scholarly journals A Sampling-Based Sensitivity Analysis Method Considering the Uncertainties of Input Variables and Their Distribution Parameters

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1095
Author(s):  
Xiang Peng ◽  
Xiaoqing Xu ◽  
Jiquan Li ◽  
Shaofei Jiang
Keyword(s):  
Sensitivity Analysis ◽  
Simulation Method ◽  
Transformation Method ◽  
Unscented Transformation ◽  
Performance Function ◽  
Gaussian Integration ◽  
Sensitivity Indices ◽  
Sensitivity Analysis Method ◽  
Distribution Parameters ◽  
Input Variables

For engineering products with uncertain input variables and distribution parameters, a sampling-based sensitivity analysis methodology was investigated to efficiently determine the influences of these uncertainties. In the calculation of the sensitivity indices, the nonlinear degrees of the performance function in the subintervals were greatly reduced by using the integral whole domain segmentation method, while the mean and variance of the performance function were calculated using the unscented transformation method. Compared with the traditional Monte Carlo simulation method, the loop number and sampling number in every loop were decreased by using the multiplication approximation and Gaussian integration methods. The proposed algorithm also reduced the calculation complexity by reusing the sample points in the calculation of two sensitivity indices to measure the influence of input variables and their distribution parameters. The accuracy and efficiency of the proposed algorithm were verified with three numerical examples and one engineering example.

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.

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.

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.

Moment Matching for Sensitivity Analysis of Probabilistic Model Output

2004 ◽  
Author(s):  
Mahmoud Awad ◽  
Agus Sudjianto ◽  
Nanua Singh
Keyword(s):  
Sensitivity Analysis ◽  
Simulation Models ◽  
Moment Matching ◽  
Model Output ◽  
Sensitivity Indices ◽  
Variance Contribution ◽  
Complex Engineering ◽  
Input Variables ◽  
The Relationship ◽  
Effective Sensitivity

With the advent of highly complex engineering simulation models that describe the relationship between input variables and output response, the need for an efficient and effective sensitivity analysis is more demanding. In this article, a generalized approach that can provide efficient as well as accurate global sensitivity indices is developed. The approach consists of two steps: running an orthogonal array based experiment using moment-matched levels of the input variables and followed by a variance contribution analysis. The benefits of the approach are demonstrated through three different examples.

scholarly journals A Study on the Application of Sensitivity Analysis for Ship Hydrodynamic Coefficients

2018 ◽  
Vol 7 (4.36) ◽  
pp. 953
Author(s):  
Khanh Toan Tran ◽  
. .
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Mathematics Model ◽  
Hydrodynamic Coefficients ◽  
Ship Manoeuvring ◽  
Multiple Input ◽  
Sensitivity Analysis Method ◽  
Ship Hydrodynamic ◽  
Input Variables ◽  
The Mathematical Model

In the mathematical model with multiple input variables, the sensitivity analysis of the input variables is an important step to ensure the reliability of the mathematical model. In order to optimize the ship manoeuvring simulation, in particular the optimization of the trajectory ship, the sensitivity analysis should be performed in the mathematical model to select the group of the most sensitive hydrodynamic coefficients. In this paper, the author applied the sensitivity analysis method in mathematics model of ship manoeuvring programming in order to optimize the ship trajectory of Esso Bernicia 193000DWT tanker model.  

scholarly journals Non-probabilistic parameter sensitivity analysis for structures based on ellipsoidal model

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401878236 ◽  
Author(s):  
Feng Zhang ◽  
Kailiang Luo ◽  
Weihao Zhai ◽  
Shiwang Tan ◽  
Yameng Wang
Keyword(s):  
Sensitivity Analysis ◽  
Analytical Solution ◽  
Parameter Sensitivity ◽  
Analysis Method ◽  
Parameter Sensitivity Analysis ◽  
Performance Function ◽  
First Order ◽  
Ellipsoidal Model ◽  
Sensitivity Analysis Method ◽  
Nonlinear Performance

Sensitivity analysis plays a crucial role in identifying the structure important parameters. In this article, a new non-probabilistic parameter sensitivity analysis method is proposed according to the ellipsoidal model. Meanwhile, an analytical solution of non-probabilistic parameter sensitivity analysis method based on the ellipsoidal model is derived for linear performance function, as well as an approximately analytical solution is obtained for nonlinear performance function using the first-order Taylor expansion to linearize the functions in design point. Finally, the proposed method is illustrated by three examples, which shows that it is reasonable and applicable.

scholarly journals Mapping-Based Hierarchical Sensitivity Analysis for Multilevel Systems With Multidimensional Correlations

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Can Xu ◽  
Ping Zhu ◽  
Zhao Liu ◽  
Wei Tao
Keyword(s):  
Sensitivity Analysis ◽  
Analysis Method ◽  
Computational Framework ◽  
Copula Theory ◽  
Multilevel Systems ◽  
Sensitivity Indices ◽  
Response Variance ◽  
Sensitivity Analysis Method ◽  
Vine Copula ◽  
Input Uncertainties

Abstract Hierarchical sensitivity analysis (HSA) of multilevel systems is to assess the effect of system’s input uncertainties on the variations of system’s performance through integrating the sensitivity indices of subsystems. However, it is difficult to deal with the engineering systems with complicated correlations among various variables across levels by using the existing hierarchical sensitivity analysis method based on variance decomposition. To overcome this limitation, a mapping-based hierarchical sensitivity analysis method is proposed to obtain sensitivity indices of multilevel systems with multidimensional correlations. For subsystems with dependent variables, a mapping-based sensitivity analysis, consisting of vine copula theory, Rosenblatt transformation, and polynomial chaos expansion (PCE) technique, is provided for obtaining the marginal sensitivity indices. The marginal sensitivity indices can allow us to distinguish between the mutual depend contribution and the independent contribution of an input to the response variance. Then, extended aggregation formulations for local variables and shared variables are developed to integrate the sensitivity indices of subsystems at each level so as to estimate the global effect of inputs on the response. Finally, this paper presents a computational framework that combines related techniques step by step. The effectiveness of the proposed mapping-based hierarchical sensitivity analysis (MHSA) method is verified by a mathematical example and a multiscale composite material.

scholarly journals Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zhiqiang Wang ◽  
Zhenyu Lei
Keyword(s):  
Sensitivity Analysis ◽  
Design System ◽  
Shield Tunnel ◽  
Random Parameters ◽  
Rubber Gasket ◽  
The Monte Carlo Method ◽  
Material Hardness ◽  
Sensitivity Analysis Method ◽  
Elastic Rubber ◽  
Input Variables

Abstract In order to study the waterproof performance of elastic rubber gasket in shield tunnel lining joints, an innovative sensitivity analysis method is proposed by combining the Monte Carlo method with the stochastic finite element method (FEM) in this paper. The sensitivity values of the waterproof performance respecting to elastic rubber gaskets are obtained via the ANSYS Probabilistic Design System (PDS) module, in which the parameters of material hardness, coordinates of the hole center, apertures are selected as random input variables. Meantime, the extent of the tolerance effect of the random parameters on the waterproof performance is explored.

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.

A new algorithm for variance-based importance measures and importance kernel sensitivity

2012 ◽  
Vol 227 (1) ◽  
pp. 16-27
Author(s):  
Changcong Zhou ◽  
Zhenzhou Lu ◽  
Guijie Li
Keyword(s):  
Numerical Simulation ◽  
Quadratic Polynomial ◽  
Point Estimate ◽  
Importance Measure ◽  
Performance Function ◽  
Point Estimate Method ◽  
Cross Terms ◽  
Distribution Parameters ◽  
Estimate Method ◽  
Input Variables

Variance-based importance measure has proven itself as an effective tool to reflect the effects of input variables on the output. Owing to the desirable properties, researchers have paid lots of attention to improving efficiency in computing a variance-based importance measure. Based on the theory of point estimate, this article proposes a new algorithm, decomposing the importance measure into inner and outer parts, and computing each part with a point estimate method. In order to discuss the impacts on the variance-based importance measure from distribution parameters of input variables, a new concept of kernel sensitivity of the variance-based importance measure is put forward, with solving algorithms respectively, based on numerical simulation and point estimate established as well. For cases where the performance function with independent and normally distributed input variables is expressed by a linear or quadratic polynomial without cross-terms, analytical results of the variance-based importance measure and the kernel sensitivity are derived. Numerical and engineering examples have been employed to illustrate the applicability of the proposed concept and algorithm.

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