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Journal of Theoretical and Applied Information Technology10th February 2016. Vol.84. No.1 2005 - 2015 JATIT & LLS. All rights reserved.ISSN: 1992-8645www.jatit.orgE-ISSN: 1817-3195IDENTIFICATION OF A PRODUCTION SYSTEM USINGHAMMERSTEIN-WIENER AND NARX MODELS112HICHAM FOURAIJI, 2BAHLOUL BENSASSIlaboratory PMMAT university HASSAN II Facultyof science Casablanca, Morocco.laboratory PMMAT university HASSAN II Facultyof science Casablanca, Morocco.E-mail:, 2 this paper we present a new approach to modeling dynamic production systems with discrete flow. Thismethod is based on the automatic knowledge domain, in order to build a mathematical model thataccurately formalizes the behavior of the studied system. The approach adopted for this study is theparametric identification of nonlinear systems (Hammerstein-Wiener system and NARX model). Theproduction system studied will be considered as a black box, which means that the inputs and outputs dataof the system will be used to identify the internal system parameters.Keywords: Production System, Hammerstein-Wiener Model, NARX Model, Parametric Identification.1.INTRODUCTIONIn recent decades, industrial companies arefacing major changes in their environment, globalcompetition, an uncertain market, and customersincreasingly demanding. These constraints requireresponsiveness and flexibility of enterprises in orderto adapt the capacity of production systems tochanges in demand and internal risks and/orexternal chains of production. Which requires athorough knowledge of the systems studied.Difficult to control, these systems continue topose serious problems in the design, modeling andcontrol. Indeed, the study of production systems, asany type of dynamic system, proves a very difficulttask to achieve, and requires very often that wehave mathematical models of these systems. Thesemodels can be derived directly from physical lawsthat govern the behavior of the system, but it isoften impossible to obtain a priori knowledgecomplete and accurate of all model parameters. Inthis case, to refine and clarify that knowledge, weuse an estimate based on observed input-outputsystem behavior model.We are referring here to the identificationapproach, which denotes the set of methodologiesfor mathematical modeling of systems based onactual measurements from the real system [1].our context we are interested in identifyingproduction logistics systems based on non-linearparametric blocks- oriented models as (NARX andHammerstein-Wiener models). Before goingfurther, let's look at what offers literature in thefield of modeling and identification of productionsystems in supply chains. It is interesting to seewhat concepts are now and what techniques orapproaches to modeling and identification havebeen discussed developed.K.LABADI and all presented a modeling andperformance analysis of logistics systems based ona new model of stochastic Petri nets. This model issuitable for modeling flow evolves in discreteamounts (lots of different sizes). It also allows totake into account more specific activities such ascustomer orders, supply inventory, production anddelivery batch fashion [2]. N.SAMATA in allproposed modeling global supply chain using Petrinets with variable speed. He transposed theconcepts developed on the traffic to the supplychain typical production (manufacturing). They alsoproposed a modular approach for modeling thedifferent actors in the supply chain is still based onthe formalism of Petri nets to variable speed [3].F.PETITJEAN and all suggested in their work amethodology for modeling global supply chainfrom a company audit. Then using the UML modelthey produced a simulation platform and they alsoproposed the principles of integrated control supplychain [4]. B.ROHEE and all used hybrid petrinetworks to develop a simulation approach offlinethat supports multiple constraints (change control,time between changes, friction .). The originality111

Journal of Theoretical and Applied Information Technology10th February 2016. Vol.84. No.1 2005 - 2015 JATIT & LLS. All rights reserved.ISSN: 1992-8645www.jatit.orgof their work lies in the fact that they havesimulated the game continues production andstudied the interactions between the continuousmodel and the discrete data exchanged with thecontrol part. This allows to simulate and control thesystem without using the actual operative part [5].H.SARIR and all exhibited a new method formodeling and controlling inventories in progress inthe production lines by analogy with themacroscopic model for controlling a hydraulic tank.They used the concept of automatic control forcontrolling and mastering inventory in progress [6].H.SARIR and all have also presented a model of aproduction line using behavioral identification indiscrete-time transfer functions, where they usedthe PEM algorithm for the construction of modelsand the simulation was carried out on the GUIidentification (IDENT) MATLAB [7].K.TAMANI and all have made an approach forcontrolling flow of products, where they brokedown the system studied as elementary productionmodules. They studied thereafter, the control flowthrough each module production and supervisionwhich was based on fuzzy logic [8].E-ISSN: 1817-3195preclude an exact mathematical description of thesystem. However, even if we have a completeknowledge of the system and sufficient data, anaccurate description is often not desirable becausethe model would be too complex to be used in anapplication. Therefore, identification of the systemis considered approximate modeling for a specificapplication on the basis of the observed data and theknowledge of the previous system.The identification procedure, in order to arrive atan appropriate mathematical model of the system isdescribed in detail in (Figure 1) .Selecting a set of models is determinedcompletely by the prior knowledge of the system.This choice of a set of candidate models is probablythe most important step and most difficult in asystem identification procedure.Then to estimate the model parameters mustchoose an algorithm to estimate or a criterion to beminimized (Figure 2).After that, a validation step model considers thequestion of whether the model is good enough forits intended use.This literature review shows us that productionsystems in logistics chains today, represent a focusfor scientific research in the identification,modeling and control field.Modeling approaches are many and varied, but itappears that the methods of analysis and design ofproduction systems combining different approachesare preferred. Indeed recent bring an ease ofanalysis or greater use or opportunities set outsimplified.Through the same literature review, we foundthat the modeling of logistics systems productionbased on non-linear parametric models orientedblocks like NARX Hammerstein-Wiener model andare rarely used.We present in the next section, the definition andidentification procedure. we present in the thirdsection nonlinear block-oriented models. the fourthsection focuses to the method of parameterestimation and model validation. in the fifth sectionwe present the case study and the results obtained.We conclude the section by presenting aconclusion and perspectives.2.IDENTIFICATION METHODA mathematical model is always anapproximation of the real system. In practice, thecomplexity of the system, limited prior knowledgeof the system and incomplete observed data112Fig 1 . Process Of System Identification

Journal of Theoretical and Applied Information Technology10th February 2016. Vol.84. No.1 2005 - 2015 JATIT & LLS. All rights reserved.ISSN: 1992-8645www.jatit.orgE-ISSN: 1817-3195The NARX model equation can be written in (1):If then the model is considered appropriate, themodel can be used, otherwise, the procedure mustbe repeated, which is most often the case inpractice. However, it is important to conclude that,because of the many important choices to be madeby the user, the system identification procedureincludes a loop to obtain a validated model.1When y is output. r are the regressors. u is inputand L is a autoregressive with exogeonoues (ARX)linear function. d is a scalar offset. g(u-r) representsoutput of nonlinear function and Q is projectionmatrix that makes the calculations well conditioned.3.2 HAMMERSTEIN-WEINER MODELThis model describes the dynamic systems usinginput and output static nonlinear blocks, in serieswith a model error output for dynamic linear block,the output of this block is distorted by the nonlinearstatic. The following structure describes theHammerstein-Wiener model.x3.The linear sequence of the Hammerstein-Wienermodel is implemented by an error output model andnonlinear blocks containing nonlinear estimators[1].NONLINEAR SYSTEMSMost dynamical systems can be betterrepresented by nonlinear models. The non-linearmodels are able to describe the behavior of theoverall system over the entire operating range,while the linear models are not able to bring thesystem about a given operating point. One of themost frequently studied classes of nonlinear modelsare called oriented blocks models, which consist ofa combination of linear and non-linear blocks [9].There are different types of nonlinear systemidentification methods. There are a number ofnonlinear models. However, two non-linear modelswill be described in the present paper.4. ESTIMATION AND VALIDATIONMETHODS4.1 Estimation MethodsNonlinear blocks identification of nonlinearsystems are implemented using non-linear functionsor estimators. In this paper, two types of estimators,containing either a network or a sigmoid waveletused with NARX, and Hammerstein-Wienermodels. Both of sigmoid and wavelet networkestimators use the neural network composing aninput layer, an output layer and a hidden layer usingwavelet and sigmoid activation functions as shownin Figure 5.3.1 Narx ModelA nonlinear autoregressive exogenous model(NARX). The estimate block of non-linearity, acombination of the non-linear function and thelinear ARX function in parallel, the output of thecard to the regressor model output. The NARXstructure is shown in Figure.3.113

Journal of Theoretical and Applied Information Technology10th February 2016. Vol.84. No.1 2005 - 2015 JATIT & LLS. All rights reserved.ISSN: 1992-8645www.jatit.orgE-ISSN: 1817-3195scaling function f (.) and the wavelet function g(.)are both radial functions, and can be written asequations (5) and (6).expdim/ 0,5 exp′ 0,5 / 56In system identification process, the waveletcoefficient (a), dilation coefficient (b) andtranslation coefficient (c) are optimized duringlearning to obtain the best performance model.5VALIDATION MODELThis step is to check whether the modelaccurately represents the system found studied.4.1.1Sigmoid network (sn) activation functionThe sigmoid network nonlinear estimatorcombines the radial basis neural network functionusing a sigmoid as the activation function. Thisestimator is based on the following expansion (2) :2when u is input and y is output. r is the theregressor. Q is a nonlinear subspace and P a linearsubspace. L is a linear coefficient. d is an outputoffset. b is a dilation coefficient., c a translationcoefficient and a an output coefficient. f is thesigmoid function, given by the following equation:14.1.21Wavelet network (wn) activation function3The term wavenet is used to describe waveletnetworks. A wavenet estimator is a nonlinearfunction by combination of a wavelet theory andneural networks [14]. Wavelet networks arefeedforward neural networks using wavelet as anactivation function, based on the followingexpansion in equation (4) :! # !#!#4u and y are input and output functions. Q and Pare a nonlinear subspace and a linear subspace. L isa linear coefficient. d is output offset. as and aw area scaling coefficient and a wavelet coefficient. bsand bw are a scaling dilation coefficient and awavelet dilation coefficient. cs and cw are scalingtranslation and wavelet translation coefficients. TheWe compare the model outputs and observedoutputs of the system until the best model isreached. This is done using criteria such as thequality of the fit to the estimation data, the finalprediction error (FPE) and Akaike informationcriterion (AIC) [12] The percentage of higheraccuracy in shape is obtained from the comparisonbetween the experimental and modeling curvessignals by the following equation (7) :!123 4 Ÿ23 45100 17Where Y is the simulated output, y is themeasured output and Y is the mean of output. FPEis Akaike Final Prediction Error for estimatedmodel which the error calculation is defined asequation (8) :7 89:11; ;8Where V is the loss function, d is the number ofestimated parameters, and N is the number ofestimation data. The loss function V is follow inequation (9) where θn represents the estimatesparameters.Final prediction Error (FPE) provides a measureof model quality by simulating the situation wherethe model is tested on a different data set. TheAkaike Information Criterion (AIC) as shown inequation (10) is used to calculate a relativecomparison of models with different structures [13].114 ?@log 92;10

Journal of Theoretical and Applied Information Technology10th February 2016. Vol.84. No.1 2005 - 2015 JATIT & LLS. All rights reserved.ISSN: 1992-86456www.jatit.orgE-ISSN: 1817-3195STUDY CASETo illustrate the parametric identificationapproach explained in Section 2, we propose tostudy the case of a production line forsingleproduct, turning inflows into outflows. Thisproduction line consists of three machines, of thesame production cadence, with a negligible timetransfer between machines.Fig 6 illustrates the processing line studied.By applying the identification procedureexplained above, we simulated each model withmultiple levels, we found that the NARX modelgives the best fit with 95.75%, while theHammerstein-Wiener system gives us a model withfit 94.74%.The figure below presents a comparison betweenthe estimated outputs and the measured outputs ofeach model.Then we represent the production system as a"black box system" when the input is u(t) andoutput is y(t).The input and output of the production lineillustrated in Figure 8, have been extracted from theinformation system of the company (ERP).These data are used to determine the modelsystem studied by comparing models (NARX andHammerstein-Wiener models), like structures in themodel. The data is divided into two parts.The first part is used to determine the model ofthe system and the second is used for the validationof the model.The following table shows the different levelstested for both models:115

Journal of Theoretical and Applied Information Technology10th February 2016. Vol.84. No.1 2005 - 2015 JATIT & LLS. All rights reserved.ISSN: 1992-8645www.jatit.org7. CONCLUSIONThe originality of this work lies in the projectioninspired methods in the field of automatic systemsfor production logistics.It has been proposed modeling "black box" of aproduction line from the observed inputs andoutputs.To estimate the parameters of the studied system,we opted for block-oriented nonlinear models(NARX and Hammerstein-Wiener), which areknown by their simplicities, and using the sigmoidnetworks and wavelet networks for estimating theparameters of models usedThe tests showed that the best fit was given bythe NARX model with a better fit of 95.57%.More future work will be in this direction,including minimization of the identification error toachieve higher rate adjustments and the applicationof other estimation models.REFRENCES:[1] L. Ljung, System Identification: Theory for theUser, 2nd Ed. New Jersey: Prentice Hall PTR,1999.[2] K.Labadi, Contribution à la modélisation etl'analyse des chaines logistique à l'aide desréseaux de Pétri, thèse de doctorat, Universitéde Technologie de Troyes 2005.[3] N.Smata, C.Tolba, D.Boudebous, S.Benmansour,J. Boukachour, Modélisation de la chaînelogistique en utilisant les réseaux de Pétricontinus, 9e Congrès International de GénieIndustriel, Canada, (Oct.2011).[4] F. Petitjean, P. Charpentier, J-Y. Bron , A.Villeminot, Modélisation globale de la chainelogistique d’un con structeur automobile, "eSTA" :La Revue électronique Sciences etE-ISSN: 1817-3195Technologies de l’Automatique, NÆ1 SpécialJD -JNMACS’ 07 2ème partie, 2008.[5] B. Rohee, B. Riera, V. Carre-Menetrier, JM.Roussel, outil d’aide à l’élaboration de modèlehybride de simulation pour les systèmesmanufacturier, "Journées doctorales du GDRMACS (JD-MACS'07), Reims, France , 2007.[6] H.Sarir, L’intégration d’un module d’a ide à ladécision (contrôle de flux entrée-sortie) basé surle modèle régulation de niveau dans le systèmeMES (ManufacturingExecution System,Colloque SIL–Concours GIL Award, (Déc.2011).[7] H. Sarir, B.Bensassi, Modélisation d’une lignede fabrication d’un sous ensemble del’inverseur de pousse par la méthoded’identification, IJAIEM : international journalof application or innovation in engineering andmanagement, ISSN 2319 – 4847 Volume 2,Issue 6, (Juin 2013).[8] K. Tamani, Développement d’une méthodologiede pilotage intelligent par régulation de fluxadaptée aux systèmes de production, thèse dedoctorat, université de Savoie, France,(Déc.2008).[9] Z.M.Yusoff, Z.Muhammad, M.H.F. Rahiman,M.N. Taib, ARX Modeling for Down-FlowingSteam Distillation System, IEEE 8thInternational Colloquium on Signal Processingand its Application, 2012.[10] Z.Muhammad, Z.M.Yusoff, M.H.F. Rahiman,M.N. Taib, Modeling of Steam Distillation Potwith ARX Model, IEEE 8th InternationalColloquium on Signal Processing and itsApplication, 2012.[11] K. Ramesh, N. Aziz and S.R. Abd Shukor,“Nonlinear Identification of Wavenet BasedHammerstein Model – Case Study on High Purity Distillation Column”, Journal of AppliedSciences Research, 3(11): 1500-1508, 2007[12] H. Akaike, “A new look at the st atistical modelidentification”, [13] IEEE Transactions onAutomatic Control 19 (1974) 716– 723.116

that the modeling of logistics systems production based on non-linear parametric models oriented blocks like NARX Hammerstein-Wiener model and are rarely used. We present in the next section, the definition and identification procedure. we present in the third section nonlinear block-oriented models. the fourth

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