Combined Parametric-Nonparametric Identification of by Grzegorz Mzyk PDF

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By Grzegorz Mzyk

ISBN-10: 3319035959

ISBN-13: 9783319035956

ISBN-10: 3319035967

ISBN-13: 9783319035963

This booklet considers an issue of block-oriented nonlinear dynamic process id within the presence of random disturbances. This category of structures contains numerous interconnections of linear dynamic blocks and static nonlinear parts, e.g., Hammerstein process, Wiener approach, Wiener-Hammerstein ("sandwich") approach and additive NARMAX platforms with suggestions. Interconnecting indications aren't obtainable for size. The mixed parametric-nonparametric algorithms, proposed within the ebook, could be chosen dependently at the earlier wisdom of the approach and indications. such a lot of them are according to the decomposition of the advanced procedure id job into less complicated neighborhood sub-problems by utilizing non-parametric (kernel or orthogonal) regression estimation. within the parametric level, the generalized least squares or the instrumental variables process is usually utilized to deal with correlated excitations. restrict homes of the algorithms were proven analytically and illustrated in easy experiments.

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10. e. the estimate cN0 ,M converges to c∗ in the same sense and with the same guaranteed speed as RM (u) to R(u). 8. We confined ourselves to the convergence in probability as such particular type of convergence has been widely examined in the literature concerning non-parametric estimation of nonlinearities (regression functions) for Hammerstein systems (see [40], [48], [49]).

006ε2max , computed according to the rule recommended in [49] (see Section 8, p. 145 there). 75. 36 = (2M ) . e. N = (2M ) each number M of data the experiment was repeated P = 10 times, and accuracy of the estimates cN0 ,M and γN,M was evaluated using the average relative estimation error δθ (N, M ) = (1/P ) P p=1 (p) θˆN,M − θ 2 / θ 2 2 2 ·100%, where (p) θˆN,M is the estimate of θ ∈ {c, γ} obtained in the pth run, and · 2 is the Euclidean vector norm. Exemplary results of two-stage identification of the nonlinear static characteristic for M = 100 and M = 500 measurement data and N SR = 5%, along with the true characteristic and the ’data’ points 0 =4 {(un , wn,M )}N n=1 (bold-faced) computed in Stage 1 by the kernel method, are visualized for a single trial in Fig.

The conditions (a) and (b) require in fact the elements of ΨN be correlated with inputs and simultaneously not correlated with the noise {z k }. g. e. g. [127], [128], [129]. 28). 28). , wk−s−p,M ) . 6. , u2−s−p ......................................... e. , s + p} required for the identification of linear dynamics. Further, {(uk , yk )}N k=1 (corresponding to r = 0) constitute first part of the data colN , used for nonparametric estimation of wk−r ’s lection {(uk , yk )}M k=1 , M in Stage 1. The time instant index k = 1 is, by assumption, attributed to the beginning of recording the input-output data employed to this end.

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Combined Parametric-Nonparametric Identification of Block-Oriented Systems by Grzegorz Mzyk

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