Time Dependent Reliability Analysis of Vibratory Systems With Random Parameters

Abstract

The field of random vibrations of largescale systems with millions of degreesoffreedom (DOF) is of significant importance in many engineering disciplines. In this paper, we propose a method to calculate the timedependent reliability of linear vibratory systems with random parameters excited by nonstationary Gaussian processes. The approach combines principles of random vibrations, the total probability theorem, and recent advances in timedependent reliability using an integral equation involving the upcrossing and joint upcrossing rates. A spacefilling design, such as optimal symmetric Latin hypercube (OSLH) sampling, is first used to sample the input parameter space. For each design point, the corresponding conditional timedependent probability of failure is calculated efficiently using random vibrations principles to obtain the statistics of the output process and an efficient numerical estimation of the upcrossing and joint upcrossing rates. A timedependent metamodel is then created between the input parameters and the output conditional probabilities allowing us to estimate the conditional probabilities for any set of input parameters. The total probability theorem is finally applied to calculate the timedependent probability of failure. The proposed method is demonstrated using a vibratory beam example.