{"title":"An efficient approximation algorithm for variance global sensitivity by Bayesian updating","authors":"Pu Chen, Zhenzhou Lu","doi":"10.1007/s10999-024-09715-7","DOIUrl":null,"url":null,"abstract":"<p>Variance global sensitivity (VGS) is defined by the mean square difference between output expectation and conditional one on input realization, and it can calculate the mean contribution of the input within its distribution region and guide the effective modulation of output variance. The Monte Carlo simulation (MCS) and quasi MCS are commonly used to estimate VGS, but they are time-consuming respectively due to double-loop framework and computation related to input dimension. Thus, a novel method is proposed to estimate VGS by elaborately using Bayesian updating. In the proposed algorithm, the input realizations are firstly treated as observations to construct a likelihood function. Then by Bayesian updating, all conditional output expectations on different input realizations, which are required in estimating VGS and most time-consuming, can be obtained as the posterior and estimated by the sample of simulating the output expectation. The proposed algorithm shares the sample of solving output expectation to obtain all conditional ones required for solving VGS, which makes the computational effort of estimating VGS equivalent to that of estimating output expectation, thus improving the efficiency of estimating VGS. Numerical and engineering examples fully substantiate the novelty and effectiveness of this algorithm.</p>","PeriodicalId":593,"journal":{"name":"International Journal of Mechanics and Materials in Design","volume":null,"pages":null},"PeriodicalIF":2.7000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mechanics and Materials in Design","FirstCategoryId":"88","ListUrlMain":"https://doi.org/10.1007/s10999-024-09715-7","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Variance global sensitivity (VGS) is defined by the mean square difference between output expectation and conditional one on input realization, and it can calculate the mean contribution of the input within its distribution region and guide the effective modulation of output variance. The Monte Carlo simulation (MCS) and quasi MCS are commonly used to estimate VGS, but they are time-consuming respectively due to double-loop framework and computation related to input dimension. Thus, a novel method is proposed to estimate VGS by elaborately using Bayesian updating. In the proposed algorithm, the input realizations are firstly treated as observations to construct a likelihood function. Then by Bayesian updating, all conditional output expectations on different input realizations, which are required in estimating VGS and most time-consuming, can be obtained as the posterior and estimated by the sample of simulating the output expectation. The proposed algorithm shares the sample of solving output expectation to obtain all conditional ones required for solving VGS, which makes the computational effort of estimating VGS equivalent to that of estimating output expectation, thus improving the efficiency of estimating VGS. Numerical and engineering examples fully substantiate the novelty and effectiveness of this algorithm.
期刊介绍:
It is the objective of this journal to provide an effective medium for the dissemination of recent advances and original works in mechanics and materials'' engineering and their impact on the design process in an integrated, highly focused and coherent format. The goal is to enable mechanical, aeronautical, civil, automotive, biomedical, chemical and nuclear engineers, researchers and scientists to keep abreast of recent developments and exchange ideas on a number of topics relating to the use of mechanics and materials in design.
Analytical synopsis of contents:
The following non-exhaustive list is considered to be within the scope of the International Journal of Mechanics and Materials in Design:
Intelligent Design:
Nano-engineering and Nano-science in Design;
Smart Materials and Adaptive Structures in Design;
Mechanism(s) Design;
Design against Failure;
Design for Manufacturing;
Design of Ultralight Structures;
Design for a Clean Environment;
Impact and Crashworthiness;
Microelectronic Packaging Systems.
Advanced Materials in Design:
Newly Engineered Materials;
Smart Materials and Adaptive Structures;
Micromechanical Modelling of Composites;
Damage Characterisation of Advanced/Traditional Materials;
Alternative Use of Traditional Materials in Design;
Functionally Graded Materials;
Failure Analysis: Fatigue and Fracture;
Multiscale Modelling Concepts and Methodology;
Interfaces, interfacial properties and characterisation.
Design Analysis and Optimisation:
Shape and Topology Optimisation;
Structural Optimisation;
Optimisation Algorithms in Design;
Nonlinear Mechanics in Design;
Novel Numerical Tools in Design;
Geometric Modelling and CAD Tools in Design;
FEM, BEM and Hybrid Methods;
Integrated Computer Aided Design;
Computational Failure Analysis;
Coupled Thermo-Electro-Mechanical Designs.