Identification of Wiener Model with Internal Noise Using a Cubic Spline Approximation-Bayesian Composite Quantile Regression Algorithm

A cubic spline approximation-Bayesian composite quantile regression algorithm is proposed to estimate parameters and structure of the Wiener model with internal noise. Firstly, an ARX model with a high order is taken to represent the linear block; meanwhile, the nonlinear block (reversibility) is approximated by a cubic spline function. Then, parameters are estimated by using the Bayesian composite quantile regression algorithm. In order to reduce the computational burden, the Markov Chain Monte Carlo algorithm is introduced to calculate the expectation of parameters’ posterior distribution. To determine the structure order, the Final Output Error and the Akaike Information Criterion are used in the nonlinear block and the linear block, respectively. Finally, a numerical simulation and an industrial case verify the effectiveness of the proposed algorithm.