An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems

A survey of nonlinear system identification algorithms and related topics is presented by extracting significant results from the literature and presenting these in an organised and systematic way. Algorithms based on the functional expansions of Wiener and Volterra, the identification of block-oriented and bilinear systems, the selection of input signals, structure detection, parameter estimation and recent results from catastrophe theory and included. The limitations, relationships and applicability of the methods are discussed throughout.

Identification of Nonlinear Systems- A Survey

An optimal two-stage identification algorithm is presented for Hammerstein–Wiener systems where two static nonlinear elements surround a linear block. The proposed algorithm consists of two steps: The first one is the recursive least squares and the second one is the singular value decomposition of two matrices whose dimensions are fixed and do not increase as the number of the data point increases. Moreover, the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise.

An Optimal Two-stage Identification Algorithm for Hammerstein―Wiener Nonlinear Systems

Identification of Hammerstein nonlinear ARMAX systems

Precise dynamic models of processes are required for many applications, ranging from control engineering to the natural sciences and economics. Frequently, such precise models cannot be derived using theoretical considerations alone. Therefore, they must be determined experimentally. This book treats the determination of dynamic models based on measurements taken at the process, which is known as system identification or process identification. Both offline and online methods are presented, i.e. methods that post-process the measured data as well as methods that provide models during the measurement. The book is theory-oriented and application-oriented and most methods covered have been used successfully in practical applications for many different processes. Illustrative examples in this book with real measured data range from hydraulic and electric actuators up to combustion engines. Real experimental data is also provided on the Springer webpage, allowing readers to gather their first experience with the methods presented in this book. Among others, the book covers the following subjects: determination of the non-parametric frequency response, (fast) Fourier transform, correlation analysis, parameter estimation with a focus on the method of Least Squares and modifications, identification of time-variant processes, identification in closed-loop, identification of continuous time processes, and subspace methods. Some methods for nonlinear system identification are also considered, such as the Extended Kalman filter and neural networks. The different methods are compared by using a real three-mass oscillator process, a model of a drive train. For many identification methods, hints for the practical implementation and application are provided. The book is intended to meet the needs of students and practicing engineers working in research and development, design and manufacturing.

Identification of Dynamic Systems: An Introduction with Applications

A noniterative method developed by Hsia for the particular case where the transfer function in the Hammerstein model has no zeros is extended to the general case where the transfer function may have zeros. Numerical examples show that the computation time by this method is considerably less than by the iteratire procedure proposed by Narendra and Gallman while the accuracy of the estimates is comparable.

F. Chang

Papers

A noniterative method for identification using Hammerstein model