Stochastic Linearization by Data Dependent Systems

Abstract

The paper presents and illustrates a method of stochastic linearization of nonlinear systems. The system response to white noise excitation is modeled by a differential equation, which provides the necessary transfer function. The linearization is optimal in the mean squared sense within the statistical limits imposed by the response. Since the linearization is accomplished purely from the response data, governing equations of the system need not be known. An application to machine tool chatter vibrations illustrates stability assessment and modal analysis. The ease with which optimal prediction and control equations can be derived and implemented is shown by an application to blast furnace operation. Detection and verification of limit cycles are illustrated by a model for airline passenger ticket sales data.