Research Papers: Design Automation

Active Resource Allocation for Reliability Analysis With Model Bias Correction

[+] Author and Article Information
Mingyang Li

Department of Mechanical Engineering-
Engineering Mechanics,
Michigan Technological University,
Houghton, MI 49931
e-mail: mli7@mtu.edu

Zequn Wang

Department of Mechanical Engineering-
Engineering Mechanics,
Michigan Technological University,
Houghton, MI 49931
e-mail: zequnw@mtu.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 13, 2018; final manuscript received December 16, 2018; published online January 11, 2019. Assoc. Editor: Gary Wang.

J. Mech. Des 141(5), 051403 (Jan 11, 2019) (13 pages) Paper No: MD-18-1565; doi: 10.1115/1.4042344 History: Received July 13, 2018; Revised December 16, 2018

To account for the model bias in reliability analysis, various methods have been developed to validate simulation models using precise experimental data. However, it still lacks a strategy to actively seek critical information from both sources for effective uncertainty reduction. This paper presents an active resource allocation approach (ARA) to improve the accuracy of reliability approximations while reducing the computational, and more importantly, experimental costs. In ARA, the Gaussian process (GP) modeling technique is employed to fuse both simulation and experimental data for capturing the model bias, and further predicting actual system responses. To manage the uncertainty due to the lack of data, a two-phase updating strategy is developed to improve the fidelity of GP models by actively collecting the most valuable simulation and experimental data. With the high-fidelity predictive models, sampling-based methods such as Monte Carlo simulation are used to calculate the reliability accurately while the overall costs of conducting simulations and experiments can be significantly reduced. The effectiveness of the proposed approach is demonstrated through four case studies.

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Chojaczyk, A. , Teixeira, A. , Neves, L. C. , Cardoso, J. , and Soares, C. G. , 2015, “ Review and Application of Artificial Neural Networks Models in Reliability Analysis of Steel Structures,” Struct. Saf., 52, pp. 78–89. [CrossRef]
Hu, Z. , and Mahadevan, S. , 2016, “ Global Sensitivity Analysis-Enhanced Surrogate (GSAS) Modeling for Reliability Analysis,” Struct. Multidiscip. Optim., 53(3), pp. 501–521. [CrossRef]
Kang, F. , Xu, Q. , and Li, J. , 2016, “ Slope Reliability Analysis Using Surrogate Models Via New Support Vector Machines With Swarm Intelligence,” Appl. Math. Modell., 40(11–12), pp. 6105–6120. [CrossRef]
Wang, S. , Chen, W. , and Tsui, K.-L. , 2009, “ Bayesian Validation of Computer Models,” Technometrics, 51(4), pp. 439–451. [CrossRef]
Zhou, Z.-B. , Dong, D.-D. , and Zhou, J.-L. , 2006, “ Application of Bayesian Networks in Reliability Analysis,” Syst. Eng.-Theory Pract., 6, pp. 95–100.
Hu, Z. , and Du, X. , 2015, “ Mixed Efficient Global Optimization for Time-Dependent Reliability Analysis,” ASME J. Mech. Des., 137(5), p. 051401. [CrossRef]
Hu, Z. , and Mahadevan, S. , 2016, “ A Single-Loop Kriging Surrogate Modeling for Time-Dependent Reliability Analysis,” ASME J. Mech. Des., 138(6), p. 061406. [CrossRef]
Wang, Z. , and Chen, W. , 2016, “ Time-Variant Reliability Assessment Through Equivalent Stochastic Process Transformation,” Reliab. Eng. Syst. Saf., 152, pp. 166–175. [CrossRef]
Schöbi, R. , Sudret, B. , and Marelli, S. , 2016, “ Rare Event Estimation Using Polynomial-Chaos Kriging,” ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A, 3(2), p. D4016002. [CrossRef]
Bourinet, J.-M. , 2016, “ Rare-Event Probability Estimation With Adaptive Support Vector Regression Surrogates,” Reliab. Eng. Syst. Saf., 150, pp. 210–221. [CrossRef]
Balesdent, M. , Morio, J. , and Brevault, L. , 2016, “ Rare Event Probability Estimation in the Presence of Epistemic Uncertainty on Input Probability Distribution Parameters,” Methodol. Comput. Appl. Probab., 18(1), pp. 197–216. [CrossRef]
Keshtegar, B. , and Meng, Z. , 2017, “ A Hybrid Relaxed First-Order Reliability Method for Efficient Structural Reliability Analysis,” Struct. Saf., 66, pp. 84–93. [CrossRef]
Wang, G. , and Ma, Z. , 2017, “ Hybrid Particle Swarm Optimization for First-Order Reliability Method,” Comput. Geotech., 81, pp. 49–58. [CrossRef]
Lim, J. , Lee, B. , and Lee, I. , 2014, “ Second-Order Reliability Method-Based Inverse Reliability Analysis Using Hessian Update for Accurate and Efficient Reliability-Based Design Optimization,” Int. J. Numer. Methods Eng., 100(10), pp. 773–792. [CrossRef]
Lim, J. , Lee, B. , and Lee, I. , 2016, “ Post Optimization for Accurate and Efficient Reliability-Based Design Optimization Using Second-Order Reliability Method Based on Importance Sampling and Its Stochastic Sensitivity Analysis,” Int. J. Numer. Methods Eng., 107(2), pp. 93–108. [CrossRef]
Piric, K. , 2015, “ Reliability Analysis Method Based on Determination of the Performance Function's PDF Using the Univariate Dimension Reduction Method,” Struct. Saf., 57, pp. 18–25. [CrossRef]
Acar, E. , Rais-Rohani, M. , and Eamon, C. D. , 2010, “ Reliability Estimation Using Univariate Dimension Reduction and Extended Generalised Lambda Distribution,” Int. J. Reliab. Saf., 4(2/3), pp. 166–187. [CrossRef]
Liang, H. , Cheng, L. , and Liu, S. , 2011, “ Monte Carlo Simulation Based Reliability Evaluation of Distribution System Containing Microgrids,” Power Syst. Technol., 10, pp. 76–81.
Miao, F. , and Ghosn, M. , 2011, “ Modified Subset Simulation Method for Reliability Analysis of Structural Systems,” Struct. Saf., 33(4–5), pp. 251–260. [CrossRef]
Bichon, B. J. , Eldred, M. S. , Swiler, L. P. , Mahadevan, S. , and McFarland, J. M. , 2008, “ Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions,” AIAA J., 46(10), pp. 2459–2468. [CrossRef]
Kaymaz, I. , and McMahon, C. A. , 2005, “ A Response Surface Method Based on Weighted Regression for Structural Reliability Analysis,” Probab. Eng. Mech., 20(1), pp. 11–17. [CrossRef]
Wong, S. , Hobbs, R. , and Onof, C. , 2005, “ An Adaptive Response Surface Method for Reliability Analysis of Structures With Multiple Loading Sequences,” Struct. Safety, 27(4), pp. 287–308. [CrossRef]
Pai, P.-F. , 2006, “ System Reliability Forecasting by Support Vector Machines With Genetic Algorithms,” Math. Comput. Modell., 43(3–4), pp. 262–274. [CrossRef]
Zhao, H. , Ru, Z. , Chang, X. , Yin, S. , and Li, S. , 2014, “ Reliability Analysis of Tunnel Using Least Square Support Vector Machine,” Tunnelling Underground Space Technol., 41, pp. 14–23. [CrossRef]
Bourinet, J.-M. , Deheeger, F. , and Lemaire, M. , 2011, “ Assessing Small Failure Probabilities by Combined Subset Simulation and Support Vector Machines,” Struct. Saf., 33(6), pp. 343–353. [CrossRef]
Chen, Z. , Qiu, H. , Gao, L. , Li, X. , and Li, P. , 2014, “ A Local Adaptive Sampling Method for Reliability-Based Design Optimization Using Kriging Model,” Struct. Multidiscip. Optim., 49(3), pp. 401–416. [CrossRef]
Lee, T. H. , and Jung, J. J. , 2008, “ A Sampling Technique Enhancing Accuracy and Efficiency of Metamodel-Based RBDO: Constraint Boundary Sampling,” Comput. Struct., 86(13), pp. 1463–1476. [CrossRef]
Wang, Z. , and Wang, P. , 2014, “ A Maximum Confidence Enhancement Based Sequential Sampling Scheme for Simulation-Based Design,” ASME J. Mech. Des., 136(2), p. 021006. [CrossRef]
Gomes, W. J. D. S. , and Beck, A. T. , 2013, “ Global Structural Optimization Considering Expected Consequences of Failure and Using ANN Surrogates,” Comput. Struct., 126(Suppl. C), pp. 56–68. [CrossRef]
Schueremans, L. , and Van Gemert, D. , 2005, “ Benefit of Splines and Neural Networks in Simulation Based Structural Reliability Analysis,” Struct. Saf., 27(3), pp. 246–261. [CrossRef]
Basudhar, A. , and Missoum, S. , 2008, “ Adaptive Explicit Decision Functions for Probabilistic Design and Optimization Using Support Vector Machines,” Comput. Struct., 86(19), pp. 1904–1917. [CrossRef]
Goswami, S. , Ghosh, S. , and Chakraborty, S. , 2016, “ Reliability Analysis of Structures by Iterative Improved Response Surface Method,” Struct. Saf., 60, pp. 56–66. [CrossRef]
Dubourg, V. , Sudret, B. , and Deheeger, F. , 2013, “ Metamodel-Based Importance Sampling for Structural Reliability Analysis,” Probab. Eng. Mech., 33, pp. 47–57. [CrossRef]
Zhao, L. , Choi, K. K. , Lee, I. , and Du, L. , “ Response Surface Method Using Sequential Sampling for Reliability-Based Design Optimization,” ASME Paper No. DETC2009-87084.
Balesdent, M. , Morio, J. , and Marzat, J. , 2013, “ Kriging-Based Adaptive Importance Sampling Algorithms for Rare Event Estimation,” Struct. Saf., 44, pp. 1–10. [CrossRef]
Hasselman, T. , Yap, K. , Lin, C.-H. , and Cafeo, J. , “ A Case Study in Model Improvement for Vehicle Crashworthiness Simulation,” 23rd International Modal Analysis Conference, Orlando, FL, Jan. 31–Feb. 3. http://citeseerx.ist.psu.edu/viewdoc/download?doi=
Roy, C. J. , and Oberkampf, W. L. , 2011, “ A Comprehensive Framework for Verification, Validation, and Uncertainty Quantification in Scientific Computing,” Comput. Methods Appl. Mech. Eng., 200(25–28), pp. 2131–2144. [CrossRef]
Xi, Z. , Fu, Y. , and Yang, R. , 2013, “ Model Bias Characterization in the Design Space Under Uncertainty,” Int. J. Performability Eng., 9(4), pp. 433–444. https://www.researchgate.net/profile/Zhimin_Xi/publication/257992981_Model_bias_characterization_in_the_design_space_under_uncertainty/links/0c960526906aa27733000000.pdf
Qian, P. Z. , and Wu, C. J. , 2008, “ Bayesian Hierarchical Modeling for Integrating Low-Accuracy and High-Accuracy Experiments,” Technometrics, 50(2), pp. 192–204. [CrossRef]
Kennedy, M. C. , and O'Hagan, A. , 2001, “ Bayesian Calibration of Computer Models,” J. R. Stat. Soc.: Ser. B, 63(3), pp. 425–464. [CrossRef]
Arendt, P. D. , Apley, D. W. , and Chen, W. , 2012, “ Quantification of Model Uncertainty: Calibration, Model Discrepancy, and Identifiability,” ASME J. Mech. Des., 134(10), p. 100908. [CrossRef]
Xia, B. , Lü, H. , Yu, D. , and Jiang, C. , 2015, “ Reliability-Based Design Optimization of Structural Systems Under Hybrid Probabilistic and Interval Model,” Comput. Struct., 160, pp. 126–134. [CrossRef]


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Fig. 1

Illustration of the active resource allocation for accurate reliability analysis

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Fig. 2

Flowchart of the model bias correction using Gaussian process modeling

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Fig. 3

Flowchart of the proposed active resource allocation approach

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Fig. 4

Iterative updating process for simulations

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Fig. 5

Iterative updating process for experiments

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Fig. 6

Cumulative confidence level and estimated reliability history during ARA in (a) phase I and (b) phase II

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Fig. 7

Comparison between true experimental responses and ARA predictions at 50 validation points

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Fig. 8

Comparison of estimated Pf for 30 repetitive runs using different methods

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Fig. 9

Comparison between true bias and ARA predictions at 50 validation points

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Fig. 10

Comparison of estimated Pf for 30 repetitive runs using different methods

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Fig. 11

Geometry of the cantilever beam

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Fig. 12

Active resource allocation predicted responses versus true experimental responses for the validation points

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Fig. 13

ANSYS results of maximum deformation (unit: m)



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