| In practical civil engineering problems,uncertainties widely exist in physical parameters,external loads and boundary conditions,etc.,and significantly effect system outputs,such as displacements,shear forces and moments.Hence,to achieve a reliable structural design and ensure the safety of structures,it is necessary to take all these uncertainties into account and implement the reliability analysis.In recent years,various methods are developed for this purpose,such as sampling-based methods,moment-based methods and surrogated models,however,exploring the efficient numerical methods for reliability analysis is still a key issue especially the application of more and more elaborate numerical models.In this thesis,an efficient sensitivity analysis method called contribution-degree analysis（CDA）is used for determining relationships of the input random variables before implementing reliability analysis.Based on the results of the contribution-degree analysis,several efficient numerical methods for structural reliability analysis are proposed as followings:（1）The original input random variables are classified into several sub-vectors:one contains variables which have obvious interactions with each other and each of the remaining sub-vectors only contains one random variable that has less interaction with other variables via the contribution-degree analysis.According to the results of CDA and an exact dimension-reduction model,a novel adaptive dimension-reduction model is established.The Gaussian-weighted integration（GWI）for calculating the statistical moments of system outputs is divided into a lower-dimensional GWI and several one-dimensional GWIs,which means that fewer model evaluations are employed for approximating the statistical moments,and by combing with a 5-7degree cubature formula,a hybrid moments estimation approach is developed.Once the statistical moments are obtained,a flexible parametric probability density function（PDF）called Pearson system is used for recovering the underlying PDF of the performance function of the system output,then the failure probability and reliability index can be easily obtained.（2）Two novel surrogate models are established for structural reliability analysis.According to the CDA-based dimension-reduction model,the original performance function of the system output is decomposed as a summation of one lower-dimensional component function and several one-dimensional component functions.Then the full polynomial chaos expansion（PCE）and sparse PCE can be employed to reconstruct the component functions.Due to avoiding building the original complicated performance function,the computational burden for building the novel PCE is eased via the CDA-based dimension-reduction model and the accuracy can be also ensured.Once the PCE surrogate model is built,the Monte Carlo simulation（MCS）can be easily implemented by using the surrogate model for structural reliability analysis.（3）An improved fractional moments-based maximum entropy（FM-MEM）method is proposed for efficient reliability analysis.First,the Laplace transform is employed to transform the fractional moments into Laplace fractional moments.By combining the CDA-based hybrid moments estimation method with a 5th-degree cubature formula,the Laplace fractional moments can be approximated efficiently.Then two useful strategies are employed to reduce the number of the initial conditions of FM-MEM,i.e.,the order of fractional moments and Lagrangian multipliers,and thus only one initial condition is required to be specified.The PDF of the performance function can be easily established and the robustness of the result is improved.（4）Considering the correlation of input random variables,a straightforward transformation method is proposed for structural reliability analysis.For moments estimation,the integration points considering the correlation between random variables are generated by combing the hybrid moments estimation method and covariance matrix.Once the statistical moments are obtained,the improved FM-MEM method can be employed for constructing the unknown PDF of performance function. |
