Non-Probabilistic Reliability Analysis Of Engineering Structural Based On Gaussian Process And Particle Swarm Optimization Algorithm

The analysis of traditional structural reliability is surrounding the uncertainty, and generally determined by the random reliability model and fuzzy reliability model which are usually based on the probability density function (PDF) of uncertain variables, but the determine of the function for the probability density function always requires a lot of data and accurate sample information, however, it is difficult to meet in the practical engineering. So some scholars put forward a method that don’t need to know the distribution of the variables, only the variable range of the probability model for structural reliability. Studies show that non-probabilistic reliability model is more reasonable, more commodiously to meet the needs of practical engineering structure than the probability model. With the development of the theory for the non-probabilistic reliability, the research of the mixed reliability between probability and non-probabilistic reliability has gradually become a hot discussion. In this paper, the non-probabilistic reliability model, probabilistic and non-probabilistic mixed model is analyzed. During to the function of the corresponding function for complex structure which has characteristics such as highly nonlinear, implicit expression is difficult to efficiently solve using the traditional method, a new reliability analysis method on the basis of Gaussian process regression (GPR) dynamic response surface hybridized into the Particle Swarm Optimization (PSO) algorithm was presented. The method using the advantage of gaussian process regression model in dealing with highly nonlinear implicit function, can be adaptive to obtain the optimal parameters, and adaptive learning on the basis of dynamic update learning samples, Thus, the function is approximated by GPR with explicit formulation under small sample condition. Then, the design point is searched quickly using PSO without any extra FEM analysis. Furthermore, an iterative algorithm is presented to reduce the errors of GPR by using information of the design point in order to improve constantly the reconstructing precision of the structural state function, then the gaussian process regression model can be enable to precisly fitting implicit functions of the structure and implementation under the small sample showed expression of implicit function, then a good global search ability of particle swarm optimization algorithm is used to search design points, and by constructing a reasonable way of iteration, using each iteration step design point information dynamic response in the face of structural functional function reconstruction precision. Finally, we use the completed final design point for the center to solve the reliable indexes. The feasibility of the presented method was demonstrated by numerical examples and the practical engineering structure. And by comparing with the traditional response surface methodology, providing an efficient and fast thought for the non-probabilistic reliability problem of complex structures.The results of study show that the proposed methods of reliability index solution between probability and non-probabilistic reliability are feasible. The method has advantages of high calculation efficiency and low computational cost and has good applicability in the non-probabilistic reliability analysis for the high computational cost of implicit function characteristics. And by compared with the traditional response surface methodology based on quadratic polynomial, the method have higher efficiency and higher accuracy and by directly taking advantage of existing engineering FEM code without modification, the method is very suitable for reliability analysis of large-scale complicated structure which have the characteristics of implicit performance function and time-consuming structural analysis.