ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Two improved methods for variance-based global sensitivity analysis' W-indices
Received date: 2015-04-10
Revised date: 2016-03-22
Online published: 2016-03-25
Supported by
National Natural Science Foundation of China (51475370);Fundamental Research Funds for the Central University (3102015BJ(II)CG009)
In the global sensitivity analysis (SA), the variance-based sensitivity indices, such as Sobol's indices and W-indices, are used widely. Sobol's indices estimate the average variation of model output when input variables are fixed in their points. W-indices measure the average reduction of model output if input variables are reduced in their distributions. Compared with Sobol's indices, W-indices include more information. The double loop repeated set Monte Carlo (DLRS MC) and double loop single set Monte Carlo (DLSS MC) are two traditional methods, but these available methods for solving W-indices are still defective. In order to calculate W-indices efficiently, two new methods are presented. They are advanced Monte Carlo simulation (AMCS) and sparse grid integration (SGI)-based method. The AMCS only needs one set of samples to estimate all W-indices. Since screening method is used to estimate the variance in the conditional interval, and the count error induced by taking an integer in DLSS MC can be avoided, the accuracy of AMCS is higher than that of DLSS MC. The SGI-based method estimates W-indices by evaluating threefold statistic moment by SGI, in which the efficiency of the SGI is inherited. Finally, two numerical examples and an engineering example are employed to demonstrate the reasonability and efficiency of the presented methods.
GONG Xiangrui , LYU Zhenzhou , ZUO Jianwei . Two improved methods for variance-based global sensitivity analysis' W-indices[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016 , 37(6) : 1888 -1898 . DOI: 10.7527/S1000-6893.2016.0090
[1] ZIO E, PODOFILLINI L. Accounting for components interactions in the differential importance measure[J]. Reliability Engineering & System Safety, 2006, 91(10-11):1163-1174.
[2] DO VAN P, BARROS A, BERENGUER C. Differential importance measure of Markov models using perturbation analysis[C]//European Safety and Reliability Conference (ESREL 2009). Abingdon, UK:Taylor & Francis, 2009:981-987.
[3] BORGONOVO E, APOSTOLAKIS G E. Comparison of global sensitivity analysis techniques and importance measures in PSA[J]. Reliability Engineering & System Safety, 2003, 79(2):175-185.
[4] VON GRIENSVEN A, MEIXNER T, GRUNWALD S, et al. A global sensitivity analysis tool for the parameters of multi-variable catchment models[J]. Journal of Hydrology, 2006, 324(1-4):10-23.
[5] SALTELLI A. Sensitivity analysis for importance assessment[J]. Risk Analysis, 2002, 22(3):579-590.
[6] HELTON J C, DAVIS F J. Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems[J]. Reliability Engineering & System Safety, 2003, 81(1):23-69.
[7] HELTON J C. Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal[J]. Reliability Engineering & System Safety, 1993, 42(2):327-367.
[8] SALTELLI A, MARIVOET J. Non-parametric statistics in sensitivity analysis for model output:A comparison of selected techniques[J]. Reliability Engineering & System Safety, 1990, 28(2):229-253.
[9] CHUN M H, HAN S J, TAK N I L. An uncertainty importance measure using a distance metric for the change in a cumulative distribution function[J]. Reliability Engineering & System Safety, 2000, 70(3):313-321.
[10] LIU H, CHEN W, SUDJIANTO A. Relative entropy based method for probabilistic sensitivity analysis in engineering design[J]. Journal of Mechanical Design, 2006, 128(2):326-336.
[11] BORGONOVO E. A new uncertainty importance measure[J]. Reliability Engineering & System Safety, 2007, 92(6):771-784.
[12] CUI L J, LU Z Z, ZHAO X P. Moment-independent importance measure of basic random variable and its probability density evolution solution[J]. Science China Technological Sciences, 2010, 53(4):1138-1145.
[13] LI L Y, LU Z Z, FENG J, et al. Moment-independent importance measure of basic variable and its state dependent parameter solution[J]. Structural Safety, 2012, 38:40-47.
[14] SOBOL' I M. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates[J]. Mathematics and Computers in Simulation, 2001, 55(1):271-280.
[15] SALTELLI A, ANNONI P, AZZINI I, et al. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index[J]. Computer Physics Communications, 2010, 181(2):259-270.
[16] ARCHER G E B, SALTELLI A, SOBOL I M. Sensitivity measures, ANOVA-like techniques and the use of bootstrap[J]. Journal of Statistical Computation and Simulation, 1997, 58(2):99-120.
[17] SOBOL' I M. On sensitivity estimation for nonlinear mathematical models[J].Matematicheskoe Modelirovanie, 1990, 2(1):112-118.
[18] SALTELLI A, TARANTOLA S. On the relative importance of input factors in mathematical models:Safety assessment for nuclear waste disposal[J]. Journal of the American Statistical Association, 2002, 97(459):702-709.
[19] WEI P, LU Z Z, SONG J. A new variance-based global sensitivity analysis technique[J]. Computer Physics Communications, 2013, 184(11):2540-2551.
[20] TARANTOLA S, KOPUSTINSKAS V, BOLADO-LAVIN R, et al. Sensitivity analysis using contribution to sample variance plot:Application to a water hammer model[J]. Reliability Engineering & System Safety, 2012, 99:62-73.
[21] RATTO M, PAGANO A, YOUNG P. State dependent parameter metamodelling and sensitivity analysis[J]. Computer Physics Communications, 2007, 177(11):863-876.
[22] BARTHELMANN V, NOVAK E, RITTER K. High dimensional polynomial interpolation on sparse grids[J]. Advances in Computational Mathematics, 2000, 12(4):273-288.
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