A functional global sensitivity measure and efficient reliability sensitivity analysis with respect to statistical parameters

Wang, Zhiheng; Ghanem, Roger

doi:10.1016/j.cma.2022.115175

A functional global sensitivity measure and efficient reliability sensitivity analysis with respect to statistical parameters

Journal Article · Mon Jun 06 00:00:00 EDT 2022 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2022.115175· OSTI ID:2422568

^[1]; ^[1]

University of Southern California, Los Angeles, CA (United States)

Sensitivity analysis and reliability assessment are two important aspects of structural and system safety. Epistemic uncertainty with respect to probabilistic model of input parameters due to lack of knowledge is present in many scarce-data applications and complicates the characterization of uncertainty in model response. In this article, we present two importance measures to evaluate the impact of distribution parameters on the probability distribution function (PDF) of the output and the failure probability. The epistemic uncertainty associated with the distribution parameters is modeled as random variables. Additionally, a modified extended polynomial chaos expansion (MEPCE) approach is introduced in which aleatory and epistemic random variables are modeled and propagated simultaneously while allowing the separate assessment for any single epistemic variable. A MEPCE-based kernel density estimation (KDE) construction provides a composite map from each epistemic variable to the response PDF. The functional global sensitivity index of the PDF with respect to the distribution parameters is thus derived, as a function of output, which is both more informative and more efficient than standard scalar sensitivity measures. Reliability sensitivity indices can be readily evaluated by integrating the global sensitivity index function over the failure zone. Three illustrative examples are used to demonstrate the proposed methodology.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). FASTMath SciDAC-5 Institute

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); National Science Foundation (NSF)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 2422568

Alternate ID(s):: OSTI ID: 1962890

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: C Vol. 402; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (40)

A nonparametric model of random uncertainties for reduced matrix models in structural dynamics Soize, C. Probabilistic Engineering Mechanics, Vol. 15, Issue 3 https://doi.org/10.1016/S0266-8920(99)00028-4	journal	July 2000
Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates Sobol′, I. M. Mathematics and Computers in Simulation, Vol. 55, Issue 1-3 https://doi.org/10.1016/S0378-4754(00)00270-6	journal	February 2001
An application of the Kriging method in global sensitivity analysis with parameter uncertainty Wang, Pan; Lu, Zhenzhou; Tang, Zhangchun Applied Mathematical Modelling, Vol. 37, Issue 9 https://doi.org/10.1016/j.apm.2013.01.019	journal	May 2013
Random matrix theory for modeling uncertainties in computational mechanics Soize, C. Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 12-16 https://doi.org/10.1016/j.cma.2004.06.038	journal	April 2005
Reliability-based shape optimization of structures undergoing fluid–structure interaction phenomena Allen, M.; Maute, K. Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 30-33 https://doi.org/10.1016/j.cma.2004.12.028	journal	August 2005
Reliability sensitivity analysis of stochastic finite element models Jensen, H. A.; Mayorga, F.; Papadimitriou, C. Computer Methods in Applied Mechanics and Engineering, Vol. 296 https://doi.org/10.1016/j.cma.2015.08.007	journal	November 2015
An extended polynomial chaos expansion for PDF characterization and variation with aleatory and epistemic uncertainties Wang, Zhiheng; Ghanem, Roger Computer Methods in Applied Mechanics and Engineering, Vol. 382 https://doi.org/10.1016/j.cma.2021.113854	journal	August 2021
Integrated stochastic analysis of fiber composites manufacturing using adapted polynomial chaos expansions Ghauch, Ziad G.; Aitharaju, Venkat; Rodgers, William R. Composites Part A: Applied Science and Manufacturing, Vol. 118 https://doi.org/10.1016/j.compositesa.2018.12.029	journal	March 2019
Reliability-based design sensitivity by efficient simulation Au, S. K. Computers & Structures, Vol. 83, Issue 14 https://doi.org/10.1016/j.compstruc.2004.11.015	journal	May 2005
A new dynamic testing method for elastic, shear modulus and Poisson’s ratio of concrete Wang, Zhiheng; Gao, Zizhen; Wang, Yunlu Construction and Building Materials, Vol. 100 https://doi.org/10.1016/j.conbuildmat.2015.09.060	journal	December 2015
Sensitivity analysis: A review of recent advances Borgonovo, Emanuele; Plischke, Elmar European Journal of Operational Research, Vol. 248, Issue 3 https://doi.org/10.1016/j.ejor.2015.06.032	journal	February 2016
Cyclic behavior modeling of reinforced concrete shear walls based on softened damage-plasticity model Feng, De-Cheng; Ren, Xiao-Dan; Li, Jie Engineering Structures, Vol. 166 https://doi.org/10.1016/j.engstruct.2018.03.085	journal	July 2018
Robustness quantification of reinforced concrete structures subjected to progressive collapse via the probability density evolution method Feng, De-Cheng; Xie, Si-Cong; Xu, Jun Engineering Structures, Vol. 202 https://doi.org/10.1016/j.engstruct.2019.109877	journal	January 2020
On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data Ghanem, Roger G.; Doostan, Alireza Journal of Computational Physics, Vol. 217, Issue 1 https://doi.org/10.1016/j.jcp.2006.01.037	journal	September 2006
Identification of Bayesian posteriors for coefficients of chaos expansions Arnst, M.; Ghanem, R.; Soize, C. Journal of Computational Physics, Vol. 229, Issue 9 https://doi.org/10.1016/j.jcp.2009.12.033	journal	May 2010
Numerical approach for quantification of epistemic uncertainty Jakeman, John; Eldred, Michael; Xiu, Dongbin Journal of Computational Physics, Vol. 229, Issue 12 https://doi.org/10.1016/j.jcp.2010.03.003	journal	June 2010
Basis adaptation in homogeneous chaos spaces Tipireddy, Ramakrishna; Ghanem, Roger Journal of Computational Physics, Vol. 259 https://doi.org/10.1016/j.jcp.2013.12.009	journal	February 2014
Reduced Wiener Chaos representation of random fields via basis adaptation and projection Tsilifis, Panagiotis; Ghanem, Roger G. Journal of Computational Physics, Vol. 341 https://doi.org/10.1016/j.jcp.2017.04.009	journal	July 2017
Survey of sampling-based methods for uncertainty and sensitivity analysis Helton, J. C.; Johnson, J. D.; Sallaberry, C. J. Reliability Engineering & System Safety, Vol. 91, Issue 10-11 https://doi.org/10.1016/j.ress.2005.11.017	journal	October 2006
Sensitivity analysis in conjunction with evidence theory representations of epistemic uncertainty Helton, J. C.; Johnson, J. D.; Oberkampf, W. L. Reliability Engineering & System Safety, Vol. 91, Issue 10-11 https://doi.org/10.1016/j.ress.2005.11.055	journal	October 2006
A new uncertainty importance measure Borgonovo, E. Reliability Engineering & System Safety, Vol. 92, Issue 6 https://doi.org/10.1016/j.ress.2006.04.015	journal	June 2007
On the use of uncertainty importance measures in reliability and risk analysis Aven, T.; Nøkland, T. E. Reliability Engineering & System Safety, Vol. 95, Issue 2 https://doi.org/10.1016/j.ress.2009.09.002	journal	February 2010
Reliability analysis under epistemic uncertainty Nannapaneni, Saideep; Mahadevan, Sankaran Reliability Engineering & System Safety, Vol. 155 https://doi.org/10.1016/j.ress.2016.06.005	journal	November 2016
Reliability-based sensitivity estimators of rare event probability in the presence of distribution parameter uncertainty Chabridon, Vincent; Balesdent, Mathieu; Bourinet, Jean-Marc Reliability Engineering & System Safety, Vol. 178 https://doi.org/10.1016/j.ress.2018.06.008	journal	October 2018
A framework for global reliability sensitivity analysis in the presence of multi-uncertainty Ehre, Max; Papaioannou, Iason; Straub, Daniel Reliability Engineering & System Safety, Vol. 195 https://doi.org/10.1016/j.ress.2019.106726	journal	March 2020
Augmented sample-based approach for efficient evaluation of risk sensitivity with respect to epistemic uncertainty in distribution parameters Wang, Zhenqiang; Jia, Gaofeng Reliability Engineering & System Safety, Vol. 197 https://doi.org/10.1016/j.ress.2019.106783	journal	May 2020
Influence of input PDF parameters of a model on a failure probability estimation Morio, Jérôme Simulation Modelling Practice and Theory, Vol. 19, Issue 10 https://doi.org/10.1016/j.simpat.2011.08.003	journal	November 2011
Reliability sensitivity method by line sampling Lu, Zhenzhou; Song, Shufang; Yue, Zhufeng Structural Safety, Vol. 30, Issue 6 https://doi.org/10.1016/j.strusafe.2007.10.001	journal	November 2008
Quantifying and communicating uncertainty in seismic risk assessment Ellingwood, Bruce R.; Kinali, Kursat Structural Safety, Vol. 31, Issue 2 https://doi.org/10.1016/j.strusafe.2008.06.001	journal	March 2009
Aleatory or epistemic? Does it matter? Kiureghian, Armen Der; Ditlevsen, Ove Structural Safety, Vol. 31, Issue 2 https://doi.org/10.1016/j.strusafe.2008.06.020	journal	March 2009
Moment-independent importance measure of basic variable and its state dependent parameter solution Luyi, Li; Zhenzhou, Lu; Jun, Feng Structural Safety, Vol. 38 https://doi.org/10.1016/j.strusafe.2012.04.001	journal	September 2012
Reliability analysis with scarce information: Comparing alternative approaches in a geotechnical engineering context Beer, Michael; Zhang, Yi; Quek, Ser Tong Structural Safety, Vol. 41 https://doi.org/10.1016/j.strusafe.2012.10.003	journal	March 2013
Meta-model-based importance sampling for reliability sensitivity analysis Dubourg, V.; Sudret, B. Structural Safety, Vol. 49 https://doi.org/10.1016/j.strusafe.2013.08.010	journal	July 2014
Measures of Structural Safety Under Imperfect States of Knowledge Kiureghian, Armen Der Journal of Structural Engineering, Vol. 115, Issue 5 https://doi.org/10.1061/(ASCE)0733-9445(1989)115:5(1119)	journal	May 1989
Displacement-Based Design of Slender Reinforced Concrete Structural Walls—Experimental Verification Thomsen, John H.; Wallace, John W. Journal of Structural Engineering, Vol. 130, Issue 4 https://doi.org/10.1061/(ASCE)0733-9445(2004)130:4(618)	journal	April 2004
Stochastic Nonlinear Behavior of Reinforced Concrete Frames. II: Numerical Simulation Feng, De-Cheng; Li, Jie Journal of Structural Engineering, Vol. 142, Issue 3 https://doi.org/10.1061/(ASCE)ST.1943-541X.0001443	journal	March 2016
Rare Event Estimation Using Polynomial-Chaos Kriging Schöbi, R.; Sudret, B.; Marelli, S. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, Vol. 3, Issue 2 https://doi.org/10.1061/AJRUA6.0000870	journal	June 2017
Asymptotic Sampling Distribution for Polynomial Chaos Representation from Data: A Maximum Entropy and Fisher Information Approach Das, Sonjoy; Ghanem, Roger; Spall, James C. SIAM Journal on Scientific Computing, Vol. 30, Issue 5 https://doi.org/10.1137/060652105	journal	January 2008
Sensitivity Analysis with Mixture of Epistemic and Aleatory Uncertainties Guo, Jia; Du, Xiaoping AIAA Journal, Vol. 45, Issue 9 https://doi.org/10.2514/1.28707	journal	September 2007
Computational methods for efficient structural reliability and reliability sensitivity analysis Wu, Y. -T. AIAA Journal, Vol. 32, Issue 8 https://doi.org/10.2514/3.12164	journal	August 1994

Similar Records

Stochastic Framework for Optimal Control of Planetary Reentry Trajectories Under Multilevel Uncertainties

Journal Article · Tue Aug 01 00:00:00 EDT 2023 · AIAA Journal · OSTI ID:2422569

Sensitivity in risk analyses with uncertain numbers.

Technical Report · Thu Jun 01 00:00:00 EDT 2006 · OSTI ID:886899

Probabilistic methods for sensitivity analysis and calibration in the NASA challenge problem

Journal Article · Wed Dec 31 23:00:00 EST 2014 · Journal of Aerospace Information Systems · OSTI ID:1141704

Related Subjects

42 ENGINEERING
Distribution parameters
Engineering
Global sensitivity analysis
Kernel density estimation
Mathematics
Mechanics
Modified extended polynomial chaos expansion
Reliability sensitivity index
Sensitivity index function

A functional global sensitivity measure and efficient reliability sensitivity analysis with respect to statistical parameters

Citation Formats

References (40)

Similar Records

Related Subjects