Point estimate methods based on Taylor Series Expansion – The perturbance moments method – A more coherent derivation of the second order statistical moment

Point estimate methods (PEMs) have found their niche in application to geotechnical problems and a few other engineering fields, where their relative simplicity matches well with the need for quick and reliable estimates of the uncertainty in model results. In some cases, however, the simplicity of...

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Bibliographic Details
Published in:Applied mathematical modelling 2012-11, Vol.36 (11), p.5445-5454
Main Authors: Franceschini, S., Tsai, C., Marani, M.
Format: Article
Language:English
Subjects:
Computer simulation
Estimates
Hydrologic response
Mathematical analysis
Mathematical models
Monte Carlo methods
Mountains
Nonlinearity
Point estimate methods
Taylor series
Uncertainty analysis
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Summary:Point estimate methods (PEMs) have found their niche in application to geotechnical problems and a few other engineering fields, where their relative simplicity matches well with the need for quick and reliable estimates of the uncertainty in model results. In some cases, however, the simplicity of the PEMs has to come to terms with the physical meaning of the stochastic variables and with the non-linearity of the model function. In this study, a general review of PEMs is presented and an improved method is proposed that requires fewer model evaluations, but still provides meaningful results for non-linear problems. Two uncertainty analyses of the hydrologic response to a rainfall event are presented: for a small synthetic basin and for a small mountain basin in Italy. The results of three PEMs are evaluated – Rosenblueth’s method, Li’s method, and the proposed perturbance moments method (PMM), along with the computationally-intensive, Monte Carlo simulation (MCS) approach. It is shown that for the same computational requirements, the derivation of the PMM is more coherent and resolves the problem of the negative variance which can occur when using other PEMs derived from the Taylor Series Expansion. The method is also computationally efficient, both compared to MCS and to other PEMs.
ISSN:0307-904X
DOI:10.1016/j.apm.2011.11.079