CA2053056A1 - Process system identification - Google Patents
Process system identificationInfo
- Publication number
- CA2053056A1 CA2053056A1 CA002053056A CA2053056A CA2053056A1 CA 2053056 A1 CA2053056 A1 CA 2053056A1 CA 002053056 A CA002053056 A CA 002053056A CA 2053056 A CA2053056 A CA 2053056A CA 2053056 A1 CA2053056 A1 CA 2053056A1
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- CA
- Canada
- Prior art keywords
- parameters
- equation
- input
- network
- terminal means
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Abandoned
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Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B17/00—Systems involving the use of models or simulators of said systems
- G05B17/02—Systems involving the use of models or simulators of said systems electric
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10S706/00—Data processing: artificial intelligence
- Y10S706/902—Application using ai with detail of the ai system
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10S706/00—Data processing: artificial intelligence
- Y10S706/902—Application using ai with detail of the ai system
- Y10S706/903—Control
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10S706/00—Data processing: artificial intelligence
- Y10S706/902—Application using ai with detail of the ai system
- Y10S706/903—Control
- Y10S706/906—Process plant
Abstract
PROCESS SYSTEM IDENTIFICATION
Abstract of Disclosure A tool, and the method of making the tool, for process system identification that is based on the general purpose learning capabilities of neural networks. The tool and method can be used for a wide variety of system identification problems with little or no analytic effort. A neural network is trained using a process model to approximate a function which relates process input and output data to process parameter values. Once trained, the network can be used as a system identification tool. In principle, this approach can be used for linear or nonlinear processes, for open or closed loop identification, and for identifying any or all process parameters.
Abstract of Disclosure A tool, and the method of making the tool, for process system identification that is based on the general purpose learning capabilities of neural networks. The tool and method can be used for a wide variety of system identification problems with little or no analytic effort. A neural network is trained using a process model to approximate a function which relates process input and output data to process parameter values. Once trained, the network can be used as a system identification tool. In principle, this approach can be used for linear or nonlinear processes, for open or closed loop identification, and for identifying any or all process parameters.
Description
2~3~
PROCESS SYSTEM IDENTIFICATION
The invention relates to a neural networX tool for proce~ system identification and a method for making the tool.
FIE~D_Q~ TH~ ~NVENTIQ~
The invention relates more specifically to a general purpose approach for proces~ system identification. Syst~m identification is viewed as a fu~ction approxi~ation problem, wher~ the input~ tQ the function are the input and output o~ th~ process, and the output~ of ths function;ar~ estimates of model parameeer~. Thi~ approach, which requires no mathema~ical analy~i~" u~ilizes the learning capabilities of neural negwcrks, and can be usled ~or a wide var~ety of applications.
Th~ identi'ication o~ model par~e rs for an unXnown or inco~pletsly known proce~ ~ystem i~ impor~ant for both contro1 and diagnosis. The ~or- dccurately a plant or proc~ can be identified, th~ b~tter it can be controllod. Estimate~ of system parameter~ arQ an e~sential a3pect o~ adaptive/predictiv~ control and auto-tuning. In addition, c~.~nges in system parameters can be valuabl~ diagnostic lnlicators. A sudden increase " - . :, : . , . , ~
. :: : , .
~ ~ ~Y 3 ~ V,J ~
in the delay of a transport process, for example, could imply a blocked pipe.
System identification is the object of extensive research in control theory and a number of techniques have been developed. Most current approache~ to system identification can be characterized as hard knowledge approache~ derived through extensive mathematical analysis.
A shortcoming of many current sy~te~
identi~ication approaches is that the assumption~
nece~sary to facilitate the mathematical analysiR for a particular application ~ay not be valid for othar application A ~ain object of the invention herein i5 to~
provide a sy~tG~ identi~ication tool having generality of application. Under thi concept, a general purpo~e techniqu~ c~n b~ used for a large vari~ty o~ syste~
identi~iration pro~lems with little or no mathematical effort re~ulr~d. In many application~ th~ short deY~lopment ~i~5 that a general purpo3~ techniqu~ would allow while still satisfying performanc~ requare~ent would be a signi~icant advantage.
In recent years, advances in the ~ield o~ neural networks hav~ produced learning rule~ ~or dev~loping arhitrary non-linear ~ultidimensional real-valued mapping~. The~e learning rules operate on examples of ', . ~ :
' . "' ' '`' "
,~
the desired functionality and no programming is required, The simplicity of neural network computational models is also an advantag~.
System identification i5 an extensively researched area of control theory with innumerable applications. When th~ purpos~ o~ the identification is to design a control system, the charactar o~ th~ problem ~ight vary wid~ly d~pending on the natur~ o~ th~ control problem~ In so~ case~ it might b~ sufficient to have a fairly crude mod~l o~ th~ syste~ dynamic~. Other cas~
might r~quir~ a fairly accurate mod~l o~ th~ ~y~
dyna~c~ o~ ~v~n a ~odel of th~ environm~nt Or th~ :
syst~.
In mo~t pxactical problems ther~ is s~ldo~
15 su~ficien~ a priori ln~ormation ahout a systeu and its en~iron~nt to de~ign a control syst-~ ~ro~ thi9 in~ormatio~ ~lon~. It will thu~ o~ten b2 nec~ssary to mak3 so~ kind oS ~xp~riment involving u~ing p~rturba~ion~ a~ input ~ignals and ob~xving th~ :~
cor~ponding ~hany~a in process variabl~s.
~ n~u~al n~tworX of the type utiliz~d by ~he invention herQin in constructed from two primitiv~
~lQment~ which ar~ processing unit and directed connQction~ b~w~on th~ processing ~nit-~ Th~ proc~ssing units ar~ den~ely interconnected with ~ach connection typically havin~ a real va'~ Jeight as~ociated with it which determinec~ the ef fect of the source unit on the destination unit. The output o~ a processing unit is som~ function of the weighted sum of its inputs:
oj f(~ wijoi + bj) (1) where oj iR the output of unit j, wij is th~ weight fro~4 unit i to unit j, and b; i~ th~ " hre~hold" or bia~ w~ight for unit j. The quantity ~ wijoi ~ b i~ usually reerred to a~ the net input to Wli'C j, 10 symbol i z ed net~ .
Proc~ ing unit~ ar~ often arranged in layer In many applica~ions thel~ networkss ar~ con$trair~d to b~
acyclic and th~ connections are c:on~tr~in~d l:o 11~
betw~en adj acent lay~r~ . A multilay~r fs~d forward 15 network of ~hi~ typ~ can realiz~ any mapping froD~ a multidi~n~nsion~l continuou~ input: spac~ to a multl di~en2~10n~1 continuous output ~pac~ wi~h a~bitrarily high ac~ur~y.
~a~y continuou~ p~ocesse~s havo proce~q delays 2 0 g~n~rally duo to transport o f f luid~, In th~se proc~sses a conv~n~ional ~edback controlle~ wolald provid~
un3ati~actoxy clo~ed-loop response.. A oon~roller which can comp~n3at~ ~or delay is requir~d ~o achi~v~ good control o~ ~h~ procQ 3. Delay comp~n~ation techniques, 25 such as th~ S~ith Pr~dictor (an example o~ which can be found in th~ work o~ Steph~ncpou10~, G. (1984); Chemica1 .. .: . . . ...
,, "
:
2 ~ .~ 3 ~ ~
Proces~ Con~rol: An Introduction to Thaory and Practice; Prentice Hall Publishers) require estimates of the process d~lay.
A further object of the invention herein is to provide a new techniqu~ for proce~ delay identification which is an open loop identification techniqu~'based on a l~arnin~ neural network approach.
Exi~ting techni ~es for delay identi~ication ar~
ba~d on ~xt~n3iv~ mathe~atical analyqes. A major advant~g~ o~ th~ techniqu~ herein i~ that it usa~ a gan~al pu~po~o neural nstwork learning archltQc~ure ~o~
which no ~ath~atical analysis of th~ proble~ i~ needed be~or~ imple~nting a neural network d~lay identi~isr.
othQr ob~ect3 and advantage~ o~ tha inv~ntion ~ -will beco~ appar~nt from the following sp~ci~ication, append~d claim~, and attached drawing~.
In thla dr~wings:
Flg. 1 ~o~ a ~chematic repres~n~atio~ o~ a prio~ ~rt tylp~ h~ating system for which param~t~r~
th~rQo~, ~uch as 'ch~ time delay paraDIetlar~ ~ay be identl~i~d wlth th~ u~a of t~le paraDI~ter id~nti~ica~ion tool o~ th~ p~ nt lnvention;
Flg. 2 ~how~ a prior art typ~ clos~d~loop temparature control sys'cem eor controlling tho temperatur~ o~ the heatin~ ~,,tem of Fig. l;
, . , , ,:.
" , . , .:
'', ~ ., /,,, : , .
2 ~ ~ 3 3 ~ ~
Fig. 3 is a schematic di.agra~ illus~rating a neural network which can b~ trained in ac~ordance with the invention to be used as a system identi~ication tool;
Fig. 4 is a block diagra~ showing a prior art adaline typo of processing element which may be used for th~ neural network of Fig. 3;
Fig. 5 i~ a block diagra~ illustrating an arrangement ~or u~ing a process mod~l for generating trainlng exa~ples for training the nstwork shown in Fig.
Fig. 6 i~ a block diagram showing an arrangelaQnt for u~ing training ~xa~ple~ to train th~ n~twork o~ Fig.
PROCESS SYSTEM IDENTIFICATION
The invention relates to a neural networX tool for proce~ system identification and a method for making the tool.
FIE~D_Q~ TH~ ~NVENTIQ~
The invention relates more specifically to a general purpose approach for proces~ system identification. Syst~m identification is viewed as a fu~ction approxi~ation problem, wher~ the input~ tQ the function are the input and output o~ th~ process, and the output~ of ths function;ar~ estimates of model parameeer~. Thi~ approach, which requires no mathema~ical analy~i~" u~ilizes the learning capabilities of neural negwcrks, and can be usled ~or a wide var~ety of applications.
Th~ identi'ication o~ model par~e rs for an unXnown or inco~pletsly known proce~ ~ystem i~ impor~ant for both contro1 and diagnosis. The ~or- dccurately a plant or proc~ can be identified, th~ b~tter it can be controllod. Estimate~ of system parameter~ arQ an e~sential a3pect o~ adaptive/predictiv~ control and auto-tuning. In addition, c~.~nges in system parameters can be valuabl~ diagnostic lnlicators. A sudden increase " - . :, : . , . , ~
. :: : , .
~ ~ ~Y 3 ~ V,J ~
in the delay of a transport process, for example, could imply a blocked pipe.
System identification is the object of extensive research in control theory and a number of techniques have been developed. Most current approache~ to system identification can be characterized as hard knowledge approache~ derived through extensive mathematical analysis.
A shortcoming of many current sy~te~
identi~ication approaches is that the assumption~
nece~sary to facilitate the mathematical analysiR for a particular application ~ay not be valid for othar application A ~ain object of the invention herein i5 to~
provide a sy~tG~ identi~ication tool having generality of application. Under thi concept, a general purpo~e techniqu~ c~n b~ used for a large vari~ty o~ syste~
identi~iration pro~lems with little or no mathematical effort re~ulr~d. In many application~ th~ short deY~lopment ~i~5 that a general purpo3~ techniqu~ would allow while still satisfying performanc~ requare~ent would be a signi~icant advantage.
In recent years, advances in the ~ield o~ neural networks hav~ produced learning rule~ ~or dev~loping arhitrary non-linear ~ultidimensional real-valued mapping~. The~e learning rules operate on examples of ', . ~ :
' . "' ' '`' "
,~
the desired functionality and no programming is required, The simplicity of neural network computational models is also an advantag~.
System identification i5 an extensively researched area of control theory with innumerable applications. When th~ purpos~ o~ the identification is to design a control system, the charactar o~ th~ problem ~ight vary wid~ly d~pending on the natur~ o~ th~ control problem~ In so~ case~ it might b~ sufficient to have a fairly crude mod~l o~ th~ syste~ dynamic~. Other cas~
might r~quir~ a fairly accurate mod~l o~ th~ ~y~
dyna~c~ o~ ~v~n a ~odel of th~ environm~nt Or th~ :
syst~.
In mo~t pxactical problems ther~ is s~ldo~
15 su~ficien~ a priori ln~ormation ahout a systeu and its en~iron~nt to de~ign a control syst-~ ~ro~ thi9 in~ormatio~ ~lon~. It will thu~ o~ten b2 nec~ssary to mak3 so~ kind oS ~xp~riment involving u~ing p~rturba~ion~ a~ input ~ignals and ob~xving th~ :~
cor~ponding ~hany~a in process variabl~s.
~ n~u~al n~tworX of the type utiliz~d by ~he invention herQin in constructed from two primitiv~
~lQment~ which ar~ processing unit and directed connQction~ b~w~on th~ processing ~nit-~ Th~ proc~ssing units ar~ den~ely interconnected with ~ach connection typically havin~ a real va'~ Jeight as~ociated with it which determinec~ the ef fect of the source unit on the destination unit. The output o~ a processing unit is som~ function of the weighted sum of its inputs:
oj f(~ wijoi + bj) (1) where oj iR the output of unit j, wij is th~ weight fro~4 unit i to unit j, and b; i~ th~ " hre~hold" or bia~ w~ight for unit j. The quantity ~ wijoi ~ b i~ usually reerred to a~ the net input to Wli'C j, 10 symbol i z ed net~ .
Proc~ ing unit~ ar~ often arranged in layer In many applica~ions thel~ networkss ar~ con$trair~d to b~
acyclic and th~ connections are c:on~tr~in~d l:o 11~
betw~en adj acent lay~r~ . A multilay~r fs~d forward 15 network of ~hi~ typ~ can realiz~ any mapping froD~ a multidi~n~nsion~l continuou~ input: spac~ to a multl di~en2~10n~1 continuous output ~pac~ wi~h a~bitrarily high ac~ur~y.
~a~y continuou~ p~ocesse~s havo proce~q delays 2 0 g~n~rally duo to transport o f f luid~, In th~se proc~sses a conv~n~ional ~edback controlle~ wolald provid~
un3ati~actoxy clo~ed-loop response.. A oon~roller which can comp~n3at~ ~or delay is requir~d ~o achi~v~ good control o~ ~h~ procQ 3. Delay comp~n~ation techniques, 25 such as th~ S~ith Pr~dictor (an example o~ which can be found in th~ work o~ Steph~ncpou10~, G. (1984); Chemica1 .. .: . . . ...
,, "
:
2 ~ .~ 3 ~ ~
Proces~ Con~rol: An Introduction to Thaory and Practice; Prentice Hall Publishers) require estimates of the process d~lay.
A further object of the invention herein is to provide a new techniqu~ for proce~ delay identification which is an open loop identification techniqu~'based on a l~arnin~ neural network approach.
Exi~ting techni ~es for delay identi~ication ar~
ba~d on ~xt~n3iv~ mathe~atical analyqes. A major advant~g~ o~ th~ techniqu~ herein i~ that it usa~ a gan~al pu~po~o neural nstwork learning archltQc~ure ~o~
which no ~ath~atical analysis of th~ proble~ i~ needed be~or~ imple~nting a neural network d~lay identi~isr.
othQr ob~ect3 and advantage~ o~ tha inv~ntion ~ -will beco~ appar~nt from the following sp~ci~ication, append~d claim~, and attached drawing~.
In thla dr~wings:
Flg. 1 ~o~ a ~chematic repres~n~atio~ o~ a prio~ ~rt tylp~ h~ating system for which param~t~r~
th~rQo~, ~uch as 'ch~ time delay paraDIetlar~ ~ay be identl~i~d wlth th~ u~a of t~le paraDI~ter id~nti~ica~ion tool o~ th~ p~ nt lnvention;
Flg. 2 ~how~ a prior art typ~ clos~d~loop temparature control sys'cem eor controlling tho temperatur~ o~ the heatin~ ~,,tem of Fig. l;
, . , , ,:.
" , . , .:
'', ~ ., /,,, : , .
2 ~ ~ 3 3 ~ ~
Fig. 3 is a schematic di.agra~ illus~rating a neural network which can b~ trained in ac~ordance with the invention to be used as a system identi~ication tool;
Fig. 4 is a block diagra~ showing a prior art adaline typo of processing element which may be used for th~ neural network of Fig. 3;
Fig. 5 i~ a block diagra~ illustrating an arrangement ~or u~ing a process mod~l for generating trainlng exa~ples for training the nstwork shown in Fig.
Fig. 6 i~ a block diagram showing an arrangelaQnt for u~ing training ~xa~ple~ to train th~ n~twork o~ Fig.
3;
Fig. 7 is a block diagram showlng th~ us~ oS a neural n~twork which has been train~d to function a~ a systeD identi~ication tool for th~ tim~ delay identi~ic~tion o~ a process;
Fig. ~ i~ a graph showiny Qr~Or in d~lay id~nti~ic3tion a~ ~ ~unction o~ rp;
Fig. 9 i~ a graph illustrating erro~ in d~lay ident1~iGation a~ a function of e;
Fig. 10 is a graph o~ error in d~lay identi~ication a~ a function of ~ ; and Fig. 11 i~ a graph of error in del~y id~nti~icatlon a~ a function of nois~.
... . , . . ~.. .
.
. ~
, 2~J~
Wi~h reference to tha drawing3, Fig. 1 show~ a schematic representation of a prior art heating system 8 which is a type o~ system for which parameter~ thereof such as thQ time delay paramet~r may b~ identi~ied with the us~ o~ a parameter identification tool to which the inv~ntion pertains. Tha illustrated heating system co~prise3 a h~ating plant 10 such a~ a ga~ ~urnac~, at leact on~ enclo~ur~ 1~ to be heated by th~ furnac~, and conduit mean~ 14 ~or conveying a heated ga~ or llguid fro~ ~h~ f~rnac~ ~o the enclosur#.
Fig. 2 show~ a prior art typ~ clo~Qd loop te~p~ratur~ control sy~teffl 20 ~or controIling th~ :
temp~ratur~ o~ th~ anclo~ure 12. T~Q control ~y ta~ 20 ha~ ~ th~r~ost~t 22 and an on/of typ~ switch 24 in ths loop with thQ h2ating plant 10.
A h~ating syst~ 8 can be approxi~ated with a ~:
Pir~t ord~r proc~ with d~lay whlCh includ~ a numb~r of oper ~in~ par~tar~ in~luding a ti~o con~ant rp, a proc~s~ galn ~ and ~ time del~y e.
The timl~ constant tp, which may bo on the ord~ o~ lû to 200 ~Qconds, relate to ~h~ rate at which thQ enclo~ur~ 12 i~ h~ated and dep~nd2~ primarily on the 3iz!~ thQ he~ting plant 10 and th~ charact~ristic~ of th~ enclo~ur~.
i. .: ~ .:. ; , ~
.
''` ~ ' ' ",~ ' . ; ' ~ ~ ~q The process gain Kp may be on the order of 00 5 to 1. 5, which is the ratio of process output to process input at steady state.
Th~ delay e, which may be on the order of 0 to 500 s~cond~, relate~ to the transport time of the h~ating mQdiu~n in th~ conduit means 14 a~ it flows from the heating plant 10 to tha ~nclosure 12 and dep~nds mainly on th~ length and flow re i~tanc~ o~ the conduit m~ans~ lg.
In c~3rtai~ in~tallations in which th6~ tim~ delay parama~r ~ of th~ conduit ~eans 14 i~ relatively larqQ, thc~ controllQr 20 of Fig. 2 will no~ b~
appropr~ats~ bRcaus~ arrat:ic operation will occur by r~ason o~ i:ha controll~r not being r6spon lva to ~ha time delay param~ . What would happen i~ tl~at th~re would b~ a lagqing ~ ct whGrein the h-ated m~diuffl would no~
r~acb t~ nclo~ur~ until a substantial tiD~ aft~r th~
then~os~at b~giru~ call ing f or heat . Aft~r th~ d~ir~d t~D~p~E~atu~ r~ach~d, th plant 10 would b~ turrl~d of f but the~re~af~r th~r~ would be an over~hoot ol~ th~ a~t poirlt 'c~mp~ratUr~ wherein ~he hea~ ediu~ (air, ~or ~xampla) wolald con~inu~ to be suppli~æd to th~3 anclosure.
Thi3 would caus~ overheating.
Irh~r~ aro a nu~ber o ~ neural ne~worlc ~odel3 and l~rning rul~ that can be used for iDlplem~nting th~
invention. A pre~erred mode I is a three-l yer ., . : ~ ,: . :: : , - . :: ,:, ::: . : . . :
,, . :::
.; ~ : :::
J
feed-forward n~twork ~0 as shown in Fig. 3 and a preferred learning rule is th~ back-propag~tion learning rule. Back-propagation is a supervised learning procedura for feed-forward networXs wher~in training examples pro~ided to the network indicate th~ desir~d network output or target for each ex~plQ input.
F~ed-~orward network~, a us~d with ~ack-propagation, comprisa an input layer of proc~ssing unitY 32, zero or mor~ hidden layer~ o~ processing units 33, and an output layer which may hav~ on~y on~
proc~Ysing uni~ 36. In the illustrat~d embodiment th~ ~ -outp~ proca~ing unit 36 output~ ths proc2 s d~lay value ~-e compu~a~ by ~:hla network 3 0 . All th~ proce~3ing unit~ output r~al value~.
~he back-p~opaga~ion learning tQchn$que p~r~orm~
gradi~nt d~csnt in a quadratic ~rror mQasur~ to ~odi~y n~tworX woight~. Th~l3 fo~ o~ Eq. ( 1) that is u~u~lly ::
~mploy~d with b~ck-propagation i9~ ~h~ sigaaoid ~unctlon: ~
~ (x) ~
1 ~ a~X (2) Back-p~opaga~ion is usually usod with ~ultilay~r fe~d-~orwaxd n~t~ork~ o~ the typ~ shown ln Fig. 3 which i~ an exa~pl~ o~ a thre~-layer network 30 with ono output unit.
The rulo u~d to modify the w~ight~ may b~:
~Wi~ ~ ~o16~ (3) _ g ,~ ~ 'J 3 ~J
wher~ q i~ a corl~tant that deterlDine~ l:he learning rate, and S~ the error ter~ for unit j (i is defined a~ in Eq. 1). ~ i9 defined dif~erently for output and hidden unlts. For output units, ~ ' ~ ' (tj-oj ~ (4) whexe o ~ ' is th~ derivativ~ of oj with respect to it~
n~t input ( i~or 'che activation function o:e Eq . ( 2 ), thi quantity i~ o~ o~ ) ) and tj i5 thQ targ~t valu~
(thG "d~ixed output"3 for unit j. For hidd~n unit~, the 10 ta~eg~t valuo i~ not knowal and th~ er~o~ t~ co~npu~d frola th~ e~ror torm~ ot l:he next "high~r~ lay~r:
~ ~ :1 ' . w~ ~Sk ( S ) FiyO 4 ho~ a prior art adalin~ type proce~ing 15 ~le~nt which could b~ the general d~ign ~or th~ hidden and output p~oc~ing ~laments 33 and 36 of th~ n~twork o~ Fig. 3. 'rh~ proC~ ing elemen~ 3~ ha~ a s~rle~ o' ~ralnabl~ w~igh~s wl ~o Wn with ?I t~r~shold or bia~
w~ight ~ b~ing connsct~d ~o a ~i~C~d inpu'c o~
F~ ho~ an arrangement Po~ an output p~o¢~ ~ng ~le~nt wh~ra the desir~d or targ~t OUtp-lt pur~uant to ~qu~t~orl (4) is availabl~ ~or tho learning al~orith~. Th~ ~rrangem2nt for hidden ~ s for which -th~a d~ir2d o~ ~argat output i~i no~ availabl~ is pu~uant 25 'co ~quation ~5).
. ," . ., ,. . ,.. .. ~ . .
2~3~
For th2 eX2rcisQ of this invention, a mathematical model o~ a syste~, containing one or morQ
parameters, is n~ce~aary (Fig. 1). It is asswled éhat the pro ::e~se~ for which the systeD~ id~ntif ication ool is S intended can be modaled with appropria'c~ accuracy for the intland~d u~ by the mathematical mod~l, for so~o spscif ic a ~iga~ nt2~ of th~ 3l0d~1 paramet~r~. It i~ also a s~n~d that rangsg~ for all ~od~el param~t~r~ can b~ sp~ci~i~d.
Thi~ a~sllmption 1~ nol: expected to pos~ prac~lcal 10 probl~m~, ~lnc~ extrsmQly broad range can b6l1 us~d. Even i~ ~o~ para~t~r valu~ that may b~ ~ncounte~rad aro axclud~d, th~ robu~tn~ properti~s~ o~ n~urz~l n~twork~ :
rend~sr it lik~ly that any resulting 10s~8 o~ ace:uracy will b~ s~ll. In ~i~apl~ cas~, or when 1itt1Q 1~ known about 15 the taxg~ proc~ , a rang~ can con~i~t oX ~ low~r limit and an uppar limi~, and al]. valu~ wit~in the rang~
can b~ con~id~r~d ~ lly probabl~. In ~oro complsx ca~e~ and wh~n adg~qua~ proces3 Jcnowlsdg~ ox~st~, th~ :
rango~ C~l b~ ~o~ ~ophi~ticated -éh~ p~oba~ility 2~ di~t~ibution ov~c t~ rango need not b~ uni~orm, s~r oven uni~odal .
~ 2~o tool ~n~ ~thod developm~nt h~rein i~ b~ 2d on ~ n~3ur~1 ns~twork approach having a two pha~
proc~dur~0 In ~h~ ~irst phase a math~m21tical n~odel of 25 tha syst~DI shown in Fig. 1 is utiliz~d ~or gQn~ tinq tr~ining data. The mathemat ical model i~ implen~nted as ~: , . . .
:: ~ ,, , 3 ~
a computer program. The training dat~ comprise3 examples o~ open loop respon ~s to a ~tep inpu'c giv~n to thsa system model. ~Equivalent procedures with impulsQ or ramp input functions, or ~ven arbitrary input func~ions, 5 could also bQ utiliz~d. ) Each ~xampl~ is generated with a uniqu~ set of para~seter values, eaoh valu~ within the s~t b~ing choson ~ro~ th~ rang~ spacifiRd ~or the para~et~r.
In th~ seGond pha~e the training da~a is applied 10 in ~ teaching or l~arning ~node to a n~ural n~twork o~ an appropriat~ typ0, ~uc:h a~ thQ n~twork 30, to trans~o~h or conv~rt tha n~two~k into a tool ~or id~ntifying at laast on~ o~ th~ paraDI~t~r~ ~uch a~ th~ tiDI~ d~lay param~t~r e.
Wlth rerer~nco to th~ s~ccand pha ~, th- lsarning ~ "3up~r~ri3ad" l~arning in which it i~ a~sumod that th~ "de~ire~d output~ to~ ~very ~ra~ning input il~ known.
~upe~vi~d l-arning can bQ use~ to train an appropr$ately con~igurQd n~lural nQtwork such a~ n~twork 30 ~o~ ~om~l 20 sp~¢i~ie ta3k by pro~ :Lding exampl6~ og d~ d behav1Or.
Th3 conc~pl: o~ n~ural net~ork b~d ~y~t2~
id~nti~ ation i~ i11ustrated hor~$ll ~g b~ing s~mbodiad in a prototyp~ dt~1ay i~ntifica~cion too1 30. Mor~
sp~s:i~ica11y, it i~ a neural network d~lay id2nti~i~r for 25 th~l op~n 1Oop ~s~ti~ation of proce~ d~lay~ ~or a linear fir3t ordlar procQs~ model.
. ' ' ~ , ~ '," '"
Th~ sy5t2m shown in Fig. 1 ~ay b~ modaled a~ a linear ~irst ord~r process with delay by th~ equation:
~ x('c), ~ 1 x(~) + ~ u(t-~3) (6, dt rp rp whQr~in x(t~ i~ th~ proces~ temperatur~ respons~ in the enclosur~ 12, rp i~ the tim~ constant o~ the proces~ th~ proce~s gain, and 0 i~ the procQ~s dQlay. ~, rp and e are th~
para~2~er~ o~ th~ model.
~h~ ~od~ling ~quation may b~ a linear or nonlin~ar di~rential equation, or an alg~b:r~lc polyno~izll aguat~ on, within th~ ~cop~ o~ th~- ~nv~ntion.
In th~ ~ir~t ph~s~ r~f~rred to abov~, training exampl~ aro gel~n~rat~d u~ing a proc~3~ mod21 40 a~ ~hown in Flg~ 5. Th~ proc~s model, with: its para~t~r~
a~ign~d to valu~ witnin pred~t,arDlin~d rang~ given a ~t~p input ~. Th~ proces~ temlporatur~ r-spons~ ou~put R or x~t) i~ ~a~pl~sl at ~om{~ p~det~nlin~l r~t- and ~h~
ro~ul~ng r~l valu~d vec~or and ~h~ re~p~ctlv~ valu~ of th~ ti~- d~lay 0 ar~ used a~ th~ tr~ining input tor th~a n~u~l n~two~k 30 a3 shown in Fi5~. 6.
Although Fig. 6 designates a proc~ inE~ut S, it will b~ und~r~tood th~ such inpllt ~ay b~ oDIitt~d in c~s~ wh~ 5 is a con~taZlt becau~ would only bo 25 varying ~alu~ o~ S that would af~ t th~ output o~ the neural network.
.. . .
, ~ ~
'' ~ '` '':
., ' , Identi~ication i~ in term~ o~ sampla~, not ab~olute units og time. By changing thQ sampling rate, the range o~ delay~ that can be identi~ied (by th~ sa~
trained na~work) can b~ ~ontrolledl I~ the ~iniDlu~ delay is Icnowr to be n s~cond, sampling may s~ar~ n ~ecorld~
af~er th~ p input is given. Th~ de ired network out put would ~h6~1l bo e-n and n would b~D add~d to ~h~
output o~ t:h~ train~2d n~twork to obtain th~ ~stiD~t0d proc~ dQlay.
Num~rou~a ~ituation~ Or trai~ing an~ op~r~tion to e~aluat~ ~h~ y~t~a ha~ b~a~n run. Our ~i~au~tion~ ~all into tw~ . Fir~t, w~ hav~ inv~tig~t~ tho Qrror o~ d~lay ~ti~tion ovar wid~ rang~ o~ proces~
paraJne'c~r~. ~eeond, w~ ha~e ifflulat6~d th~ 3~t-up o~ Fig.
7 and d~D~onstrat~d ~eh~ proYed eon~rol that c:an ~ -aehi~v~d usling ~sur d~l~y identiPl,~r. Tha r~ult~
da~erib~d bllslow ~ploysd a thr~-lay~r n~tworlc with 15 hid~n unlt~.
In on~ aue~ 2~i~ulation th~ trz~ in~ d~t~ ~oP ~h~
n~worX 30 eor.~ dl of 6,000,000 dynaD~ lly g~r~rRt0d ~xa~ s. ~h~- rang~l o~ param0t~r~ eonsid~r~d wer~
rp ~ro2l 10 to 200 sQeond~; e fro~ O to 50û
oeonds~: and Xp ~roDI 0.5 to 1.5. Unlror~ dis~ribution~
w~r~ u~sd ~or all rang~.
T~ining on a rang~ of Kp valuo~ i~ not ` .
strietly n~eQ~ry if the correct valuo is availabl~ in ~ 14 --" :
2 ~ ~g 3 ~ ~, 6 op~ration. As th~ procecs model i~ lin~ar, th~ proc~
output can ~aslly b~ nor~alized. Howevar, wi'chout training on a rang~ of Kp, ev0n ~all chang~ in th~
value o~ thl~ par~m~1:er can reqult in ~lgnif~cant ~rror S in d~ y ~tilaa~ion. Th~3 noi~ in ~raining inpu~ was gausvian with 99% (3 tar~dard deviatlon~ falling within 5% o~ ~h~ rang~ o~ p~OCQ5~ outpu~ valull3.., wh~ch wa~
nons lizad b~two~n 0 and 1. The output o~ ~h~ proces~
wa~ ~amplod ~v~ry 10 s~cond3 aft~r th~ skQp irlput w~
yiv~n. 50 s~D~pl~ wer~ collected and u~ed as input to tha natwork.
Durinsl th~ q~nora~on of training d~tza Yia proc~ l 40, ~ch v~ctor of 50 ~ampl~ had on~ s~t o~ valu~s o~ tho para~t0r~ p, e an~ Kp as~oci~t~ ~ith itc During thel training o~ th~s n~twork 30, ~ach ~ucb. ~ tor o~ 50 sa~pl~ h~ th~ 2~3p~cl:iv~
v~lu~ o~ ~ ti~ d-llay e a ociat~ with it, wbich in ~ach ca~0 ~ ~o targ~ Yalu~ ~o~ ad~u~ing t~
w~ight~ oi~ n~t~ork.
rh~ n~orlt 30 h~d 50 input u~ on~ S~or Q~ch ~a~3pl~, 15 hldd~n un~ and 1 ou~:pu~ (thl~ d~la~
. ~ei~ato) O Th~ Y~luo o~ th~ learning ~tal pz~ to~
~7 W21~ 0.1 9~oE t:ho ~ir~t l,ooO,000 t~ainir ilt~r~'cions" an~ 0 . 01 thQrea~ter.
Agt~ tralning, th~ network 30 w21~ t~a~ on BlQW
(alao rando~ly g~n~ratQd) data. ~e~t~ w~ p~r~orm~d to ., ' ~ ',, 3 ~
dQtermin~ th~a ~f~ectivene~s o~ delay identiflcation a3 a furlction o~ delay, as a function o~ rp, and a function ot Kp, and as a function o~ th~ aD~ount o~
nois~. A nol3~ ~igur~ ol~, ~ay, S p~cent iD~plle~ tha~ 99 5 perc~nt ol~ tho gau~3ian noisQ (~ 3 ~'candard d~viations) wa~ within ~ 5 perc~nt o~ th~ rany~ o~
proce~ output ~or that simulation.
Figur~s 8 through 11 depict th~ re~ult~ o~
variou~ tosst3l. Each o~ thesQ grapho ~hows th~ ~tlm~tion 10 er~o~ ov~ a r~ng~ op valu~3 o~ a particulaE param~t~r.
'rh~ r~lnlrlg para~tor~ wera h~ld con. tant a1~ or n~ar 'sh~ ~idpoint~ o~ thQir range~.
~s~d on th~ t~ts~, the Sollow~n~ ol~ t~on~
w~r~ mado:
$ho av~rzlg- e~ti~ation error i~ w$~in 2 . 5 p~rc~nt o~raE a wide rang~l og d~l~y~ an~
p:~oc~ cona'cant~ fo~ ro~ tic~ a~ount~
ot noi~
For ~ a~ value~ withir~lning ~ang~
~ a~ti~tlon ~rror is small. Th~ro i~ on~
O~ ~xc:~ption. For v~11 d~llay~, p~lrG~nt~gl~ orror iY larg~ to -expoct~d. Th~ ~ampled proco~ output in thl~
c~ p~ov~dls~ little r~lovan'c d~t~
li~c~ly that a non-uni~orm ~pling ~ang~
would ovorc:oms this probl~
~ .:
. . , In many ca~e~, estiD!ation ~rror is accep'cablo avan for parameter valus~ out~id~ training ranges~. For ~xample, th~ avarago error for rp ~ 280 less than 4%. Ev~an ~or gain~
t~wic~ a~ high a~ any tha netwo~X wa~ l:rained on, tho avarag~ error is around 4 % .
E~ ation i~ robu~t with re~p~ct to noi~.
For ~5% nois~, the averag~ e:~ror i~ a~o 6.5%.
10 . ~ft~r th~ n~twork 30 ha bo~n tr~in~d, 1~ can b~
u3~d ~or on-lin~ d~lay ldenti~ication. Th~l input to tho n~twork i~ no~ actuall ~not ~imul~t~d) proc~ output ~ut th~ outpu~ og ~he~ n~éwo~k i~ a~x~n ~ d~l~y ~ti~t-.
Thi~ dolay a~ti~t~ can th~n b~ u~d S~o~ control and/or diagnos~tlcl o~ ~xaDlpl~ if th~ proc~--~ controll~P
ins::orpor~ S~i~ Pr~dictor or oth~r d~lay co~pQn~tion 'c~lqu~, th6~ d~lay e~timllt~ can ~o giv~n a~ input to lt,.
Flg. 7 d~ cl:~ how d~lay id~ntl~ 50 e~abodylng 20 th~ n~t~ork 30 ~-n b~ appl ied to a unit 52 whi-;:h comp~ controll2r having an a~oct~tQ~ ~ith Pr~dicltor. Wh~n ~ d~lay estima~o 1~ n~d~, th~a control loop is brok~n ~ ia ~ switch 54 and ~ top input p~rturbation i- ~p~ d to a proc~ 56 th~o~ b~ir.g~
25 controll~d, by unit 52, via step input g~ner~tor 58. The r~ponse oP th~ procçl~s s6 to tha per~cur~a~lon i9 sampled ,. .., . . - . .
,~,, . , ,; . ~
,,, , . , .
.
and ~tore~d in a bur t'~r 60 . When a ~u~icient numbQr o~
samples hav~ b~n ~ec~ived, th~ vector o~ sampl~ caled appropriately) i~ u~ad as input to th~ trained neural nQtwork 30. Thel~ output of the network i~ subj~ctQd to so~ po~t proc~ ing ~scaling and/or tr n~lation) in a po~t proc~or 62 to obtain a d~lay estimat~ eQ5~t.
onc~ th~ d~l~y o~timat~ ha~ been input to th~ S~aith Pr~dic~s~, ~witch 54 may b~ clo ~d again and th~ prsc~s plat b~ck und~r clo~oed loop con'crol.
A ~i~ulat~d s~t-up o~ Fi~. 7 ha~ b~n utiliz~ to in~o~ti~8t~ th~ ct on clo~d loop cont~ol o~ d~l~y ide~ iclltlorl. A Pi~t ord~r p~oce~ an~ a ~ pl~
proportion~l controll~r w~rQ u~e~d ~or ~:hs~ ulatlon. It wa~ round th~t ~ign~ antly bett~r c:ontrol 1~ achlsvæd 15 wi~h a gosd ~o~ dg~a o~ ~h~ proc~ d~lay.
Thl~ proa~ d~ sy ig ~u~t on~ proc~ pa~m~1:or.
Alt~lough o~tl~at~- o~ timaa con~t~nt~, ~2in9~, otc.
~lso ~quir~l ~rO~ cont~ol, it has~ baon Poun~l ~h~t.
pros:le~ y 1~ tho DlOOt critical parala~t~r.
Signl9!1c~2t ov~r 08~ und~r ~stimat~ ln proco~-s d-lay can C~U8~ Wo~O eon'crol thzm propor~iona~ly poo~ ti~.
ln tho proc~ tlao con~nt or th~ proco~ g~In.
1=1 roaeh h~r~in for d~rolopi.ng ~y~t~
25 lda~ti~iGation toolsl ig ~xtrem~ly g~n~ral-pu~po~ 'C
can b~ u~3Qd ~or c:lo:~d loop or open loop idQnt~ic~tiorl, -- 18 ~
.
, r'or ~stim2~ting any and all mod~l parame~ers, and ~or lialear and non-linQar proc~s~ Diodsls. For spaci~lc application~, 3i~plification may b~ po~sibl~. For example, i~ the id~ntification techniqu~ is arl OpQn loop 5 on~, thQ input p~rturbation can be id~ntical ~or all t~inin~ ~xample~. It thQn ne~d not be provid~d a2~ input to th- n~twork 3 0 . Th~ constra~rlt thi . i~po~a3 i~ that th~ sa~ input p~rturbation, or ( i~ th~ proc~ mod~
lln~a~ c2~ d v~r~ion o~ it, mu~t bc u~d during ~ho 10 opar~tion.
Th~ dosc:~ip~cion oP th~ inv~ntion h~3roin ha~ ~or l:h~ o~t p~t b~n d~r~:t~d to op~n loop ~y~t~
ideJItl~ication. Th~ , it i~ a~u~o~ th t ~n input can b~ glvor~ h~ proe~ nd its r~3pon~0 ob~enr~ w~thou~
15 th~ con~oun~in~ ct~ o~ ~e~d~ack. ~ pli~ but r~alis~ic ~or~n o~ clo~d loop delay id~nti~icatio~a h~
al30 b~n con~i~Qr~d, how~v~r.
T~ æn¢~ o~ ~ho invQntion i~ tho ~pp~oxl~a~tlon o~ a ~un~ti~ o~ proc~ input~o~ltpu1: to pa~o~-~
20 valu~ ~tl~ato-. For g~neral closod loop ld~nti~ at~on, e3tl~t~ ha~r~ to ~ produced giv~n cont~nuou~ly (~nd unpr~dlctably3 va~ying inpu~ In princ:~plo, t~lor~
appea~ to b~ no roa30n why a ne'cwork coul~ not b-train~d ~o~ thi~ cas~ ~9 well; n~ural n~twork~ ha~ b~n u~d to app~o~ unetion~ a~ co~pl~x a~ ch~otlc: time .
:. . , . . . :
.
' ;:, serie~. A simulation of the proces~ under closed loopcontrol could be uced.
we have investigated a constrained form o~
closed-loop identification: delay identi~ication under "bang-bang" control. In closed-loop bang-bang con~rol, th~ proce~ can b~ switched on or of~. WhenQver the output ~xc~eds an upper bound, the proce~ i8 turn~d of~;
whenever thQ outpuk falls below a lower bound, th~
proces~ i~ turn~d on. Bang~bang control $~ co~only used wh~n highly accurat~ control i8 not required - e.g., in HVAC sy~t~
For d~lay id~nti~ica~ion und~r ban~-b2ng control, WQ assu~e that th~ collection of output ~a~ple~ i~
initiated when the proce ~ i~ turned on. A~ter th~
pr~det~r~ined nu~ber of ampl~ hav~ b~n coll~cted, ~n ~sti~at~ i3 produced~ Giv~n tA~ ~c~nario, ther~ i~ only on~ signi~ic~nt dl~rsncQ b~tw~en op~n-loop and bang-bang d~lay i~Qntifica~ion. In th~ ~orm~ ca~, th~
.
procQ~s i~ as~u~d to b~ at a con~tant value (~xcopt ~or noi~ ro~ whon th* ~tep input i8 given until tha d~lay expl~o~; in th~ bang-bang case, thQ procQ~ output is decaying during ~h~ d~lay. Th~ deGaying and ri~ing re~pon~es can b~ governed by di~cr~nt dynamic~.
~ hav~ traln~d a network to identi~y th~ d~l~y of a proc~ under bang-bang control. It wa~ a~um~d that both th~ "on~ process and ~he l~o~N procsss w~r~
e,i ~^;
first-ordJ~r with independent (and therefore dif~erent) ti~a constants. Tha procsss input wa~ again constant over the duration of a training example and wa3 not provided to the networX. An av~rag~ error rate o~ around 5 7% was achiev~d in 100, 000 iterations. The networX
converge~ ~ignificantly fa~ter than for th~ open-loop delay identi~icatic~n, and we exp~ct that a coD~parably long simulation would produc~ lower error rat23. The better per~or~ance ln the~ bang-bang clo~ed-loop c~
not too surprising: a transition betw~n falllng and ri~ing CUrV128 is easier to det~ct than a transition b~tw2en con~ant and ri~ing curvas.
, : ' :
Fig. 7 is a block diagram showlng th~ us~ oS a neural n~twork which has been train~d to function a~ a systeD identi~ication tool for th~ tim~ delay identi~ic~tion o~ a process;
Fig. ~ i~ a graph showiny Qr~Or in d~lay id~nti~ic3tion a~ ~ ~unction o~ rp;
Fig. 9 i~ a graph illustrating erro~ in d~lay ident1~iGation a~ a function of e;
Fig. 10 is a graph o~ error in d~lay identi~ication a~ a function of ~ ; and Fig. 11 i~ a graph of error in del~y id~nti~icatlon a~ a function of nois~.
... . , . . ~.. .
.
. ~
, 2~J~
Wi~h reference to tha drawing3, Fig. 1 show~ a schematic representation of a prior art heating system 8 which is a type o~ system for which parameter~ thereof such as thQ time delay paramet~r may b~ identi~ied with the us~ o~ a parameter identification tool to which the inv~ntion pertains. Tha illustrated heating system co~prise3 a h~ating plant 10 such a~ a ga~ ~urnac~, at leact on~ enclo~ur~ 1~ to be heated by th~ furnac~, and conduit mean~ 14 ~or conveying a heated ga~ or llguid fro~ ~h~ f~rnac~ ~o the enclosur#.
Fig. 2 show~ a prior art typ~ clo~Qd loop te~p~ratur~ control sy~teffl 20 ~or controIling th~ :
temp~ratur~ o~ th~ anclo~ure 12. T~Q control ~y ta~ 20 ha~ ~ th~r~ost~t 22 and an on/of typ~ switch 24 in ths loop with thQ h2ating plant 10.
A h~ating syst~ 8 can be approxi~ated with a ~:
Pir~t ord~r proc~ with d~lay whlCh includ~ a numb~r of oper ~in~ par~tar~ in~luding a ti~o con~ant rp, a proc~s~ galn ~ and ~ time del~y e.
The timl~ constant tp, which may bo on the ord~ o~ lû to 200 ~Qconds, relate to ~h~ rate at which thQ enclo~ur~ 12 i~ h~ated and dep~nd2~ primarily on the 3iz!~ thQ he~ting plant 10 and th~ charact~ristic~ of th~ enclo~ur~.
i. .: ~ .:. ; , ~
.
''` ~ ' ' ",~ ' . ; ' ~ ~ ~q The process gain Kp may be on the order of 00 5 to 1. 5, which is the ratio of process output to process input at steady state.
Th~ delay e, which may be on the order of 0 to 500 s~cond~, relate~ to the transport time of the h~ating mQdiu~n in th~ conduit means 14 a~ it flows from the heating plant 10 to tha ~nclosure 12 and dep~nds mainly on th~ length and flow re i~tanc~ o~ the conduit m~ans~ lg.
In c~3rtai~ in~tallations in which th6~ tim~ delay parama~r ~ of th~ conduit ~eans 14 i~ relatively larqQ, thc~ controllQr 20 of Fig. 2 will no~ b~
appropr~ats~ bRcaus~ arrat:ic operation will occur by r~ason o~ i:ha controll~r not being r6spon lva to ~ha time delay param~ . What would happen i~ tl~at th~re would b~ a lagqing ~ ct whGrein the h-ated m~diuffl would no~
r~acb t~ nclo~ur~ until a substantial tiD~ aft~r th~
then~os~at b~giru~ call ing f or heat . Aft~r th~ d~ir~d t~D~p~E~atu~ r~ach~d, th plant 10 would b~ turrl~d of f but the~re~af~r th~r~ would be an over~hoot ol~ th~ a~t poirlt 'c~mp~ratUr~ wherein ~he hea~ ediu~ (air, ~or ~xampla) wolald con~inu~ to be suppli~æd to th~3 anclosure.
Thi3 would caus~ overheating.
Irh~r~ aro a nu~ber o ~ neural ne~worlc ~odel3 and l~rning rul~ that can be used for iDlplem~nting th~
invention. A pre~erred mode I is a three-l yer ., . : ~ ,: . :: : , - . :: ,:, ::: . : . . :
,, . :::
.; ~ : :::
J
feed-forward n~twork ~0 as shown in Fig. 3 and a preferred learning rule is th~ back-propag~tion learning rule. Back-propagation is a supervised learning procedura for feed-forward networXs wher~in training examples pro~ided to the network indicate th~ desir~d network output or target for each ex~plQ input.
F~ed-~orward network~, a us~d with ~ack-propagation, comprisa an input layer of proc~ssing unitY 32, zero or mor~ hidden layer~ o~ processing units 33, and an output layer which may hav~ on~y on~
proc~Ysing uni~ 36. In the illustrat~d embodiment th~ ~ -outp~ proca~ing unit 36 output~ ths proc2 s d~lay value ~-e compu~a~ by ~:hla network 3 0 . All th~ proce~3ing unit~ output r~al value~.
~he back-p~opaga~ion learning tQchn$que p~r~orm~
gradi~nt d~csnt in a quadratic ~rror mQasur~ to ~odi~y n~tworX woight~. Th~l3 fo~ o~ Eq. ( 1) that is u~u~lly ::
~mploy~d with b~ck-propagation i9~ ~h~ sigaaoid ~unctlon: ~
~ (x) ~
1 ~ a~X (2) Back-p~opaga~ion is usually usod with ~ultilay~r fe~d-~orwaxd n~t~ork~ o~ the typ~ shown ln Fig. 3 which i~ an exa~pl~ o~ a thre~-layer network 30 with ono output unit.
The rulo u~d to modify the w~ight~ may b~:
~Wi~ ~ ~o16~ (3) _ g ,~ ~ 'J 3 ~J
wher~ q i~ a corl~tant that deterlDine~ l:he learning rate, and S~ the error ter~ for unit j (i is defined a~ in Eq. 1). ~ i9 defined dif~erently for output and hidden unlts. For output units, ~ ' ~ ' (tj-oj ~ (4) whexe o ~ ' is th~ derivativ~ of oj with respect to it~
n~t input ( i~or 'che activation function o:e Eq . ( 2 ), thi quantity i~ o~ o~ ) ) and tj i5 thQ targ~t valu~
(thG "d~ixed output"3 for unit j. For hidd~n unit~, the 10 ta~eg~t valuo i~ not knowal and th~ er~o~ t~ co~npu~d frola th~ e~ror torm~ ot l:he next "high~r~ lay~r:
~ ~ :1 ' . w~ ~Sk ( S ) FiyO 4 ho~ a prior art adalin~ type proce~ing 15 ~le~nt which could b~ the general d~ign ~or th~ hidden and output p~oc~ing ~laments 33 and 36 of th~ n~twork o~ Fig. 3. 'rh~ proC~ ing elemen~ 3~ ha~ a s~rle~ o' ~ralnabl~ w~igh~s wl ~o Wn with ?I t~r~shold or bia~
w~ight ~ b~ing connsct~d ~o a ~i~C~d inpu'c o~
F~ ho~ an arrangement Po~ an output p~o¢~ ~ng ~le~nt wh~ra the desir~d or targ~t OUtp-lt pur~uant to ~qu~t~orl (4) is availabl~ ~or tho learning al~orith~. Th~ ~rrangem2nt for hidden ~ s for which -th~a d~ir2d o~ ~argat output i~i no~ availabl~ is pu~uant 25 'co ~quation ~5).
. ," . ., ,. . ,.. .. ~ . .
2~3~
For th2 eX2rcisQ of this invention, a mathematical model o~ a syste~, containing one or morQ
parameters, is n~ce~aary (Fig. 1). It is asswled éhat the pro ::e~se~ for which the systeD~ id~ntif ication ool is S intended can be modaled with appropria'c~ accuracy for the intland~d u~ by the mathematical mod~l, for so~o spscif ic a ~iga~ nt2~ of th~ 3l0d~1 paramet~r~. It i~ also a s~n~d that rangsg~ for all ~od~el param~t~r~ can b~ sp~ci~i~d.
Thi~ a~sllmption 1~ nol: expected to pos~ prac~lcal 10 probl~m~, ~lnc~ extrsmQly broad range can b6l1 us~d. Even i~ ~o~ para~t~r valu~ that may b~ ~ncounte~rad aro axclud~d, th~ robu~tn~ properti~s~ o~ n~urz~l n~twork~ :
rend~sr it lik~ly that any resulting 10s~8 o~ ace:uracy will b~ s~ll. In ~i~apl~ cas~, or when 1itt1Q 1~ known about 15 the taxg~ proc~ , a rang~ can con~i~t oX ~ low~r limit and an uppar limi~, and al]. valu~ wit~in the rang~
can b~ con~id~r~d ~ lly probabl~. In ~oro complsx ca~e~ and wh~n adg~qua~ proces3 Jcnowlsdg~ ox~st~, th~ :
rango~ C~l b~ ~o~ ~ophi~ticated -éh~ p~oba~ility 2~ di~t~ibution ov~c t~ rango need not b~ uni~orm, s~r oven uni~odal .
~ 2~o tool ~n~ ~thod developm~nt h~rein i~ b~ 2d on ~ n~3ur~1 ns~twork approach having a two pha~
proc~dur~0 In ~h~ ~irst phase a math~m21tical n~odel of 25 tha syst~DI shown in Fig. 1 is utiliz~d ~or gQn~ tinq tr~ining data. The mathemat ical model i~ implen~nted as ~: , . . .
:: ~ ,, , 3 ~
a computer program. The training dat~ comprise3 examples o~ open loop respon ~s to a ~tep inpu'c giv~n to thsa system model. ~Equivalent procedures with impulsQ or ramp input functions, or ~ven arbitrary input func~ions, 5 could also bQ utiliz~d. ) Each ~xampl~ is generated with a uniqu~ set of para~seter values, eaoh valu~ within the s~t b~ing choson ~ro~ th~ rang~ spacifiRd ~or the para~et~r.
In th~ seGond pha~e the training da~a is applied 10 in ~ teaching or l~arning ~node to a n~ural n~twork o~ an appropriat~ typ0, ~uc:h a~ thQ n~twork 30, to trans~o~h or conv~rt tha n~two~k into a tool ~or id~ntifying at laast on~ o~ th~ paraDI~t~r~ ~uch a~ th~ tiDI~ d~lay param~t~r e.
Wlth rerer~nco to th~ s~ccand pha ~, th- lsarning ~ "3up~r~ri3ad" l~arning in which it i~ a~sumod that th~ "de~ire~d output~ to~ ~very ~ra~ning input il~ known.
~upe~vi~d l-arning can bQ use~ to train an appropr$ately con~igurQd n~lural nQtwork such a~ n~twork 30 ~o~ ~om~l 20 sp~¢i~ie ta3k by pro~ :Lding exampl6~ og d~ d behav1Or.
Th3 conc~pl: o~ n~ural net~ork b~d ~y~t2~
id~nti~ ation i~ i11ustrated hor~$ll ~g b~ing s~mbodiad in a prototyp~ dt~1ay i~ntifica~cion too1 30. Mor~
sp~s:i~ica11y, it i~ a neural network d~lay id2nti~i~r for 25 th~l op~n 1Oop ~s~ti~ation of proce~ d~lay~ ~or a linear fir3t ordlar procQs~ model.
. ' ' ~ , ~ '," '"
Th~ sy5t2m shown in Fig. 1 ~ay b~ modaled a~ a linear ~irst ord~r process with delay by th~ equation:
~ x('c), ~ 1 x(~) + ~ u(t-~3) (6, dt rp rp whQr~in x(t~ i~ th~ proces~ temperatur~ respons~ in the enclosur~ 12, rp i~ the tim~ constant o~ the proces~ th~ proce~s gain, and 0 i~ the procQ~s dQlay. ~, rp and e are th~
para~2~er~ o~ th~ model.
~h~ ~od~ling ~quation may b~ a linear or nonlin~ar di~rential equation, or an alg~b:r~lc polyno~izll aguat~ on, within th~ ~cop~ o~ th~- ~nv~ntion.
In th~ ~ir~t ph~s~ r~f~rred to abov~, training exampl~ aro gel~n~rat~d u~ing a proc~3~ mod21 40 a~ ~hown in Flg~ 5. Th~ proc~s model, with: its para~t~r~
a~ign~d to valu~ witnin pred~t,arDlin~d rang~ given a ~t~p input ~. Th~ proces~ temlporatur~ r-spons~ ou~put R or x~t) i~ ~a~pl~sl at ~om{~ p~det~nlin~l r~t- and ~h~
ro~ul~ng r~l valu~d vec~or and ~h~ re~p~ctlv~ valu~ of th~ ti~- d~lay 0 ar~ used a~ th~ tr~ining input tor th~a n~u~l n~two~k 30 a3 shown in Fi5~. 6.
Although Fig. 6 designates a proc~ inE~ut S, it will b~ und~r~tood th~ such inpllt ~ay b~ oDIitt~d in c~s~ wh~ 5 is a con~taZlt becau~ would only bo 25 varying ~alu~ o~ S that would af~ t th~ output o~ the neural network.
.. . .
, ~ ~
'' ~ '` '':
., ' , Identi~ication i~ in term~ o~ sampla~, not ab~olute units og time. By changing thQ sampling rate, the range o~ delay~ that can be identi~ied (by th~ sa~
trained na~work) can b~ ~ontrolledl I~ the ~iniDlu~ delay is Icnowr to be n s~cond, sampling may s~ar~ n ~ecorld~
af~er th~ p input is given. Th~ de ired network out put would ~h6~1l bo e-n and n would b~D add~d to ~h~
output o~ t:h~ train~2d n~twork to obtain th~ ~stiD~t0d proc~ dQlay.
Num~rou~a ~ituation~ Or trai~ing an~ op~r~tion to e~aluat~ ~h~ y~t~a ha~ b~a~n run. Our ~i~au~tion~ ~all into tw~ . Fir~t, w~ hav~ inv~tig~t~ tho Qrror o~ d~lay ~ti~tion ovar wid~ rang~ o~ proces~
paraJne'c~r~. ~eeond, w~ ha~e ifflulat6~d th~ 3~t-up o~ Fig.
7 and d~D~onstrat~d ~eh~ proYed eon~rol that c:an ~ -aehi~v~d usling ~sur d~l~y identiPl,~r. Tha r~ult~
da~erib~d bllslow ~ploysd a thr~-lay~r n~tworlc with 15 hid~n unlt~.
In on~ aue~ 2~i~ulation th~ trz~ in~ d~t~ ~oP ~h~
n~worX 30 eor.~ dl of 6,000,000 dynaD~ lly g~r~rRt0d ~xa~ s. ~h~- rang~l o~ param0t~r~ eonsid~r~d wer~
rp ~ro2l 10 to 200 sQeond~; e fro~ O to 50û
oeonds~: and Xp ~roDI 0.5 to 1.5. Unlror~ dis~ribution~
w~r~ u~sd ~or all rang~.
T~ining on a rang~ of Kp valuo~ i~ not ` .
strietly n~eQ~ry if the correct valuo is availabl~ in ~ 14 --" :
2 ~ ~g 3 ~ ~, 6 op~ration. As th~ procecs model i~ lin~ar, th~ proc~
output can ~aslly b~ nor~alized. Howevar, wi'chout training on a rang~ of Kp, ev0n ~all chang~ in th~
value o~ thl~ par~m~1:er can reqult in ~lgnif~cant ~rror S in d~ y ~tilaa~ion. Th~3 noi~ in ~raining inpu~ was gausvian with 99% (3 tar~dard deviatlon~ falling within 5% o~ ~h~ rang~ o~ p~OCQ5~ outpu~ valull3.., wh~ch wa~
nons lizad b~two~n 0 and 1. The output o~ ~h~ proces~
wa~ ~amplod ~v~ry 10 s~cond3 aft~r th~ skQp irlput w~
yiv~n. 50 s~D~pl~ wer~ collected and u~ed as input to tha natwork.
Durinsl th~ q~nora~on of training d~tza Yia proc~ l 40, ~ch v~ctor of 50 ~ampl~ had on~ s~t o~ valu~s o~ tho para~t0r~ p, e an~ Kp as~oci~t~ ~ith itc During thel training o~ th~s n~twork 30, ~ach ~ucb. ~ tor o~ 50 sa~pl~ h~ th~ 2~3p~cl:iv~
v~lu~ o~ ~ ti~ d-llay e a ociat~ with it, wbich in ~ach ca~0 ~ ~o targ~ Yalu~ ~o~ ad~u~ing t~
w~ight~ oi~ n~t~ork.
rh~ n~orlt 30 h~d 50 input u~ on~ S~or Q~ch ~a~3pl~, 15 hldd~n un~ and 1 ou~:pu~ (thl~ d~la~
. ~ei~ato) O Th~ Y~luo o~ th~ learning ~tal pz~ to~
~7 W21~ 0.1 9~oE t:ho ~ir~t l,ooO,000 t~ainir ilt~r~'cions" an~ 0 . 01 thQrea~ter.
Agt~ tralning, th~ network 30 w21~ t~a~ on BlQW
(alao rando~ly g~n~ratQd) data. ~e~t~ w~ p~r~orm~d to ., ' ~ ',, 3 ~
dQtermin~ th~a ~f~ectivene~s o~ delay identiflcation a3 a furlction o~ delay, as a function o~ rp, and a function ot Kp, and as a function o~ th~ aD~ount o~
nois~. A nol3~ ~igur~ ol~, ~ay, S p~cent iD~plle~ tha~ 99 5 perc~nt ol~ tho gau~3ian noisQ (~ 3 ~'candard d~viations) wa~ within ~ 5 perc~nt o~ th~ rany~ o~
proce~ output ~or that simulation.
Figur~s 8 through 11 depict th~ re~ult~ o~
variou~ tosst3l. Each o~ thesQ grapho ~hows th~ ~tlm~tion 10 er~o~ ov~ a r~ng~ op valu~3 o~ a particulaE param~t~r.
'rh~ r~lnlrlg para~tor~ wera h~ld con. tant a1~ or n~ar 'sh~ ~idpoint~ o~ thQir range~.
~s~d on th~ t~ts~, the Sollow~n~ ol~ t~on~
w~r~ mado:
$ho av~rzlg- e~ti~ation error i~ w$~in 2 . 5 p~rc~nt o~raE a wide rang~l og d~l~y~ an~
p:~oc~ cona'cant~ fo~ ro~ tic~ a~ount~
ot noi~
For ~ a~ value~ withir~lning ~ang~
~ a~ti~tlon ~rror is small. Th~ro i~ on~
O~ ~xc:~ption. For v~11 d~llay~, p~lrG~nt~gl~ orror iY larg~ to -expoct~d. Th~ ~ampled proco~ output in thl~
c~ p~ov~dls~ little r~lovan'c d~t~
li~c~ly that a non-uni~orm ~pling ~ang~
would ovorc:oms this probl~
~ .:
. . , In many ca~e~, estiD!ation ~rror is accep'cablo avan for parameter valus~ out~id~ training ranges~. For ~xample, th~ avarago error for rp ~ 280 less than 4%. Ev~an ~or gain~
t~wic~ a~ high a~ any tha netwo~X wa~ l:rained on, tho avarag~ error is around 4 % .
E~ ation i~ robu~t with re~p~ct to noi~.
For ~5% nois~, the averag~ e:~ror i~ a~o 6.5%.
10 . ~ft~r th~ n~twork 30 ha bo~n tr~in~d, 1~ can b~
u3~d ~or on-lin~ d~lay ldenti~ication. Th~l input to tho n~twork i~ no~ actuall ~not ~imul~t~d) proc~ output ~ut th~ outpu~ og ~he~ n~éwo~k i~ a~x~n ~ d~l~y ~ti~t-.
Thi~ dolay a~ti~t~ can th~n b~ u~d S~o~ control and/or diagnos~tlcl o~ ~xaDlpl~ if th~ proc~--~ controll~P
ins::orpor~ S~i~ Pr~dictor or oth~r d~lay co~pQn~tion 'c~lqu~, th6~ d~lay e~timllt~ can ~o giv~n a~ input to lt,.
Flg. 7 d~ cl:~ how d~lay id~ntl~ 50 e~abodylng 20 th~ n~t~ork 30 ~-n b~ appl ied to a unit 52 whi-;:h comp~ controll2r having an a~oct~tQ~ ~ith Pr~dicltor. Wh~n ~ d~lay estima~o 1~ n~d~, th~a control loop is brok~n ~ ia ~ switch 54 and ~ top input p~rturbation i- ~p~ d to a proc~ 56 th~o~ b~ir.g~
25 controll~d, by unit 52, via step input g~ner~tor 58. The r~ponse oP th~ procçl~s s6 to tha per~cur~a~lon i9 sampled ,. .., . . - . .
,~,, . , ,; . ~
,,, , . , .
.
and ~tore~d in a bur t'~r 60 . When a ~u~icient numbQr o~
samples hav~ b~n ~ec~ived, th~ vector o~ sampl~ caled appropriately) i~ u~ad as input to th~ trained neural nQtwork 30. Thel~ output of the network i~ subj~ctQd to so~ po~t proc~ ing ~scaling and/or tr n~lation) in a po~t proc~or 62 to obtain a d~lay estimat~ eQ5~t.
onc~ th~ d~l~y o~timat~ ha~ been input to th~ S~aith Pr~dic~s~, ~witch 54 may b~ clo ~d again and th~ prsc~s plat b~ck und~r clo~oed loop con'crol.
A ~i~ulat~d s~t-up o~ Fi~. 7 ha~ b~n utiliz~ to in~o~ti~8t~ th~ ct on clo~d loop cont~ol o~ d~l~y ide~ iclltlorl. A Pi~t ord~r p~oce~ an~ a ~ pl~
proportion~l controll~r w~rQ u~e~d ~or ~:hs~ ulatlon. It wa~ round th~t ~ign~ antly bett~r c:ontrol 1~ achlsvæd 15 wi~h a gosd ~o~ dg~a o~ ~h~ proc~ d~lay.
Thl~ proa~ d~ sy ig ~u~t on~ proc~ pa~m~1:or.
Alt~lough o~tl~at~- o~ timaa con~t~nt~, ~2in9~, otc.
~lso ~quir~l ~rO~ cont~ol, it has~ baon Poun~l ~h~t.
pros:le~ y 1~ tho DlOOt critical parala~t~r.
Signl9!1c~2t ov~r 08~ und~r ~stimat~ ln proco~-s d-lay can C~U8~ Wo~O eon'crol thzm propor~iona~ly poo~ ti~.
ln tho proc~ tlao con~nt or th~ proco~ g~In.
1=1 roaeh h~r~in for d~rolopi.ng ~y~t~
25 lda~ti~iGation toolsl ig ~xtrem~ly g~n~ral-pu~po~ 'C
can b~ u~3Qd ~or c:lo:~d loop or open loop idQnt~ic~tiorl, -- 18 ~
.
, r'or ~stim2~ting any and all mod~l parame~ers, and ~or lialear and non-linQar proc~s~ Diodsls. For spaci~lc application~, 3i~plification may b~ po~sibl~. For example, i~ the id~ntification techniqu~ is arl OpQn loop 5 on~, thQ input p~rturbation can be id~ntical ~or all t~inin~ ~xample~. It thQn ne~d not be provid~d a2~ input to th- n~twork 3 0 . Th~ constra~rlt thi . i~po~a3 i~ that th~ sa~ input p~rturbation, or ( i~ th~ proc~ mod~
lln~a~ c2~ d v~r~ion o~ it, mu~t bc u~d during ~ho 10 opar~tion.
Th~ dosc:~ip~cion oP th~ inv~ntion h~3roin ha~ ~or l:h~ o~t p~t b~n d~r~:t~d to op~n loop ~y~t~
ideJItl~ication. Th~ , it i~ a~u~o~ th t ~n input can b~ glvor~ h~ proe~ nd its r~3pon~0 ob~enr~ w~thou~
15 th~ con~oun~in~ ct~ o~ ~e~d~ack. ~ pli~ but r~alis~ic ~or~n o~ clo~d loop delay id~nti~icatio~a h~
al30 b~n con~i~Qr~d, how~v~r.
T~ æn¢~ o~ ~ho invQntion i~ tho ~pp~oxl~a~tlon o~ a ~un~ti~ o~ proc~ input~o~ltpu1: to pa~o~-~
20 valu~ ~tl~ato-. For g~neral closod loop ld~nti~ at~on, e3tl~t~ ha~r~ to ~ produced giv~n cont~nuou~ly (~nd unpr~dlctably3 va~ying inpu~ In princ:~plo, t~lor~
appea~ to b~ no roa30n why a ne'cwork coul~ not b-train~d ~o~ thi~ cas~ ~9 well; n~ural n~twork~ ha~ b~n u~d to app~o~ unetion~ a~ co~pl~x a~ ch~otlc: time .
:. . , . . . :
.
' ;:, serie~. A simulation of the proces~ under closed loopcontrol could be uced.
we have investigated a constrained form o~
closed-loop identification: delay identi~ication under "bang-bang" control. In closed-loop bang-bang con~rol, th~ proce~ can b~ switched on or of~. WhenQver the output ~xc~eds an upper bound, the proce~ i8 turn~d of~;
whenever thQ outpuk falls below a lower bound, th~
proces~ i~ turn~d on. Bang~bang control $~ co~only used wh~n highly accurat~ control i8 not required - e.g., in HVAC sy~t~
For d~lay id~nti~ica~ion und~r ban~-b2ng control, WQ assu~e that th~ collection of output ~a~ple~ i~
initiated when the proce ~ i~ turned on. A~ter th~
pr~det~r~ined nu~ber of ampl~ hav~ b~n coll~cted, ~n ~sti~at~ i3 produced~ Giv~n tA~ ~c~nario, ther~ i~ only on~ signi~ic~nt dl~rsncQ b~tw~en op~n-loop and bang-bang d~lay i~Qntifica~ion. In th~ ~orm~ ca~, th~
.
procQ~s i~ as~u~d to b~ at a con~tant value (~xcopt ~or noi~ ro~ whon th* ~tep input i8 given until tha d~lay expl~o~; in th~ bang-bang case, thQ procQ~ output is decaying during ~h~ d~lay. Th~ deGaying and ri~ing re~pon~es can b~ governed by di~cr~nt dynamic~.
~ hav~ traln~d a network to identi~y th~ d~l~y of a proc~ under bang-bang control. It wa~ a~um~d that both th~ "on~ process and ~he l~o~N procsss w~r~
e,i ~^;
first-ordJ~r with independent (and therefore dif~erent) ti~a constants. Tha procsss input wa~ again constant over the duration of a training example and wa3 not provided to the networX. An av~rag~ error rate o~ around 5 7% was achiev~d in 100, 000 iterations. The networX
converge~ ~ignificantly fa~ter than for th~ open-loop delay identi~icatic~n, and we exp~ct that a coD~parably long simulation would produc~ lower error rat23. The better per~or~ance ln the~ bang-bang clo~ed-loop c~
not too surprising: a transition betw~n falllng and ri~ing CUrV128 is easier to det~ct than a transition b~tw2en con~ant and ri~ing curvas.
, : ' :
Claims (14)
1. A method for developing a tool for identifying at least one parameter of a process which is modeled by an equation having m parameters p1, p2,...pm;
comprising the steps:
determining ranges for each of said m parameters;
modeling said equation via a computer program;
utilizing said program to generate a set of training examples, each of said examples having (1) selected values of said parameters from within said respective ranges and (2) process output data resulting from said program when said selected values of said parameters are used; and using said set of training examples to train an artificial neural network such that (1) the input to said network comprises for each of said training examples respective values of at least said process output data and (2) the output of said network comprises respectively for each of said training examples at least one of said selected values of said parameter.
comprising the steps:
determining ranges for each of said m parameters;
modeling said equation via a computer program;
utilizing said program to generate a set of training examples, each of said examples having (1) selected values of said parameters from within said respective ranges and (2) process output data resulting from said program when said selected values of said parameters are used; and using said set of training examples to train an artificial neural network such that (1) the input to said network comprises for each of said training examples respective values of at least said process output data and (2) the output of said network comprises respectively for each of said training examples at least one of said selected values of said parameter.
2. A method according to claim 1 wherein said equation is a linear differential equation.
3. A method according to claim 1 wherein said equation is a nonlinear differential equation.
4. A method according to claim 1 wherein said equation is an algebraic polynomial equation with said parameters being represented as coefficients.
5. A method according to claim 1 wherein each of aid training examples includes input data employed in said program for said selected values of said parameters.
6. A method according to claim 5 wherein said input to said network includes varying values of said input data.
7. A method according to claim 1 wherein said equation has the form:
wherein x(t) is the process response, rp is the time constant parameter of the system, Kp is the system gain parameter and .THETA. is the system delay parameter.
wherein x(t) is the process response, rp is the time constant parameter of the system, Kp is the system gain parameter and .THETA. is the system delay parameter.
8. A method for making a neural network tool for identifying parameters of a system which may be modeled by the equation:
wherein x (t) is the system response, rp is the time constant: parameter of the system, Kp is the system gain parameter and .THETA. is the system delay parameter, comprising the steps:
providing a neural network having an arrangement of processing element and adjustable weights connecting the outputs of some of said elements to the inputs of other of said elements, said network having input and output terminal means and target setting terminal means;
providing learning algorithm operational means for said network for adjusting said weights wherein output values on said output terminal means are biased to converge respectively to target values applied to said target selecting terminal means;
making a model of said equation and utilizing said model to generate sets of training data for said neural network with each of said sets having selected values of said parameters within respective predetermined ranges and a resulting response which is said x (t); and sequentially applying said sets of training data to said neural network with each of said sets having said response thereof applied to said input terminal means and said value of said parameters beings applied to said target setting terminal means.
wherein x (t) is the system response, rp is the time constant: parameter of the system, Kp is the system gain parameter and .THETA. is the system delay parameter, comprising the steps:
providing a neural network having an arrangement of processing element and adjustable weights connecting the outputs of some of said elements to the inputs of other of said elements, said network having input and output terminal means and target setting terminal means;
providing learning algorithm operational means for said network for adjusting said weights wherein output values on said output terminal means are biased to converge respectively to target values applied to said target selecting terminal means;
making a model of said equation and utilizing said model to generate sets of training data for said neural network with each of said sets having selected values of said parameters within respective predetermined ranges and a resulting response which is said x (t); and sequentially applying said sets of training data to said neural network with each of said sets having said response thereof applied to said input terminal means and said value of said parameters beings applied to said target setting terminal means.
9. A method according to claim 8 wherein said system is a linear first order system.
10. A method according to claim 8 wherein each of said sets applied to said network has only one of said parameters applied to said target setting terminal means.
11. A method according to claim 10 wherein said one of said parameters is said system delay parameter .theta..
12. A method according to claim 8 wherein each of said sets of training data includes a stimulus value for said model which is applied to said input terminal means of said network.
13. A method according to claim 12 wherein said stimulus value is a step input.
14. The tool developed as the product of the process of claim 1.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US59492790A | 1990-10-10 | 1990-10-10 | |
| US07/594,927 | 1990-10-10 |
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|---|---|
| CA2053056A1 true CA2053056A1 (en) | 1992-04-11 |
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| CA002053056A Abandoned CA2053056A1 (en) | 1990-10-10 | 1991-10-09 | Process system identification |
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| US (2) | US5740324A (en) |
| EP (1) | EP0480654B1 (en) |
| JP (1) | JPH0628007A (en) |
| AT (1) | ATE163777T1 (en) |
| CA (1) | CA2053056A1 (en) |
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| US6017143A (en) * | 1996-03-28 | 2000-01-25 | Rosemount Inc. | Device in a process system for detecting events |
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- 1991-10-07 ES ES91309163T patent/ES2112853T3/en not_active Expired - Lifetime
- 1991-10-09 CA CA002053056A patent/CA2053056A1/en not_active Abandoned
- 1991-10-11 JP JP3290441A patent/JPH0628007A/en not_active Withdrawn
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1996
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1997
- 1997-03-13 US US08/816,470 patent/US5924086A/en not_active Expired - Fee Related
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| ES2112853T3 (en) | 1998-04-16 |
| EP0480654A3 (en) | 1993-04-14 |
| US5740324A (en) | 1998-04-14 |
| US5924086A (en) | 1999-07-13 |
| EP0480654B1 (en) | 1998-03-04 |
| DE69128996T2 (en) | 1998-09-10 |
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