Refined Stratified Sampling for efficient Monte Carlo based uncertainty quantification

• Published in: Reliability engineering & system safety Vol. 142; pp. 310 - 325
• Main Authors: Shields, Michael D., Teferra, Kirubel, Hapij, Adam, Daddazio, Raymond P.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2015
• Subjects: Floating structures; Latin hypercube sampling; Monte Carlo methods; Monte Carlo simulation; Optimization; Reduction; Reliability engineering; Sample size extension; Sampling; Stratified sampling; Uncertainty; Uncertainty quantification; Variance; Stratified sampling; Uncertainty quantification; Latin hypercube sampling; Monte Carlo simulation; Sample size extension
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2015.05.023

A 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 adaptive process, rooted in stratified sampling, is proposed for Monte Carlo-based uncertainty quantification.•Space-filling, orthogonality, and projective properties of stratified sampling are investigated•Stratified sampling is shown to possess attractive properties for certain classes of problems.•Refined Stratified Sampling, a new sampling method is proposed that enables the adaptive UQ process.•Optimality of RSS stratum division is explored.