[Back]

C. Gasser, C. Bucher:
"An improved strategy for using asymptotic sampling for reliability analysis";
Talk: 2016 EMI International Conference (EMI IC 2016), Metz, France; 2016-10-25 - 2016-10-27.

Reliability of high-dimensional nonlinear systems can be analysed by applying Monte Carlo simulation. Whereas the computational effort of crude Monte Carlo is not adversely affected by the dimensionality of the problem, it becomes prohibitively large when very small failure probabilities are to be calculated. For example, for a failure probability of , the number of samples should be at least to obtain enough failures.
A recently developed method to overcome these deficiencies is the so-called asymptotic sampling. The method aims at obtaining more failures by artificially increasing the variance of the basic variables. Asymptotic properties of the reliability index regarding the scaling of the basic variables are exploited to construct a regression model which allows to determine the reliability index for extremely small failure probabilities.
Efficiency and accuracy of asymptotic sampling depend on the supporting points of the regression model. These supporting points basically represent scaled safety indices for scaled systems; i.e., modifications of the original system with increased variances of the variables.
A strategy is presented for the optimal choice of the number and positions of supporting points. An extrapolation algorithm is shown which allows an unbiased prediction of the reliability index with high precision using a moderate number of Monte Carlo samples. Furthermore, a new technique is presented for stabilising supporting points by employing the CDF of the safety margin obtained from the Monte Carlo samples.
It is shown that the proposed strategy is suitable for a broad spectrum of applications, especially, also for nonlinear systems and for a diversity of excitations. Advantages of using low discrepancy sampling as well as its application limits are discussed.

Asymptotic sampling, Structural reliability, Reliability index, Failure probability, Computational stochastic analysis