An island particle algorithm for rare event analysis

• Estimation of the law of random phenomena that leads to critical events.
• Presentation of two algorithms to estimate this kind of targeted laws derived from the PMCMC and the SMC2.
• Application on different realistic aerospace test cases.

Estimating rare event probability with accuracy is of great interest for safety and reliability applications. In this paper, we focus on rare events which can be modeled by a threshold exceedance of a deterministic input–output function with random inputs. Some parameters of this function or density parameters of input random variables may be fixed by an experimenter for simplicity reasons. From a risk analysis point of view, it is not only interesting to evaluate the probability of a critical event but it is also important to determine the impact of such tuning of parameters on the realization of a critical event, because a bad estimation of these parameters can strongly modify rare event probability estimations. In the present paper, we present an example of island particle algorithm referred to as sequential Monte Carlo square (SMC2). This algorithm gives an estimate of the law of random phenomena that leads to critical events. The principles of this statistical technique are described throughout this article and its results are analysed on different realistic aerospace test cases.