Linear Stochastic Dynamical System under Uncertain Load: Inverse Reliability Analysis

Abstract

The reliability of a linear dynamical system driven by a partially known Gaussian load process, specified only through its total average energy, is studied. A simple dynamic parallel and series system reliability network is investigated for the failure analysis using the crossing theory of stochastic processes. The critical input power spectral density of the load process which maximizes the mean crossing rate of a parallel or series system network emerges to be fairly narrow banded and hence fails to represent the erratic nature of the random input realistically. Consequently, a tradeoff curve between the maximum mean crossing rate of the reliability network and the disorder in the input, quantitatively measured through its entropy rate, is generated. Mathematically, the generation of the tradeoff curve of nondominated solutions, known as the Pareto optimal set, leads to a nonlinear, nonconvex, and multicriteria optimization problem with conflicting objectives. A recently developed Pareto optimization te...