An numerical procedure of evaluating approximately first passage probabilities of discrete linear and nonlinear MDOF systems subjected to non-stationary random loading is presented. The procedure is based on advanced Monte Carlo simulation techniques such as "Double and Clump" and "Splitting and Russian Roulette". The basic algorithms of both procedures are introduced briefly. In a next step one of the procedures is verified by comparing the results obtained by utilizing Double & Clump with available analytical solutions. In a final step, the applicability to a hysteretic MDOF system is demonstrated.
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