Hybrid Reliability Analysis Method Based On Probabilistic And Non-probabilistic Convex Model

Uncertainties widely exist in engineering structures design and analysis, and howto deal with these uncertainties correctly is an important factor for the accuracy ofreliability design. Traditional reliability analysis bases on probability model, andwhich requires the probability distributions of variables. In many engineeringapplications, the probability distributions of some variables may not be known due tolacking of samples information, but they are only known within certain intervals,which are more suitable to be described by convex model. Therefore, the research onthe hybrid reliability analysis is very necessary. Based on hybrid reliability modelwith random and interval variables, it aims at doing some researches and trials on theinvestigation of hybrid reliability. The major contents and achievement of thisdissertation are listed as follows:1. Combined interval analysis with the asymptotic approximations forprobability integrals method, a method is given to solve probability-interval hybridreliability problem. At first, the point with maximum probability density is located inthe original space， and then combined with the asymptotic approximations forprobability integrals method, the maximum probability of failure of the hybrid modelis calculated. This method is much more efficient because of avoiding the nestingoptimization.2. Based on the RS (Response surface) approach, an efficient reliabilityanalysis method for structures with random and interval mixed uncertainties isdeveloped. At first, a quadratic RS model is constructed by using axial experimentaldesign method for approximating the actual limit-state function, which may beexplicit or implicit. An approximate hybrid reliability model is created based on theRS model, which is solved by a decoupling approach, and then an updating strategy issuggested to improve the accuracy of the response surface.3. The vector projection technique is applied to the hybrid uncertainly problem,a high efficient method is proposed to deal with reliability analysis of hybridstructures with random and interval variables. Sampling points are located by Bucherdesign combined with vector projection method, which is more close to the originallimited-state surface. Linear RS is constructed based on these sampling points, andthen an approximate hybrid reliability model is created based on the RS model, which is solved by a decoupling approach. Finally, using iteration technique to ensureanalysis precision.