Generalized distribution reconstruction based on the inversion of characteristic function curve for structural reliability analysis

Recovering the probability distribution of the performance function with an arbitrary shape is still a difficult task for structural reliability analysis. Since working with the characteristic function curve provides an alternative and frequently much simpler route than working directly with the pro...

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Bibliographic Details
Published in:Reliability engineering & system safety Vol. 229; p. 108768
Main Authors: Xu, Jun, Song, Jinheng, Yu, Quanfu, Kong, Fan
Format: Journal Article
Language:English
Published: Barking Elsevier Ltd 01.01.2023
Elsevier BV
Subjects:
Characteristic function
Characteristic functions
Complex fractional moments
Curve fitting
Fourier transform
Fourier transforms
Limit states
Mellin transform
Probability distribution
Probability distribution functions
Reconstruction
Reliability analysis
Reliability engineering
Structural reliability
Characteristic function
Complex fractional moments
Reliability analysis
Fourier transform
Curve fitting
Mellin transform
ISSN:0951-8320, 1879-0836
Online Access:Get full text
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Summary:Recovering the probability distribution of the performance function with an arbitrary shape is still a difficult task for structural reliability analysis. Since working with the characteristic function curve provides an alternative and frequently much simpler route than working directly with the probability distribution, this paper proposes a generalized density reconstruction method based on the inversion of characteristic function, which is estimated based on the complex fractional moments. First, the complex fractional moments of the limit state function are numerically evaluated by using the sample estimator. Then, the characteristic function is numerically determined in terms of complex fractional moments. Since inverting the numerical version of characteristic function to be the corresponding probability distribution is not an easy task, two analytical expressions of characteristic function are proposed according to its different features, where the undetermined parameters are obtained via fitting an analytical expression based on the data estimated by complex fractional moments. Then, the probability distribution of the limit state function is obtained by using the inverse Fourier transform of characteristic function, where a one-to-one mapping relationship is involved. Finally, the failure probability can be readily obtained. Several analytical distributions and numerical examples are extensively investigated to validate the proposed method. •The proposed method is applicable to both unimodal and multimodal distributions.•Analytical expressions are proposed for CF fitting according to different characteristics.•The proposed method outperforms the conventional Mellin transform.•Numerical examples validate the effectiveness of the proposed method.
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ISSN:0951-8320
1879-0836
DOI:10.1016/j.ress.2022.108768