Research On Reliability Analysis Method Based On Multi-fidelity Approximation Model

With the increase of people's requirements for the safety and reliability of engineering product structures,reliability analysis has become an integral part of the engineering product design process.While reliability analysis has received widespread attention,finding efficient and accurate methods for reliability analysis has become a research hotspot.At present,the reliability analysis methods based on approximate models have been widely used.However,due to the increasing complexity of product structures and more stringent use conditions,the difficulty of reliability analysis continues to increase.In order to ensure the balance between reliability calculation cost and prediction accuracy,the multi-fidelity approximation model has received extensive attention from researchers.The multi-fidelity approximation model can use the information of high and low fidelity sample points to build an approximation model,using a large number of low credibility sample points to reduce the use of high fidelity sample points,thereby reducing the amount of calculation.However,it is not efficient that applying the multifidelity approximation model directly to existing reliability analysis methods in all cases.Therefore,this paper studies the reliability analysis method based on the multi-fidelity approximation model,and applies the method to the component and system reliability analysis problems.The main research work is as follows:Aiming at the problems of low efficiency and slow convergence of update points in the existing active learning methods of approximate models,a UE(Uncertainty-Effect)active learning function is proposed,which uses the uncertainty of the candidate point's own symbol and the probability density of the variables to construct uncertainty parameters and influence.Parameters to maximize the prediction accuracy of each failure probability,improve the efficiency of point selection,and speed up the convergence.Combined with numerical and engineering examples for verification and comparison with other active learning functions,the results show that the proposed reliability analysis method based on UE active learning functions has higher computational efficiency and accuracy.Combining the advantages of the multi-fidelity approximation model that can reduce the use of high fidelity sample points through low fidelity sample points,a multi-fidelity approximation model is introduced in the reliability analysis.Aiming at its shortcoming of poor adaptability in different problems,a component reliability analysis method based on a multifidelity approximation model was proposed.This method builds a co-kriging approximation model based on high fidelity sample points and low fidelity sample points,and builds a kriging approximation model based on existing high fidelity sample points.Finally,the Kalman filter method is used to fuse the prediction information of the two models to calculate the failure probability of the structural elements.The numerical examples and engineering examples are used to verify the results.The results show that the proposed method can effectively balance the contradiction between the failure probability calculation cost and the calculation accuracy in the reliability analysis.At the same time,the method has high adaptability.Aiming at the problem of system reliability analysis for multiple failure modes,it is proposed that a system reliability analysis method based on a multi-fidelity approximation model and Kalman filter.This method extends the component reliability analysis method based on the multi-fidelity approximation model and Kalman filter,and uses the composite criterion approach to reduce the calculation cost.Approximate models for various failure modes are constructed separately.In each approximate model,areas are ignored that have no effect on the accuracy of the limit state of the system or have a small effect.Only look for update sample points near the limit state of the system,and then update each approximate model separately.The test results show that the proposed method can calculate the system failure probability efficiently and accurately.Finally,the full text is summarized.Future directions worthy of further research are prospected.