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The Potential Applications of Artificial Neural Nets in Quality Control
Copyright © IFAC Distributed Intelli gence Systems, Virginia, USA, 199 1
THE POTENTIAL APPLICATIONS OF ARTIFICIAL NEURAL NETS IN QUALITY CONTROL Yong-zai Lu Research Institute oJ Industrial Process Control, Zhejiang University. Hangzhou 310027. PRC
KEY WORDS: Quality Control, Statistical Process Control, Artificial Neural Nets, Pattern Mapping, Back Propagation Learning, Associative Me.ory, Intelligent Quality Control. ABSTRACT: This paper addresses the develop.ent of an application of Artificial Neural Nets (ANNs) in Quality Control (QC). This study first Addresses the anAlysis of QC in the real industrial processes, such a s bAtch, discrete as well as continuous productions to show the potentials in co.bining the existing Statistical Process Control (SPC), Process Control (PC) with ANN and Artificial Intelligence (AI). The general structure, strategy and Algorith. of ANN with BACk Propagation (BP) learning for process quality .odel and the quality control .odel have been developed. The resulting ANNs can be used for various processes (batch, discrete, and continuous as well) and the production .anage.ent. The co.puter si.ulations show the re.arkable learning, .e.ory and decision ability. Finally, the concept and fra.e of the Intelligent Quality Control (IQC) has also been proposed.
ShewhArt ChArt, Cusu. Chart, etc. shown in Fig.l and Fig.2 respectively. The • .ajor objective of QC is to .aintain the quality variables as close as possible to desired target area,or the set point. The statistical approach associated with the QC charts provides the analysis for i.proving the product quality. It should be noted that the hu.an factors or socalled knowledge plays critical role in .aking the analysis and / or decisions, which are hardly possible to be e.ulated by the traditional .athe.atical tools.
INTRODUCTION
Statistical Process Control (SPC) has been playing .ore and .ore i.portant role in i.proving process productivity and product quality in traditional and .odern industries. Here we .ust .ention that De.ing [ll has .ade great contributions, first in Japan, and .ore recently in North A.erica to convince .Anage.ent putting product quality being the top priority. In fact,the quality revolution has provided the high reputation of the Japanese products.
The latest technology of Artificial Intelligence ( AI ) and Artificial Neural
The Quality Control ( QC ) based on SPC .ainly involves process design, Analysis and on-line qual ity control, etc •• It is obvious thAt the later beco.es A very i.portant AreA of overlAp between SPC and Process or Production Control ( PC ) However, in .as noted by l1acQregor [2J. general, the product quality is hardly possible or too costly to be on-line .easured by sensors, i nst ead, d i scret e dAt.a infrequently obt.ained fro. product anAlysis lAboratory are used to guide the operat ion. This .akes it extre.ely difficult to design a control syste. bAsed on such discrete dat.a for process control engineers.
Nets (ANN) has shown the powerful func tions in e.ulating so.e hu.an being, such as,leArning, .e.ory, reAsoning and decisions, obviously, which will be an effective tool to solve the QC proble •• This study will topics:
* *
* * *
In order to deal with discrete data QC proble.,a nu.ber of .approaches have been developed. The .ost popular .ethods .are different kinds of QC Charts, such as
address
the following
Proble. State.ent of Quality Model and Qu.ality Control; ANN b.ased Process Quality Model ANN QC Control Model; Design of ANN for QC; Si.ulation Results; Intelligent QC PROBLEM STATEMENT
107
The relationships between the product quality and the operating conditions can be illustrated by the following .ath. • odel: Y
Where Y
E
U
D
F
F
( E,
U
) + D
learning are developed to carry out the QC for continuous, batch and discrete product ions •
(1)
DEVELOPMENT OF ANN FOR QC
=[
y, ' Y2 , •••. , y" JT ER" A vector Denoting the quality variables in the qualit~ space; [E" E 2 , • • • • • , Em J ER'" A vector denoting the production environ.ent,which usually involves the uncontrollable variables (analog, discrete, or digital/logical); r [ U, , U. , •.••• , U r JT E R The control vector denoting the control actions and I or .anipulat ing variables, which can also be in analog, discrete, or digital I logical for.s; [ D, , D 2 , • • • • • , D... ERn A vector denoting the rando. disturbance; Representing the stochastical funct ion.
In order to .odel a co.plex syste.,an ANN with hidden layer and BP-learning as has been developed. The function of the input layer is to carry out the signal nor.alization, here the input I output signal are scaled within the range of 0 to 1.0, or for binary ANN, the signals are represented by 0 and 1 integer data sequence. Both hidden and output layers consist of a nu.ber of neurons with the sig.oidal functions. All of the neurons at the different layers are weighted connected to transfer the infor.ation. The BP-learning provides the upgraded weights based on the errors between the syste. output which serves as the teaching signal and the output given by the ANN. The ANN configuration with BPlearning is shown in Fig. 4. The Basic Structure of ANN The transfer function of the can be described a5 follows:
Si.ilarly, the relevant QC .odel can be written in the following for.:
U
=G
(1 + exp
(2)
/ T »
Ni
~
(4)
Wji Ui + Wj
i=l Yj
However, since the relationships between the product quality and the production environ.ent and other conditions are so sophisticated, that in .ost production processes, it is hardly possible to establish the quality .odel, even its structure as shown in Eq. (1), as a result, the existing approaches, such as Kal.an Filtering, identification and esti.ation, can not be used. The .ajor reasons are as follows:
*
(et. j
Where
Where Ys denotes the desired product quality , and G represents the functional relationship between the control actions and both Ys and E.
*
(3)
Yj ( Vs, E,
neuron j
dj
Ui Wji Wj
The output of the neuron j; The state of the neuron j ; The input fro. the neuron i at the lower level of the layer; The connection strength fro. neuron i to j ; The bias of the neuron j ; The te.perature .achine.
T
in
Based on the Eqs (3) and (4), the input I output relationship for both hidden and output layer can then be described as the .atrix for. [3J:
All of those .ethods are heavily dependent upon the .ath. .odel, at least the .odel structure; It is i.possible to deal with the digital I logical variables.
In this study, a concept of pattern .apping is proposed to replace the traditinal Math. concepts. In fact, the relationships between production variables can be considered as a hyperspace .apping proble. as shown in Fig.3. As a result, the quantitative relationships are only based on the production data without knowing the .odel structure.
Yh
S
Yo
S
(5)
B
(6)
Where Wh U B
S
The proble.s addressed in this paper are .ainly to establish both production quality and QC .odels by .eans of ANN techno 1 ogy.
Yo Yh U
A
The proble. of ANN based QC .odeling is ~ develop an ANN .odel which can dupllcate
B
the input/output relationship just based on the production data. An ANN with BP-
Wo
108
Wo Yh
Wh
+
+
Wo
(7) (8)
The sig.oidal function; The output vector of the output layer; The output vector of the hidden layer; The nor.alized input of the ANN; The state vector of the hidden layer; The state vector of the output layer; The connective .atrix between hidden and output layers;
Wh
The connective .atrix between input and hidden layers; The bias vl!ctor of thl! output laYl!r;
Wo Wh
The bias laYl!r
vl!ctor of
Basl!d on thl! abovl! processing stl!ps. we can then I!stablish .any pairs of the pattl!rns using thl! production data relatl!d to thl! product quality V. production environ.ent E. and control actions and/or .anipulates U. As a rl!sult. the functions F and G in Eqs. (1). and (2) are convl!rtl!d in to thl! relevant pattern .apping without thl! knowledge of thl! .athe.atical structurl!. The input / output data gatherl!d fro. thl! production can bl! used to I!stablish a data file describing thl! V -E -U pattl!rns as shown
thl! hidden
Thl! ANN-BP Learning Algorith. Thl! cost function of ANN-BP ll!arning is to .ini.izl! the .ean square I!rror betwl!l!n thl! tl!aching signals and thl! actual output of ANN. which can bl! dl!scribl!d as follows: 2 Min J (Wh. Wo) = Z. L,( Vs (k) -Vo (k» (q) I<
in Tabll! 1.
.,.
Tabll! 1
(t+1) = Wkj
Wkj
(t) + Lr De Vhj
* *
(10)
V2.
••• • ••
Vn. J T
which can gl!o.l!trically illustratl!d in Fig. S. Thl! product quality can be classified into a nu.bl!r of groups based on thl! following ways:
*
Product grades. such as • A. B•••••• which arl! rl!late to thl! spl!cific area in thl! quality spacl!. as a result. thl! product grade can then bl! dl!scribl!d by thl! rl!ll!vant digital nu.bl!rs;
*
The quality vl!ctor. V. which rl!prl!sl!nts a point in thl! qual i ty space. in this casl! the product quality is directly .I!asured by thl! physical variables.
* *
1 1
* *
* ..... . * ..... .
1 1 1
Using the ANN - BP structure as introduced in thl! previous section, { E, U} and {V} are placl!d as ANN input and tl!aching pattl!rns rl!spectively as shown in Fig.D. Based on the "V -E -un pattl!rns as shown in Table 1, Thl! ANN will start to learn fro. the supl!rvised ll!arning pattl!rns. If Wl! sl!lect thl! suitable initial learning rate and the tl!.pl!raturl!, thl! error bl!twl!l!n thl! tl!aching signals and thl! ANN output will rl!ducl!d stl!P by stl!P, and finally, thl! error will bl! close to zero and thl! wl!ights will bl! frozl!n. The nu.bl!r of itl!rations to co.pll!tl! the ll!arning is .ainly dl!tl!r.inl!d based on thl! sizl! of ANN and the nu.bl!r of the pattl!rns bl!ing trained. Obviously both ll!arning rat I! and thl! tl!.peraturl! will also significantly influencl! the convergl!nt rate as wl!ll as stability.
SUppOSI! that thl! quality variables constructs a .ultipll! di.l!nsional spacl! •
* *
Th. Structure of ANN QC Mod.l
In order to I!stablish thl! .apping bl!tween the quality spacl! and the space of the opl!rating conditions and the production I!nviron.l!nt. Wl! will first .akl! thl! classification in thl! quality spacl!.
CV I
1 1
------------1--------------1-- -----------
In this study. both ll!arning rate Lr and thl! tl!.perature T are designed to be the dl!crl!asing functions. which benefit thl! convl!rgl!nt ratl!. In ordl!r to spl!ed up thl! ll!arning ratl! .the .0.l!ntu. ter. is introduced in thl! ll!arning algorith. C4J.
=
* *
1 1 1
In Eq. (10). Wkj are weights fro. layer j to the layer k at the iterativl! ti •• t. Vhj is the input signal fro. the layer j to the layer k. The co.putation of the error t.r. De for both hidden and output layers can refer to C3J.
V
V - E - U Patterns
------------1--------------1------------VIE 1 U ------------1--------------1------------V V .•••• 1 E E •••.•. I U U ••••.• ------------1--------------1-------------
Using the gradil!nt sl!arch tl!chnique. the wl!ights can bl! upgradl!d by using the following rl!cursivl! algorith. starting at thl! output nodes and working back to the first hidden laYl!r :
If thl! ll!arning / training has been co.pll!tl!d. thl! pattl!rn .apping is I!stablishl!d and this ANN has both short tl!r. and long ter. .e.ory which are rl!latl!d to thl! nl!uron states and the connectivl! wl!ights respl!ctivl!ly. Whl!n we entl!r thl! input pattl!rns { E. U }. the ANN will providl! thl! output patterns. which will .atch thl! systl!.'s rl!al output. Howl!ver. if thl! pattl!rns are not locatl!d in the arl!a which has bl!en trainl!d. the results will not bl! good I!nough to .atch the real output .50 it beco.es a critical proble. to select the trained patterns which can cover the operating area. The orthogonal procl!ssing for the trained pattl!rns will bl! helpful for thl! learning / training.
In addition. both production environ.ent and control actions can also described by the digital nu.ber and / or thl! physical variabll!. For instancl!. thl! diffl!rl!nt product ion schl!.l!s and / or thl! raw .atl!rials can bl! .arked with differl!nt tag nu.bers. Obviously. thl!Y can also bl! describl!d by the analog variables. such as thl! t •• pl!rature. flow ratl!. or .achine running speed • • tc ••
~n addition.
The ANN QC proble •• in fact. a rl!vl!rse proble. of what Wl! dl!scribed abovl!, na.l!ly, finding the control actions based on thl! production I!nviron.ent to satisfy thl! dl!sired product quality. Obviously, this probll!. can also be governl!d by of a pattern 1S
109
.Apping which Addressed above.
is
si.ilAr to
whAt
we REFERENCES
SIMULATION RESULTS
Deming, W. E. Ind. Qual. Contr, 24, P.89, 19&7 (2] MacGregor, J. F. Che.. Engng. Prog. P.21, 1988 (3] Ru me1hat't, D. E. et a1 PArallel Distributed Procesiing , MIT Pt' ess, 1988 [4] Lippmann, R. P. IEEE ASSP Magazine, P.4, 1987 [1J
Based on the developed ANN-QC .odel and the nonlinear si.ulated plant with .ultiple variable rando. input and output signals (siK inputs and three outputs >, the co.puter si.ulation study on ANN -BP learning and ANN running is shown in Fig. 7. The co.puter si.ulation results are given in Figs. 8 -10. An ANN with hidden layer and deco.posed structure can have .e.ory of one thousand patterns after thousands of thousands learning. The Average relative error between the actual output and the ANN output , ARE, are less thAn 3 " •
UCL
_....£.
THE INTELLIGENT QC
o
o
o
As we noted before that the hu.an knowledge is one of .ost i.portant factors in carrying out QC. It should be noted that since the ANN can deal with rule base, fuzzy logical and the relevant reasoning, a structure of Intelligent Quality Control (IQC > can be establishl!d as shown in Fig. 11. Thl! key issue here is how to convert the factors related to both production environ.ent And control actions into the input signals which can be dealt with by ANN. Sincl! ANN CAn process VArious signals,
0-
0-
o
t t
TARQET
o
o LCL
ACTIONS
Fig.l The Sa.ple of Shewhart Chart for QC
it will hAve no proble. to convl!rt a physical syste. into a relevant ANN. CONCLUSIONS This study show the potential Applications of ANN in QC, and also propose the structurl! of IQC, which will be the futurl! of the QC. Co.paring with thl! traditional QC tools and the eKpert syste. for QC, thl! ANN based QC has the following .Ajor .I!rits:
*
*
The ANN QC .odl!l is .ainly based on not is production data, it the nl!cessary to have .athe.atical .odel required in is which structure QC the approaches or tradition base which is onl! of the knowledge .ost difficult probll!. in I!stablishing An eKpert syste ••
o
o
o
o OUT OF CONTROL
SAI'PLE NUI'1BER
Sincl! the ANN has powerful functions in learning / .e.ory, the resulting ANN QC syste. can readily adapt the production I!nviron.ent chAngl!s through thl! rl!leArning whl!n thl! new pAttl!rnS introduced. As a result, an Adaptive ANN QC can be constructed.
Fig.2 Thl! Sa.ple of Cusu. Chart for QC
*
Since ANN CAn deal with various signals, the resulting ANN QC tools CAn be widely used for batch, continuous as well as discrl!te eVl!nt production syste.s.
*
The author's present address is " Co.puter Eng. Dept., Bethlehe. Steel Co., P.O.BoK 248, Chesterton, IN 4&304
110
a
y SYSTEM
1
--- ---
+
J
--
Fig4. ANN Configuration With BP Learning
Fig.3 The Illustrative Mapping for QC in The Hyper Space
11.y A.B • ...• RELATED TO PRODUCT QUALITY GRADES
1_________________________________
~
Fig.& The Place.ent of Input & Teaching
".<
Pattern in an ANN
Fig.5 The Classification in the Quality Variable Space
lE .[(I
r-
-;+
-
SIMULATED PLANT
"'ANN MODEL LEARNING PHASE
-
_J ________ I
o -- - - - (
I
r--
o (
FROZEN WEIGHTS
ANN MODEL
t- -
T
d
LEARNING
~
-k
o
~.
f
l
-~
-
__l _____ I
---- -----
__ J_
A,
Y
o
r--
(
o I
Fig.7 The Sche.e of Si.ulation for Training
I
~J__ - - - - - - - - -
J I
I
I
2
ANN MODEL OUTPUT ......... SYSTEM OUTPUT ...... LEARNING ITERATIONS: 147'
and On-l in!! Running
Fig.8 Th!! Si.ulation Rl!sults for Binary Input/Output Patterns
III
(OOry.-·--------------------------------------------------~ OUTPUTS: :3 INPUTS : 6 NUMBER OF PATTERNS : BOO ITERATIONS OF THE TRAININQ : 20.000
80
Ik
III
~ ~
c bo
0..
~ fI:
III
40
S 20
~3X
.3
J~S- /.
S
7- 1°/:
7
.r-77,
;Yc
10
RELATIVE ERROR BETWEEN ANN AND REAL OUTPUT Fig.9 The relative Error Distribution for Continuous Input/Output Patterns
%, I§ fI: k 1&1
...~ ~
C .J 1&1
A
~
3
t
2
t
•
•
~
•
Ill:
1&1
~
0
!
-(
ITERATIONS OF TRAININQ : 20. 000 0
Ill:
11. 112
• 4
~
C
0
loo
200
•
I
1/00 Sl'O NUMBER OF PATTERNS
.300
&00
;7t?o
I
I
800
lOO(>
-,
I-_K_NOW~>,..L-E-CQ-E-BA-SE--...II r---------------~
r
Va
ANN GC I'1ODEL
LEARNINQ
ANN GC I'1ODEL
--u
E
PRODUCTION SYSTEM
V--Product Qualit\l Vr-Ai.ed Product Qualit\l
112
\1
:
I I v
3
THE POTENTIAL APPLICATIONS OF ARTIFICIAL NEURAL NETS IN QUALITY CONTROL Yong-zai Lu Research Institute oJ Industrial Process Control, Zhejiang University. Hangzhou 310027. PRC
KEY WORDS: Quality Control, Statistical Process Control, Artificial Neural Nets, Pattern Mapping, Back Propagation Learning, Associative Me.ory, Intelligent Quality Control. ABSTRACT: This paper addresses the develop.ent of an application of Artificial Neural Nets (ANNs) in Quality Control (QC). This study first Addresses the anAlysis of QC in the real industrial processes, such a s bAtch, discrete as well as continuous productions to show the potentials in co.bining the existing Statistical Process Control (SPC), Process Control (PC) with ANN and Artificial Intelligence (AI). The general structure, strategy and Algorith. of ANN with BACk Propagation (BP) learning for process quality .odel and the quality control .odel have been developed. The resulting ANNs can be used for various processes (batch, discrete, and continuous as well) and the production .anage.ent. The co.puter si.ulations show the re.arkable learning, .e.ory and decision ability. Finally, the concept and fra.e of the Intelligent Quality Control (IQC) has also been proposed.
ShewhArt ChArt, Cusu. Chart, etc. shown in Fig.l and Fig.2 respectively. The • .ajor objective of QC is to .aintain the quality variables as close as possible to desired target area,or the set point. The statistical approach associated with the QC charts provides the analysis for i.proving the product quality. It should be noted that the hu.an factors or socalled knowledge plays critical role in .aking the analysis and / or decisions, which are hardly possible to be e.ulated by the traditional .athe.atical tools.
INTRODUCTION
Statistical Process Control (SPC) has been playing .ore and .ore i.portant role in i.proving process productivity and product quality in traditional and .odern industries. Here we .ust .ention that De.ing [ll has .ade great contributions, first in Japan, and .ore recently in North A.erica to convince .Anage.ent putting product quality being the top priority. In fact,the quality revolution has provided the high reputation of the Japanese products.
The latest technology of Artificial Intelligence ( AI ) and Artificial Neural
The Quality Control ( QC ) based on SPC .ainly involves process design, Analysis and on-line qual ity control, etc •• It is obvious thAt the later beco.es A very i.portant AreA of overlAp between SPC and Process or Production Control ( PC ) However, in .as noted by l1acQregor [2J. general, the product quality is hardly possible or too costly to be on-line .easured by sensors, i nst ead, d i scret e dAt.a infrequently obt.ained fro. product anAlysis lAboratory are used to guide the operat ion. This .akes it extre.ely difficult to design a control syste. bAsed on such discrete dat.a for process control engineers.
Nets (ANN) has shown the powerful func tions in e.ulating so.e hu.an being, such as,leArning, .e.ory, reAsoning and decisions, obviously, which will be an effective tool to solve the QC proble •• This study will topics:
* *
* * *
In order to deal with discrete data QC proble.,a nu.ber of .approaches have been developed. The .ost popular .ethods .are different kinds of QC Charts, such as
address
the following
Proble. State.ent of Quality Model and Qu.ality Control; ANN b.ased Process Quality Model ANN QC Control Model; Design of ANN for QC; Si.ulation Results; Intelligent QC PROBLEM STATEMENT
107
The relationships between the product quality and the operating conditions can be illustrated by the following .ath. • odel: Y
Where Y
E
U
D
F
F
( E,
U
) + D
learning are developed to carry out the QC for continuous, batch and discrete product ions •
(1)
DEVELOPMENT OF ANN FOR QC
=[
y, ' Y2 , •••. , y" JT ER" A vector Denoting the quality variables in the qualit~ space; [E" E 2 , • • • • • , Em J ER'" A vector denoting the production environ.ent,which usually involves the uncontrollable variables (analog, discrete, or digital/logical); r [ U, , U. , •.••• , U r JT E R The control vector denoting the control actions and I or .anipulat ing variables, which can also be in analog, discrete, or digital I logical for.s; [ D, , D 2 , • • • • • , D... ERn A vector denoting the rando. disturbance; Representing the stochastical funct ion.
In order to .odel a co.plex syste.,an ANN with hidden layer and BP-learning as has been developed. The function of the input layer is to carry out the signal nor.alization, here the input I output signal are scaled within the range of 0 to 1.0, or for binary ANN, the signals are represented by 0 and 1 integer data sequence. Both hidden and output layers consist of a nu.ber of neurons with the sig.oidal functions. All of the neurons at the different layers are weighted connected to transfer the infor.ation. The BP-learning provides the upgraded weights based on the errors between the syste. output which serves as the teaching signal and the output given by the ANN. The ANN configuration with BPlearning is shown in Fig. 4. The Basic Structure of ANN The transfer function of the can be described a5 follows:
Si.ilarly, the relevant QC .odel can be written in the following for.:
U
=G
(1 + exp
(2)
/ T »
Ni
~
(4)
Wji Ui + Wj
i=l Yj
However, since the relationships between the product quality and the production environ.ent and other conditions are so sophisticated, that in .ost production processes, it is hardly possible to establish the quality .odel, even its structure as shown in Eq. (1), as a result, the existing approaches, such as Kal.an Filtering, identification and esti.ation, can not be used. The .ajor reasons are as follows:
*
(et. j
Where
Where Ys denotes the desired product quality , and G represents the functional relationship between the control actions and both Ys and E.
*
(3)
Yj ( Vs, E,
neuron j
dj
Ui Wji Wj
The output of the neuron j; The state of the neuron j ; The input fro. the neuron i at the lower level of the layer; The connection strength fro. neuron i to j ; The bias of the neuron j ; The te.perature .achine.
T
in
Based on the Eqs (3) and (4), the input I output relationship for both hidden and output layer can then be described as the .atrix for. [3J:
All of those .ethods are heavily dependent upon the .ath. .odel, at least the .odel structure; It is i.possible to deal with the digital I logical variables.
In this study, a concept of pattern .apping is proposed to replace the traditinal Math. concepts. In fact, the relationships between production variables can be considered as a hyperspace .apping proble. as shown in Fig.3. As a result, the quantitative relationships are only based on the production data without knowing the .odel structure.
Yh
S
Yo
S
(5)
B
(6)
Where Wh U B
S
The proble.s addressed in this paper are .ainly to establish both production quality and QC .odels by .eans of ANN techno 1 ogy.
Yo Yh U
A
The proble. of ANN based QC .odeling is ~ develop an ANN .odel which can dupllcate
B
the input/output relationship just based on the production data. An ANN with BP-
Wo
108
Wo Yh
Wh
+
+
Wo
(7) (8)
The sig.oidal function; The output vector of the output layer; The output vector of the hidden layer; The nor.alized input of the ANN; The state vector of the hidden layer; The state vector of the output layer; The connective .atrix between hidden and output layers;
Wh
The connective .atrix between input and hidden layers; The bias vl!ctor of thl! output laYl!r;
Wo Wh
The bias laYl!r
vl!ctor of
Basl!d on thl! abovl! processing stl!ps. we can then I!stablish .any pairs of the pattl!rns using thl! production data relatl!d to thl! product quality V. production environ.ent E. and control actions and/or .anipulates U. As a rl!sult. the functions F and G in Eqs. (1). and (2) are convl!rtl!d in to thl! relevant pattern .apping without thl! knowledge of thl! .athe.atical structurl!. The input / output data gatherl!d fro. thl! production can bl! used to I!stablish a data file describing thl! V -E -U pattl!rns as shown
thl! hidden
Thl! ANN-BP Learning Algorith. Thl! cost function of ANN-BP ll!arning is to .ini.izl! the .ean square I!rror betwl!l!n thl! tl!aching signals and thl! actual output of ANN. which can bl! dl!scribl!d as follows: 2 Min J (Wh. Wo) = Z. L,( Vs (k) -Vo (k» (q) I<
in Tabll! 1.
.,.
Tabll! 1
(t+1) = Wkj
Wkj
(t) + Lr De Vhj
* *
(10)
V2.
••• • ••
Vn. J T
which can gl!o.l!trically illustratl!d in Fig. S. Thl! product quality can be classified into a nu.bl!r of groups based on thl! following ways:
*
Product grades. such as • A. B•••••• which arl! rl!late to thl! spl!cific area in thl! quality spacl!. as a result. thl! product grade can then bl! dl!scribl!d by thl! rl!ll!vant digital nu.bl!rs;
*
The quality vl!ctor. V. which rl!prl!sl!nts a point in thl! qual i ty space. in this casl! the product quality is directly .I!asured by thl! physical variables.
* *
1 1
* *
* ..... . * ..... .
1 1 1
Using the ANN - BP structure as introduced in thl! previous section, { E, U} and {V} are placl!d as ANN input and tl!aching pattl!rns rl!spectively as shown in Fig.D. Based on the "V -E -un pattl!rns as shown in Table 1, Thl! ANN will start to learn fro. the supl!rvised ll!arning pattl!rns. If Wl! sl!lect thl! suitable initial learning rate and the tl!.pl!raturl!, thl! error bl!twl!l!n thl! tl!aching signals and thl! ANN output will rl!ducl!d stl!P by stl!P, and finally, thl! error will bl! close to zero and thl! wl!ights will bl! frozl!n. The nu.bl!r of itl!rations to co.pll!tl! the ll!arning is .ainly dl!tl!r.inl!d based on thl! sizl! of ANN and the nu.bl!r of the pattl!rns bl!ing trained. Obviously both ll!arning rat I! and thl! tl!.peraturl! will also significantly influencl! the convergl!nt rate as wl!ll as stability.
SUppOSI! that thl! quality variables constructs a .ultipll! di.l!nsional spacl! •
* *
Th. Structure of ANN QC Mod.l
In order to I!stablish thl! .apping bl!tween the quality spacl! and the space of the opl!rating conditions and the production I!nviron.l!nt. Wl! will first .akl! thl! classification in thl! quality spacl!.
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1 1
------------1--------------1-- -----------
In this study. both ll!arning rate Lr and thl! tl!.perature T are designed to be the dl!crl!asing functions. which benefit thl! convl!rgl!nt ratl!. In ordl!r to spl!ed up thl! ll!arning ratl! .the .0.l!ntu. ter. is introduced in thl! ll!arning algorith. C4J.
=
* *
1 1 1
In Eq. (10). Wkj are weights fro. layer j to the layer k at the iterativl! ti •• t. Vhj is the input signal fro. the layer j to the layer k. The co.putation of the error t.r. De for both hidden and output layers can refer to C3J.
V
V - E - U Patterns
------------1--------------1------------VIE 1 U ------------1--------------1------------V V .•••• 1 E E •••.•. I U U ••••.• ------------1--------------1-------------
Using the gradil!nt sl!arch tl!chnique. the wl!ights can bl! upgradl!d by using the following rl!cursivl! algorith. starting at thl! output nodes and working back to the first hidden laYl!r :
If thl! ll!arning / training has been co.pll!tl!d. thl! pattl!rn .apping is I!stablishl!d and this ANN has both short tl!r. and long ter. .e.ory which are rl!latl!d to thl! nl!uron states and the connectivl! wl!ights respl!ctivl!ly. Whl!n we entl!r thl! input pattl!rns { E. U }. the ANN will providl! thl! output patterns. which will .atch thl! systl!.'s rl!al output. Howl!ver. if thl! pattl!rns are not locatl!d in the arl!a which has bl!en trainl!d. the results will not bl! good I!nough to .atch the real output .50 it beco.es a critical proble. to select the trained patterns which can cover the operating area. The orthogonal procl!ssing for the trained pattl!rns will bl! helpful for thl! learning / training.
In addition. both production environ.ent and control actions can also described by the digital nu.ber and / or thl! physical variabll!. For instancl!. thl! diffl!rl!nt product ion schl!.l!s and / or thl! raw .atl!rials can bl! .arked with differl!nt tag nu.bers. Obviously. thl!Y can also bl! describl!d by the analog variables. such as thl! t •• pl!rature. flow ratl!. or .achine running speed • • tc ••
~n addition.
The ANN QC proble •• in fact. a rl!vl!rse proble. of what Wl! dl!scribed abovl!, na.l!ly, finding the control actions based on thl! production I!nviron.ent to satisfy thl! dl!sired product quality. Obviously, this probll!. can also be governl!d by of a pattern 1S
109
.Apping which Addressed above.
is
si.ilAr to
whAt
we REFERENCES
SIMULATION RESULTS
Deming, W. E. Ind. Qual. Contr, 24, P.89, 19&7 (2] MacGregor, J. F. Che.. Engng. Prog. P.21, 1988 (3] Ru me1hat't, D. E. et a1 PArallel Distributed Procesiing , MIT Pt' ess, 1988 [4] Lippmann, R. P. IEEE ASSP Magazine, P.4, 1987 [1J
Based on the developed ANN-QC .odel and the nonlinear si.ulated plant with .ultiple variable rando. input and output signals (siK inputs and three outputs >, the co.puter si.ulation study on ANN -BP learning and ANN running is shown in Fig. 7. The co.puter si.ulation results are given in Figs. 8 -10. An ANN with hidden layer and deco.posed structure can have .e.ory of one thousand patterns after thousands of thousands learning. The Average relative error between the actual output and the ANN output , ARE, are less thAn 3 " •
UCL
_....£.
THE INTELLIGENT QC
o
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As we noted before that the hu.an knowledge is one of .ost i.portant factors in carrying out QC. It should be noted that since the ANN can deal with rule base, fuzzy logical and the relevant reasoning, a structure of Intelligent Quality Control (IQC > can be establishl!d as shown in Fig. 11. Thl! key issue here is how to convert the factors related to both production environ.ent And control actions into the input signals which can be dealt with by ANN. Sincl! ANN CAn process VArious signals,
0-
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t t
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Fig.l The Sa.ple of Shewhart Chart for QC
it will hAve no proble. to convl!rt a physical syste. into a relevant ANN. CONCLUSIONS This study show the potential Applications of ANN in QC, and also propose the structurl! of IQC, which will be the futurl! of the QC. Co.paring with thl! traditional QC tools and the eKpert syste. for QC, thl! ANN based QC has the following .Ajor .I!rits:
*
*
The ANN QC .odl!l is .ainly based on not is production data, it the nl!cessary to have .athe.atical .odel required in is which structure QC the approaches or tradition base which is onl! of the knowledge .ost difficult probll!. in I!stablishing An eKpert syste ••
o
o
o
o OUT OF CONTROL
SAI'PLE NUI'1BER
Sincl! the ANN has powerful functions in learning / .e.ory, the resulting ANN QC syste. can readily adapt the production I!nviron.ent chAngl!s through thl! rl!leArning whl!n thl! new pAttl!rnS introduced. As a result, an Adaptive ANN QC can be constructed.
Fig.2 Thl! Sa.ple of Cusu. Chart for QC
*
Since ANN CAn deal with various signals, the resulting ANN QC tools CAn be widely used for batch, continuous as well as discrl!te eVl!nt production syste.s.
*
The author's present address is " Co.puter Eng. Dept., Bethlehe. Steel Co., P.O.BoK 248, Chesterton, IN 4&304
110
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Fig4. ANN Configuration With BP Learning
Fig.3 The Illustrative Mapping for QC in The Hyper Space
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112
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