Modeling and Identification of Discrete Second-Order Systems via Stochastic Mechanics

Abstract

For a class of second-order mechanical or structural systems subjected to random disturbances, their discrete-time models are derived. Since the output of stochastic system is random and has no longer its velocity in the ordinary sense, the notion of the Nelson process which is a stochastic process having forward and backward mean velocities is introduced to describe the action integral. Then the stochastic version of the Euler-Lagrange equation is derived from the Hamilton's principle. The discrete-time second-order model is obtained by discretizing the stochastic Euler-Lagrange equation and/or Hamilton's principle. The structural matrices are identified using the discrete second-order model.