Sequential importance sampling for structural reliability analysis

TL;DR: In this paper , the authors discuss the mathematical foundation of the importance sampling technique and discuss two general classes of methods to construct the importance sample density (or probability measure) for reliability analysis, and explore the performances of the two classes of importance sampling methods through several benchmark numerical examples.

TL;DR: In this paper , a generalized modular framework is proposed to build on-the-fly efficient active learning strategies by combining the following four ingredients or modules: surrogate model, reliability estimation algorithm, learning function and stopping criterion.

TL;DR: A stratified importance sampling method with an adaptive Kriging strategy to estimate failure probabilities and the efficiency of the proposed method is demonstrated using several analytic examples and then transferred to a carbon dioxide storage benchmark problem.

TL;DR: In this work, based on the FORM, the structural reliability analysis problem is transformed into a sequential surrogate constrained optimization problem and a reliability analysis method is developed that an adaptive radial basis function (RBF) metamodeling is adopted to approximate the performance function and the genetic algorithm (GA) is employed to solve the constrained optimized problem.

TL;DR: A generalization of the sampling method introduced by Metropolis et al. as mentioned in this paper is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates.

TL;DR: The important role of finite mixture models in the statistical analysis of data is underscored by the ever-increasing rate at which articles on mixture applications appear in the mathematical and statistical literature.

TL;DR: The important role of finite mixture models in statistical analysis of data is underscored by the ever-increasing rate at which articles on mixture applications appear in the statistical and geospatial literature.

TL;DR: This book presents the first comprehensive treatment of Monte Carlo techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modeling, neural networks, optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection.