## 5 Conclusions  
(1) This study proposes a multi-software interaction approach for active-learning reliability analysis, using BIW as a case study, to address the multi-dimensional implicit response relationships and time-consuming computational costs. MATLAB programming and secondary development are used to achieve multi-software interaction and automate the execution of pre-processing, solving and post-processing tasks, thereby minimizing manual interventions and enhancing efficiency. Subsequently, the PCK active-learning method is introduced to establish locally accurate surrogate models and reduce the number of DOE training samples. Active learning required 31 samples using the LF-based criterion and 68 samples with the bounds on \(P_{\text{f}}\) criterion. The resulting failure probabilities are consistent with those obtained using the response surface method with 132 samples. This significantly reduces the sample size, thereby minimizing computational demands and further improving efficiency, specifically by reducing the number of finite element simulations required. Therefore, this method not only improves the design efficiency, but also provides an interactive modeling framework that is easy to understand and apply, enabling the  
Figure 11: Iterative process for torsional stiffness with 30 initial samples: (**a**) The random seed is set to 1; (**b**) The random seed is set to 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Method**} & **Convergence** & **Sample Size** & \(P_{\text{b}}\) & \(P_{\text{t}}\) \\ \hline Active learning & LF-based & 31 & \(1.51\times 10^{-4}\) & \(3.25\times 10^{-4}\) \\  & Bounds on \(P_{\text{t}}\) & 68 & \(1.65\times 10^{-4}\) & \(3.36\times 10^{-4}\) \\ Response surface & – & 132 & \(1.53\times 10^{-4}\) & \(3.33\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of results between the response surface method and active-learning method. rapid application of the technology to real-world engineering problems. This is conducive to promoting the innovation and development of automotive structural design, and brings tangible value to the field of engineering design;  
(2) The efficiency and accuracy of active learning may be affected by a number of factors, such as the initial sample size, random seed, convergence criterion and degree of nonlinearity. Among these factors, the initial sample size and convergence criterion are easier to control. Therefore, during application, continuous practice is needed to balance the efficiency and accuracy by adjusting the initial sample size and convergence criteria;  
(3) In terms of uncertainty quantification, as engineering problems become increasingly complex, future research can further explore and develop in the following three aspects. Firstly, intelligent parameter design needs to be enhanced to improve the stability and validity of models as parameters change. This will simplify the system design process and improve adaptability for various engineering applications. Secondly, capabilities for secondary software development need to be strengthened to improve flexibility and scalability. This will help provide tailored solutions for engineering analysis and meet the different needs of users. Finally, reliability methods need to be continuously refined and improved to address potential challenges and shortcomings for engineering applications, including how to improve efficiency and robustness when addressing multi-dimensional and nonlinear implicit response issues. Conceptualization, J.W. and J.C.; methodology, J.W. ; software, J.W. and Y.Z. ([PERSON]); validation, J.C. and F.L. ; formal analysis, F.L. and J.C.; investigation, J.W. and Y.Z. ([PERSON]); resources, F.L. ; data curation, Y.Z. ([PERSON]); writing--original draft preparation, J.W. ; writing--review and editing, J.C. and F.L. ; visualization, J.W. ; supervision, [PERSON] and Y.Z. ([PERSON]); project administration, Y.Z. ([PERSON]) and F.L. ; funding acquisition, Y.Z. ([PERSON]).