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

Summary 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.