| 翻訳と辞書 |
| Fourier amplitude sensitivity testing ： ウィキペディア英語版 |
Fourier amplitude sensitivity testing
Fourier amplitude sensitivity testing (FAST) is a variance-based global sensitivity analysis method. The sensitivity value is defined based on conditional variances which indicate the individual or joint effects of the uncertain inputs on the output.
FAST first represents conditional variances via coefficients from the multiple Fourier series expansion of the output function. Then the ergodic theorem is applied to transform the multi-dimensional integral to a one-dimensional integral in evaluation of the Fourier coefficients. A set of incommensurate frequencies is required to perform the transform and most frequencies are irrational. To facilitate computation a set of integer frequencies is selected instead of the irrational frequencies. The integer frequencies are not strictly incommensurate, resulting in an error between the multi-dimensional integral and the transformed one-dimensional integral. However, the integer frequencies can be selected to be incommensurate to any order so that the error can be controlled meeting any precision requirement in theory. Using integer frequencies in the integral transform, the resulted function in the one-dimensional integral is periodic and the integral only needs to evaluate in a single period. Next, since the continuous integral function can be recovered from a set of finite sampling points if the Nyquist–Shannon sampling theorem is satisfied, the one-dimensional integral is evaluated from the summation of function values at the generated sampling points.
FAST is more efficient to calculate sensitivities than other variance-based global sensitivity analysis methods via Monte Carlo integration. However the calculation by FAST is usually limited to sensitivities referring to “main effect” or “total effect”.
== History ==
The FAST method originated in study of coupled chemical reaction systems in 1973〔Cukier, R.I., C.M. Fortuin, K.E. Shuler, A.G. Petschek and J.H. Schaibly (1973). Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I Theory. ''Journal of Chemical Physics'', 59, 3873–3878.〕〔Schaibly, J.H. and K.E. Shuler (1973). Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. II Applications. ''Journal of Chemical Physics'', 59, 3879–3888.〕 and the detailed analysis of the computational error was presented latter in 1975.〔Cukier, R.I., J.H. Schaibly, and K.E. Shuler (1975). Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. III. Analysis of the approximations. ''Journal of Chemical Physics'', 63, 1140–1149.〕 Only the first order sensitivity indices referring to “main effect” were calculated in the original method. A FORTRAN computer program capable of analyzing either algebraic or differential equation systems was published in 1982.〔McRae, G.J., J.W. Tilden and J.H. Seinfeld (1982). Global sensitivity analysis—a computational implementation of the Fourier Amplitude Sensitivity Test (FAST). ''Computers & Chemical Engineering'', 6, 15–25.〕 In 1990s, the relationship between FAST sensitivity indices and Sobol’s ones calculated from Monte-Carlo simulation was revealed in the general framework of ANOVA-like decomposition 〔Archer G.E.B., A. Saltelli and I.M. Sobol (1997). Sensitivity measures, ANOVA-like techniques and the use of bootstrap. ''Journal of Statistical Computation and Simulation'', 58, 99–120.〕 and an extended FAST method able to calculate sensitivity indices referring to “total effect” was developed.〔Saltelli A., S. Tarantola and K.P.S. Chan (1999). A quantitative model-independent method for global sensitivity analysis of model output. ''Technometrics'', 41, 39–56.〕
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「Fourier amplitude sensitivity testing」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|