Research On Reliability Evaluation Considering Temporal And Spatial Variations

Structural reliability is a function of time and space in practical engineering.Most of existing reliability analysis methods ignore the uncertain impact of spatial variables on the structure,which may cause large errors.In order to guarantee that engineering structures can perform their intended function safely,it is of great scientific and practical significance to study efficient and accurate methods for evaluating reliability problem with temporal and spatial variations.Aiming at the reliability problems with temporal and spatial variations,the main contents in this thesis are listed as follows:(1)A kernel density estimation approach is proposed for the reliability analysis with temporal and spatial variations based on response extreme value.This method firstly uses the good lattice point method based partially stratified sampling to generate random samples.Then time interval is decomposed into a group of sub-time intervals and extreme value analysis is performed in each subtime interval to obtain the corresponding samples of extreme value.Finally,the kernel density estimation is employed to fit the extreme value distribution.This method shows a good accuracy and computational efficiency in practical examples.(2)An adaptive kriging method is developed to solve the reliability problem of temporal-spatial variations with small failure probability.The latin hypercube sampling is employed to generate random samples firstly.Then the samples of spatial response extreme value at discrete time instants are obtained by the sequential quadratic programming.Kriging surrogate model is constructed for spatial response extreme value and samples are selected by U learning function to update the surrogate model until convergence.Three examples demonstrate that this method can balance efficiency and accuracy well.(3)A polynomial chaos expansion method is proposed to construct the surrogate model of spatial response extreme value at discrete times with a few random samples.Therefore,the structural response hypersurface in time and space domain is transformed into a trajectory of spatial response extreme value in time,and then the reliability analysis is carried out accordingly.This method is compared with Monte Carlo simulation in examples,which proves that it has good performance in accuracy and efficiency.(4)Compare the above three methods and analyze their performances.All the three methods require training sample sets,but only the adaptive kriging method has an updated strategy.The parameters used in the kernel density estimation method are fewer than the adaptive kriging and polynomial chaos expansion methods.However,the adaptive kriging and polynomial chaos expansion methods have better computational accuracy and efficiency.