TY - JOUR

T1 - Relationship between sensitivity indices defined by variance- and covariance-based methods

AU - Li, Genyuan

AU - Rabitz, Herschel

N1 - Funding Information:
H.R. acknowledges the support of the National Science Foundation (CHE-1464569); G.L. acknowledges the support of the Department of Energy (DE-FG02-02ER15344).
Publisher Copyright:
© 2017 Elsevier Ltd

PY - 2017/11

Y1 - 2017/11

N2 - Sensitivity analysis is a challenge to perform with correlated variables, as often occur in practice. The variance-based methods for correlated variables use the same sensitivity indices defined for independent variables. The associate algorithms to determine the sensitivity indices are computationally demanding, and require explicit knowledge of the joint and conditional probability density function (pdf) of the input variables. As an alternative, a method referred to as structural and correlative sensitivity analysis (SCSA) based on a covariance decomposition has also been developed to fully quantify the deterministic and statistical contributions of independent and correlated variables, which can be applied in simulations as well as for laboratory/field data where the explicit forms of the function f(x) and the pdf are unknown. In this paper, we show that the sensitivity indices defined by the variance-based method may be re-expressed in terms of the SCSA sensitivity indices without further numerical computation, if the function f(x) and the pdf are known. If f(x) and the pdf are not known, the indices can still be accurately calculated from a single modest set of input-output data samples with SCSA.

AB - Sensitivity analysis is a challenge to perform with correlated variables, as often occur in practice. The variance-based methods for correlated variables use the same sensitivity indices defined for independent variables. The associate algorithms to determine the sensitivity indices are computationally demanding, and require explicit knowledge of the joint and conditional probability density function (pdf) of the input variables. As an alternative, a method referred to as structural and correlative sensitivity analysis (SCSA) based on a covariance decomposition has also been developed to fully quantify the deterministic and statistical contributions of independent and correlated variables, which can be applied in simulations as well as for laboratory/field data where the explicit forms of the function f(x) and the pdf are unknown. In this paper, we show that the sensitivity indices defined by the variance-based method may be re-expressed in terms of the SCSA sensitivity indices without further numerical computation, if the function f(x) and the pdf are known. If f(x) and the pdf are not known, the indices can still be accurately calculated from a single modest set of input-output data samples with SCSA.

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U2 - 10.1016/j.ress.2017.05.038

DO - 10.1016/j.ress.2017.05.038

M3 - Article

AN - SCOPUS:85020036918

SN - 0951-8320

VL - 167

SP - 136

EP - 157

JO - Reliability Engineering and System Safety

JF - Reliability Engineering and System Safety

ER -