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Analytical global sensitivity analysis with Gaussian processes

Published online by Cambridge University Press:  03 August 2017

Ankur Srivastava ,
Arun K. Subramaniyan  and
Liping Wang
Ankur Srivastava*
Affiliation:
GE Global Research Center, Niskayuna, New York, USA
Arun K. Subramaniyan
Affiliation:
GE Global Research Center, Niskayuna, New York, USA
Liping Wang
Affiliation:
GE Global Research Center, Niskayuna, New York, USA
*
Reprint requests to: Ankur Srivastava, GE Global Research Center, 1 Research Circle, Niskayuna, NY 12309, USA. E-mail: ankur.rice@gmail.com
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Abstract

Methods for efficient variance-based global sensitivity analysis of complex high-dimensional problems are presented and compared. Variance decomposition methods rank inputs according to Sobol indices that can be computationally expensive to evaluate. Main and interaction effect Sobol indices can be computed analytically in the Kennedy and O'Hagan framework with Gaussian processes. These methods use the high-dimensional model representation concept for variance decomposition that presents a unique model representation when inputs are uncorrelated. However, when the inputs are correlated, multiple model representations may be possible leading to ambiguous sensitivity ranking with Sobol indices. In this work, we present the effect of input correlation on sensitivity analysis and discuss the methods presented by Li and Rabitz in the context of Kennedy and O'Hagan's framework with Gaussian processes. Results are demonstrated on simulated and real problems for correlated and uncorrelated inputs and demonstrate the utility of variance decomposition methods for sensitivity analysis.

Keywords

Bayesian QuadratureEffect FunctionsGaussian ProcessesSobol Indices
Type
Special Issue Articles
Information
AI EDAM , Volume 31 , Special Issue 3: Uncertainty Quantification for Engineering Design , August 2017 , pp. 235 - 250
Copyright
Copyright © Cambridge University Press 2017 

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