Research On Non-probabilistic Reliability Analysis Method Of Mechanical Structure Based On Convex Set Model

There are many uncertainties related to load,material characteristics,assembly errors and measurement errors in mechanical structures.The traditional probability model is an effective method for dealing with uncertainty,but its sample information acquisition cost is large.The non-probabilistic convex set model only needs to know the boundary or boundary information of the sample to evaluate the safety of the structure,and therefore it is widely concerned by researchers.In this paper,the non-probabilistic reliability analysis of mechanical structure based on convex set model is studied.The main contents include:(1)A non-probabilistic reliability index of polygonal convex set model is proposed,in which the ratio of mean of structural function function to its deviation is used to measure the safety degree of mechanical structures,The invariance problem in the above-mentioned reliability index is then revealed.The applicability of geometric reliability index of traditional regular convex set model to polygonal convex set model is also discussed.A numerical example and three engineering examples are used to illustrate the effectiveness of the proposed nonprobabilistic reliability index by comparing the results obtained by polygonal convex set model.interval model and principal component analysis interval model.(2)The incompleteness of distance ratio non-probabilistic reliability index proposed by Xie Ling is supplemented and an improved version is given.The non-probabilistic reliability index of the polygonal convex set model proposed in this paper and the improved non-probabilistic reliability index of the distance ratio are compared and studied.The two non-probabilistic reliability indexes are compared from two aspects of definition and inconsistency.The two indexes are quantitatively compared through three highly nonlinear numerical examples and two engineering examples.A three-bar truss example is used to compare the optimization design based on two kinds of non-probabilistic reliability indexes.The results show that both indexes indexes can consider the influence of uncertain variables.(3)Non-probabilistic reliability analysis of structures integrating PSO and Kriging model:In view of the problems with implicit performance functions and limited experimental data in the reliability analysis of complex structures,a non-probabilistic reliability method combining particle swarm optimization(PSO)with Kriging model is presented.A multidimensional ellipsoid is first used to characterize the uncertain parameters of structures.The Kriging model is then constructed for a implicit performance function,wherein its optimal relative parameters is determined by the PSO.Based on the proposed model the reliability analysis is explicitly conducted.The results by three numerical show that the proposed method is effectiveness and feasibility,and has a higher accuracy and efficiency than the one based on traditional Kriging model.