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A two-step methodology to apply low-discrepancy sequences in reliability assessment of structural dynamic systems

Abstract

This study introduces various low-discrepancy sequences and then develops a new methodology for reliability assessment for structural dynamic systems. In this methodology, a two-step algorithm is first proposed, in which the most uniformly scattered point set among the low-discrepancy sequences is selected according to the centered L2-discrepancy (CL2 discrepancy) and then rearranged to minimize the generalized F-discrepancy (GF discrepancy). After that, the developed point set is incorporated into the maximum entropy method to capture the fractional moments for deriving the extreme value distribution for reliability assessment of structural dynamic systems. Numerical examples are investigated, where the results are compared with those obtained from Monte Carlo simulations, demonstrating the accuracy and efficiency of the proposed methodology.

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Acknowledgements

The support of the National Natural Science Foundation of China (Grant No.: 51608186) and the Fundamental Research Funds for the Central Universities (No.531107040890) is highly appreciated. The anonymous reviewers are greatly acknowledged for their constructive criticisms to the original version of the paper.

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Correspondence to Jun Xu.

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Xu, J., Wang, D. A two-step methodology to apply low-discrepancy sequences in reliability assessment of structural dynamic systems. Struct Multidisc Optim 57, 1643–1662 (2018). https://doi.org/10.1007/s00158-017-1834-x

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  • DOI: https://doi.org/10.1007/s00158-017-1834-x

Keywords

  • Low-discrepancy sequence
  • Reliability
  • Structural dynamic systems
  • CL2 discrepancy
  • GF discrepancy
  • Extreme value distribution
  • Fractional moments