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A new framework for comprehensive, robust, and efficient global sensitivity analysis: 1. Theory
Author(s) -
Razavi Saman,
Gupta Hoshin V.
Publication year - 2016
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2015wr017558
Subject(s) - sobol sequence , sensitivity (control systems) , robustness (evolution) , computer science , dimension (graph theory) , variance (accounting) , mathematical optimization , econometrics , data mining , mathematics , engineering , biochemistry , chemistry , accounting , electronic engineering , pure mathematics , business , gene
Computer simulation models are continually growing in complexity with increasingly more factors to be identified. Sensitivity Analysis (SA) provides an essential means for understanding the role and importance of these factors in producing model responses. However, conventional approaches to SA suffer from (1) an ambiguous characterization of sensitivity, and (2) poor computational efficiency, particularly as the problem dimension grows. Here, we present a new and general sensitivity analysis framework (called VARS), based on an analogy to “variogram analysis,” that provides an intuitive and comprehensive characterization of sensitivity across the full spectrum of scales in the factor space. We prove, theoretically, that Morris (derivative‐based) and Sobol (variance‐based) methods and their extensions are special cases of VARS, and that their SA indices can be computed as by‐products of the VARS framework. Synthetic functions that resemble actual model response surfaces are used to illustrate the concepts, and show VARS to be as much as two orders of magnitude more computationally efficient than the state‐of‐the‐art Sobol approach. In a companion paper, we propose a practical implementation strategy, and demonstrate the effectiveness, efficiency, and reliability (robustness) of the VARS framework on real‐data case studies.