An intuitive basis of the probability density evolution method (PDEM) for stochastic dynamics

Abstract

The recently developed Probability Density Evolution Method (PDEM) is described in intuitive terms in order to permit a better understanding and wider application of the PDEM in practical engineering problems, particularly for assessing the risk and reliability of large and complex engineering systems. In implementation, the PDEM is similar, in a limited sense, to the basic Monte Carlo simulation (MCS) in that it also requires deterministic response solutions of a system. However, in principle and in theory it is very different from the MCS. The practical effectiveness of the PDEM is emphasized and illustrated.