## 5 Example Analysis and Discussion
### Reliability Analysis of a Latch Lock Mechanism  
A structural reliability problem for a latch lock mechanism of hatch is considered, as shown in Figure 2a [42]. The latch lock mechanism can be visualized as a crank slider schematically shown in Figure 2b. According to the kinematic analysis of the crank slider  
Figure 1: Flowchart of the proposed hybrid intelligent algorithm.  
mechanism, the horizontal distance between the fulcrum and the endpoint of the latch lock is expressed as:  
\[L(\alpha_{1},r,L_{1},L_{2},e)=r\cos\alpha_{1}+\sqrt{L_{1}^{2}-\left(e-r\sin \alpha_{1}\right)^{2}}+L_{2} \tag{15}\]  
where \(\alpha_{1}\) is the angle between the horizontal direction and the crank, \(r,L_{1},L_{2},\text{ and }e\) are dimensional parameters.  
When \(L\) is not less than \(L_{3}(\text{mm})\), the latch lock can be normally locked. Otherwise, the latch lock cannot normally operate. Therefore, the LSF of the latch lock mechanism can be established as follows:  
\[g(\alpha_{1},r,L_{1},L_{2},e)=L(\alpha_{1},r,L_{1},L_{2},e)-L_{3} \tag{16}\]  
In this work, it is assumed that the input factors \(\xi=(\alpha_{1},r,L_{1},L_{2},e)^{\text{T}}\) are uncertain variables with independent normal uncertainty distributions under insufficient sample data. Relevant distribution parameters of input factors are listed in Table 1. The reliability assessment of the latch lock mechanism can be implemented based on the two uncertainty reliability methods presented in Section 3.  
To verify the credibility of the proposed structural reliability analysis methods, the traditional FORM-based on probability theory is provided as a reference. In this case, all input factors are regarded as random variables with normal probability distribution shown in Table 1. Comparative reliability results of the aforementioned three analysis methods in \(L_{3}\in[286,\ 291]\) are shown in Figure 3.  
As presented in Figure 3, with an increase \(L_{3}\), both URI and probabilistic reliability indicator (PRI) decrease. It is worth noting that the uncertainty theory-based URI trend is consistent with the probability theory-based PRI trend. When \(L_{3}\) increases, the URI decreases, and the belief degree of the mechanism reliability becomes lower. Therefore, the URI introduced in Section 3 is effectively describes the trend of mechanism reliability with epistemic uncertainties. It clearly shows that the reliability estimated by the presented method is lower than the one calculated by the classical probabil  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Input Factors** & **Proposed Method** & **Probabilistic Method** \\ \hline \(\alpha_{1}(\text{rad})\) & \(\mathcal{N}(0.7844,0.02)\) & \(N(0.7844,0.02^{2})\) * \\ \(r(\text{mm})\) & \(\mathcal{N}(44.4162,0.02)\) & \(N(44.4162,0.02^{2})\) \\ \(L_{1}(\text{mm})\) & \(\mathcal{N}(114,0.02)\) & \(N(114,0.02^{2})\) \\ \(L_{2}(\text{mm})\) & \(\mathcal{N}(114,0.02)\) & \(N(144,0.02^{2})\) \\ \(e(\text{mm})\) & \(\mathcal{N}(41,0.02)\) & \(N(41,0.02^{2})\) \\ \hline \hline \end{tabular}  
* \(0.02^{2}\) is the variance of normal probability distribution.  
\end{table}
Table 1: Distribution parameters of input factors.  
Figure 2: The latch lock mechanism of hatch. (**a**) The simulation model; (**b**) The visualized model.  
Furthermore, as shown in Figure 3, the URI estimated based on the equivalent analytical model is highly consistent with the one calculated by the US approach. Therefore, it can be inferred that the US approach meets the requirements of prediction accuracy. The URI can be used to help structural engineers make the most reasonable prediction when the input factors are obtained from epistemic uncertainty with insufficient sample data.