Time Dependent Reliability Analysis Using the Total Probability Theorem

Abstract

A new reliability analysis method is proposed for timedependent problems with explicit in time limitstate functions of input random variables and input random processes using the total probability theorem and the concept of composite limit state. The input random processes are assumed Gaussian. They are expressed in terms of standard normal variables using a spectral decomposition method. The total probability theorem is employed to calculate the timedependent probability of failure using timedependent conditional probabilities which are computed accurately and efficiently in the standard normal space using the firstorder reliability method (FORM) and a composite limit state of linear instantaneous limit states. If the dimensionality of the total probability theorem integral is small, we can easily calculate it using Gauss quadrature numerical integration. Otherwise, simple Monte Carlo simulation (MCS) or adaptive importance sampling are used based on a Kriging metamodel of the conditional probabilities. An example from the literature on the design of a hydrokinetic turbine blade under timedependent river flow load demonstrates all developments.