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Über dieses Buch

The purpose of this volume is to provide a brief review of the previous work on model reduction and identifi cation of distributed parameter systems (DPS), and develop new spatio-temporal models and their relevant identifi cation approaches.

In this book, a systematic overview and classifi cation on the modeling of DPS is presented fi rst, which includes model reduction, parameter estimation and system identifi cation. Next, a class of block-oriented nonlinear systems in traditional lumped parameter systems (LPS) is extended to DPS, which results in the spatio-temporal Wiener and Hammerstein systems and their identifi cation methods. Then, the traditional Volterra model is extended to DPS, which results in the spatio-temporal Volterra model and its identification algorithm. All these methods are based on linear time/space separation. Sometimes, the nonlinear time/space separation can play a better role in modeling of very complex processes.

Thus, a nonlinear time/space separation based neural modeling is also presented for a class of DPS with more complicated dynamics. Finally, all these modeling approaches are successfully applied to industrial thermal processes, including a catalytic rod, a packed-bed reactor and a snap curing oven. The work is presented giving a unifi ed view from time/space separation. The book also illustrates applications to thermal processes in the electronics packaging and chemical industry. This volume assumes a basic knowledge about distributed parameter systems, system modeling and identifi cation. It is intended for researchers, graduate students and engineers interested in distributed parameter systems, nonlinear systems, and process modeling and control.

Inhaltsverzeichnis

Frontmatter

Introduction

Abstract
This chapter is an introduction of the book. Starting from typical examples of distributed parameter systems (DPS) encountered in the real-world, it briefly introduces the background and the motivation of the research, and finally the contributions and organization of the book.
Han-Xiong Li, Chenkun Qi

Modeling of Distributed Parameter Systems: Overview and Classification

Abstract
This chapter provides a systematic overview of the distributed parameter system (DPS) modeling and its classification. Three different problems in DPS modeling are discussed, which includes model reduction for known DPS, parameter estimation for DPS, and system identification for unknown DPS. All approaches are classified into different categories with their limitations and advantages briefly discussed. This overview motivates us to develop new methods for DPS modeling.
Han-Xiong Li, Chenkun Qi

Spatio-Temporal Modeling for Wiener Distributed Parameter Systems

Abstract
For Wiener distributed parameter systems (DPS), a spatio-temporal Wiener model (a linear DPS followed by a static nonlinearity) is constructed in this chapter. After the time/space separation, it can be represented by the traditional Wiener system with a set of spatial basis functions. To achieve a low-order model, the Karhunen-Loève (KL) method is used for the time/space separation and dimension reduction. Finally, unknown parameters of the Wiener system are estimated with the least-squares estimation and the instrumental variables method to achieve consistent estimation under noisy measurements. The simulation on the catalytic rod and the experiment on snap curing oven are presented to illustrate the effectiveness of this modeling method.
Han-Xiong Li, Chenkun Qi

Spatio-Temporal Modeling for Hammerstein Distributed Parameter Systems

Abstract
A spatio-temporal Hammerstein modeling approach is presented in this chapter. To model the nonlinear distributed parameter system (DPS), a spatio-temporal Hammerstein model (a static nonlinearity followed by a linear DPS) is constructed. After the time/space separation, it can be represented by the traditional Hammerstein system with a set of spatial basis functions. To achieve a low-order model, the Karhunen-Loève (KL) method is used for the time/space separation and dimension reduction. Then a compact Hammerstein model structure is determined by the orthogonal forward regression, and their unknown parameters are estimated with the least-squares method and the singular value decomposition. The simulation and experiment are presented to show the effectiveness of this spatio-temporal modeling method.
Han-Xiong Li, Chenkun Qi

Multi-channel Spatio-Temporal Modeling for Hammerstein Distributed Parameter Systems

Abstract
A multi-channel spatio-temporal Hammerstein modeling approach is presented in this chapter. As a special case of the model described in Chapter 4, a spatio-temporal Hammerstein model is constructed with a static nonlinearity followed by a linear spatio-temporal kernel. When the model structure is matched with the system, a basic single-channel identification algorithm with the algorithm used in the Chapter 4 can work well. When there is unmodeled dynamics, a multi-channel modeling framework can provide a better performance, because more channels used can attract more information from the process. The modeling convergence can be guaranteed under noisy measurements. The simulation example and the experiment on snap curing oven are presented to show the effectiveness of this modeling method.
Han-Xiong Li, Chenkun Qi

Spatio-Temporal Volterra Modeling for a Class of Nonlinear DPS

Abstract
To model the nonlinear distributed parameter system (DPS), a spatio-temporal Volterra model is presented with a series of spatio-temporal kernels. It can be considered as a nonlinear generalization of Green’s function or a spatial extension of the traditional Volterra model. To obtain a low-order model, the Karhunen-Loève (KL) method is used for the time/space separation and dimension reduction. Then the model can be estimated with a least-squares algorithm with the convergence guaranteed under noisy measurements. The simulation and experiment are conducted to demonstrate the effectiveness of the presented modeling method.
Han-Xiong Li, Chenkun Qi

Nonlinear Dimension Reduction Based Neural Modeling for Nonlinear Complex DPS

Abstract
A nonlinear principal component analysis (NL-PCA) based neural modeling approach is presented for a lower-order or more accurate solution for nonlinear distributed parameter systems (DPS). One NL-PCA network is trained for the nonlinear dimension reduction and the nonlinear time/space reconstruction. The other neural model is to learn the system dynamics with a linear/nonlinear separated model structure. With the powerful capability of dimension reduction and the intelligent learning, this approach can model the nonlinear complex DPS with much more complexity. The simulation on the catalytic rod and the experiment on the snap curing oven will demonstrate the effectiveness of the presented method.
Han-Xiong Li, Chenkun Qi

Conclusions

Abstract
This chapter summarizes all the methods introduced in the book, and discusses future challenges in this area.
Han-Xiong Li, Chenkun Qi

Backmatter

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