Refined Stratified Sampling for efficient Monte Carlo based uncertainty quantification

Abstract

a b s t r a c tA general adaptive approach rooted in stratified sampling (SS) is proposed for sample-based uncertainty quantification (UQ). To motivate its use in this context the space-filling, orthogonality, and projective properties of SS are compared with simple random sampling and Latin hypercube sampling (LHS). SS is demonstrated to provide attractive properties for certain classes of problems. The proposed approach, Refined Stratified Sampling (RSS), capitalizes on these properties through an adaptive process that adds samples sequentially by dividing the existing subspaces of a stratified design. RSS is proven to reduce variance compared to traditional stratified sample extension methods while providing comparable or enhanced variance reduction when compared to sample size extension methods for LHS -which do not afford the same degree of flexibility to facilitate a truly adaptive UQ process. An initial investigation of optimal stratification is presented and motivates the potential for major advances in variance reduction through optimally designed RSS. Potential paths for extension of the method to high dimension are discussed. Two examples are provided. The first involves UQ for a low dimensional function where convergence is evaluated analytically. The second presents a study to asses the response variability of a floating structure to an underwater shock.

An innovative framework for probabilistic-based structural assessment with an application to existing reinforced concrete structures

“…Accordingly, an open source Latin Hypercube Sampling (LHS) [28][29][30] toolbox is used in the present work. There are some algorithms, such as the well-known Iman and Conover [31] or the more advanced Simulated Annealing [32] that might be used in sampling to consider the correlation between parameters.…”

“…From all these algorithms, the stratified sampling procedures, in particular the LHS, was commonly used due to its lower computational cost [4,28,29]. Accordingly, a LHS toolbox with an incorporated Iman and…”

“…In this case, an Iman and Conover algorithm [31] is integrated in the LHS toolbox to generate samples of the correlated random variables [28,29]. Used correlation values (Table 10) are obtained from bibliography [3,4,27].…”

Targeted random sampling: a new approach for efficient reliability estimation for complex systems

“…The methodology proposed herein is built upon the RSS concept developed by Shields et al (2015). RSS provides an effective means of adding samples to a stratified design by dividing the existing strata and sampling in the newly produced empty strata.…”

“…The method has its underpinnings in stratified sampling for Monte Carlo simulation, particularly the Refined Stratified Sampling (RSS) method developed by Shields et al (2015). The method is demonstrated for two problems with complex limit states in a moderate number of dimensions and is shown to improve both the accuracy (in terms of reduced solution variability) and the efficiency of probability of failure estimates when compared with existing methods.…”