Reliability Numerical Solution Method Based On Occurrence Function Method And Its Engineering Application

The reliability calculation of simple structure usually can be obtained by integrating the probability density function, but if there are many random variables, or the probability density function is not integrable, partially missing, unknown, using the generating function method for structural reliability calculation is a new feasible way.Generating function method is an important tool for structural reliability analysis and performance assessment of multi-state systems. In view of existing problems of low computational efficiency and poor accuracy, the following work has been done:(1) According to the problem that the discrete data is less and existing error, the window estimation method was introduced and improved to obtain accurate variable generating function. This method has provided the safeguard for precise calculation of structure reliability.(2) The technology of approximate merger was put forward, according to the principle of a few merge in the failure domain and a lot merge in the security domain, which reduces the amount of calculation in the situation that the calculation precision is unchanged.(3) The technology of failure domain segmentation was put forward, which limiting increases failure domain number of discrete points, and improves the accuracy of probability in the failure domain, eventually improves the reliability of structure calculation accuracy. Meanwhile, the paper does in-depth research on the relationship between inspection domain number of discrete points and accuracy of the calculation.(4) The technology of variables non-uniform discretization was put forward, which arranges discrete points in accordance with the certain rules of the density in the situation that the number of all discrete points is unchanged, makes the discrete points of failure domain concentrated to ensure the high precision of probability, and makes the discrete points of security domain dispersed to ensure efficient operations, eventually improves the reliability of structure calculation accuracy and efficiency.(5) According to above research method and technologies, non-uniform discretization method was put forward. A general numerical software packages is edited by MATLAB software based on the Non-uniform discretization method.(6) The study of engineering example was performed. The new method was applied to analyse reliability of cantilever beam, roof structure and hit. The correctness of the method is verified by the results of calculation.The new method and technology take the error of the formation mechanism of calculation of structural reliability and feasibility of MATLAB programming into consideration. The numerical software package contains rather complete functions, stable operation, easy to use, and it also provides an effective tool, for the reliability of the limit state function fast and efficient computing with multi-variable nonlinear structure.