A copula-function-based structural system reliability analysis method

• Published in: Acta mechanica Vol. 233; no. 4; pp. 1371 - 1391
• Main Authors: Mi, D., Zhang, W., Li, J. W., Jiang, C.
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.04.2022; Springer; Springer Nature B.V
• Subjects: Analysis; Bivariate analysis; Classical and Continuum Physics; Control; Distribution (Probability theory); Dynamical Systems; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Failure modes; Heat and Mass Transfer; Maximum likelihood estimation; Methods; Monte Carlo method; Monte Carlo simulation; Original Paper; Probability density functions; Reliability analysis; Reliability engineering; Solid Mechanics; Structural reliability; System reliability; Theoretical and Applied Mechanics; Vibration
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-022-03160-3

In this study, a copula-function-based system reliability analysis method is proposed for reliability evaluation of structures with multiple failure modes. The vine copula function is used to process the correlations that exist between performance functions. The joint probability density function of the performance function random vector is then converted into multiple bivariate copula functions. The maximum likelihood estimation method and Akaike information criteria are used for optimal selection of each bivariate copula function. Based on this process, a joint probability density function of the performance function random vector is constructed. Then, based on the joint probability density function, a Monte Carlo simulation method is given to calculate the system reliability of the structure. Finally, the effectiveness of the method proposed in this study is verified using 4 numerical examples.