| Uncertainties commonly exist in the practical engineering structures.Reliability theory is an effective method to deal with uncertain factors.The exploring research is performed in order to solve the problem of reliability and optimization computation from two different theoretical sys tems of probability theory and non-probability theory.The research includes non-probabilistic reliability model,Kriging model-based active learning method and reliability-based design optimization.An exponential convex model is proposed for improving the precision characterization of the non-probabilistic reliability model.To solve the problem of low efficiency of reliability analysis and optimization,an efficient and robust Kriging model-based active learning algorithm is proposed.The main content is as the following three aspects:(1)This study aims to create a novel data-driven exponential convex model to achieve accurate approximation for experiment data,in which the dimension reduction minimum volume method plays the key role.Furthermore,a novel relaxed exponential nominal value method is developed to calculate the corresponding non-probabilistic reliability index robustly and efficiently,and the sensitivities are also derived based on the straight forward perturbation method to guarantee its efficiency.Through numerical and experimental studies,the accuracy and validity of the proposed data-drive exponential convex model are validated compared to the interval and ellipsoid models,and the robustness and efficiency of the proposed method are also demonstrated for solving both linear and nonlinear problems.(2)An active weight learning method based upon the Kriging model is well proposed for reliability analysis.Firstly,An active weight learning function based on the optimization theory is built to replace the traditional learning function,in which the important degrees of sampling points on the limit state function are assigned as different weight indices.The Kriging s urrogate model is updated according to the proposed active weight learning function.In addition,the proposed strategy is extended to solve the system reliability problem,which can effectively avoid the nonlinearity of composite function in the traditional approach.A novel stopping criterion is also exploited to guarantee the convergence of the proposed method.(3)A new active learning method for reliability-based design optimization(RBDO)combining with Kriging metamodel and accelerated chaotic single loop approach(AK-ACSLA)is developed,in which the most probable learning function is proposed to search the most probable failure point.To ensure the high efficiency,the system’s most probable learning function is further constructed to solve the RBDO problem of series system with multiple probabilistic constraints,and then the ACSLA is proposed by taking full advantage of chaos feedback control methodology for guaranteeing the validity of AK-ACSLA.The high efficiency and accuracy of AK-ACSLA are illustrated by comparing with both existing gradient-based methods and active learning methods. |
