Integrating subset simulation with probabilistic re-analysis to estimate reliability of dynamic systems

It is often expensive to estimate the failure probability of highly reliable systems by Monte Carlo simulation. Subset Simulation breaks the original problem of estimating a small probability into the estimation of a sequence of large conditional probabilities, which is more efficient. The conditional probabilities are estimated by Markov Chain simulation. Uncertainty in the power spectral density of the excitation makes it necessary to re-evaluate the reliability for many power spectral densities that are consistent with the evidence about the system excitation. Subset Simulation is more efficient than Monte Carlo simulation, but still requires a new simulation for each admissible power spectral density. This paper presents an efficient method to re-evaluate the reliability of a dynamic system under stationary Gaussian stochastic excitation for different load spectra. We accomplish that by re-weighting the results of a single Subset Simulation. This method is applicable to both linear and nonlinear systems provided that all of the spectra contain the same amount of energy. The authors are currently working on an extension of the method to nonlinear systems, even when the sampling and true power spectral density functions contain different amounts of energy.