Global Reliabillity And Sensitivity Analysis Of Structures Based On Stochastic Response Surface Methods

There are a lot of uncertainties in the design and construction of building structures, which will influence the behavior and performance of structures.The loadings in the service period of structures, such as wind load, and seismic actions, are also stochastic in nature. The combination of these two kinds fo uncertainties leads to the occasionality of failures of structures. Therefore, it is necssary to investigate the global reliability and sensitivity of structures under uncertain conditions. The analysis results of the global reliability and sensitivity of structures can guide the design of structures, improving the knowledge level of design.There are many methods to analyze structural reliability. In this thesis, the stochastic response surface methods(SRSM) based on polynomial chaos expansions(PCE) are selected. An explict meta-model based on PCE can be constructed by the regression method, which has good effects in the globa ldomain of definition. The main research contents of this thesis are summarized as follows:(1) Based on the basic theory of PCE, the process of constructing the meta-model is determined. Besides, different collocation methods have been compared to analyze their advantages and disadvantages.(2) Based on the constructed explict meta-model, the reliability indices can be calculated by the Monte Carlo Simulation(MCS) method or the first order reliability method(FORM). In this thesis, the stochastic response surface model is combined with the high order moment methods(HOMM). A high order moment method basd on the generalized lambda distribution method is proposed, and compared with maximum entropy principle. Through numerical examples, the accuracy and application scopes of the propsed method are given. By use of the approximate probability distribution function and statistical moments of the state variable of structures, the reliability indices of structures can be obtained.(3) Global senstivity analysis of structures based on the stochastic response surface method. When there are too many input variables, the construction of the meta-model will be pretty complex. Thus, the sensitivity indices of the input variables based on analysis of variance(ANOVA) have been calculated by the stochastic response surface methods to analyze the effects of input variables on the state variable. Through replaciong the variables whose sensitivity indices are very small as constant values, the computational burden of the subsequent analysis can be greatly reduced. Moreover, the sensitivity indices that calculated by the stochastic response surfaces have been compared with the results gotten by the Monte Carlo Simulation and the quasi-Monte Carlo, and the accuracy of this method is verified.(4) Global seismic reliability and senstivity analysis of structures based on the stochastic response surface method. To know the application effects in practical engineering of the stochastic response surface method, three reinforce concrete(RC) frame structures whose floor numbers are different have been modelled, and their global reliability and sensitivity indices for the load carrying capacity limite state and the deformation limit state of structures have been calculated respectively. The results by the stochastic response surface method are compared with those by the Monte Carlo Simulation, and the applicability of this method is verified.Through the study of this thesis, some conclusions can be summarized. When the polynomial order and the amount of collocation points are enough, then the explict metamodels of structures van have good perofrmance, and the accury of the reliability indices calculated by the stochastic response surface method is better. In addition, the global sensitivity indices by the proposed method are in agreement with the engineering empirical judgments.