Analytical Uncertainty Quantification Approach Based On Gaussian Process Metamodel

Uncertainty exists in various engineering structures,such as high-rise structures,bridges,spatial structures,etc.The sources of uncertainty can be divided into four categories:parameter uncertainty,model uncertainty,computational uncertainty and test uncertainty.Parameter uncertainty is the most studied uncertainty,which can be caused by many factors,including manufacturing error,assembly tolerance,material aging,environmental corrosion and incomplete structural information(such as unclear definition of boundary conditions).The uncertainty of structural parameters will inevitably lead to the uncertainty of structural response.Ignoring uncertainty may lead to the decline of structural design quality and even major accidents.Therefore,structural analysis and design should consider the influence of parameter uncertainty and quantify structural uncertainty,that is,the uncertainty of parameters transmitted to structural response should be accurately quantified.In this paper,the Gaussian process metamodel(GPM)method is improved,and the analytical method of structural uncertainty based on adaptive GPM,generalized co-GPM(GC-GPM)and adaptive GC-GPM are further proposed.The analytical expressions of response statistical moments are derived,which can quickly and accurately obtain the analytical solution of the mean and variance of structural response.This paper mainly carried out the following research work:(1)This paper proposes an analytical method for structural uncertainty based on adaptive GPM by combining sequential design and GPM.The optimal sample points are iteratively selected by the filling criterion,and an adaptive GPM is established to improve the uncertainty quantification accuracy.Within the framework of the established adaptive GPM,the highdimensional integrals of the response statistical moments are transformed into onedimensional integrals and can be obtained analytically.The fitting process of the adaptive GPM is demonstrated by two mathematical functions.The proposed method is applied to the natural frequency statistical moments of a cylindrical reticulated shell,and compared with the traditional GPM and MCS.The results show that the analytical method of uncertainty quantification based on the adaptive GPM has higher accuracy and lower computational cost.(2)An analytical approach for structural uncertainty quantification based on generalized co-Gaussian process metamodel is proposed.High-fidelity samples can establish high accuracy surrogate model,but obtaining high-fidelity samples requires the establishment of complex high-precision finite element models,which leads to high cost.The computational cost of obtaining low-fidelity samples is low,but the accuracy of the established surrogate model is poor.In order to combine the advantages of high and low precision samples,this paper proposes a generalized co-Gaussian process metamodel(GC-GPM)that integrates high and low fidelity training samples.Based on the framework,the analytical expressions of mean and variance of structural response are derived,and the analytical quantification of structural uncertainty is realized.The fitting of a mathematical function proves that the GC-GPM has good prediction performance under nested and non-nested samples.Three engineering structures are used to verify the reliability of the analytical method of structural uncertainty,and the results are compared with those of traditional MCS,co-GPM and GPM.The results show that the proposed method has advantages in computational accuracy and efficiency.(3)An analytical uncertainty quantification approach based on adaptive generalized coGaussian process model is proposed.Based on the GC-GPM,an adaptive sampling method is introduced,and a filling criterion suitable for two fidelities is proposed.The optimal high/lowfidelity samples are selected by iteration to fill into the initial sample sets,and the current GCGPM is updated adaptively.The iterative mechanism of the adaptive GC-GPM is demonstrated by the fitting process of a two-dimensional six-hump function.The proposed adaptive GC-GPM is applied to three engineering structures.The calculation results are very close to the results of the MCS method,indicating that the adaptive method has high accuracy.At the same time,compared with the traditional GC-GPM,the adaptive GC-GPM only needs fewer samples to achieve higher accuracy,indicating that the adaptive sampling method further reduces the computational cost and improves the efficiency.