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Time-variant reliability analysis via approximation of the first-crossing PDF

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Abstract

Time-variant reliability analysis can effectively estimate the safe state of structures under dynamic uncertainties during their lifecycle. However, one of its key challenging issues is computational efficiency. To improve the efficiency, this paper develops an approximation of the first-crossing probability density function (PDF) method, termed AFC-PDFM, based on the first-crossing theory. The response surface of the first-crossing time point (FCTP) about input variables is first estimated by using the moving least squares method (MLSM) and uniform design. Furthermore, an iterative algorithm is developed to compute the origin moments of the FCTP based on the MLSM response surface. Finally, the PDF of the FCTP is obtained by combining the origin moments and the maximum entropy method to avoid direct calculations of the first-crossing rate, which is often intractable, and then the time-variant reliability is estimated. Three examples are implemented to testify and validate the effectiveness of the proposed method and potential applications to engineering problems.

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Replication of results

The results presented in this work are based on the flowchart in Fig. 2. To further understand the proposed method for time-variant reliability analysis and replicate the solutions presented in this paper, the MATLAB codes of the proposed ACF-PDFM for the numerical example are provided as the supplementary material.

Funding

This research was financially supported in part by the Dongguan University of Technology under research grant (KCYKYQD2017014), National Key R&D Program of China under the Contract No. 2017YFB1302301, and the National Natural Science Foundation of China under the Contract No. 11472075.

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Authors and Affiliations

  1. Industry 4.0 Artificial Intelligence Laboratory, and School of Computer Science and Technology, Dongguan University of Technology, Dongguan, 523808, China

    Shui Yu & Yun Li

  2. School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Shui Yu, Yanwei Zhang & Zhonglai Wang

Authors
  1. Shui Yu
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  2. Yanwei Zhang
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  3. Yun Li
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  4. Zhonglai Wang
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Corresponding authors

Correspondence to Yun Li or Zhonglai Wang.

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The authors declare that they have no conflict of interest.

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Responsible Editor: Byeng D Youn

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Yu, S., Zhang, Y., Li, Y. et al. Time-variant reliability analysis via approximation of the first-crossing PDF. Struct Multidisc Optim 62, 2653–2667 (2020). https://doi.org/10.1007/s00158-020-02635-y

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  • DOI: https://doi.org/10.1007/s00158-020-02635-y

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