Structural Reliability Analysis Based On Sampling By The Direct Optimization Algorithm And Support Vector Machine

Modern engineering structure becomes more complex,and various large complex structures have emerged all over the world.The function functions of complex structures are usually highly nonlinear and implicit.There are problems of large amount of calculation and low efficiency in solving them directly.In order to reduce the complexity of structural reliability analysis,it is necessary to develop an efficient and high-precision response surface method.Amongst,the response surface method of support vector machine can realize the nonlinear mapping into high dimensional space by the inner product kernel function,which has excellent adaptability in nonlinear problems and can avoid dimensional disaster.This thesis puts forward an efficient sampling method,construct samples by means of Direct optimization algorithm.The sampling objective function is discussed,and combined with the response surface method of support vector machine,it is applied to structural reliability analysis with randomness or random-interval hybrid uncertainty.The main contents are as follows:(1)Structural reliability analysis method based on sampling by the Direct optimization algorithm and support vector machine.The objective function of Direct optimization algorithm is set up to sample.Monte Carlo simulation and structural reliability analysis are performed in virtue of the support vector machine trained by those sampling points.The practicability and effectiveness of the method are illustrated by numerical examples.(2)Response surface method of support vector machine for reliability analysis based on the Direct optimization algorithm and two-sample point updating.The Direct optimization algorithm was firstly used to build rough samples.In the safety domain and failure domain respectively,an adaptive point selection rule in terms of Euclidean distance is given,two sample points are continuously added to the training set after a finite number of iterations.A support vector machine with high accuracy is established by these small number of samples.Monte Carlo method is used for structural reliability analysis,and the effectiveness,accuracy and efficiency of the method are verified by several numerical examples.(3)A response surface method of support vector machine for random-interval hybrid reliability analysis of structure based on Direct optimization algorithm and a small number of sample updating.For the random variables and intervals simultaneously exist in problems of structure reliability analysis,first of all,via Direct optimization algorithm with an appropriate objective function,coarse sample plan is obtained,and then in the safe domain and unsafe domain respectively,an adaptive selection rule based on Euclidean distance and some optimization algorithm,a small amount of sample points are continuously updated in the training set.Response surface function of support vector machine with high accuracy is established.Monte Carlo method is used for structural reliability analysis,and several examples demonstrate the effectiveness,efficiency and accuracy of the proposed method for structural reliability analysis with random and interval variables existing simultaneously.