Importance sampling for first passage problems of nonlinear structures

This article deals with reliability assessment of mechanical structures subjected to random excitation. The probability of failure is formulated as first passage probability of a given threshold within the observation period. A solution for arbitrary structures exhibiting nonlinear behaviour can be obtained by the Monte Carlo simulation. In order to reduce the sample size, an importance sampling concept is proposed, which automatically adapts the simulation densities in two subsequent simulation runs. The excitation process is simulated by the so-called spectral representation method, where the random variables are the amplitudes and phase angles of a Fourier series expansion. It is proposed to adapt the simulation densities of the amplitudes with respect to the power spectral density of the observed structural response. An example demonstrates the applicability of the procedure.