Research On Gaussian Process Based Dynamic Response Surface Method Of Reliability Analysis For Complex Structure

China is at a golden opportunity to develop civil construction industry.With the rapid appearance of large-scale structures, complexity is higher and higher, uncertain factors are increasing, security problem following is more and more important. It is required that the new theory and analysis methods are proposed to face new challenges in the area of structure reliability assessment. The performance function of large-scale complex structures has many features, such as high computational cost, implicit expression, highly nonlinear and the traditional method is often difficult to solve it. Because GP model is good at dealing with high dimensions, small samples, nonlinear complexities problems and can obtain optimal super-parameter self-adaptively and forecast results of probability, this paper will focus on approximating the implicit performance function by GP model and combining traditional structure reliability analysis method to handle the issues of structure reliability assessment, which is based on dynamic updating of learning samples.Four methods are proposed in this paper for reliability analysis which are based on GP model:GPC-based MCS, which combined the GPC with MCS simulation (MCS),GPR-based Breitung, which combined the GPR with Breitung method, GPR-based MCS,which combined the GPR with MCS simulation (MCS) and GPR-based PSO,which combined the GPR with Particle Swarm Optimization (PSO).Then, those methods are applied to large-scale structure existed, which provides a new choice to solve this problem quickly and accurately. In sum, the main works and results are listed as follows: 1. MCS-GPC. Based on markov chain sample generation mechanism and GPC model which is used to approximate the implicit performance function,GPC are combined with MCS to solve the issues of structure reliability assessement.In this method,fitting error is self-adaptively in the aspects of approximating the response surface,which provides a new choice to solve this problem quickly and accurately.2. Breitung-.GPR. The small number of training samples were created using Finite Element method (FEM) code for building the GPR response surface. Thus, the implicit performance and its derivatives were approximated by the GPR with explicit formulation. Then, an iterative algorithm is presented to reduce the errors of GPR response surface by information of design point in order to improve constantly the reconstructing precision at the important region, which contributes to the failure probability significantly. Then, the classical Breitung method combined with GRP response surface was applied to calculate the structural reliability index. The results show that the proposed method has higher efficiency and higher accuracy compared to traditional response surface method. It can directly take advantage of existing engineering FEM code without modification.3. MCS-GPR.The small number of training samples were created using FEM code for building the GPR response surface. The highly nonlinear and implicit performance function is approximated by GPR with explicit formulation under small sample condition. Then, the most probable point (MPP) is predicted quickly using MCS Simulation without any extra FEM analysis. Furthermore, an iterative algorithm is presented to reduce the errors of GPR by using information of MPP in order to improve constantly the reconstructing precision at the important region, which contributes to the failure probability significantly. Then, MCS method combined with GRP surface is applied to get the structure of failure probability. The proposed method has advantages of high efficiency and high precision compared to traditional response surface method.and thus it is very suitable for reliability analysis of large-scale complicated engineering structure.4. PSO-GPR. The calculation of reliability index converted to optimization problem. Then, the small number of training samples were created using Finite Element method (FEM) code for building the GPR response surface. Thus, the highly nonlinear and implicit performance function is approximated by GPR with explicit formulation under small sample condition. Then, the most probable point (MPP) is searched quickly using PSO without any extra FEM analysis. Furthermore, an iterative algorithm is presented to reduce the errors of GPR by using information of MPP in order to improve constantly the reconstructing precision at the important region, which contributes to the failure probability significantly. Finally, Important simulation method (ISM) combined with GRP surface is applied to calculate the failure probability.It is a effective method to solve the issues of structure reliability assessment which involve multiple peak values function.Finally,the methods above are applied to calculate the structural reliability index for large-scale complex structures. It show that a series of methods proposed in this paper are more accurate, efficient, scientific and feasible, which can be a good reference for large-scale complex structure reliability assessment.