Local Polynomial Estimation for Sensitivity Analysis on Models With Correlated Inputs

存在相关输入变量时基于方差的敏感性分析

Variance-based sensitivity analysis in the presence of correlated input variables

针对相关输入变量下的方差敏感性分析，提出扩展 Sobol' 估计量，通过线性相关模型分解相关与不相关贡献，并直接依据联合分布采样计算模型输出。

Shapley效应在具有相关输入的可靠性导向敏感性分析中的发展与应用

Developments and applications of Shapley effects to reliability-oriented sensitivity analysis with correlated inputs

本文提出基于Shapley值的“目标Shapley效应”新敏感性指数，用于在相关输入条件下度量输入对关键失效事件的影响，并给出两种估计算法及实际应用验证。

Generating correlated random vector by polynomial normal transformation

This paper develops a polynomial normal transformation model, whereby various non-normal probability distributions can be simulated by the standard normal distribution. Two methods are presented to determine the coefficients of polynomial model: (1) probability weighted moment (PWM) matching (2) percentile matching. Compared to the existing raw moment or L-moment matching, the proposed methods are more computationally convenient, and can be used to estimate the coefficients of polynomial model with a higher degree. Furthermore, for two correlated random variables, a polynomial equation is deri…

具有相关输入的高维模型的敏感性分析

Sensitivity Analysis of High-Dimensional Models with Correlated Inputs

针对输入参数随机相关导致传统敏感性分析失真的问题，本文结合多项式混沌展开与 Rosenblatt、Cholesky 变换，在方差及导数敏感性分析中量化依赖影响。

Data-Driven Sensitivity Indices for Models With Dependent Inputs Using the Polynomial Chaos Expansion

Uncertainties exist in both physics-based and data-driven models. Variance-based sensitivity analysis characterizes how the variance of a model output is propagated from the model inputs. The Sobol index is one of the most widely used sensitivity indices for models with independent inputs. For models with dependent inputs, different approaches have been explored to obtain sensitivity indices in the literature. Typical approaches are based on procedures of transforming the dependent inputs into independent inputs. However, such transformation requires additional information about the inputs, su…

Proportional marginal effects for global sensitivity analysis

Performing (variance-based) global sensitivity analysis (GSA) with dependent inputs has recently benefited from cooperative game theory concepts.By using this theory, despite the potential correlation between the inputs, meaningful sensitivity indices can be defined via allocation shares of the model output's variance to each input. The ``Shapley effects'', i.e., the Shapley values transposed to variance-based GSA problems, allowed for this suitable solution. However, these indices exhibit a particular behavior that can be undesirable: an exogenous input (i.e., which is not explicitly included…