By Andrzej Janczak
This monograph systematically provides the prevailing id tools of nonlinear platforms utilizing the block-oriented technique It surveys a variety of recognized methods to the id of Wiener and Hammerstein structures that are appropriate to either neural community and polynomial versions. The e-book supplies a comparative learn in their gradient approximation accuracy, computational complexity, and convergence premiums and moreover offers a few new and unique equipment about the version parameter adjusting with gradient-based thoughts. "Identification of Nonlinear platforms utilizing Neural Networks and Polynomal types" comes in handy for researchers, engineers and graduate scholars in nonlinear structures and neural community thought.
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Extra info for Identification of Nonlinear Systems Using Neural Networks and Polynomial Models: A Block-Oriented Approach
The recursive least squares scheme is used in the orthonormal basis functionbased identiﬁcation method proposed by Marciak et al. . They use a noninverted model of the linear system composed of Laguerre ﬁlters and an inverse polynomial model of the nonlinear element. In the frequency approach to the identiﬁcation of Wiener systems of Bai , the phase estimate of the linear dynamic system output is determined based on the discrete Fourier transform (DFT) of the ﬁltered system output. Having the phase estimate, the structure of nonlinearity can be determined from the graph of the system output versus an estimated linear dynamic system output and approximated by a polynomial.
Due to output error formulation of the prediction error, parallel Wiener models are also useful for the identiﬁcation of systems disturbed additively by the white output noise. 2. 3. 4 contains details of diﬀerent gradient calculation algorithms and an analysis of gradient computation accuracy with the truncated BPTT method. 6 to compare the convergence rates of the algorithms. 7. 8 summarizes the essential results. 2 Problem formulation Consider a two-block structure composed of a linear dynamic system and a static nonlinear element in a cascade, referred to as the SISO Wiener system – Fig.
To achieve a signiﬁcantly higher convergence rate, higher order approximations of the cost function should be used. Examples of such learning techniques are the Levenberg-Marquard method, quasi-Newton methods, conjugate gradient methods [68, 123], and the RLS learning algorithms . To extract information from the training data and increase the the eﬀectiveness of learning, some data preprocessing such as ﬁltering, removing redundancy, and removing outliers is usually necessary. 18 1 Introduction Also, scaling the data is essential to make learning algorithms robust and decrease the learning time.
Identification of Nonlinear Systems Using Neural Networks and Polynomial Models: A Block-Oriented Approach by Andrzej Janczak