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

by   Zhanlin Liu, et al.

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. A typical approach is based on a procedure 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 partition to generate orthogonal polynomials solely 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 new sensitivity indices provide intuitive interpretations on how the dependent inputs affect the variance of the output without a priori knowledge on the dependence structure of the inputs. Two numerical examples are used to validate the proposed approach.


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