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A novel maximum entropy method based on the B-spline theory and the low-discrepancy sequence for complex probability distribution reconstruction

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  • He, Wanxin
  • Wang, Yiyuan
  • Li, Gang
  • Zhou, Jinhang

Abstract

The maximum entropy method (MEM) is a powerful tool for the recovery of unknown probability density functions (PDF) and has growing popularity in the reliability analysis community. However, MEM may be inaccurate for PDFs with a complex shape (e. g. multiple modals or a long tail), influencing the accuracy of the reliability analysis greatly. To overcome this deficiency, this study proposes a novel MEM paradigm based on the B-spline theory and the low-discrepancy sequence. Firstly, to enhance the performance of MEM for complex PDFs, the B-spline functions are used to construct the MEM PDF. Correspondingly, the iteration formulation is derived for the undetermined parameter estimation of the B-spline-based MEM PDF based on the closed solution for minimizing the Kullback-Leibler divergence. Then, we adopt the low-discrepancy sequence to calculate the objective function of minimizing the Kullback-Leibler divergence efficiently. Compared with MEM and other moment-based reliability analysis methods, the proposed method does not require the statistical moments, and integrates the advantages of the B-spline theory and MEM. To illustrate the benefits of our method, five examples are analyzed and compared with some classical reliability analysis methods.

Suggested Citation

  • He, Wanxin & Wang, Yiyuan & Li, Gang & Zhou, Jinhang, 2024. "A novel maximum entropy method based on the B-spline theory and the low-discrepancy sequence for complex probability distribution reconstruction," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    • Handle: RePEc:eee:reensy:v:243:y:2024:i:c:s0951832023008232
    DOI: 10.1016/j.ress.2023.109909
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    References listed on IDEAS

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    1. Wang, Yuhao & Gao, Yi & Liu, Yongming & Ghosh, Sayan & Subber, Waad & Pandita, Piyush & Wang, Liping, 2021. "Bayesian-entropy gaussian process for constrained metamodeling," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    2. Zhang, Dequan & Shen, Shuoshuo & Wu, Jinhui & Wang, Fang & Han, Xu, 2023. "Kinematic trajectory accuracy reliability analysis for industrial robots considering intercorrelations among multi-point positioning errors," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    3. Mehni, Moien Barkhori & Mehni, Mohammad Barkhori, 2023. "Reliability analysis with cross-entropy based adaptive Markov chain importance sampling and control variates," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    4. Xu, Jun & Kong, Fan, 2018. "A new unequal-weighted sampling method for efficient reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 94-102.
    5. Francesco Di Maio & Chiara Pettorossi & Enrico Zio, 2023. "Entropy-driven Monte Carlo simulation method for approximating the survival signature of complex infrastructures," Post-Print hal-04103855, HAL.
    6. Erdem Acar & Masoud Rais-Rohani & Christopher D. Eamon, 2010. "Reliability estimation using univariate dimension reduction and extended generalised lambda distribution," International Journal of Reliability and Safety, Inderscience Enterprises Ltd, vol. 4(2/3), pages 166-187.
    7. Echard, B. & Gayton, N. & Lemaire, M. & Relun, N., 2013. "A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 232-240.
    8. Zhang, Xiaobo & Lu, Zhenzhou & Cheng, Kai, 2022. "Cross-entropy-based directional importance sampling with von Mises-Fisher mixture model for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 220(C).
    9. Xu, Jun & Song, Jinheng & Yu, Quanfu & Kong, Fan, 2023. "Generalized distribution reconstruction based on the inversion of characteristic function curve for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    Full references (including those not matched with items on IDEAS)

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