Study On Surrogate Model Methods For Structural Reliability Analysis

Surrogate model methods are widely used in structural reliability to alleviatethe computational burden of engineering analysis at present. Existing methodsinclude the traditional Response Surface Method (RSM) and recently devolopedArtificial Neural Network (ANN) and kriging et al. The basic idea of these methodsis to create approximate models and provide functional relationships between theresponses and variables to replace the implicit limit state function. However, thesemethods are often confronted with kinds of difficulties such as the low accuracy andthe inefficiency for realistic engineering problems, especially in high-dimensionalsystems. Based on the existing methods, this study throughly investigates thesurrogate model methods for structural reliability analysis. Several new methodsthat have the higher accuracy and the improved efficiency when compared with thetraditional methods are proposed. The main work of this study is as follows:(1) The experiment design methods in applied statistics are briefly introduced.Suggestions for the selection of experiment design methods in traditional responsesurface method are provided through the comparison of some experiment designmethods for response surface fitting in reliability analysis. For the response surfacemethods of multidimensional variables with the uniform design, the limitation of th eoriginal Least Squares (LS) regression induced by multidimensional correlation ofdata in model fitting is analysized. To deal with the limitation, a new approachcalled quasi-linearal Partial Least Squares (PLS) response surface method based onthe traditional polynomial has been proposed. This method combines the uniformdesign and Partial Least Squares technique to estimate the response surface andperform reliability analysis. It can effectively cope with the multidimensionalcorrelation of data and high error when building the regression model under thecondition of small samples. The results of several examples show that the proposedmethod based on the polynomial functions is suitable for structural reliabilityanalysis and has higher accuracy, especially in the high dimensional problem.(2) Due to the restriction of polynomial functions, the traditional responsesurface method cannot attain satisfactory accuracy for multidimensional variablesand high non-linearity problems. This paper presents the partial least squaresnon-linear regression methods based on the B-spline transform and kernel transformsubstitute for the surrogate model for the calculation of reliability, and the main ideais to first map the input space into a high-dimensional feature space via a nonlinearkernel function or a B-spline function, then to apply partial least squares regressionin the feature space, which can make full use of the sample space information and effectively capture the nonlinear relationship between input variables and outputvariables compared to linear partial least square. Thus the methods can not onlyavoid the influence of assuming the type of the limit state function but also handlethe correlation among variables after space transform. Numerical examples indicatethat the accuracy and efficiency of the two proposed methods are both superior tothe traditional response surface method.(3) To improve the accuracy and efficiency of the widely used kriging method,especially in multidimensional systems, this paper explores the use of the cokrigingmethod by incorporating the secondary information such as the gradients of thefunction. The improvement of the new method is verified by numerical examples.Then, a simulated importance sampling approach, which combines the importancesampling technique with the cokriging method, is presented for structural reliabilityevaluation. Numerical examples illustrate that the proposed method can greatlydecrease the sample number of Monte Carlo method and improve the efficiency withcomparable accuracy.(4) To overcome the flaws of artificial neural network (ANN) such as thedifficulty to determine the network struture and the lack of theoretical basis forparameter seletion, two kinds of hybrid artificial neural networks (HANN)integrating Radial Basis Function (RBF) networks and Back Propagation (BP)networks with partial least square technique respectively are proposed. Then thecorresponding structural reliability analysis methods utilizing the hybrid model asthe surrogate model are presented. The results of the numerical examplesdemonstrate that the proposed methods are superior to the traditional artificialneural networks in terms of accuracy and efficiency.