Assessment of low probability events of dynamical systems by controlled Monte Carlo simulation

Various procedures to extend the applicability and to increase the efficiency of Monte Carlo simulation (MCS) for the analysis of complex dynamical systems are discussed. In particular, the capabilities of the methods denoted Russian Roulette and Splitting (RR&S) and Double and Clump (D&C) are reviewed with regard to their capabilities to analyze such systems. In this context, the difficulties in identifying the `importantʹ regions for simulation are detailed. It is shown that these difficulties may be circumvented by a newly introduced `distance controlledʹ MCS. This procedure, which allows the prediction of very low probability events and the analysis of systems of higher dimension, is applicable not only to mechanical systems and structures but also to complex dynamical systems encountered, for example, in economics, physics, etc. The procedure is shown to be particularly suited to cases where exact analytical methods and direct Monte Carlo simulation are infeasible, hence, being well suited for practical application.