Identification of Wiener systems based on the variable forgetting factor multierror stochastic gradient and the key term separation

Abstract

The identification of Wiener systems is very difficult because of the output nonlinearity and the parameter product term. To identify the Wiener system, a novel stochastic gradient algorithm based on the multierror and the key term separation is proposed. Firstly, the Wiener system is parameterized as a pseudo-linear model to avoid the products of the parameters. Secondly, a parzen window is used to estimate the probability density function of the error. Thirdly, a stochastic information gradient algorithm with the multierror is adopted to estimate the parameters. The multierror takes the place of the scalar error by the stacked error, which accelerates the algorithm greatly. Fourthly, a variable forgetting factor considering errors is integrated to further speed the algorithm up. Finally, the proposed algorithm is validated by a numerical example and an industrial case. The estimation results indicate that the proposed algorithm can obtain accurate estimates with fast convergence speed.

Identification of series–parallel systems composed of linear and nonlinear blocks

“…Several studies have been focused on the identification of nonlinear systems constituted by the series connection of linear and nonlinear blocks 4,5 . Most papers on nonlinear system identification have addressed the problem of Wiener and Hammerstein models 6–11 . The problem has been addressed following several approaches and methods, for example, stochastic methods, 12–14 deterministic recursive techniques, 15 frequency methods 16,17 …”

“…4,5 Most papers on nonlinear system identification have addressed the problem of Wiener and Hammerstein models. [6][7][8][9][10][11] The problem has been addressed following several approaches and methods, for example, stochastic methods, [12][13][14] deterministic recursive techniques, 15 frequency methods. 16,17 To increase modeling capability, more complex models have been proposed involving parallel connections.…”

Bias compensated stochastic gradient algorithm for identification of an ARX‐type nonlinear rational model and its application in modeling of the dynamic of the cellular toxicity

“…To decrease the complexity, the stochastic gradient (SG) algorithm is an alternative because it costs only flops each iteration 29,30 . There are many gradient‐based algorithms, such as information gradient algorithms and accelerated gradient algorithms 31‐34 . Among these algorithms, a key term separation gradient iterative algorithm was derived to identify a fractional‐order nonlinear system, 30 a recursive gradient algorithm was proposed to estimate the nonlinear parameters using multifrequency sine signals, 35 a maximum likelihood gradient iterative algorithm was developed for identifying the parameters of bilinear systems, 36 a gradient‐based recursive least squares estimator was applied in the model‐free extremum seeking control 37 …”

“…29,30 There are many gradient-based algorithms, such as information gradient algorithms and accelerated gradient algorithms. [31][32][33][34] Among these algorithms, a key term separation gradient iterative algorithm was derived to identify a fractional-order nonlinear system, 30 a recursive gradient algorithm was proposed to estimate the nonlinear parameters using multifrequency sine signals, 35 a maximum likelihood gradient iterative algorithm was developed for identifying the parameters of bilinear systems, 36 a gradient-based recursive least squares estimator was applied in the model-free extremum seeking control. 37 However, the estimate for the NRM given by the traditional SG algorithm is biased because the output y(k) in the information vector is correlated to the noise v(k) (see Equation (6) for detail).…”

Iterative parameter identification algorithms for the generalized time‐varying system with a measurable disturbance vector

“…The measurable disturbance can be a function of the system load in the thermal power plant temperature control system or a function of excitation current in the DC variable speed motor system. 20 Many identification methods were proposed for generalized time-varying systems with white noises, [21][22][23] Ding et al proposed the least squares identification method for generalized time-varying systems. 24 The recursive identification and the iterative identification are two important branch of parameter estimation methods.…”