The Analysis And Application Of Structural Reliability Using Response Surface Methods

The response surface method(RSM)has the advantages of simple principle and strong applicability,so that it can be widely used in the analysis and calculation method of engineering reliability.However,the classical RSM may be more nonlinear to calculate the function function of complex structure,and it is easy to cause inaccurate or non-converged calculation results.In this paper,the RSM is studied,the above problems are improved,and the improved RSM is applied to the reliability calculation of a mesh frame,the specific research contents are as follows:1)For the analysis of classical RSM test point distribution,this thesis based on the center point rotation arrangement and the updating test point of the response surface function(RSF)is introduced.The test points obtained by this method will be better distributed around the RSF,and the constructed RSF can be better approximated to the limit state function(LSF).In this way,The number of test points required in the reliability calculation process will be significantly less than that of the traditional RSM,and the reliability index obtained will be closer to the exact solution.2)Due to the problem that the classical RSM iteration is difficult to converge,a response surface reliability analysis method based on simplex optimization is proposed,and the simplex algorithm is introduced to reduce the dimension processing.In this method,those failure points deviating from the error of the original limit state function can be corrected and reducing the number of iterations of the overall iteration.For some high dimensional nonlinear implicit limit state equation reliability calculation convergence problem,it can improve the calculation accuracy and calculation efficiency,and bring a certain engineering applicability.3)Starting with the geometrical significance of the reliability index,this thesis proposes an improved RSM based on the minimum Norm Point,which selects a new test point near the minimum norm point on RSM.These sample points are calibrated in two polynomial interpolation to construct the response surface form which is more approximate to the LSF.This improves the accuracy of the calculation to some extent.In addition,this paper introduces a double convergence criterion to evaluate the judgment.It can effectively save the iterative process and improve the efficiency of the calculation.Finally,the rationality and applicability of the method are verified by numerical examples.4)This theory is based on the analysis of the finite element model of a trestle prestressed mesh frame structure.This method adopts the reliability analysis method of the improved RSM based on simplex optimization and that based on the minimum norm point proposed in the fourth chapter respectively,and the reliability analysis of the cross-middle deflection of the trestle is analyzed.Then,Compare the calculation results with the Monte Carlo method for efficiency and accuracy.From the calculation results,we can obtain that the method in this paper can give accurate results and the processing method is both simple and effective.Moreover,it has certain applicability and high efficiency in engineering practice.