Novel design of weighted differential evolution for parameter estimation of Hammerstein-Wiener systems

Abstract

Introduction: Knacks of evolutionary computing paradigm-based heuristics has been exploited exhaustively for system modeling and parameter estimation of complex nonlinear systems due to their legacy of reliable convergence, accurate performance, simple conceptual design ease implementation ease and wider applicability. Objectives: The aim of the presented study is to investigate in evolutionary heuristics of weighted differential evolution (WDE) to estimate the parameters of Hammerstein-Wiener model (HWM) along with comparative evaluation from state-of-the-art counterparts. The objective function of the HWM for controlled autoregressive systems is efficaciously formulated by approximating error in mean square sense by computing difference between true and estimated parameters. Methods: The adjustable parameters of HWM are estimated through heuristics of WDE and genetic algorithms (GAs) for different degrees of freedom and noise levels for exhaustive, comprehensive, and robust analysis on multiple autonomous trials. Results: Comparison through sufficient large number of graphical and numerical illustrations of outcomes for single and multiple execution of WDE and GAs through different performance measuring metrics of precision, convergence and complexity proves the worth and value of the designed WDE algorithm. Statistical assessment studies further prove the efficacy of the proposed scheme. Conclusion: Extensive simulation based experimentations on measure of central tendency and variance authenticate the effectiveness of the designed methodology WDE as precise, efficient, stable, and robust computing platform for system identification of HWM for controlled autoregressive scenarios.

Keywords

• Hammerstein-Wiener system
• Parameter estimation
• Evolutionary heuristics
• Weighted differential evolution
• Genetic algorithms