scholarly journals A Novel Global Sensitivity Measure Based on Probability Weighted Moments

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 90
Author(s):  
Shufang Song ◽  
Lu Wang
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Small Samples ◽  
Double Loop ◽  
Numerical Estimation ◽  
Global Sensitivity ◽  
Sensitivity Measure ◽  
Probability Weighted Moments ◽  
Input Variables ◽  
Single Set

Global sensitivity analysis (GSA) is a useful tool to evaluate the influence of input variables in the whole distribution range. Variance-based methods and moment-independent methods are widely studied and popular GSA techniques despite their several shortcomings. Since probability weighted moments (PWMs) include more information than classical moments and can be accurately estimated from small samples, a novel global sensitivity measure based on PWMs is proposed. Then, two methods are introduced to estimate the proposed measure, i.e., double-loop-repeated-set numerical estimation and double-loop-single-set numerical estimation. Several numerical and engineering examples are used to show its advantages.

scholarly journals New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2425
Author(s):  
Zdeněk Kala
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Binary Outcome ◽  
Global Sensitivity ◽  
First Order ◽  
Sensitivity Measure ◽  
Sensitivity Indices ◽  
Alternative Measures ◽  
Input Variables ◽  
Dome Shape

This article presents new sensitivity measures in reliability-oriented global sensitivity analysis. The obtained results show that the contrast and the newly proposed sensitivity measures (entropy and two others) effectively describe the influence of input random variables on the probability of failure Pf. The contrast sensitivity measure builds on Sobol, using the variance of the binary outcome as either a success (0) or a failure (1). In Bernoulli distribution, variance Pf(1 − Pf) and discrete entropy—Pfln(Pf) − (1 − Pf)ln(1 − Pf) are similar to dome functions. By replacing the variance with discrete entropy, a new alternative sensitivity measure is obtained, and then two additional new alternative measures are derived. It is shown that the desired property of all the measures is a dome shape; the rise is not important. Although the decomposition of sensitivity indices with alternative measures is not proven, the case studies suggest a rationale structure of all the indices in the sensitivity analysis of small Pf. The sensitivity ranking of input variables based on the total indices is approximately the same, but the proportions of the first-order and the higher-order indices are very different. Discrete entropy gives significantly higher proportions of first-order sensitivity indices than the other sensitivity measures, presenting entropy as an interesting new sensitivity measure of engineering reliability.

scholarly journals Global Sensitivity Analysis to Assess Salt Precipitation for CO2 Geological Storage in Deep Saline Aquifers

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Yuan Wang ◽  
Jie Ren ◽  
Shaobin Hu ◽  
Di Feng
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Injection Rate ◽  
Injection Well ◽  
Saline Aquifers ◽  
Salt Precipitation ◽  
Empirical Parameter ◽  
Global Sensitivity ◽  
Morris Method ◽  
Input Variables

Salt precipitation is generated near the injection well when dry supercritical carbon dioxide (scCO2) is injected into saline aquifers, and it can seriously impair the CO2 injectivity of the well. We used solid saturation (Ss) to map CO2 injectivity. Ss was used as the response variable for the sensitivity analysis, and the input variables included the CO2 injection rate (QCO2), salinity of the aquifer (XNaCl), empirical parameter m, air entry pressure (P0), maximum capillary pressure (Pmax), and liquid residual saturation (Splr and Sclr). Global sensitivity analysis methods, namely, the Morris method and Sobol method, were used. A significant increase in Ss was observed near the injection well, and the results of the two methods were similar: XNaCl had the greatest effect on Ss; the effect of P0 and Pmax on Ss was negligible. On the other hand, with these two methods, QCO2 had various effects on Ss: QCO2 had a large effect on Ss in the Morris method, but it had little effect on Ss in the Sobol method. We also found that a low QCO2 had a profound effect on Ss but that a high QCO2 had almost no effect on the Ss value.

scholarly journals Global Sensitivity Analysis of Fuzzy Distribution Parameter on Failure Probability and Its Single-Loop Estimation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Lei Cheng ◽  
Zhenzhou Lu ◽  
Luyi Li
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Single Loop ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Distribution Parameters ◽  
Input Variables ◽  
Sampling Probability

An extending Borgonovo’s global sensitivity analysis is proposed to measure the influence of fuzzy distribution parameters on fuzzy failure probability by averaging the shift between the membership functions (MFs) of unconditional and conditional failure probability. The presented global sensitivity indices can reasonably reflect the influence of fuzzy-valued distribution parameters on the character of the failure probability, whereas solving the MFs of unconditional and conditional failure probability is time-consuming due to the involved multiple-loop sampling and optimization operators. To overcome the large computational cost, a single-loop simulation (SLS) is introduced to estimate the global sensitivity indices. By establishing a sampling probability density, only a set of samples of input variables are essential to evaluate the MFs of unconditional and conditional failure probability in the presented SLS method. Significance of the global sensitivity indices can be verified and demonstrated through several numerical and engineering examples.

Investigation of the uncertainty of the in-plane mechanical properties of composite laminates

2011 ◽  
Vol 226 (7) ◽  
pp. 1739-1750 ◽  
Author(s):  
Tian Longfei ◽  
Lu Zhenzhou ◽  
Hao Wenrui
Keyword(s):  
Mechanical Properties ◽  
Sensitivity Analysis ◽  
Composite Laminates ◽  
Global Sensitivity Analysis ◽  
Nonlinear Models ◽  
Analysis Method ◽  
Global Sensitivity ◽  
Response Variance ◽  
Sensitivity Analysis Method ◽  
Input Variables

The uncertainty of the in-plane mechanical properties of the laminate used in an aircraft wing structure is investigated. Global sensitivity analysis is used to identify the source of the uncertainties of the response performance. Due to the limitations of the existing global sensitivity analysis method for nonlinear models with correlated input variables, a new one using nonlinear regression is proposed. Furthermore, a contribution matrix is defined for engineering convenience. Two nonlinear numerical examples are employed in this article to demonstrate the ability of the proposed global sensitivity analysis method. After applying the proposed global sensitivity analysis method to the laminate model, the contribution matrices are obtained; from these matrices, researchers can identify the dominant variance contributions that contribute the most to the response variance. Factor analysis is then employed to analyze the global sensitivity analysis results and determine the most efficient methods to decrease the variances of the in-plane elastic constants. Monte Carlo simulation is used to demonstrate the efficiency of the methods in decreasing the variances.

Analytical Variance-Based Global Sensitivity Analysis in Simulation-Based Design Under Uncertainty

2004 ◽  
Author(s):  
Wei Chen ◽  
Ruichen Jin ◽  
Agus Sudjianto
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Simulation Models ◽  
Design Under Uncertainty ◽  
Global Sensitivity ◽  
Functional Relationships ◽  
Simulation Based Design ◽  
Simulation Based ◽  
Input Variables ◽  
The Impact

The importance of sensitivity analysis in engineering design cannot be over-emphasized. In design under uncertainty, sensitivity analysis is performed with respect to the probabilistic characteristics. Global sensitivity analysis (GSA), in particular, is used to study the impact of variations in input variables on the variation of a model output. One of the most challenging issues for GSA is the intensive computational demand for assessing the impact of probabilistic variations. Existing variance-based GSA methods are developed for general functional relationships but require a large number of samples. In this work, we develop an efficient and accurate approach to GSA that employs analytic formulations derived from metamodels of engineering simulation models. We examine the types of GSA needed for design under uncertainty and derive generalized analytical formulations of GSA based on a variety of metamodels commonly used in engineering applications. The benefits of our proposed techniques are demonstrated and verified through both illustrative mathematical examples and the robust design for improving vehicle handling performance.

A Global Sensitivity Analysis Method for Multi-Input Multi-Output System and its Application in Structural Design

2021 ◽  
pp. 2141005
Author(s):  
Qiming Liu ◽  
Nichen Tong ◽  
Xu Han
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Sensitivity Index ◽  
Response Functions ◽  
Analysis Method ◽  
Order Function ◽  
Global Sensitivity ◽  
Sensitivity Analysis Method ◽  
Output System ◽  
Input Variables

Commonly, variance-based global sensitivity analysis methods are popular and applicable to quantify the impact of a set of input variables on output response. However, for many engineering practical problems, the output response is not single but multiple, which makes some traditional sensitivity analysis methods difficult or unsuitable. Therefore, a novel global sensitivity analysis method is presented to evaluate the importance of multi-input variables to multi-output responses. First, assume that a multi-input multi-output system (MIMOS) includes [Formula: see text] variables and [Formula: see text] responses. A set of summatory functions [Formula: see text] and [Formula: see text] are constructed by the addition and subtraction of any two response functions. Naturally, each response function is represented using a set of summatory function. Subsequently, the summatory functions [Formula: see text] and [Formula: see text] are further decomposed based on the high dimensional model representation (HDMR), respectively. Due to the orthogonality of all the decomposed function sub-terms, the variance and covariance of each response function can be represented using the partial variances of all the decomposed function sub-terms on the corresponding summatory functions, respectively. The total fluctuation of MIMOS is calculated by the sum of the variances and covariances on all the response functions. Further, the fluctuation is represented as the sum of the total partial variances for all the [Formula: see text]-order function sub-terms, and the total partial variance is the sum of [Formula: see text] partial variances for the corresponding [Formula: see text]-order function sub-terms. Then, the function sensitivity index (FSI) [Formula: see text] for s-order function sub-terms is defined by the ratio of the total partial variance and total fluctuation, which includes first-order, second-order, and high-order FSI. The variable sensitivity index [Formula: see text] of variable [Formula: see text] is calculated by the sum of all the FSIs including the contribution of variable [Formula: see text]. Finally, numerical example and engineering application are employed to demonstrate the accuracy and practicality of the presented global sensitivity analysis method for MIMOS.

scholarly journals Variable Selection in Regression Models Using Global Sensitivity Analysis

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
William Becker ◽  
Paolo Paruolo ◽  
Andrea Saltelli
Keyword(s):  
Sensitivity Analysis ◽  
Variable Selection ◽  
Regression Models ◽  
Global Sensitivity Analysis ◽  
Physical Models ◽  
Model Fit ◽  
Global Sensitivity ◽  
Testing Sequence ◽  
Input Variables

Abstract Global sensitivity analysis is primarily used to investigate the effects of uncertainties in the input variables of physical models on the model output. This work investigates the use of global sensitivity analysis tools in the context of variable selection in regression models. Specifically, a global sensitivity measure is applied to a criterion of model fit, hence defining a ranking of regressors by importance; a testing sequence based on the ‘Pantula-principle’ is then applied to the corresponding nested submodels, obtaining a novel model-selection method. The approach is demonstrated on a growth regression case study, and on a number of simulation experiments, and it is found competitive with existing approaches to variable selection.

scholarly journals A Vine Copula-Based Global Sensitivity Analysis Method for Structures with Multidimensional Dependent Variables

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2489
Author(s):  
Zhiwei Bai ◽  
Hongkui Wei ◽  
Yingying Xiao ◽  
Shufang Song ◽  
Sergei Kucherenko
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Joint Probability ◽  
Copula Functions ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Sensitivity Analysis Method ◽  
Input Variables ◽  
Vine Copula ◽  
Bivariate Copula

For multidimensional dependent cases with incomplete probability information of random variables, global sensitivity analysis (GSA) theory is not yet mature. The joint probability density function (PDF) of multidimensional variables is usually unknown, meaning that the samples of multivariate variables cannot be easily obtained. Vine copula can decompose the joint PDF of multidimensional variables into the continuous product of marginal PDF and several bivariate copula functions. Based on Vine copula, multidimensional dependent problems can be transformed into two-dimensional dependent problems. A novel Vine copula-based approach for analyzing variance-based sensitivity measures is proposed, which can estimate the main and total sensitivity indices of dependent input variables. Five considered test cases and engineering examples show that the proposed methods are accurate and applicable.

A global sensitivity analysis method based on ANOVA with convex set model and its state-dependent parameter solution

2018 ◽  
Vol 233 (11) ◽  
pp. 4039-4051
Author(s):  
Qing Guo ◽  
Yongshou Liu ◽  
Xiangyu Chen
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Convex Set ◽  
The State ◽  
Analysis Method ◽  
Global Sensitivity ◽  
State Dependent ◽  
Sensitivity Analysis Method ◽  
Dependent Parameter ◽  
Input Variables

Convex set model is most widely applied around nonprobabilistic uncertainty description. This paper combines the convex model with global sensitivity analysis theory of variance, and then proposes an index based on convex set model and variance-based global sensitivity analysis method to illustrate the effect of the nonprobability variables on the dangerous degree. The proposed index consists of two parts, including the main and total indices. The main index can quantitatively reflect the effect of uncertainties of input variables on the variance of output response, and the total index reflects the influence of interaction with other variables in addition to the individual influence of input variables. Furthermore, an efficient state-dependent parameter solution for solving the variance-based global sensitivity analysis of nonprobabilistic convex uncertainty is given in this paper. The state-dependent parameter solution not only greatly improves the efficiency but also guarantees the computational accuracy, and the times of performance functions evaluation decrease from [Formula: see text] in single-loop Monte Carlo solution to 2048 in the state-dependent parameter method. Finally, three numerical examples and a finite element example are used to verify the feasibility and rationality of the proposed method.

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