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International Journal for Uncertainty Quantification
Главный редактор: Habib N. Najm (open in a new tab)
Ассоциированный редакторs: Dongbin Xiu (open in a new tab) Tao Zhou (open in a new tab)
Редактор-основатель: Nicholas Zabaras (open in a new tab)

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ISSN Печать: 2152-5080

ISSN Онлайн: 2152-5099

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SHAPLEY EFFECT ESTIMATION IN RELIABILITY-ORIENTED SENSITIVITY ANALYSIS WITH CORRELATED INPUTS BY IMPORTANCE SAMPLING

Том 13, Выпуск 3, 2023, pp. 1-37
DOI: 10.1615/Int.J.UncertaintyQuantification.2022043692
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Краткое описание

Reliability-oriented sensitivity analysis aims at combining both reliability and sensitivity analyses by quantifying the influence of each input variable of a numerical model on a quantity of interest related to its failure. In particular, target sensitivity analysis focuses on the occurrence of the failure, and more precisely aims to determine which inputs are more likely to lead to the failure of the system. The Shapley effects are quantitative global sensitivity indices which are able to deal with correlated input variables. They have been recently adapted to the target sensitivity analysis framework. In this article, we investigate two importance-sampling-based estimation schemes of these indices which are more efficient than the existing ones when the failure probability is small. Moreover, an extension to the case where only an i.i.d. input/output N-sample distributed according to the importance sampling auxiliary distribution is proposed. This extension allows us to estimate the Shapley effects only with a data set distributed according to the importance sampling auxiliary distribution stemming from a reliability analysis without additional calls to the numerical model. In addition, we study theoretically the absence of bias of some estimators as well as the benefit of importance sampling. We also provide numerical guidelines and finally, realistic test cases show the practical interest of the proposed methods.

ЛИТЕРАТУРА
  1. Davis, P. J. and Rabinowitz, P., Methods of Numerical Integration, Amsterdam, the Netherlands: Elsevier, 2007.

  2. Rubinstein, R.Y. and Kroese, D.P., Simulation and the Monte Carlo Method, Vol. 10, New York: John Wiley & Sons, 2016.

  3. Morio, J. and Balesdent, M., Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems: A Practical Approach, Sawston, UK: Woodhead Publishing, 2015.

  4. Bucklew, J., Introduction to Rare Event Simulation, Berlin: Springer Science & Business Media, 2004.

  5. Saltelli, A., Tarantola, S., Campolongo, F., and Ratto, M., Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models, Vol. 1, Wiley Online Library, 2004.

  6. Marrel, A. and Chabridon, V., Statistical Developments for Target and Conditional Sensitivity Analysis: Application on Safety Studies for Nuclear Reactor, Reliab. Eng. Syst. Saf., 214:107711, 2021.

  7. Sobol, I.M., Sensitivity Analysis for Non-Linear Mathematical Models, Math. Modell. Comput. Exp., 1:407-414,1993.

  8. Wei, P., Lu, Z., Hao, W., Feng, J., and Wang, B., Efficient Sampling Methods for Global Reliability Sensitivity Analysis, Comput. Phys. Commun., 183(8):1728-1743,2012.

  9. Perrin, G. and Defaux, G., Efficient Evaluation of Reliability-Oriented Sensitivity Indices, J. Sci. Comput:., 79(3):1433-1455, 2019.

  10. Chastaing, G., Gamboa, F., and Prieur, C., Generalized Hoeffding-Sobol Decomposition for Dependent Variables-Application to Sensitivity Analysis, Electron. J. Stat., 6:2420-2448, 2012.

  11. Shapley, L.S., A Value for n-Person Games, in Contributions to the Theory of Games, H. Kuhnand A. Tucker, Eds., Princeton, NJ: Princeton University Press, pp. 307-317, 1953.

  12. Owen, A.B., Sobol' Indices and Shapley Value, SIAM/ASA J. Uncertainty Quantif., 2(1):245-251, 2014.

  13. Il Idrissi, M., Chabridon, V., and Iooss, B., Developments and Applications of Shapley Effects to Reliability-Oriented Sensitivity Analysis with Correlated Inputs, Env. Model. Software, 143:105115,2021.

  14. Broto, B., Bachoc, F., and Depecker, M., Variance Reduction for Estimation of Shapley Effects and Adaptation to Unknown Input Distribution, SIAM/ASA J. Uncertainty Quantif, 8(2):693-716, 2020.

  15. Hoeffding, W., A Class of Statistics with Asymptotically Normal Distribution, Ann. Math. Stat., 19(3):293-325, 1948.

  16. Homma, T. and Saltelli, A., Importance Measures in Global Sensitivity Analysis of Nonlinear Models, Reliab. Eng. Syst. Saf, 52(1):1-17, 1996.

  17. Song, E., Nelson, B.L., and Staum, J., Shapley Effects for Global Sensitivity Analysis: Theory and Computation, SIAM/ASA J. Uncertainty Quantif., 4(1):1060-1083,2016.

  18. Owen, A.B. and Prieur, C., On Shapley Value for Measuring Importance of Dependent Inputs, SIAM/ASA J. Uncertainty Quantif., 5(1):986-1002, 2017.

  19. Iooss, B. and Prieur, C., Shapley Effects for Sensitivity Analysis with Correlated Inputs: Comparisons with Sobol' Indices, Numerical Estimation and Applications, Int. J. Uncertainty Quantif, 9(5):493-514, 2019.

  20. Castro, J., Gomez, D., and Tejada, J., Polynomial Calculation of the Shapley Value Based on Sampling, Comput. Oper. Res, 36(5):1726-1730, 2009.

  21. Plischke, E., Rabitti, G., and Borgonovo, E., Computing Shapley Effects for Sensitivity Analysis, SIAM/ASA J. Uncertainty Quantif., 9(4):1411-1437,2021.

  22. Benoumechiara, N. and Elie-Dit-Cosaque, K., Shapley Effects for Sensitivity Analysis with Dependent Inputs: Bootstrap and Kriging-Based Algorithms, ESAIM: Proc. Surv, 65:266-293, 2019.

  23. Benard, C., Biau, G., Da Veiga, S., and Scornet, E., SHAFF: Fast and Consistent SHApley EFfect Estimates via Random Forests, Int. Conf. on Artificial Intelligence and Statistics, pp. 5563-5582, PMLR, 2022.

  24. Broto, B., Bachoc, F., Clouvel, L., and Martinez, J.M., Block-Diagonal Covariance Estimation and Application to the Shapley Effects in Sensitivity Analysis, Math. Stat. Theory, arXiv:1907.12780, 2019.

  25. Broto, B., Bachoc, F., Depecker, M., and Martinez, J.M., Sensitivity Indices for Independent Groups of Variables, Math. Comput. Simul., 163:19-31, 2019.

  26. Sun, Y., Apley, D.W., and Staum, J., Efficient Nested Simulation for Estimating the Variance of a Conditional Expectation, Oper. Res, 59(4):998-1007, 2011.

  27. Da Veiga, S. and Gamboa, F., Efficient Estimation of Sensitivity Indices, J. Nonparametric Stat., 25(3):573-595, 2013.

  28. Hasofer, A.M. and Lind, N.C., Exact and Invariant Second-Moment Code Format, J. Eng. Mech. Div., 100(1):111-121,1974.

  29. Breitung, K., Asymptotic Approximations for Multinormal Integrals, J. Eng. Mech, 110(3):357-366,1984.

  30. Cerou, F., Del Moral, P., Furon, T., and Guyader, A., Sequential Monte Carlo for Rare Event Estimation, Stat. Comput:., 22(3):795-908,2012.

  31. Koutsourelakis, P.S., Pradlwarter, H., and Schueller, G., Reliability of Structures in High Dimensions, Part I: Algorithms and Applications, Probab. Eng. Mech, 19(4):409-417,2004.

  32. Kahn, H. and Harris, T.E., Estimation of Particle Transmission by Random Sampling, Nat. Bureau Stand. Appl. Math. Ser., 12:27-30, 1951.

  33. Shinozuka, M., Basic Analysis of Structural Safety, J. Struct. Eng. ASCE, 109:721-740, 1983.

  34. Harbitz, A., Efficient and Accurate Probability of Failure Calculation by the Use of Importance Sampling Technique, Proc. of ICASP, Vol. 4, pp. 825-836, 1983.

  35. Zhang, P., Nonparametric Importance Sampling, J. Am. Stat. Assoc., 91(435):1245-1253, 1996.

  36. De Boer, P.T., Kroese, D.P., Mannor, S., and Rubinstein, R.Y., A Tutorial on the Cross-Entropy Method, Ann. Oper. Res., 134(1):19-67, 2005.

  37. Rubinstein, R.Y. and Kroese, D.P., The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning, Berlin: Springer Science & Business Media, 2013.

  38. Raguet, H. and Marrel, A., Target and Conditional Sensitivity Analysis with Emphasis on Dependence Measures, Stat. Methodol, arXiv:1801.10047,2018.

  39. Geyer, S., Papaioannou, I., and Straub, D., Cross Entropy-Based Importance Sampling Using Gaussian Densities Revisited, Struct. Saf., 76:15-27, 2019.

  40. Zhou, C., Lu, Z., Zhang, L., and Hu, J., Moment Independent Sensitivity Analysis with Correlations, Appl. Math. Modell., 38(19-20):4885-4896, 2014.

  41. Li, B., Zhang, L., Zhu, X., Yu, X., and Ma, X., Reliability Analysis Based on aNovel Density Estimation Method for Structures with Correlations, Chin. J. Aeronaut., 30(3):1021-1030,2017.

  42. Rothermel, R.C., A Mathematical Model for Predicting Fire Spread in Wildland Fuels, Res. Pap. INT-115, Ogden, UT: U.S. Department of Agriculture, Intermountain Forest & Range Experiment Station, 1972.

  43. Salvador, R., Pinol, J., Tarantola, S., and Pla, E., Global Sensitivity Analysis and Scale Effects of a Fire Propagation Model Used over Mediterranean Shrublands, Ecol. Modell, 136(2-3):175-189,2001.

  44. Albini, F.A., Estimating Wildfire Behavior and Effects, INT-GTR-30, Ogden, UT: U.S. Department of Agriculture, Forest Service, Intermountain Forest and Range, 1976.

  45. Catchpole, E.A. and Catchpole, W.R., Modelling Moisture Damping for Fire Spread in a Mixture of Live and Dead Fuels, Int. J Wildland Fire, 1:101-106, 1991.

  46. Clark, R., Hope, A., Tarantola, S., Gatelli, D., Dennison, P.E., and Moritz, M.A., Sensitivity Analysis of a Fire Spread Model in a Chaparral Landscape, Fire Ecol., 4(1):1-13, 2008.

  47. Janon, A., Klein, T., Lagnoux, A., Nodet, M., and Prieur, C., Asymptotic Normality and Efficiency of Two Sobol Index Estimators, ESAIM: Probab. Stat, 18:342-364, 2014.

  48. Zahm, O., Cui, T., Law, K., Spantini, A., and Marzouk, Y., Certified Dimension Reduction in Nonlinear Bayesian Inverse Problems, Math. Probab, arXiv:1807.03712,2018.

  49. Echard, B., Gayton, N., Lemaire, M., and Relun, N., A Combined Importance Sampling and Kriging Reliability Method for Small Failure Probabilities with Time-Demanding Numerical Models, Reliab. Eng. Syst. Saf., 111:232-240, 2013.

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