Importance Sampling Technique for Simulating Time Histories for Efficient Rainflow Fatigue Analysis

Abstract

Frequency domain analysis of a dynamical system yields the response spectral density. There are many spectral fatigue methods for evaluating the mean fatigue damage from a stress spectrum, but they are only approximate. The only accurate method is to simulate the time history from the spectrum, succeeded by rainflow counting. However, this procedure is time-consuming because of the need for numerous realizations to achieve statistical convergence, making it incompatible with the high efficiency of frequency domain analysis. To overcome the slow convergence rate of conventional Monte Carlo simulation (MCS), this paper proposes an efficient simulation approach, which to date, appears to be the first of its kind for such an application. The proposed approach reduces the variance of the fatigue damage samples by invoking the technique of importance sampling, and entails only the coefficient of variation (CoV) of the damage to construct the importance sampling density. The CoV can be estimated initially using an analytical approach, and subsequently updated adaptively. The proposed approach is implemented on a diversity of spectral shapes, and is found to provide a substantial computational advantage over MCS.