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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.

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  • 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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    3. Wu, Shengnan & Hu, Yiming & Zhang, Laibin & Liu, Shujie & Xie, Renjun & Yin, Zhiming, 2024. "Intelligent risk identification for drilling lost circulation incidents using data-driven machine learning," Reliability Engineering and System Safety, Elsevier, vol. 252(C).

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