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GLOBAL SENSITIVITY ANALYSIS OF RARE EVENT PROBABILITIES USING SUBSET SIMULATION AND POLYNOMIAL CHAOS EXPANSIONS

卷 13, 册 1, 2023, pp. 53-67
DOI: 10.1615/Int.J.UncertaintyQuantification.2022041624
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摘要

By their very nature, rare event probabilities are expensive to compute; they are also delicate to estimate as their value strongly depends on distributional assumptions on the model parameters. Hence, understanding the sensitivity of the computed rare event probabilities to the hyper-parameters that define the distribution law of the model parameters is crucial. We show that by (i) accelerating the calculation of rare event probabilities through subset simulation and (ii) approximating the resulting probabilities through a polynomial chaos expansion, the global sensitivity of such problems can be analyzed through a double-loop sampling approach. The resulting method is conceptually simple and computationally efficient; its performance is illustrated on a subsurface flow application and on an analytical example.

参考文献
  1. Ullmann, E. and Papaioannou, I., Multilevel Estimation of Rare Events, SIAM/ASA J. Uncertainty Quantif., 3(1):922-953, 2015.

  2. Tong, S., Vanden-Eijnden, E., and Stadler, G., Extreme Event Probability Estimation Using PDE-Constrained Optimization and Large Deviation Theory, with Application to Tsunamis, Commun. Appl. Math. Comput. Sci., 16(2):181-225, 2021.

  3. Beck, J.L. and Zuev, K.M., Rare-Event Simulation, in Handbook of Uncertainty Quantification, R. Ghanem, D. Higdon, and H. Owhadi, Eds., Cham, Switzerland: Springer, pp. 1075-1100, 2017.

  4. Morio, J., Influence of Input PDF Parameters of a Model on a Failure Probability Estimation, Simul. Modell. Practice Theory, 19(10):2244-2255, 2011.

  5. Sobol', I.M., On Sensitivity Estimation for Nonlinear Mathematical Models, Mat. Model, 2(1):112-118,1990.

  6. Sobol', I.M., Sensitivity Estimates for Nonlinear Mathematical Models, Math. Modell. Comput., 1:407-414,1993.

  7. Sobol', I.M., Global Sensitivity Indices for Nonlinear Mathematical Models and Their Monte Carlo Estimates, Math. Comput. Simul., 55:271-280,2001.

  8. Owen, A., Better Estimation of Small Sobol' Sensitivity Indices, ACM Trans. Model. Comput. Simul., 23:11-1-11-17, 2013.

  9. Ashraf, M., Oladyshkin, S., and Nowak, W., Geological Storage of CO2: Application, Feasibility and Efficiency of Global Sensitivity Analysis and Risk Assessment Using the Arbitrary Polynomial Chaos, Int. J. Greenhouse Gas Control, 19:704-719,2013.

  10. Sochala, P. and Le Maitre, O., Polynomial Chaos Expansion for Subsurface Flows with Uncertain Soil Parameters, Adv. Water Res, 62:139-154, 2013.

  11. Guo, L., Fahs, M., Hoteit, H., Gao, R., and Shao, Q., Uncertainty Analysis of Seepage-Induced Consolidation in a Fractured Porous Medium, Comput. Model. Eng. Sci, 129(1):279-297,2021.

  12. Alexanderian, A., Winokur, J., Sraj, I., Srinivasan, A., Iskandarani, M., Thacker, W.C., and Knio, O.M., Global Sensitivity Analysis in an Ocean General Circulation Model: A Sparse Spectral Projection Approach, Comput. Geosci., 16(3):757-778, 2012.

  13. Sraj, I., Mandli, K.T., Knio, O.M., Dawson, C.N., and Hoteit, I., Uncertainty Quantification and Inference of Manning's Friction Coefficients Using DART Buoy Data during the Tohoku Tsunami, Ocean Modell, 83:82-97,2014.

  14. Navarro Jimenez, M., Le Maitre, O., and Knio, O., Global Sensitivity Analysis in Stochastic Simulators of Uncertain Reaction Networks, J. Chem. Phys, 145(24):244106, 2016.

  15. Hantouche, M., Sarathy, S.M., and Knio, O.M., Global Sensitivity Analysis of n-Butanol Reaction Kinetics Using Rate Rules, Combust. Flame, 196:452-465,2018.

  16. Merritt, M., Alexanderian, A., and Gremaud, P.A., Multiscale Global Sensitivity Analysis for Stochastic Chemical Systems, Multiscale Model. Simul., 19(1):440-459,2021.

  17. Olivares, A. and Staffetti, E., Uncertainty Quantification of a Mathematical Model of COVID-19 Transmission Dynamics with Mass Vaccination Strategy, Chaos, Solitons Fractals, 146:110895, 2021.

  18. Lu, X. and Borgonovo, E., Global Sensitivity Analysis in Epidemiological Modeling, Eur. J. Oper. Res, in press, 2021.

  19. Hart, J., Gremaud, P., and David, T., Global Sensitivity Analysis of High-Dimensional Neuroscience Models: An Example of Neurovascular Coupling, Bull. Math. Biol, 81(6):1805-1828, 2019.

  20. Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., and Tarantola, S., Global Sensitivity Analysis: The Primer, New York: Wiley, 2008.

  21. Iooss, B. and Lemaitre, P., A Review on Global Analysis Methods, in Uncertainty Management in Simulation-Optimization of Complex Systems, G. Dellino and C. Meloni, Eds., Chapter 5, Berlin: Springer, pp. 101-122, 2015.

  22. Chabridon, V., Balesdent, M., Bourinet, J.M., Morio, J., and Gayton, N., Reliability-Based Sensitivity Estimators of Rare Event Probability in the Presence of Distribution Parameter Uncertainty, Reliab. Eng. Syst. Saf., 178:164-178, 2018.

  23. Lemaitre, P., Sergienko, E., Arnaud, A., Bousquet, N., Gamboa, F., and Iooss, B., Density Modification-Based Reliability Sensitivity Analysis, J. Stat. Comput. Simul., 85(6):1200-1223, 2015.

  24. Dupuis, P., Katsoulakis, M.A., Pantazis, Y., and Rey-Bellet, L., Sensitivity Analysis for Rare Events Based on Renyi Divergence, Ann. Appl. Probab., 30(4):1507-1533,2020.

  25. Ehre, M., Papaioannou, I., and Straub, D., A Framework for Global Reliability Sensitivity Analysis in the Presence of Multi-Uncertainty, Reliab. Eng. Syst. Saf., 195:106726, 2020.

  26. Wang, Z. and Jia, G., Augmented Sample-Based Approach for Efficient Evaluation of Risk Sensitivity with Respect to Epistemic Uncertainty in Distribution Parameters, Reliab. Eng. Syst. Saf., 197:106783, 2020.

  27. Wang, P., Li, C., Liu, F., and Zhou, H., Global Sensitivity Analysis of Failure Probability of Structures with Uncertainties of Random Variable and Their Distribution Parameters, Eng. Comput, 126:1-19,2021.

  28. Chabridon, V., Reliability-Oriented Sensitivity Analysis under Probabilistic Model Uncertainty-Application to Aerospace Systems, PhD, Universite Clermont Auvergne, 2018.

  29. Sehic, K. and Karamehmedovic, M., Estimation of Failure Probabilities via Local Subset Approximations, Stat. Comput:., arXiv:2003.05994, 2020.

  30. Papaioannou, I., Betz, W., Zwirglmaier, K., and Straub, D., MCMC Algorithms for Subset Simulation, Probab. Eng. Mech., 41:89-103,2015.

  31. Bhatia, R. and Davis, C., A Better Bound on the Variance, Am. Math. Mon., 107(4):353-357,2000.

  32. Au, S.K. and Beck, J.L., Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation, Probab. Eng. Mech, 16(4):263-277,2001.

  33. Schueller, G., Pradlwarter, H., and Koutsourelakis, P.S., A Critical Appraisal of Reliability Estimation Procedures for High Dimensions, Probab. Eng. Mech, 19(4):463-474, 2004.

  34. Zuev, K.M., Beck, J.L., Au, S.K., and Katafygiotis, L.S., Bayesian Post-Processor and Other Enhancements of Subset Simulation for Estimating Failure Probabilities in High Dimensions, Comput. Struct., 92:283-296, 2012.

  35. Melchers, R.E. and Beck, A.T., Structural Reliability Analysis and Prediction, New York: John Wiley & Sons, 2018.

  36. Peherstorfer, B., Kramer, B., and Willcox, K., Combining Multiple Surrogate Models to Accelerate Failure Probability Estimation with Expensive High-Fidelity Models, J. Comput. Phys., 341:61-75, 2017.

  37. Li, J. and Xiu, D., Evaluation of Failure Probability via Surrogate Models, J. Comput. Phys, 229(23):8966-8980, 2010.

  38. Li, J., Li, J., and Xiu, D., An Efficient Surrogate-Based Method for Computing Rare Failure Probability, J. Comput. Phys, 230(24):8683-8697,2011.

  39. Butler, T. and Wildey, T., Utilizing Adjoint-Based Error Estimates for Surrogate Models to Accurately Predict Probabilities of Events, Int. J. Uncertainty Quantif., 8(2):143-159, 2018.

  40. Bourinet, J.M., Rare-Event Probability Estimation with Adaptive Support Vector Regression Surrogates, Reliab. Eng. Syst. Saf., 150:210-221,2016.

  41. Ebeida, M.S., Mitchell, S.A., Swiler, L.P., Romero, V.J., and Rushdi, A.A., Pof-Darts: Geometric Adaptive Sampling for Probability of Failure, Reliab. Eng. Syst. Saf, 155:64-77, 2016.

  42. Bichon, B.J., McFarland, J.M., and Mahadevan, S., Efficient Surrogate Models for Reliability Analysis of Systems with Multiple Failure Modes, Reliab. Eng. Syst. Saf., 96(10):1386-1395, 2011.

  43. Le Maitre, O. and Knio, O.M., Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics, Berlin: Springer Science & Business Media, 2010.

  44. Crestaux, T., Le Maitre, O., and Martinez, J.M., Polynomial Chaos Expansion for Sensitivity Analysis, Reliab. Eng. Syst. Saf., 94(7):1161-1172, 2009.

  45. Asmussen, S. and Glynn, P.W., Stochastic Simulation: Algorithms and Analysis, Vol. 57, Berlin: Springer Science & Business Media, 2007.

  46. Blatman, G. and Sudret, B., Efficient Computation of Global Sensitivity Indices Using Sparse Polynomial Chaos Expansions, Reliab. Eng. Syst. Saf., 95(11):1216-1229, 2010.

  47. Fajraoui, N., Marelli, S., and Sudret, B., Sequential Design of Experiment for Sparse Polynomial Chaos Expansions, SIAM/ASA J Uncertainty Quantif, 5(1):1061-1085, 2017.

  48. Hampton, J. and Doostan, A., Compressive Sampling Methods for Sparse Polynomial Chaos Expansions, in Handbook of Uncertainty Quantification, R. Ghanem, D. Higdon, and H. Owhadi, Eds., Springer International Publishing, pp. 827-855, 2017.

  49. van den Berg, E. and Friedlander, M.P., SPGL1: A Solver for Large-Scale Sparse Reconstruction, from https://friedlander.io/ spgl1, 2019.

  50. Alexanderian, A., On Spectral Methods for Variance Based Sensitivity Analysis, Probab. Surv., 10:51-68, 2013.

  51. Saltelli, A., Annoni, P., Azzini, I., Campolongo, F., Ratto, M., and Tarantola, S., Variance Based Sensitivity Analysis of Model Output. Design and Estimator for the Total Sensitivity Index, Comput. Phys. Commun., 181:259-270, 2010.

  52. Cleaves, H.L., Alexanderian, A., Guy, H., Smith, R.C., and Yu, M., Derivative-Based Global Sensitivity Analysis for Models with High-Dimensional Inputs and Functional Outputs, SIAMJ. Sci. Comput., 41(6):A3524-A3551,2019.

  53. SPE International, SPE Comparative Solution Project: Description of Model 2, from https://www.spe.org/web/csp/datasets/ set02.htm, 2001.

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