Distribution Tail Approximation of Performance Function Via Tail Moment-Based Squared Normal Distribution

DOI: https://doi.org/10.62517/jes.202602222

Author(s)

Haoran Yu1,2,*

Affiliation(s)

1State Key Laboratory of Bridge Safety and Resilience (Beijing), Beijing University of Technology, Beijing, China 2Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing, China *Corresponding Author

Abstract

The probability distribution of the performance function serves as an essential tool for quantifying the uncertainty of structural responses. Traditional methods can construct the main body of the probability distribution but often fail to effectively capture information from the tail region, or require a considerable computational cost. Since the probability density estimation in the tail region requires particular attention, the accurate reconstruction of this region is particularly important. To address this challenge, a new method based on the squared normal distribution is proposed, in which the shape parameters are determined through the first three tail moments. As the information used for tail moment computation is extracted from the tail region corresponding to the design threshold, the final distribution achieves higher accuracy in the target tail region. Furthermore, the proposed method is applied to several different examples involving a simple performance function, a strongly nonlinear function and complex examples characterized by implicit relationships, and high dimensionality, demonstrating its superior accuracy and efficiency of the distribution tail approximation.

Keywords

Tail Moment; Squared Normal Distribution; Tail Fitting; Structural Reliability Assessment

References

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