Hyper-rectangle Domain Decomposing Response Surface Method Based On Non-linearity For Reliability Analysis

Reliability analysis guarantees the safety and durability of engineering structures,which is beneficial to the national economic security.A great deal of research with considerable progress was done on the structural reliability analysis methods.However,for those large engineering structures with implicit limit state functions,it is difficult to take partial derivatives in the first-order reliability method(FORM)or can consume too much computation in the Monte Carlo simulation(MCS)method.The solution by means of the classical response surface method for those multidimensional and highly nonlinear problems has poor precision and results are easily affected by the interpolation coefficients.A deepgoing research based on the theories of star shape design,non-linearity and Kriging interpolation is thus performed in this paper.The main part of this thesis works as follows(1)In the light of theories of central composite design and roughness of non-linearity,hyper-rectangle domain decomposition method is first proposed.Centred at an initial point(design point or mean point)in the standard normal space,the initial domain is decomposed into series of sub-domains that are sufficiently smooth and approximating to the real failure limit state surface along the direction with the maximum roughness(non-linearity).A weighted response surface is fitted on a set of appropriate sample points obtained by the previous domain decomposition method and the reliability index is then calculated by the FORM.The results of numerical examples show that the proposed method is superior to the traditional quadratic polynomial response surface method with more efficiency and accuracy.(2)A new local coordinate system along the tangent and normal direction of the response surface is built,and rotational hyper-rectangle domain decomposition method for reliability analysis is proposed in this chapter.This method constructs a rotational coordinate matrix based on the direction from the origin to the design point,starts the domain decomposition from the design point,then splits the domain along the tangent or normal direction of the response surface.Several numerical examples indicate that this method further improves the precision of hyper-rectangle domain decomposition method.(3)In view of low precision made by the classical response surface method in structuralreliability analysis,Kriging response surface method based on hyper-rectangle domain decomposition is proposed in this chapter,which obtains the response surface via the Kriging interpolation after the hyper-rectangle domain decomposition.Numerical examples verify the applicability,effectiveness and accuracy of the method.