Journal ArticleDOI
Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I Theory
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In this article, the sensitivity of the solutions of large sets of coupled nonlinear rate equations to uncertainties in the rate coefficients is investigated, and it is shown via an application of Weyl's ergodic theorem that a subset of the Fourier coefficients is related to ∂ci/∂kl ǫ, the rate of change of the concentration of species i with respect to the rate constant for reaction l averaged over the uncertainties of all the other rate coefficients.Abstract:
A method has been developed to investigate the sensitivity of the solutions of large sets of coupled nonlinear rate equations to uncertainties in the rate coefficients. This method is based on varying all the rate coefficients simultaneously through the introduction of a parameter in such a way that the output concentrations become periodic functions of this parameter at any given time t. The concentrations of the chemical species are then Fourier analyzed at time t. We show via an application of Weyl's ergodic theorem that a subset of the Fourier coefficients is related to 〈∂ci/∂kl〉, the rate of change of the concentration of species i with respect to the rate constant for reaction l averaged over the uncertainties of all the other rate coefficients. Thus a large Fourier coefficient corresponds to a large sensitivity, and a small Fourier coefficient corresponds to a small sensitivity. The amount of numerical integration required to calculate these Fourier coefficients is considerably less than that requi...read more
Citations
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Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index
Andrea Saltelli,Paola Annoni,Ivano Azzini,Francesca Campolongo,Marco Ratto,Stefano Tarantola +5 more
TL;DR: Existing and new practices for sensitivity analysis of model output are compared and recommendations on which to use are offered to help practitioners choose which techniques to use.
Journal ArticleDOI
A Methodology For Performing Global Uncertainty And Sensitivity Analysis In Systems Biology
TL;DR: This work develops methods for applying existing analytical tools to perform analyses on a variety of mathematical and computer models and provides a complete methodology for performing these analyses, in both deterministic and stochastic settings, and proposes novel techniques to handle problems encountered during these types of analyses.
Journal ArticleDOI
Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems
Jon C. Helton,Freddie J. Davis +1 more
TL;DR: The following techniques for uncertainty and sensitivity analysis are briefly summarized: Monte Carlo analysis, differential analysis, response surface methodology, Fourier amplitude sensitivity test, Sobol' variance decomposition, and fast probability integration.
Journal ArticleDOI
Importance measures in global sensitivity analysis of nonlinear models
Toshimitsu Homma,Andrea Saltelli +1 more
TL;DR: In this paper, a new method of global sensitivity analysis of nonlinear models is proposed based on a measure of importance to calculate the fractional contribution of the input parameters to the variance of the model prediction.
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A quantitative model-independent method for global sensitivity analysis of model output
TL;DR: In this paper, the Fourier amplitude sensitivity test (FAST) has been extended to include all the interaction terms involving a factor and the main effect of the factor's main effect.
References
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Numerical Evaluation of Multiple Integrals
TL;DR: A survey of the main methods for numerical evaluation of multiple integrals can be found in this article, where the Monte Carlo method and its generalizations are discussed, as well as number-theoretical methods, based essentially on the ideas of Diophantine approximation and equidistribution modulo 1; functional analysis approach, in which the quadrature error is regarded as a linear functional and one attempts to minimize its norm.