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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 6976301, 12 pages
Research Article

The Method of Solving Structural Reliability with Multiparameter Correlation Problem

College of Science, Inner Mongolia University of Technology, Hohhot 010051, China

Correspondence should be addressed to Haibin Li

Received 1 July 2017; Revised 12 November 2017; Accepted 16 November 2017; Published 11 December 2017

Academic Editor: Fiorenzo A. Fazzolari

Copyright © 2017 Juan Du et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Correlation among variables must be considered to accurately reflect the level of structure reliability. This problem has referential value to engineering practice and has attracted attention from relevant scholars and industries. In this paper, Copula function was used to build the joint probability density function among all variables. The key is to describe the correlation among variables, solve the correlation parameter of Copula function, and select the type of correlation structure among variables. The correlation parameter of Copula function was solved using Pearson linear correlation coefficient and maximum likelihood estimation. Based on the Akaike information criteria (AIC) and Bayesian information criteria (BIC), the optimal Copula function was selected, and the correlation structure among variables was determined. Monte Carlo method, which is based on Nataf inverse transformation, was introduced and used to evaluate the reliability of the correlated variable. Finally, this paper proposed the reliability calculation method based on dual neural network and direct integration by establishing the dual neural network of original and integrand functions. Compared with the Monte Carlo method, the proposed method can be utilized to efficiently and precisely calculate the structure reliability of multiple correlated random variables.