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To address the shortcomings of the traditional back propagation (BP) neural network agent model, such as insufficient fitting accuracy and low computational efficiency, an improved method is proposed.

In this study, an improved sparrow search algorithm (ISSA) is developed to optimize the reliability calculation of the BP neural network (ISSA-BP) using an enhanced BP neural network model. The traditional sparrow search algorithm is enhanced by incorporating a golden sine strategy to improve its position-updating mechanism, thereby overcoming its tendency to converge prematurely to local optima. Additionally, an opposition-based learning strategy is integrated to explore the reverse solution around the optimal solution of the sparrow search algorithm, mitigating the risk of local optima.

The results of the test function demonstrate that the proposed method significantly enhances fitting accuracy while maintaining computational efficiency. Finally, by applying this approach to the metro bogie frame as a case study, the structural reliability of the bogie frame is evaluated using the Monte Carlo method, providing valuable insights for subsequent analysis and structural optimization.

The use of the surrogate model approach for structural reliability analysis significantly improves solution efficiency. Furthermore, the integration of ISSA with the BP neural network enhances both fitting accuracy and computational efficiency, demonstrating the superiority and practicality of the proposed method.

Aiming at the inefficiency of solving the Sobol index using the traditional mathematical analytical method, a Sobol global sensitivity analysis method is proposed.

In this paper, a support vector regression (SVR) surrogate model is constructed to solve the Sobol index. The optimal combination of SVR hyperparameters is obtained by using the improved beluga whale optimization (IBWO). Meanwhile, in order to solve the problem that Sobol sequences will form correlation regions in high-dimensional space leading to the uneven distribution of sampling points, a scrambled strategy is introduced in the Sobol sensitivity analysis using IBWO-SVR. Thus, the IBWO-SVR-SS sensitivity analysis model is established.

The results of two test functions show that the method further improves the accuracy of the sensitivity analysis. Finally, the first-order Sobol index and second-order Sobol index are solved by the IBWO-SVR-SS method using the metro bogie frame as an engineering example. Through the analysis results, the key design parameters of the frame and the design parameter combinations with more obvious coupling relationships are identified, providing a strong reference for the subsequent analysis and structural optimization.

Sobol sensitivity analysis using the surrogate model method can effectively improve the efficiency of the solution. In addition, IBWO is used for the optimization of the SVR hyperparameters to improve the accuracy and efficiency of the optimization, and finally, the correction of the Sobol sequence through the introduction of the disruption strategy also further improves the accuracy of the sensitivity analysis of Sobol.