Solution to non-probabilistic reliability indices based on improved synthetic minority oversampling technique
The existing algorithm cannot solve the non-probabilistic reliability indices(NPRIs)effectively when the functional function of the structure presents a high degree of nonlinearity and the limit state surface is multi-regional.To solve such problems,a synthetic minority oversampling technique(SMOTE)was improved and the NPRIs solution method was proposed.Firstly,based on the geometric meaning of NPRIs,an improved SMOTE algorithm was proposed to further improve the sampling efficiency of the algorithm near the critical surface by combining the sample classification strategy,hypersphere restriction strategy and the standard SMOTE algorithm.Then the improved SMOTE algorithm was combined to fit the local limit state surface in the normalized space with high accuracy,and the NPRIs were searched.Finally,the main flow of the NPRIs solution based on the improved SMOTE algorithm was given.The numerical example shows that when the limit state surface presents the characteristics of local closure and multiple regions,the improved SMOTE algorithm can efficiently produce the sample points located near the limit state surface,and then fits the limit state surface with high accuracy.Comparing the calculation results with that of the analytical solution,the relative errors are less than the maximum error limit of 5%in engineering,which indicates that the improved SMOTE algorithm can better handle the highly nonlinear functional functions and verifies the effectiveness and practicality of the proposed algorithm.