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Efficient Sensitivity/Uncertainty Analysis Using the Combined Stochastic Response Surface Method and Automated Differentiation: Application to Environmental and Biological Systems
Author(s) -
Isukapalli S. S.,
Roy A.,
Georgopoulos P. G.
Publication year - 2000
Publication title -
risk analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.972
H-Index - 130
eISSN - 1539-6924
pISSN - 0272-4332
DOI - 10.1111/0272-4332.205054
Subject(s) - latin hypercube sampling , monte carlo method , sampling (signal processing) , sensitivity (control systems) , propagation of uncertainty , mathematics , series (stratigraphy) , algorithm , stochastic modelling , set (abstract data type) , mathematical optimization , component (thermodynamics) , computer science , statistics , engineering , filter (signal processing) , physics , computer vision , paleontology , electronic engineering , biology , programming language , thermodynamics
Estimation of uncertainties associated with model predictions is an important component of the application of environmental and biological models. “Traditional” methods for propagating uncertainty, such as standard Monte Carlo and Latin Hypercube Sampling, however, often require performing a prohibitive number of model simulations, especially for complex, computationally intensive models. Here, a computationally efficient method for uncertainty propagation, the Stochastic Response Surface Method (SRSM) is coupled with another method, the Automatic Differentiation of FORTRAN (ADIFOR). The SRSM is based on series expansions of model inputs and outputs in terms of a set of “well‐behaved” standard random variables. The ADIFOR method is used to transform the model code into one that calculates the derivatives of the model outputs with respect to inputs or transformed inputs. The calculated model outputs and the derivatives at a set of sample points are used to approximate the unknown coefficients in the series expansions of outputs. A framework for the coupling of the SRSM and ADIFOR is developed and presented here. Two case studies are presented, involving (1) a physiologically based pharmacokinetic model for perchloroethylene for humans, and (2) an atmospheric photochemical model, the Reactive Plume Model. The results obtained agree closely with those of traditional Monte Carlo and Latin hypercube sampling methods, while reducing the required number of model simulations by about two orders of magnitude.