Concerning the issue of high-dimensions, hybrid uncertainties of randomness and intervals including implicit and highly nonlinear limit state function, reliability analysis based on the hybrid uncertainty reliability mode combining with back propagation neural network (HU-BP neural network) is proposed in this paper. Random variables and interval variables are as input layer of the neural network, after the training and approximation of the neural network, the response variables are obtained through the output layer. Reliability index is calculated by solving the optimization model of the most probable point (MPP) searching in the limit state band. Two numerical cases are used to demonstrate the method proposed in this paper, and finally the method is employed to solving an engineering problem of the aerospace friction plate. For this high nonlinear, small failure probability problem with interval variables, this method could achieve a good analysis result.
The random variables are always truncated in aerospace engineering and the truncated distribution is more feasible and effective for the random variables due to the limited samples available. For high-reliability aerospace mechanism with truncated random variables, a method based on artificial bee colony (ABC) algorithm and line sampling (LS) is proposed. The artificial bee colony-based line sampling (ABCLS) method presents a multi-constrained optimization model to solve the potential non-convergence problem when calculating design point (is also as most probable point, MPP) of performance function with truncated variables; by implementing ABC algorithm to search for MPP in the standard normal space, the optimization efficiency and global searching ability are increased with this method dramatically. When calculating the reliability of aerospace mechanism with too small failure probability, the Monte Carlo simulation method needs too large sample size. The ABCLS method could overcome this drawback. For reliability problems with implicit functions, this paper combines the ABCLS with Kriging response surface method, therefore could alleviate computational burden of calculating the reliability of complex aerospace mechanism. A numerical example and an engineering example are carried out to verify this method and prove the applicability.
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