Systems of random differential equations and model reduction

Ralf Wunderlich

Habilitationsschrift, TU Chemnitz, 1999

Abstract :

This monograph is devoted to systems of ordinary differential equations with stationary random excitation terms. For stable linear systems as well as systems with polynomial nonlinearities the existence of stationary solutions and the computation of their distribution characteristics as second-order moment functions are considered. Such questions arise in the investigation of the long-time behaviour of the system response to permanently acting excitations. The results can be directly applied to discrete vibration systems with damping and an external random excitation.

The presented results are essentially based on the work of J. vom Scheidt and his research group on weakly correlated random functions and their application to random equations of mathematical physics. They can be considered as extensions and generalizations of the work on random vibration systems. In particular, such topics are chosen where the author himself contributed to the development: modeling of random excitations, higher-order expansions of correlation functions, systems with polynomial nonlinearities and model reduction. Several results have not been presented before.

The monograph is organized into 12 sections which form four chapters: