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Uncertainties exist in both physics-based and data-driven models.Variance-based sensitivity analysis characterizes how the variance of a modeloutput is propagated from the model inputs. The Sobol index is one of the mostwidely used sensitivity indices for models with independent inputs. For modelswith dependent inputs, different approaches have been explored to obtainsensitivity indices in the literature. Typical approaches are based onprocedures 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 densityfunctions. In this paper, data-driven sensitivity indices are proposed formodels with dependent inputs. We first construct ordered partitions of linearlyindependent polynomials of the inputs. The modified Gram-Schmidt algorithm isthen applied to the ordered partitions to generate orthogonal polynomials withrespect to the empirical measure based on observed data of model inputs andoutputs. Using the polynomial chaos expansion with the orthogonal polynomials,we obtain the proposed data-driven sensitivity indices. The sensitivity indicesprovide intuitive interpretations of how the dependent inputs affect thevariance of the output without a priori knowledge on the dependence structureof the inputs. Three numerical examples are used to validate the proposedapproach.

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