High Dimensional Reliability Analysis Method Based On Surrogate Model

With the increasing complexity and large scale of modern engineering structures,the coupling degree and dimension of input and output variables are also increasing.The existing structural reliability theories and methods are usually very effective in low dimensional space,but difficult to apply to high dimensional problems.The reason lies in the " curse of dimensionality ",the geometric increase of computation amount,the difficulty of constructing surrogate model and the difficulty of ensuring the validity of high dimensional reliability analysis.In view of the above problems,this paper makes an in-depth study of high dimensional reliability analysis,and is committed to building an organic bridge between dimension reduction method and surrogate model,so as to achieve the balance between accuracy and efficiency.The research results of this thesis can be summarized as follows:(1)Reliability analysis method based on principal component analysis and Kriging model for high dimensional output system.In the existing methods,dimension reduction and surrogate modeling are usually independently in two stages and lack of effective coupling mechanism between them.Therefore,problems such as waste of training samples,low efficiency of surrogate modeling and lack of accuracy will be caused.To solve these problems,this thesis proposes a new high dimensional reliability analysis method based on principal component analysis and Kriging model.This method makes full use of the information provided by principal component analysis and surrogate model,and uses new learning functions and iterative strategies to construct an organic bridge between dimension reduction method and surrogate model,which effectively improves the computational efficiency and accuracy.(2)Reliability analysis method based on active subspace and neural network for high dimensional input systems.At present,most studies on high dimensional adaptive surrogate models focus on the Kriging model,because the Kriging model provides predictive mean and variance information of unknown samples that can be used to construct learning functions for active learning.However,the Kriging model requires a lot of computation and cannot be applied to the problem of discontinuous function,so it has poor robustness.Therefore,this thesis proposes a high dimensional reliability analysis method based on active subspace and neural network.This method uses a learning function that considers both the input space distance information and the output space response value to guide the adaptive updating of the neural network in the low dimensional space,so that the surrogate model is no longer limited to Kriging.(3)An efficient and adaptive surrogate model construction method for complex and high-dimensional input and output systems.Most of the existing methods are aimed at single high dimensional input or output,and there are problems such as low computational efficiency and insufficient accuracy.High dimensional reliability methods integrating input and output coupling dimension reduction and adaptive surrogate models are rare.To solve these problems,this thesis proposes an efficient adaptive surrogate modeling method for complex and high dimensional systems.The method reduces dimension of input and output simultaneously and constructs an adaptive surrogate model in low dimensional space.Moreover,a parallel strategy is introduced on the premise of ensuring accuracy.Multiple sample points are selected for model updating in one iteration to make full use of computing resources and improve computing efficiency.