Data-driven statistical nonlinearization technique based on information entropy

Abstract

For a given nonlinear stochastic system, an exact stationary probability density function, which is important for system response prediction and control, is not always available. Owing to the development of various sensors and measurement systems, data acquisition and processing have become increasingly convenient. Inspired by traditional statistical nonlinearization techniques and measured data, a data-driven statistical nonlinearization technique was developed in this study based on information entropy. First, a class of appropriate equivalent systems with exact solutions was selected. Subsequently, the optimal parameters of the equivalent systems were determined based on the minimization of the Shannon information entropy and some statistical moments of the system state from the measured data. The derivation of the optimal parameters of the equivalent systems was then converted into an extremum problem of the entropy function of several variables. Finally, three typical nonlinear stochastic systems were presented to illustrate and validate the effectiveness and accuracy of the proposed procedure. The proposed data-driven statistical nonlinearization technique can be used to provide more comprehensive information on the system response, which is important for system response evaluation and control.