Research On Efficient Reliability Analysis Methods Using Multi-objective Optimization Theory

In engineering practice,the first order second moment method(FOSM)is a common reliability analysis method.For the reliability analysis with the lowly nonlinear performance function,traditional gradient-based iterative algorithms of the FOSM generally have high accuracy and efficiency.However,when the nonlinearity of the performance function is high,traditional algorithms may fail in convergence with chaotic oscillation or periodic oscillation,or find the local optimal solution.In addition,when increasing the nonlinear degree of the performance function,the error of the failure probability between the result of the FOSM and true result could increase.In order to analyze reliability efficiently and accurately,various reliability methods have been proposed,and many of them need the most probable point(MPP)provided by the FOSM.Therefore,how to improve the accuracy and efficiency of searching the MPP is of great significance.In the dissertation,the fundamental reasons affecting the convergence of the FOSM are studied and the corresponding improved methods are proposed from the viewpoint of multi-objective optimization,and then the reliability analysis is extended from the reliability index calculation of the FOSM to the high-precision failure probability calculation.The main research contents are as follows:1.The traditional gradient-based iterative algorithms are introduced,which are uniformly defined as the gradient-based direct method(GDM)in the dissertation.In the solving framework of the GDM,the computational performance is enhanced.Firstly,the oscillation control methods in the traditional gradient-based iterative algorithms are reviewed and classified as step-length control method and directional control method.Then,a unified relationship of these two types of control methods are derived by formulas,defined as the gradient-based direct method.Finally,combining the characteristics of the two control methods,the Armijo-based hybrid control algorithm is proposed to improve computational performance of the GDM further.2.When dealing with highly nonlinear problems,the GDM could fail in convergenc,such as oscillation and the local optimal result.In the dissertation,the fundamental reasons affecting the convergence of the GDM are discussed from the perspective of multi-objective optimization.Firstly,a multi-objective optimization formula of the FOSM is established,and it is pointed out that the GDM is actually an interactive multi-objective optimization process based on the ?-constraint method.Then,two fundamental reasons affecting the convergence of the GDM are revealed through analysis and verification,which are passive decision-making of the target reliability index and single-step search without sufficient accuracy,respectively.They may result in convergence failure of the GDM in that the target reliability indexs oscillate on the axis of relaibility index,and the successive iteration points are not located on the Pareto front in the objective function space.3.Aiming at the problem of single-step search without sufficient accuracy in the GDM,the efficient and accurate search method based on the inverse reliability analysis is proposed to improve the search accuracy and efficiency under the given target reliability index.Firstly,the inherent relation between inverse reliability analysis and reliability analysis is emphasized,and the traditional inverse reliability analysis algorithms are briefly introduced.Then,the suitable chaos control factor for each iteration step is obtained by using a cyclic update strategy without additional computation,based on which the improved adaptive chaos control algorithm(IACC)is proposed.The inverse reliability analysis with IACC is used as an efficient and accurate search method for MPP.Finally,the IACC algorithm is compared with traditional inverse reliability analysis algorithms.It is verified that the IACC algorithm has the advantages of high efficiency and accuracy,and can avoid the local optimum effectively.4.In order to solev the problem of passive decision-making of the target reliability index in the GDM,the active decision-making method of target reliability index by the secant method is proposed.The adaptive PMA-IACC algorithm(APMA-IACC)is further established to solve the MPP efficiently and robustly based on the improved search method and decision-making method.Firstly,according to the multi-objective optimization formula of the FOSM,the active decision-making method of target reliability index by the secant method is proposed to assure that target reliability index can converge to MPP under the active control of the decision maker.Then,two improved algorithms of the GDM are proposed,namely the PMA-IACC algorithm and the adaptive PMA-IACC algorithm.Finally,the performances of the improved algorithms are verified by the examples,which show that the adaptive PMA-IACC algorithm has the best efficiency and accuracy.5.For the balance between efficiency and accuracy of failure probability calculation method,the AK-IS(reliability method combining the active learning Kriging and importance sampling)method based on the APMA-IACC algorithm is proposed to calculate failure probability efficiently and accurately.Firstly,two participation strategies(complete APMA-IACC participation and partial APMA-IACC participation)are presented.Then,the above participation strategies are combined with the AK-IS to establish the efficient and accurate failure probability calculation method based on the APMA-IACC algorithm.Finally,the proposed method is compared with MCS,FOSM,traditional importance sampling(IS)and GDM-based AK-IS,and it is verified that the performance of the AK-IS method is further improved with combining the APMA-IACC algorithm by the numerical examples and engineering examples.