Research On The Improvement Of Subset Simulation Algorithm

Structural reliability analysis, a branch of reliability engineering, plays an important role inguaranteeing the safety of products. As the development of the modern finite element techniques anddynamic simulation methods, structural reliability analysis has made a good progress in its basis, butit is still faced with many problems, especially for dealing with high-dimensional and complicatedstructures. Recent several decades, a number of methods have been developed to handle this problem.Subset simulation (SS) method is one of the most successful methods, which performs greatefficiency and robustness in high-dimensional problems.It should be noted that SS can only estimate the failure probability of single stochastic response.However, estimating the failure probabilities of multiple stochastic responses, e.g. multiple limit statefunctions, with a single run of reliability method remains quite a challenging problem in structuralreliability analysis. In the first part of the thesis, an improved Subset Simulation (ISS) algorithm isproposed to resolve this drawback associated with the original Subset Simulation (SS). It bypasses thesorting difficulty arising in the multiple stochastic responses case by defining a unified event. Thisunified event, considered as the only driving variable, guides the whole simulation procedureprogressively approaching failure regions in a single run of SS. All failure probabilities are alsoestimated simultaneously from this single run instead of repeated calculating them using the originalSS. Two representative examples and two high-dimensional dynamical benchmark problems are usedto illustrate the efficiency and accuracy of the proposed ISS through comparing with the crude MonteCarlo Simulation (MCS) and the original subset simulation.Meantime, as its application and improvement expands, SS has already been developed to deal withstructural optimization with continuous design variables. However, it still makes no contribution inthat with discrete design variables. Thus, the next part of this thesis deals with the design optimizationof truss structures with discrete design variables, which remains quite a challenging task in structuraldesign. A new discrete search strategy based on the recently developed subset simulation optimizationalgorithm is proposed in details for this type of structural optimization. The discrete design variablesare transformed into standard normal variable space to implement the sampling procedure in subsetsimulation optimization, while the optimization is processed in the discrete design space in the meantime. The performance of the proposed method is illustrated by four representative benchmarkoptimization problems. Comparisons are made with other well known stochastic optimizationalgorithms. It is found that the proposed method can produce optimum designs as good as or betterthan those of other stochastic optimization algorithms.