GLOBAL SENSITIVITY ANALYSIS: AN EFFICIENT NUMERICAL METHOD FOR APPROXIMATING THE TOTAL SENSITIVITY INDEX

2016 ◽  
Vol 6 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Matieyendou Lamboni
Keyword(s):  
Sensitivity Analysis ◽  
Numerical Method ◽  
Global Sensitivity Analysis ◽  
Sensitivity Index ◽  
Global Sensitivity ◽  
Total Sensitivity

Global Sensitivity Analysis for Stay Vane and Casing Design of Reaction Hydraulic Turbine

2019 ◽  
Author(s):  
Hyunkyoo Cho ◽  
Ujjwal Shrestha ◽  
Young-Do Choi ◽  
Jungwan Park
Keyword(s):  
Sensitivity Analysis ◽  
Design Process ◽  
Performance Measures ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Surrogate Models ◽  
Sensitivity Index ◽  
Global Sensitivity ◽  
Design Variables ◽  
Hydraulic Turbines

Abstract Global sensitivity analysis (GSA) estimates influence of design variables in the entire design domain on performance measures. Hence, using GSA, important design variables could be found for an engineering application with high dimension which require computationally expensive analyses. Then, similar engineering applications could use selected variables to carry out design process with smaller dimension and affordable computational cost. In this study, GSA has been carried out for the performance measures in design of stay vane and casing of reaction hydraulic turbines. Global sensitivity index method is used for GSA because it can fully capture the effect of interaction between the design variables. For efficiency, genetic aggregation surrogate models are constructed using the responses of computational fluid dynamic (CFD) analysis. Global sensitivity indices for the performance measures of stay vane and casing have been evaluated using the surrogate models. It is found that less than three design variables among 12 are effective in the design process of stay vane and casing in reaction hydraulic turbines.

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.

Global Sensitivity Analysis for a Bayesian Network

2016 ◽  
Author(s):  
Chenzhao Li ◽  
Sankaran Mahadevan
Keyword(s):  
Sensitivity Analysis ◽  
Bayesian Network ◽  
Prior Distribution ◽  
Global Sensitivity Analysis ◽  
Auxiliary Variable ◽  
Uncertainty Reduction ◽  
Sensitivity Index ◽  
Global Sensitivity ◽  
First Order ◽  
Deterministic Function

In a Bayesian network, how a node of interest is affected by the observation of another node is of interest in both forward propagation and backward inference. The proposed global sensitivity analysis (GSA) for Bayesian network aims to calculate the Sobol’ sensitivity index of a node with respect to the node of interest. The desired GSA for Bayesian network confronts two challenges. First, the computation of the Sobol’ index requires a deterministic function while the Bayesian network is a stochastic model. Second, the computation of the Sobol’ index can be expensive, especially if the model inputs are correlated, which is common in a Bayesian network. To solve the first challenge, this paper uses the auxiliary variable method to convert the path between two nodes in the Bayesian network to a deterministic function, thus making the Sobol’ index computation feasible in a Bayesian network. To solve the second challenge, this paper proposes an efficient algorithm to directly estimate the first-order Sobol’ index from Monte Carlo samples of the prior distribution of the Bayesian network, so that the proposed GSA for Bayesian network is computationally affordable. Before the updating, the proposed algorithm can predict the uncertainty reduction of the node of interest purely using the prior distribution samples, thus providing quantitative guidance for effective observation and updating.

A global sensitivity analysis-assisted sequential optimization tool for plant-fin heat sink design

2019 ◽  
Vol 37 (2) ◽  
pp. 591-614
Author(s):  
Enying Li ◽  
Zheng Zhou ◽  
Hu Wang ◽  
Kang Cai
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Optimization Method ◽  
Sequential Optimization ◽  
Support Vector ◽  
Sensitivity Index ◽  
Content Type ◽  
Global Sensitivity ◽  
Design Variables ◽  
Heat Sink Design

Purpose This study aims to suggest and develops a global sensitivity analysis-assisted multi-level sequential optimization method for the heat transfer problem. Design/methodology/approach Compared with other surrogate-assisted optimization methods, the distinctive characteristic of the suggested method is to decompose the original problem into several layers according to the global sensitivity index. The optimization starts with the several most important design variables by the support vector regression-based efficient global optimization method. Then, when the optimization process progresses, the filtered design variables should be involved in optimization one by one or the setting value. Therefore, in each layer, the design space should be reduced according to the previous optimization result. To improve the accuracy of the global sensitivity index, a novel global sensitivity analysis method based on the variance-based method incorporating a random sampling high-dimensional model representation is introduced. Findings The advantage of this method lies in its capability to solve complicated problems with a limited number of sample points. Moreover, to enhance the reliability of optimum, the support vector regression-based global efficient optimization is used to optimize in each layer. Practical implications The developed optimization tool is built by MATLAB and can be integrated by commercial software, such as ABAQUS and COMSOL. Lastly, this tool is integrated with COMSOL and applied to the plant-fin heat sink design. Compared with the initial temperature, the temperature after design is over 49°. Moreover, the relationships among all design variables are also disclosed clearly. Originality/value The D-MORPH-HDMR is integrated to obtain the coupling relativities among the design variables efficiently. The suggested method can be decomposed into multiplier layers according to the GSI. The SVR-EGO is used to optimize the sub-problem because of its robustness of modeling.

Dynamic Reliability and Global Sensitivity Analysis for Hydraulic Pipe Based on Sparse Grid Integral Method

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Guo Qing ◽  
Lv Tangqi ◽  
Liu Yongshou ◽  
Chen Bingqian
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Random Variable ◽  
Sparse Grid ◽  
Working Environment ◽  
Cumulative Distribution ◽  
Sensitivity Index ◽  
Dynamic Reliability ◽  
Curved Pipe ◽  
Global Sensitivity

Abstract Due to the extremely rough working environment, aero-hydraulic pipes face serious dynamic failure problems in applications for practical engineering. This paper proposes a dynamic reliability and moment-independent global sensitivity analysis (GSA) method to evaluate the dynamic reliability and the effects of random input variables on the dynamic reliability of aero-hydraulic pipes. Based on the Miner criterion for the cumulative damage of structural fatigue, this paper establishes the dynamic reliability analysis method under the condition of double random vibration. In order to further analyze the influence of the uncertainty of each random variable of pipe on its dynamic reliability, a moment-independent global sensitivity index for dynamic reliability based on cumulative distribution function is proposed in this paper. The index can reflect the effects of random variables on dynamic reliability quantitatively. Based on the proposed GSA method of dynamic reliability, a sparse grid integral (SGI) method is introduced to solve the dynamic reliability and moment-independent global sensitivity index, with high computational efficiency. Finally, the effects of clamp supports, diameters, and curvature of curved pipe on the dynamic reliability and GSA are analyzed through a hydraulic piping example.

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