Probabilistic Sensitivity Analysis Methods for Design Under Uncertainty

Abstract

Sensitivity analysis (SA) is an important procedure in engineering design to obtain valuable information about the model behavior to guide a design process. For design under uncertainty, probabilistic sensitivity analysis (PSA) methods have been developed to provide insight into the probabilistic behavior of a model. In this paper, the goals of PSA at different design stages are investigated. In the prior-design stage, PSA can be utilized to identify those probabilistically non-significant variables and reduce the dimension of a random design space. It can reduce the computational cost associated with uncertainty assessment without much sacrifice on the optimum solution. For post-design analysis, probabilistic sensitivity analysis can be used to identify where to spend design resources for the largest potential improvement of a performance. Based on the interested distribution range of a random response, the PSA methods can be categorized into two types: the global response probabilistic sensitivity analysis (GRPSA) and the regional response probabilistic sensitivity analysis (RRPSA). Four widely-used PSA methods: Sobol' indices, Wu's sensitivity coefficients, the MPP based sensitivity coefficients, and the Kullback-Leibler entropy based method are selected for comparison. The merits behind each method are reviewed in details. Their advantages, limitations, and applicability are investigated. Their effectiveness and applicability under different design scenarios are compared in two numerical examples and two engineering design problems.

Cross-wind effects on road and rail vehicles

“…To investigate the global influence of the excitation and design parameters, the correlation matrix for the performance function g(z), with respect to these variables, can be computed Downloaded by [Nipissing University] at 19:04 10 October 2014 and also a principal component analysis concerning the calculated correlation matrix can be undertaken [32]. A global method, which is less numerically costly than correlation analysis, and which gives also a good insight into nonlinearities of the system, is the Morris method [33].…”

Robust design optimization of electro-thermal microactuator using probabilistic methods

“…There are many methods for SA; a good overview of these methods is presented by Saltelli et al 2000). Probabilistic sensitivity analysis (PSA) takes into account all the variation of the inputs, and tries to relate the output uncertainty to the uncertainty in the input factors (Liu et al 2004). Among PSA techniques, variance-based methods are the most often used.…”

“…Robust optimization becomes an important topic in MEMS for developing reliable applications. Liu et al (2004) used analytical equations to determine the effects of feature width variation on MEMS resonators and developed analytical equations for making resonators robust to width variations. Mawardi and Pitchumani (2004) applied a more general robust optimization approach to the design of microresonators.…”

Monte Carlo simulation-based sensitivity analysis of the model of a thermal–hydraulic passive system

“…In the framework of reliability sensitivity, the sensitivity to a given uncertain input variable is defined as the partial derivative of the system failure probability with respect to the parameters (e.g., the mean, the standard deviation, …) of the probability distribution of the input variable itself [65], [70], [77]- [79].…”