An efficient approximation algorithm for variance global sensitivity by Bayesian updating

IF 2.7 3区 材料科学 Q2 ENGINEERING, MECHANICAL International Journal of Mechanics and Materials in Design Pub Date : 2024-08-05 DOI:10.1007/s10999-024-09715-7
Pu Chen, Zhenzhou Lu
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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.

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贝叶斯更新方差全局灵敏度的高效近似算法
方差全局灵敏度(VGS)由输出期望值与输入实现条件期望值之间的均方差定义,它可以计算输入在其分布区域内的平均贡献,并指导输出方差的有效调节。蒙特卡罗模拟(MCS)和准 MCS 是估算 VGS 的常用方法,但它们分别因双环框架和与输入维度相关的计算而耗时。因此,本文提出了一种通过精心使用贝叶斯更新来估计 VGS 的新方法。在所提出的算法中,首先将输入实现值作为观测值来构建似然函数。然后,通过贝叶斯更新,可以得到所有不同输入变现上的条件输出期望作为后验,并通过模拟输出期望的样本进行估计,这在估计 VGS 时是必需的,也是最耗时的。所提出的算法通过共享求解输出期望的样本来获得求解 VGS 所需的所有条件期望,使得估计 VGS 的计算量等同于估计输出期望的计算量,从而提高了估计 VGS 的效率。数值和工程实例充分证明了该算法的新颖性和有效性。
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来源期刊
International Journal of Mechanics and Materials in Design
International Journal of Mechanics and Materials in Design ENGINEERING, MECHANICAL-MATERIALS SCIENCE, MULTIDISCIPLINARY
CiteScore
6.00
自引率
5.40%
发文量
41
审稿时长
>12 weeks
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.
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Strength and stability analysis of composite inverted conical structure Interface design of a neutral spheroidal piezoelectric inhomogeneity in a transversely isotropic piezoelectric matrix Multi-objective topology optimization for materials with negative Poisson’s ratio and thermal insulation An efficient approximation algorithm for variance global sensitivity by Bayesian updating Theoretical prediction and experimental verification of thermomechanical deflection responses of geometrically nonlinear porous graded curved structure
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