Study On Simulation Methods For Structural Reliability Analysis

Structural reliability theory which takes account of randomicities of structuralparameters is advanced for structural analysis. Calculation of structural failureprobability is one of the fundamental tasks of structural reliability analysis, and failureprobability can be estimated by simulation methods, which simulate the randomicitiesof structural parameters via random samples. With the development of computertechnique, various simulation methods have been developed and widely applied toreliability analyses of actual structures.However, there are some problems in applications of simulation methods. Forexample, we don’t know how to increase samples to achieve needed accuracy, and fortraditional Solver-Surrogate Method, simulation accuracy according to different modeltype can not be evaluated, and so on. In this thesis, Importance Sampling and SubsetSimulation are studied.First, Importance Sampling is studied. Considering the situation that theimportance sampling density function is a probability density function of independent ndimensional normal distribution, comparative analysis of several methods to determinethe parameters of importance sampling density function is made, and a new method isproposed. The proposed method is summarized as follows: firstly generate samples viaMarkov Chain Monte Carlo, secondly estimate simulation variance via these samples,lastly parameters’ values are determined by solving nonlinear optimization problemwhich minimizes the variance. Numerical examples show that the proposed method candetermine the parameters with fewer samples and is more accurate than existingmethods.Subset Simulation is studied. In order to reach the needed simulation accuracy withthe least samples, the relationship between simulation accuracy and the number ofsamples is studied, and four strategies of increasing samples are proposed. Comparativeanalysis of the four strategies is made via numerical examples. The strategy whichconsiders the Characteristic of intermediate failure regions, increases samples byincreasing the number of Markov Chains, is the best among the fours.The performance functions of actual structures are generally implicit, and in order to get performance function value, structural analysis is often needed. The number ofstructural analysis is the key for simulation accuracy. Kriging model which is aSolver-Surrogate Method is combined with Importance Sampling or Subset Simulation,and two algorithms are proposed. The proposed algorithms search and add the besttraining samples via Learning Function to adapt the model parameters’ values, andfinally the Kriging model which can divide samples correctly are established. Then, theKriging values are used instead of true performance function values to estimate thefailure probability. By doing this, the number of structural analyses is reduced. Thenumerical examples demonstrate the feasibility of the proposed methods.