Reliability analysis based on combination of universal generating function and discrete approach

Uncertainty exists in the engineering practices widely. Since a multidimensional integration problem should be dealt with during the process of reliability-based analysis and design, it is the key problem to develop new method to improve the efficiency and accuracy for the reliability-based analysis and design in the complex systems. Hence a new method is proposed, and the procedure of the proposed method is summarized as follows. First, transform continuous random variable into discrete random variables modeled by probability mass function (PMF). The PMF of a limit-state function can be acquired through universal generating function (UGF) and different moments can be calculated by using derivative. Second, maximum entropy principle is used to calculate the probability density function (PDF) of the limit-state function. The proposed method, based on the PMF and UGF, is suitable for the cases that discrete variables exist in the system and the limit-state function is a highly non-linear problem. The reason is that the proposed method needs neither derivative nor the most probable point (MPP) search. A numerical example is provided to demonstrate the effectiveness of the proposed method, and furthermore a comparison is made between the results from the proposed method and Monte Carlo simulation (MCS).