V.O. Lazarev
USING THE ALGORITHM OF BACK-PROPAGATION FOR QUALITY
MANAGEMENT SYSTEM OF PRODUCTS.
Summary. The publication is dedicated to the use of back-propagation algorithm to
control the quality management system of production.
Key words: artificial neural networks, quality control of production, back-propagation
algorithm.
Formulation of the problem. Quality control of products is a problem of
the first magnitude for any enterprise. For this reason, most manufacturers are not
only willing to invest in a classic automated quality control system, but also ready
to introduce new advanced development. In describing the production process can
be distinguished input characteristics, such as temperature, density, chemical
composition, geometric parameters of blanks and other parameters, and output
quality criteria derived products, their composition is usually described state
standards and other industry standards, and sometimes the finished products to
customer requirements [1; p.9]. Input characteristics can in turn be divided into
modified during the manufacturing process and unchanging; the latest features are
mostly blanks and semi-finished products produced by other industries. Thus, the
manufacturing process is always possible to identify the relationship of input
variable characteristics of the production process with the criteria for quality of the
resulting output product. In the case of a large number of these characteristics and,
possibly, quality criteria, manual control of such a process is impossible,
distributed automatic control system (ACS), working in conjunction with expert
systems (ES) require a very long and time-consuming to change the rules and
parameters in case of change of the output criteria or fluctuations in input
characteristics. For similar production processes, we obtain a nonlinear mapping of
input characteristics on the set of output quality criteria for the finished product.
This model can be described with the help of an artificial neural network [2; p.21],
with the back-propagation algorithm [3; p.51] implements a robust set of feedback
from the output criteria to the input characteristics.
Analysis of the latest research and publications. The first description of
the method of back-propagation as one of the options for training artificial neural
networks gave A. I. Galushkin in 1974 at the same time it did P. J. Verbos. In a
further development of the method involved D. I. Rumelhart, G. E. Hinton, and R.
J. Williams, and S. I. Bartsev and V. A. Okhonin.
Sufficiently complete and detailed classification of neural network control
systems can be found in S. G. Chernyy "Application of a model of intelligent
information in automatic control systems" published in the Journal of HNTU
number 1 (44), 2012 This publication examines the joint work on the adoption of
management solutions of an artificial neural network and a mathematical model of
the control system.
The purpose of this publication is to consider the possibility of using
artificial neural networks to manage the complex process of production and the use
of back-propagation algorithm for the feedback to the control system.
The presentation of the basic material of the research. In solving the
problem of the control system for the production process described above, we
arrive at the map multiple input multiple output characteristics on the quality
criteria of the finished product, it can be illustrated by the scheme shown in Figure
1:
1
2
3
Fig. 1. The mapping of input characteristics on the quality criteria.
Zone 1 features a variety of input characteristics of the production process.
Zone 3 represents a set of linkable criteria of product quality. To better improve the
averaging and smoothing of sharp emission undesired interaction region of the
input data and output results is expedient to introduce the intermediate combiners
shown in area 2.
The above circuit can be easily described in the artificial neural network
architecture which is the n-layer perceptron [4; p.222].
Artificial neural network is a collection of artificial neurons (AN) connected
weighted connections (synapses). Each AN has a certain number of inputs and
outputs. The main objective of AN include 3 stages:
1. Acceptance input information which is transmitted as a set of pieces of
output signals of previous AN weights and incoming connections
2. Processing the received signals by applying thereto an activation function
AN [2; p.22].
3. Transmission of the activation function of the input of the following AN.
Back-propagation algorithm belongs to a group of teaching methods of
artificial neural networks (ANN) with the teacher. This means that the ANN
training phase compares the results obtained with the reference network output
values. After each pass through the training data for the ANN 2 options are
possible outcomes:
• The result of the ANN is the reference;
• The result of the ANN is different from the reference;
In the first case it is assumed that the state weighting ties AN (synapses)
does not require changes. In the second case requires correction weights.
To carry out the correction weights must calculate the difference of the ANN
and the resulting benchmark result for the members of the training set of
characteristics. The resulting difference initiates the return passage network, in
which the inputs and outputs are reversed AN and activation function works
similarly. The process of return passage on the network is accompanied by a
weight correction, a detailed description of the error back-propagation algorithm
can be found in [2] and [3].
In the case of an interest to us, the process control scheme in the form of
MLP in general, there are several stages of preparation and operation of the
system:
• Clarify the use of ANN architecture
• Develop rules for the incoming data and results
• Create a standard set of inputs and outputs for the ANN training
• Just learning the INS, including the adjustment of the weights and their
subsequent fixation.
• The process of refining and scaling that determines the outcome of the
ANN change from subtle changes in the various input parameters.
Clarify the use of ANN architecture. Having defined, in general, the
architecture of the ANN as a MLP, it remains to determine the number of hidden
layers, AN, as well as the number of AN in each layer. It is worth noting that to
date there is no generally accepted method accurately calculate these parameters. A
priori, these parameters depend on the complexity of the task, the number of inputs
and outputs of the network and the number of training samples. When choosing
these parameters should take into account the hardware resources of the computer,
which is expected to operate the control system.
For a small number of hidden layers and TI in them ANN can not learn or do
not learn well it will cause sharp fluctuations in the resulting function. A large
number of hidden layers and the AN they entail retraining the network disappears
ability to generalize and dramatically increase the load on the hardware resources,
which will lead to excessive demands. Thus, such a configuration of ANN is made
directly for a specific target.
Develop rules for the incoming data and results. Application data "raw"
(unprocessed) form of treatment in most cases ANN impossible. This is due
primarily to the different dimensions of the data, whereby the first to convert the
data so that the values are within at least one order. With non-linear activation
function AN (this is a must use back-propagation algorithm, since it requires
differentiability of the activation function at any point) to provide input in the
range of (-1, 1) or (0, 1) it will take them to scale.
Create a standard set of inputs and outputs for the ANN training. When
creating the training set must be guided primarily principle completeness, it should
include all possible embodiments wherein the training set should not be excessive.
Detailed procedures of preparation of training data and the learning process of
ANN are described in [5], [6] and [7].
The process of refining and scaling the system. After the refined design,
creation and training of ANN weights are fixed, and the mechanism will provide
the algorithm back-propagation switch to operational mode.
The essence of the method is the use of mathematical and algorithmic
apparatus, method, back-propagation, and possibly ready software and hardware
implementations of it, not only for the ANN training, as well as to manage the
production of the finished product in real time.
The system can implement two major functions:
• Control of the resulting product and automatically adjusts the input
parameters of the production process in real time;
• Smooth adjustment to the required quality criteria and functional when
they are changed without stopping the production process.
After training, the ANN output by a set of criteria will be considered the
current standard, as the system of weights is fixed then the deviation from the
standard will only occur through the fault of the input characteristics of the
process. Fixing the deviation of output parameters of the current standard, the
system activates the error back-propagation, but the weight of the AN will not
change as a result of the return passage by the ANN will be calculated which of the
incoming characteristics have changed and to what extent, activating the
appropriate controllers, the system compensates for the difference by increasing or
decreasing the supply of the desired input component, which in turn will change
the output parameters. Thus, as a result of an iterative comparison with the current
standard and the tuning parameter changes will be leveled and the process will be
terminated before the next move beyond the set of output codes.
Another possibility is implicit in the proposed method, is to smooth the fine
tuning of the input parameters in response to changing exit criteria of quality and
functionality of the finished product. In this case, there is a sequence: the output
parameters of the ANN are adjusted in line with the new requirements, resulting in
the formation of a new current standard, therefore, a set of criteria, the former past
the current standard, becomes invalid, the mechanisms activated by implementing
back-propagation algorithm, which computes difference between the states of
nodes in the reverse pass, and determines which of the input parameters and the
extent to which you want to change, to ensure that the coincidence of the final set
of criteria with the new standard.
Fig. 2. The use of back-propagation to define and configure influencing the outcome of the input parameters.
As is known, the error back-propagation algorithm is based on the fact that
the correction synapse weights for training the ANN is made depending on the
weights themselves [2; p.41], i.e. the value of the error function given node on the
reverse pass network is divided between the input current node is proportional to
the weights of incoming synaptic connections. As a result, we get the return
passage to change the weights of all edges of the ANN, including the difference
between the weights of synapses coming from the inputs of ANN to the first
hidden layer; these differences can be used to change the numerical characteristics
of the relevant input parameters. Figure 2 shows schematically a backward pass by
ANN influencing nodes and synapses allocated more dense of grayscale.
Conclusions. The use of artificial neural networks in different areas of
production activities for a long time is not surprising. ANN took place alongside
the other tools and technologies. In order to use neural network techniques
developed serious mathematical, algorithmic and technological apparatus.
The method proposed in this document proposes to consider the application
of the well-known back-propagation algorithm, not only for its intended purpose as a tool of ANN training, but also as a method of analyzing and managing the
process of production of finished products.
It should be noted that the feasibility of this technique will very much
depend on the specific conditions of production, in particular the number of input
and output parameters. The preferred method is to use, manufacturing processes
with a maximum number of incoming bad parameterized properties that are
managed by the operating composition greatly complicated, costly or not optimal
due to the low reaction rate.
Literature
1.
Гиссин В. И. Управление качеством продукции / В.И. Гиссин. Ростов-на-Дону : Феникс, 2000. – 300 с.
2.
Заенцев И. В. Нейронные сети: основные модели / И.В.Заенцев. Воронеж : Воронеж, 1999. – 76 c.
3.
Каллан Р. Основные концепции нейронных сетей / Р. Каллан. - М.
: Издательский дом «Вильямс», 2001. – 287 c.
4.
Хайкин С. Нейронные сети: полный курс. 2-е изд. / Хайкин С. М. : Издательский дом "Вильямс", 2006. – 1103 c.
5.
Комарцова Л. Г. Нейрокомпьютеры. / Комарцова Л. Г., Максимов
А. В. - М. : Изд-во МГТУ им. Баумана, 2004. – 250 c.
6.
Галушкин А. И. Нейронные сети. Основы теории / А.И.
Галушкин. - М. : Горячая линия - Телеком, 2010. – 320 c.
7.
Kosko B. Neural Networks and Fuzzy Systems. A Dynamical Systems
Approach to Machine Intelligence / В. Kosko. - Prentice Hall : Englewood Cliffs,
1992. – 400 c.