For structures with both random and fuzzy uncertainty parameters, a novel method for obtaining the membership function of reliability in the fuzziness failure criterion is presented using a Random Fuzzy Support Vector Machine based on the Particle Swarm Optimization method (PSO-RFSVM). The proposed method is used to solve the structural reliability problem with implicit limit state function in the presence of mixed variables. Under each cut level, a new distance measure between the mixed variables is presented, named the advanced Yang distance; then, the RFSVM model can be constructed using the kernel function built by the advanced Yang distance and random fuzzy mixed sampling points. Furthermore, to obtain satisfactory fitting, a PSO algorithm is used to optimize the super-parameters in RFSVM. The limit state function is subsequently approximated at the given cut level, and then, the reliability bound under the given cut level is readily obtained. The PSO-RFSVM method provides a new efficient analysis framework in the case of implicit approximation under mixed uncertainty when the classical method has excessive consumption in virtual prototype simulation. Two examples are used to demonstrate the validity and advantage of PSO-RFSVM compared to the Extreme Response Surface based on Simulated Annealing (SAERS) method and Monte Carlo simulation (MCS).
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This research is supported by the National Natural Science Foundation of China (No. 51675026) and Aeronautical Science Foundation of China (2018ZC74001).
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You, LF., Zhang, JG., Zhou, S. et al. A novel mixed uncertainty support vector machine method for structural reliability analysis. Acta Mech 232, 1497–1513 (2021). https://doi.org/10.1007/s00707-020-02906-1