Data-driven sensitivity indices for models with dependent inputs using polynomial chaos expansions
Data-driven sensitivity indices for models with dependent inputs using polynomial chaos expansions
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DOI：
10.1016/j.strusafe.2020.101984
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发表时间：
2018-03
影响因子：
5.8
通讯作者：
Zhanlin Liu;Youngjun Choe
中科院分区：
文献类型：
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作者：
Zhanlin Liu;Youngjun Choe
基于物理的模型和数据驱动的模型都存在不确定性。基于方差的敏感性分析表征了模型输出的方差如何从模型输入传播。Sobol指数是具有独立输入的模型的最广泛使用的灵敏度指数之一。对于具有相关输入的模型，文献中已经探索了不同的方法来获得敏感性指数。典型的方法是基于将相关输入转换为独立输入的过程。然而，这种转换需要关于输入的附加信息，例如依赖结构或条件概率密度函数。本文提出了数据驱动的灵敏度指标模型与相关的输入。我们首先构造有序分区的线性无关的多项式的输入。然后将改进的Gram-Schmidt算法应用于有序分区，以基于模型输入和输出的观测数据生成关于经验度量的正交多项式。利用正交多项式混沌展开，我们得到了建议的数据驱动的灵敏度指数。灵敏度指数提供了直观的解释，依赖的输入如何影响的方差的输出，没有先验知识的依赖结构的输入。四个数值例子被用来验证所提出的方法。
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, such as the dependency structure or the conditional probability density functions. In this paper, data-driven sensitivity indices are proposed for models with dependent inputs. We first construct ordered partitions of linearly independent polynomials of the inputs. The modified Gram-Schmidt algorithm is then applied to the ordered partitions to generate orthogonal polynomials with respect to the empirical measure based on observed data of model inputs and outputs. Using the polynomial chaos expansion with the orthogonal polynomials, we obtain the proposed data-driven sensitivity indices. The sensitivity indices provide intuitive interpretations of how the dependent inputs affect the variance of the output without a priori knowledge on the dependence structure of the inputs. Four numerical examples are used to validate the proposed approach.