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.

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.

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.

scholarly journals Hierarchical sensitivity analysis for a large-scale process-based hydrological model applied to an Amazonian watershed

2020 ◽  
Vol 24 (10) ◽  
pp. 4971-4996
Author(s):  
Haifan Liu ◽  
Heng Dai ◽  
Jie Niu ◽  
Bill X. Hu ◽  
Dongwei Gui ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Large Scale ◽  
Global Sensitivity Analysis ◽  
Hydrological Models ◽  
Climate Scenarios ◽  
Analysis Method ◽  
Global Sensitivity ◽  
Uncertainty Sources ◽  
Sensitivity Indices ◽  
Sensitivity Analysis Method

Abstract. Sensitivity analysis methods have recently received much attention for identifying important uncertainty sources (or uncertain inputs) and improving model calibrations and predictions for hydrological models. However, it is still challenging to apply the quantitative and comprehensive global sensitivity analysis method to complex large-scale process-based hydrological models (PBHMs) because of its variant uncertainty sources and high computational cost. Therefore, a global sensitivity analysis method that is capable of simultaneously analyzing multiple uncertainty sources of PBHMs and providing quantitative sensitivity analysis results is still lacking. In an effort to develop a new tool for overcoming these weaknesses, we improved the hierarchical sensitivity analysis method by defining a new set of sensitivity indices for subdivided parameters. A new binning method and Latin hypercube sampling (LHS) were implemented for estimating these new sensitivity indices. For test and demonstration purposes, this improved global sensitivity analysis method was implemented to quantify three different uncertainty sources (parameters, models, and climate scenarios) of a three-dimensional large-scale process-based hydrologic model (Process-based Adaptive Watershed Simulator, PAWS) with an application case in an ∼ 9000 km2 Amazon catchment. The importance of different uncertainty sources was quantified by sensitivity indices for two hydrologic outputs of interest: evapotranspiration (ET) and groundwater contribution to streamflow (QG). The results show that the parameters, especially the vadose zone parameters, are the most important uncertainty contributors for both outputs. In addition, the influence of climate scenarios on ET predictions is also important. Furthermore, the thickness of the aquifers is important for QG predictions, especially in main stream areas. These sensitivity analysis results provide useful information for modelers, and our method is mathematically rigorous and can be applied to other large-scale hydrological models.

Efficient Sensitivity Analysis for Multibody Dynamics Systems Using an Iterative Steps Method With Application in Topology Optimization

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi ◽  
Sudhakar Arepally ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Multibody Dynamics ◽  
Optimization Problem ◽  
Finite Difference Methods ◽  
Analysis Method ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Rotational Motions

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

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