Issn: Identification Of A Production System Using Hammerstein-wiener .

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: 1hicham.fouraiji@gmail.com, 2 b.bensassi@fsac.ac.maABSTRACTIn 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