Quantum mechanics

Algorithm

Engineering

Reliability engineering

Uncertainty quantification

Statistics

Importance sampling

Power (physics)

Computer science

Mathematical optimization

Probability distribution

Physics

Parameterized complexity

Rare events

Mathematics

Estimator

Electronic engineering

Stochastic simulation

Reliability (semiconductor)

Sensitivity (control systems)

Monte Carlo method

Machine learning

Mechanical Systems and Signal Processing

Structural reliability analysis for rare failure events in the presence of hybrid uncertainties is a challenging task drawing increasing attentions in both academic and engineering fields. Based on the new imprecise stochastic simulation framework developed in the companion paper, this work aims at developing efficient methods to estimate the failure probability functions subjected to rare failure events with the hybrid uncertainties being characterized by imprecise probability models. The imprecise stochastic simulation methods are firstly improved by the active learning procedure so as to reduce the computational costs. For the more challenging rare failure events, two extended subset simulation based sampling methods are proposed to provide better performances in both local and global parameter spaces. The computational costs of both methods are the same with the classical subset simulation method. These two methods are also combined with the active learning procedure so as to further substantially reduce the computational costs. The estimation errors of all the methods are analyzed based on sensitivity indices and statistical properties of the developed estimators. All these new developments enrich the imprecise stochastic simulation framework. The feasibility and efficiency of the proposed methods are demonstrated with numerical and engineering test examples.

Non-intrusive stochastic analysis with parameterized imprecise probability models: II. Reliability and rare events analysis