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Moment‐independent regional sensitivity analysis of complicated models with great efficiency
Author(s) -
Zhang Leigang,
Lu Zhenzhou,
Cheng Lei,
Hong Dongpao
Publication year - 2015
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4931
Subject(s) - sensitivity (control systems) , moment (physics) , monte carlo method , probability density function , mathematical optimization , computer science , entropy (arrow of time) , transformation (genetics) , variable (mathematics) , function (biology) , range (aeronautics) , sparse grid , grid , mathematics , algorithm , statistics , engineering , mathematical analysis , biochemistry , physics , chemistry , geometry , classical mechanics , quantum mechanics , electronic engineering , evolutionary biology , biology , gene , aerospace engineering
Summary Moment‐independent regional sensitivity analysis (RSA) is a very useful guide tool for assessing the effect of a specific range of an individual input on the uncertainty of model output, while large computational burden is involved to perform RSA, which would certainty lead to the limitation of engineering application. Main tasks for performing RSA are to estimate the probability density function (PDF) of model output and the joint PDF of model output and the input variable by some certain smart techniques. Firstly, a method based on the concepts of maximum entropy, fractional moment and sparse grid integration is utilized to estimate the PDF of the model output. Secondly, Nataf transformation is applied to obtain the joint PDF of model output and the input variable. Finally, according to an integral transformation, those regional sensitivity indices can be easily computed by a Monte Carlo procedure without extra function evaluations. Because all the PDFs can be estimated with great efficiency, and only a small amount of function evaluations are involved in the whole process, the proposed method can greatly decrease the computational burden. Several examples with explicit or implicit input–output relations are introduced to demonstrate the accuracy and efficiency of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.