC) and one valve position
(VE). It can be said that, except the PO_feed, five of them
(TCO, FWC, TRC, TR_dis, TWI) are about the condenser side,
and the other two at the evaporator side (TEO, VE). See
Appendix B for their locations in the system.
4) The four faults, ConFoul, ReduCF, NonCon and ReduEF, are
easy to be detected and identified, even with the slightest
severity level (level 1). The two faults, RefLeak and RefOver,
are the most difficult to be hit, especially when all features
are included. The three faults, Normal, RefLeak and ExcsOil,
are the easiest to be falsely alarmed.
Generally speaking, the feature selection schemes and the
machine learning method employed in this study proved to
be effective in improving FDD performance, reducing computational time and saving initial cost on sensors in terms of both
type and quantity. It represents a useful effort, in a sense, not
only for the researchers but for the chiller manufacturers.
Future study includes further test with more samples, other FS
methods, SVM parameter tuning, improved multi-class SVM
algorithm, and other FDD technology such as combining
different techniques for fault detection and fault diagnosis, etc.
The practical implementation will be the final testing ground.
Acknowledgement
This project was supported by the National Natural Science
Foundation of China (NSFC) under Grant No. 50876059. The
authors would also like to thank Prof. James Braun with Purdue
University and Dr. Donna Daniel with ASHRAE for their kind
help in providing the detailed experimental data, Dr. Peng
Hanchuan with University of California at Berkeley, for his
informative discussions about mutual information and Harri
M.T. Saarikoski, PhD candidate with Helsinki University,
Finland, for his valuable advices on feature selection.
Appendix A. Further information about features.
Both Appendix A and B are from Comstock and Braun (1999a),
for information only.
Table A1 e Exported data from experimental test runs.
Designation
Source
Description
Units
1
2
3
4
5
6
7
8
9
Time
TWE_set
TEI
TWEI
TEO
TWEO
TCI
TWCI
TCO
TWCO
TSI
VisSim
Micro Tech
JCI AHU (RTD)
Micro Tech (Thermistor)
JCI AHU (RTD)
Micro Tech (Thermistor)
JCI AHU (RTD)
Micro Tech (Thermistor)
JCI AHU (RTD)
Micro Tech (Thermistor)
JCI AHU (RTD)
Second
F
F
F
F
F
F
F
F
F
F
10
TSO
JCI AHU (RTD)
11
TBI
JCI AHU (RTD)
12
TBO
JCI AHU (RTD)
13
14
15
Cond Tons
Cooling Tons
Shared Cond Tons
VisSim
VisSim
VisSim
16
Cond Energy Balance
VisSim
17
18
Evap Tons
Shared Evap Tons
VisSim
VisSim
19
Building Tons
VisSim
Real time counter
Chilled water setpointdcontrol variable
Temperature of Evaporator Water In
Temperature of Evaporator Water In
Temperature of Evaporator Water Out
Temperature of Evaporator Water Out
Temperature of Condenser Water In
Temperature of Condenser Water In
Temperature of Condenser Water Out
Temperature of Condenser Water Out
Temperature of Shared HX Water In (in
Condenser Water Loop)
Temperature of Shared HX Water Out (in
Condenser Water Loop)
Temperature of Building Water In (in
Evaporator Water Loop)
Temperature of Building Water Out (in
Evaporator Water Loop)
Calculated Condenser Heat Rejection Rate
Calculated City Water Cooling Rate
Calculated Shared HX Heat Transfer (only
valid with no water bypass)
Calculated 1st Law Energy Balance for
Condenser Water Loop (only valid with no
water bypass)
Calculated Evaporator Cooling Rate
Calculated Shared HX Heat Transfer
(should equal Shared Cond Tons with no
water bypass)
Calculated Steam Heating Load
F
F
F
Tons
Tons
Tons
Tons
Tons
Tons
Tons
597
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 5 8 6 e5 9 9
Table A1 (continued).
Designation
Source
20
Evap Energy Balance
VisSim
21
kW
JCI AHU
22
23
24
25
26
COP
kW/ton
FWC
FEW
TEA
VisSim
VisSim
JCI AHU
JCI AHU
Micro Tech
27
TCA
Micro Tech
28
TRE
Micro Tech
29
30
PRE
TRC
Micro Tech
Micro Tech
31
32
PRC
TRC_sub
Micro Tech
Micro Tech
33
34
T_suc
Tsh_suc
Micro Tech
Micro Tech
35
36
TR_dis
Tsh_dis
Micro Tech
Micro Tech
37
38
P_lift
Amps
Micro Tech
Micro Tech
39
40
RLA%
Heat Balance (kW)
Micro Tech
VisSim
41
Heat Balance%
VisSim
42
Tolerance%
VisSim
43
44
45
46
47
48
49
Unit Status
Active Fault
TO_sump
TO_feed
PO_feed
PO_net
TWCD
Micro Tech
Micro Tech
Micro Tech
Micro Tech
Micro Tech
Micro Tech
Micro Tech
50
TWED
Micro Tech
51
52
53
54
55
56
57
58
59
60
61
62
63
64
VSS
VSL
VH
VM
VC
VE
VW
TWI
TWO
THI
THO
FWW
FWH
FWB
JCI AHU
JCI AHU
JCI AHU
JCI AHU
JCI AHU
JCI AHU
JCI AHU
JCI AHU
JCI AHU
JCI AHU
JCI AHU
VisSim
VisSim
VisSim
(RTD)
(RTD)
(RTD)
(RTD)
*Please consult the corresponding tables in Comstock and Braun (1999a).
Description
Calculated 1st Law Energy Balance for
Evaporator Water Loop
Watt Transducer Measuring
Instantaneous Compressor Power
Calculated Coefficient of Performance
Calculated Compressor Efficiency
Flow Rate of Condenser Water
Flow Rate of Evaporator Water
Evaporator Approach Temperature
(TWEO-TRE)
Condenser Approach Temperature (TRCTWCO)
Saturated Refrigerant Temperature in
Evaporator
Pressure of Refrigerant in Evaporator
Saturated Refrigerant Temperature in
Condenser
Pressure of Refrigerant in Condenser
Liquid-line Refrigerant Subcooling from
Condenser
Refrigerant Suction Temperature
Refrigerant Suction Superheat
Temperature
Refrigerant Discharge temperature
Refrigerant Discharge Superheat
temperature
Pressure Lift Across Compressor
Current Draw Across One Leg of Motor
Input
Percent of Maximum Rated Load Amps
Calculated 1st Law Energy Balance for
Chiller
Calculated 1st Law Energy Balance for
Chiller
Calculated Heat Balance Tolerance (ARI
550 defined as allowable test tolerance on
heat balance)
Consult Table B.4 in Appendix*
Consult Table B.3 in Appendix*
Temperature of Oil in Sump
Temperature of Oil Feed
Pressure of Oil Feed
Oil Feed minus Oil Vent Pressure
Condenser Water Temperature Difference
(TWCO-TWCI)
Evaporator Water Temperature Difference
(TWEI-TWEO)
Small Steam Valve Position
Large Steam Valve Position
Hot Water Valve Position
3-way Mixing Valve Position
Condenser Valve Position
Evaporator Valve Position
City Water Valve Position
Temperature of City Water In
Temperature of City Water Out
Temperature of Hot Water In
Temperature of Hot Water Out
Calculated City Water Flow Rate
Calculated Hot Water Flow Rate
Calculated Condenser Water Bypass Flow
Rate
Units
Tons
kW
kW/ton
GPM
GPM
F
F
F
PSIG
F
PSIG
F
F
F
F
F
PSIG
Amps
%
kW
%
%
0e27
0e44
F
F
PSIG
PSI
F
F
%Open
%Open
%Open
%Open
%Open
%Open
%Open
F
F
F
F
GMP
GMP
GMP
598
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 5 8 6 e5 9 9
Appendix B. Position of sensors
Fig. B1 e Sensors mounted in condenser water circuit and city water supply.
Fig. B2 e Sensors mounted on evaporator water circuit and steam supply.
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 5 8 6 e5 9 9
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