## 6 Validation  
Under the same experimental conditions, thirty specimens of unknown weld defect levels had been selected to verify the modified MLE MMM model based on the D-S theory. Take specimen 17 as an example, after 980 fatigue kilocycles, the specimen, which showed no macroscopic crack visible to the naked eye, was examined by X-rays. The result of X-ray detection showed that there were no hidden cracks on both sides of the prefabricated defect shown in Figure 7.  
Then, by analyzing the MMM data, the tangential and normal components of \(\Delta H_{p}\), \(G\) and \(Z\) are (28.9, 5.75, 2.441) and (9.6, 6.5, 5.007), respectively. Then, the tangential and normal MLE probabilities are calculated, respectively, by Formulas (10) and (11), the results are 0.16 and 0.12. The proximity of the unknown defect level are obtained by Formulas (12) and (13), and the results are listed in Table 5. Then, the basic reliability allocation is calculated by Formulas (17) and (18), shown in Table 6.  
It can be seen that the basic reliability allocations of the normal and hidden crack are similar. It is still difficult to identify the unknown defect level only based on the basic reliability allocation. So, it is necessary to use the information fusion. The information fusion results are listed in Table 7. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Basic Reliability Allocation** & **Tangential Signal** & **Normal Signal** \\ \hline Normal state & 0.47 & 0.41 \\ Hidden crack & 0.47 & 0.48 \\ Macroscopic crack & 0.01 & 0.08 \\ Uncertainty degree & 0.047 & 0.033 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Basic reliability allocation of the identifying damage state. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(m_{\text{hel1}}=D_{\text{1}}\)**0.41)** & \(m_{\text{hel1}}=D_{\text{2}}\)**(0.48)** & \(m_{\text{hel1}}=D_{\text{3}}\)**(0.08)** & \(m_{\text{hel1}}=\)**(0.033)** \\ \hline \(m_{\text{hel2}}=\) C\({}_{1}\)(0.47) & C\({}_{1}\)(0.1927) & \(\Phi\)(0.2256) & \(\Phi\)(0.0376) & C\({}_{1}\)(0.01551) \\ \(m_{\text{hel2}}=\) C\({}_{2}\)(0.47) & \(\Phi\)(0.1927) & C\({}_{2}\)(0.2256) & \(\Phi\)(0.0376) & C\({}_{2}\)(0.01551) \\ \(m_{\text{hel2}}=\) C\({}_{3}\)(0.01) & \(\Phi\)(0.0041) & \(\Phi\)(0.0048) & \(C_{3}\)(0.0008) & \(C_{3}\)(0.00033) \\ \(m_{\text{hel2}}=\)\(\Theta\)(0.047) & C\({}_{1}\)(0.01927) & C\({}_{2}\)(0.02256) & C\({}_{3}\)(0.00376) & \(\Theta\)(0.00155) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Information fusion results. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Proximity** & **Tangential Signal** & **Normal Signal** \\ \hline Normal state & 0.84 & 0.99 \\ Hidden crack & 0.99 & 0.98 \\ Macroscopic crack & 0.17 & 0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: MLE probability proximity of the identifying damage state. Figure 7: Result of X-ray detection of specimen 17#. The inconsistency factor \(k\) is calculated by Formula (23), and the result is as follows:  
\[k=0.2256+0.04+0.0376+0.1458+0.1927+0.0376+0.0041+0.0048=0.5024\]  
So, the basic reliability allocation of the evidence \(Bel_{1}\) and \(Bel_{2}\) is calculated by Formula (22). And the reliability allocation after information fusion is shown in Table 8.  
According to the decision rules of the D-S theory, \(\varepsilon_{1}\) and \(\varepsilon_{2}\) are taken as 0.01 and 0.001, then the prediction result is hidden crack. The results show the reliability is 53% and uncertainty degree \(m(\Theta)\) is 0.3%. In order to determine the unknown defect level from the experimental point of view, a scanning electron microscopy (SEM) has been applied to test the selected specimen. At the end of the prefabricated defect, the wire-electrode cutting was used to obtain the SEM specimen as shown in the dashed box in Figure 8. The cutting surface 1 is the SEM observation surface with the length of 15 mm. The distance from the cutting surface 2 to 1 was 10 mm.