On advanced Monte Carlo simulation procedures in stochastic structural dynamics

As analytical methods to predict the response of MDOF-systems under stochastic loading are quite limited, numerical procedures, such as Monte Carlo simulation techniques, are frequently applied. Direct Monte Carlo simulation, however, particularly for reliability analyses, is not suitable for providing sufficient information on the tails of the distribution of the response. In this paper Monte Carlo methods, applicable to Markov processes are further advanced, i.e. by leading the generated samples towards the low probability range which is practically not accessible by direct Monte Carlo methods. In this context, notions as developed for variance reduction techniques are introduced and discussed. Based on criteria denoting those realizations which lead most likely to failure, a numerical procedure called ''Double & Clump'' (D&C) is discussed briefly. It is shown that the rather numerically involved D&C procedure can be simplified by a technique known as ''Russian Roulette and Splitting'' (RR&S). In two numerical examples, both procedures D&C and RR&S are compared with direct Monte Carlo simulation as well as the Response Surface Method (RSM) demonstrating comparable accuracy. (C) 1997 Elsevier Science Ltd.