Markov chain simulation for fast evaluation of failure probability

Based on fast Markov chain simulation for the samples distributed in failure region, an evaluation method was presented for fast evaluation of the small Failure Probability (FP) with nonlinear limit state equation (LSE). The small FP of non-linear LSE was transformed into a product of the FP of the linear LSE and a feature ratio factor, which was the basic concept of the presented method. The linear LSE was obtained by the samples distributed in the failure region of the non-linear LSE and generated by the fast Markov chain simulation. The linear LSE and the non-linear one have the same maximum likelihood points in the failure regions. The feature ratio factor was computed by means of multiplicative rule of probability; it exposed the relation between the FP of the non-linear LSE and that of the linear LSE. Since the FP of the linear LSE can be calculated analytically and accurately, and the feature ratio factor can fast be computed by the samples distributed in the failure regions of the non-linear LSE and of the linear LSE, the presented method possesses high precision and high efficiency. These advantages were demonstrated by the given examples.