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An enhanced unified uncertainty analysis approach based on first order reliability method with single-level optimization

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  • Yao, Wen
  • Chen, Xiaoqian
  • Huang, Yiyong
  • van Tooren, Michel

Abstract

In engineering, there exist both aleatory uncertainties due to the inherent variation of the physical system and its operational environment, and epistemic uncertainties due to lack of knowledge and which can be reduced with the collection of more data. To analyze the uncertain distribution of the system performance under both aleatory and epistemic uncertainties, combined probability and evidence theory can be employed to quantify the compound effects of the mixed uncertainties. The existing First Order Reliability Method (FORM) based Unified Uncertainty Analysis (UUA) approach nests the optimization based interval analysis in the improved Hasofer–Lind–Rackwitz–Fiessler (iHLRF) algorithm based Most Probable Point (MPP) searching procedure, which is computationally inhibitive for complex systems and may encounter convergence problem as well. Therefore, in this paper it is proposed to use general optimization solvers to search MPP in the outer loop and then reformulate the double-loop optimization problem into an equivalent single-level optimization (SLO) problem, so as to simplify the uncertainty analysis process, improve the robustness of the algorithm, and alleviate the computational complexity. The effectiveness and efficiency of the proposed method is demonstrated with two numerical examples and one practical satellite conceptual design problem.

Suggested Citation

  • Yao, Wen & Chen, Xiaoqian & Huang, Yiyong & van Tooren, Michel, 2013. "An enhanced unified uncertainty analysis approach based on first order reliability method with single-level optimization," Reliability Engineering and System Safety, Elsevier, vol. 116(C), pages 28-37.
    • Handle: RePEc:eee:reensy:v:116:y:2013:i:c:p:28-37
    DOI: 10.1016/j.ress.2013.02.014
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    References listed on IDEAS

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    1. Zaman, Kais & Rangavajhala, Sirisha & McDonald, Mark P. & Mahadevan, Sankaran, 2011. "A probabilistic approach for representation of interval uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(1), pages 117-130.
    2. Helton, Jon C. & Johnson, Jay D., 2011. "Quantification of margins and uncertainties: Alternative representations of epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1034-1052.
    3. Urbina, Angel & Mahadevan, Sankaran & Paez, Thomas L., 2011. "Quantification of margins and uncertainties of complex systems in the presence of aleatoric and epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1114-1125.
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    Cited by:

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    5. Zheng, Xiaohu & Yao, Wen & Xu, Yingchun & Chen, Xiaoqian, 2020. "Algorithms for Bayesian network modeling and reliability inference of complex multistate systems: Part I – Independent systems," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    6. Rocchetta, Roberto & Crespo, Luis G., 2021. "A scenario optimization approach to reliability-based and risk-based design: Soft-constrained modulation of failure probability bounds," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    7. Mathpati, Yogesh Chandrakant & More, Kalpesh Sanjay & Tripura, Tapas & Nayek, Rajdip & Chakraborty, Souvik, 2023. "MAntRA: A framework for model agnostic reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    8. Izquierdo, J. & Crespo Márquez, A. & Uribetxebarria, J., 2019. "Dynamic artificial neural network-based reliability considering operational context of assets," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 483-493.
    9. Qu, Pengfei & Zhang, Limao & Zhu, Qizhi & Wu, Maozhi, 2023. "Probabilistic reliability assessment of twin tunnels considering fluid–solid coupling with physics-guided machine learning," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    10. Zheng, Xiaohu & Yao, Wen & Zhang, Yunyang & Zhang, Xiaoya, 2022. "Consistency regularization-based deep polynomial chaos neural network method for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    11. Zheng, Xiaohu & Yao, Wen & Xu, Yingchun & Chen, Xianqi, 2019. "Improved compression inference algorithm for reliability analysis of complex multistate satellite system based on multilevel Bayesian network," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 123-142.

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