This paper reviews the mathematical foundation of the importance sampling technique and
discusses two general classes of methods to construct the importance sampling density (or …

Monte Carlo methods have attracted constant and even increasing attention in structural
reliability analysis with a wide variety of developments seamlessly presented over decades …

Active learning methods have recently surged in the literature due to their ability to solve
complex structural reliability problems within an affordable computational cost. These …

The main task of structural reliability analysis is to estimate failure probability of a studied
structure taking randomness of input variables into account. To consider structural behavior …

Structural reliability analysis is typically evaluated based on a multivariate function that
describes underlying failure mechanisms of a structural system. It is necessary for a …

With complex performance functions and time-demanding computation of structural
responses, the estimation of small failure probabilities is a challenging problem in …

Polynomial chaos expansions (PCE) have seen widespread use in the context of uncertainty
quantification. However, their application to structural reliability problems has been hindered …

The reliability analysis of complex structures usually involves implicit performance function
and expensive-to-evaluate computational models, which pose a great challenge for the …

Assessing rare event probabilities still suffers from its computational cost despite some
available methods widely accepted by researchers and engineers. For low to moderately …

The ever-increasing complexity of numerical models and associated computational
demands have challenged classical reliability analysis methods. Surrogate model-based …