Overview of Structural Reliability Analysis Methods — Part II : Sampling Methods

Abstract

ABSTRACT. In Part II of the overview of structural reliability analysis methods, the category of sampling methods is reviewed. The basic Monte Carlo simulation is the foundation for sampling methods of reliability analysis. Sampling methods can evaluate the failure probability defined by both explicit and implicit performance function. With sufficient number of samples, simulation methods can give accurate results. However, for complex problem the computational cost is expensive. Thus, based on variance reduction techniques, some variants of basic Monte Carlo simulation method are proposed to reduce the computational cost. Monte Carlo simulation and its variants, including importance sampling, adaptive sampling, Latin hypercube sampling, directional simulation, and subset simulation, are presented and summarized in this paper.

Calibration and validation of fatigue design models for railway car bodies considering uncertainty

“…For the reliability analysis, sampling methods are applied. 48 The commonly used Monte-Carlo sampling covers the complete range of the input parameters and allows evaluating the mean value and variance of the life span distribution. The failure probability PðFÞ that the life span is below the required value l target , thus PðFÞ ¼ Pðl < l target Þ, is given by the fraction of samples for which l < l target corresponding to the P-th percentile of the distribution.…”

“…49 In order to obtain a more precise estimation of the failure probability, adapted sampling methods exist, which focus on the distribution around the failure probability. The subset sampling 48 transforms the computation of the rare failure probability into a series of more frequent failure events using conditional probabilities. By using importance sampling, 50 a larger fraction of samples is situated in the region of the failure probability.…”

Effect of shape factor on structural reliability analysis of a surface cracked pipeline-parametric study

“…3 shows the design point in the normal space witch accomplish the criterion of highest probability density. This point is situated on the limit state function and has the smallest distance to the origin of normal space [15]. The key aspect of the method is to define the design point using First Order Reliability Method "FORM".…”

Performance-Based Analysis in Civil Engineering: Overview of Applications

“…This can be expensive and time-consuming for problems with implicit limit state functions or where failure probability is low. Further details on the preceding analytical and numerical reliability methods can be found in the literature, see for example [162][163][164]. Note that MC simulation has also been used to verify PBA analytical tools.…”