Modeling of chromatographic separation process with Wiener-MLP representation

Abstract Dynamic input–output-models have been identified for columns of an industrial sequential ion-exclusive chromatographic separation unit. Models are aimed at describing motion and form transformation of the fronts of different substances in the columns so that changes in “limit cycles” dynamics and drifts to undesired disturbed states could be observed on-line with model based simulations. The model structure has been innovated on the basis of classical Wiener representation, in which nonlinear dynamic system is described with a combination of linear Laguerre dynamics and static nonlinear mapping. The static mapping is realized here with MLP-type neural network. A separate delay model is needed for describing the movement of the front. The delay time adapts on variations of the process flow rate. Form transformation of the front is described with a dispersion model, which is smoother type Wiener-MLP model. Forward and backward Laguerre presentations are calculated with Laguerre filters. These Laguerre presentations are mapped to the output with a neural network. Dynamics of “salt” and two important compounds have been modeled on the basis of analyzed samples, which were taken in a factory experiment during normal production. A priori information about the process dynamics can be included in the dispersion model by choosing a suitable Laguerre parameter, but otherwise representativeness of the identification data determines validity of the model.

[1]  K S Narendra,et al.  IDENTIFICATION AND CONTROL OF DYNAMIC SYSTEMS USING NEURAL NETWORKS , 1990 .

[2]  Pertti M. Mäkilä,et al.  Approximation of stable systems by laguerre filters , 1990, Autom..

[3]  Arto Visala,et al.  Quality assurance in bioprocesses by model based fault diagnosis and state estimation , 1996 .

[4]  Arto Visala,et al.  Wiener-NN models and robust identification , 1999, IJCNN'99. International Joint Conference on Neural Networks. Proceedings (Cat. No.99CH36339).

[5]  Stephen A. Billings,et al.  Non-linear system identification using neural networks , 1990 .

[6]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[7]  B. Bavarian,et al.  Introduction to neural networks for intelligent control , 1988, IEEE Control Systems Magazine.

[8]  M. Schetzen The Volterra and Wiener Theories of Nonlinear Systems , 1980 .

[9]  Pierre Roussel-Ragot,et al.  Training recurrent neural networks: why and how? An illustration in dynamical process modeling , 1994, IEEE Trans. Neural Networks.

[10]  J. Calvin Giddings,et al.  Unified Separation Science , 1991 .

[11]  Lennart Ljung,et al.  Nonlinear black-box modeling in system identification: a unified overview , 1995, Autom..

[12]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.

[13]  Paul W. Broome,et al.  Discrete Orthonormal Sequences , 1965, JACM.

[14]  Vasilis Z. Marmarelis,et al.  Volterra models and three-layer perceptrons , 1997, IEEE Trans. Neural Networks.

[15]  N. V. Bhat,et al.  Use of neural nets for dynamic modeling and control of chemical process systems , 1990 .

[16]  N. Wiener,et al.  Nonlinear Problems in Random Theory , 1964 .

[17]  B. Wahlberg System identification using Laguerre models , 1991 .

[18]  A. G. Ivakhnenko,et al.  Polynomial Theory of Complex Systems , 1971, IEEE Trans. Syst. Man Cybern..

[19]  Andrew R. Barron,et al.  Universal approximation bounds for superpositions of a sigmoidal function , 1993, IEEE Trans. Inf. Theory.

[20]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[21]  Bo Wahlberg,et al.  On approximation of stable linear dynamical systems using Laguerre and Kautz functions , 1996, Autom..

[22]  A. Halme,et al.  Generalized polynomial operators for nonlinear systems analysis , 1972 .

[23]  A. J. Krijgsman,et al.  System Identification with Orthogonal Basis Functions and Neural Networks , 1996 .

[24]  Arto Visala,et al.  Wiener Type SOM- and MLP-classifiers for Recognition of Dynamic Modes , 1997, ICANN.

[25]  Bernard Delyon,et al.  Nonlinear black-box models in system identification: Mathematical foundations , 1995, Autom..