## 3 Case Study
### Collapse Risk Assessment Based on Multi-Source Data Fusion Method  
In order to solve the problem of unreliable evaluation results of a single information source, the improved D-S theory is used to fuse multi-source data. This method combines the different results of the above three single evaluation models. The importance value is  
Figure 5: Classification probability distribution for different parameters. (**a**) C are 0.05, 0.1, 0.15 and 0.2. (**b**) gamma are 0.001, 0.002, 0.004 and 0.006. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multicolumn{2}{c}{**Probability**} & \multicolumn{2}{c  
chosen based on the classification measures of each model by the rule (min[F1-scores]). The classification performance for the above three models is summarized by Equation (11). The result is shown in Table 9. According to the rule (min[classwise F1-scores]), the importance values of each model in the fusion process are [0.5; 0.33; 0.57]. To illustrate the fusion process, six test samples were selected for analysis. The three-source information fusion training results are compared with three single-source training results, as shown in Table 10. In the table, bold values represent the probability of the maximum risk level obtained by the model. The following conclusions can be obtained:  
1. The multi-source information fusion model has good fault tolerance. The fusion model can correct the wrong classifier result by the important rating and reliability. Taking the test sample section No. 5 as an example, the collapse failure probability value obtained by the three single-information source model are \(p_{\theta,1}=[0.1,\ 0.1,\ 0.65,\ 0.15]\), \(p_{\theta,2}=[0.3,\ 0.4,\ 0,\ 0.3]\) and \(p_{\theta,3}=[0,\ 0.1,\ 0.4,\ 0.5]\). According to Equation (10), the credibility can be obtained as \([r_{1},\ r_{2},\ r_{3}]=[0.733,\ 0.685,\ 0.707]\). It can be seen from Table 9 that the importance value of the fusion model is \([t_{1},t_{2},t_{3}]=[0.5,0.33,0.57]\). According to Equation (12), the value of BPA, which is combined credibility and importance rating, can be obtained as \[ \begin{bmatrix}\widetilde{m}_{I,1}&\widetilde{m}_{II,1}&\widetilde{m}_{II,1}& \widetilde{m}_{IV,1}\\ \widetilde{m}_{I,2}&\widetilde{m}_{II,2}&\widetilde{m}_{II,2}&\widetilde{m}_ {IV,2}\\ \widetilde{m}_{I,3}&\widetilde{m}_{II,3}&\widetilde{m}_{II,3}&\widetilde{m}_ {IV,3}\end{bmatrix} = \begin{bmatrix}0.068&0.068&0.438&0.109\\ 0.000&0.297&0.243&0.135\\ 0.050&0.153&0.102&0.256\end{bmatrix} .\] Firstly, evidence \(e_{1}\) and evidence \(e_{2}\) are fused, and the probability distribution result after fusion is \([\widetilde{m}_{I,e(2)},\ \widetilde{m}_{II,e(2)},\ \widetilde{m}_{III,e(2)},\ \widetilde{m}_{III,e(2)}]=[0.020,\ 0.119,\ 0.2 99,\ 0.083]\). Then it is fused with evidence \(e_{3}\), and the probability distribution result after fusion is \([\widetilde{m}_{I,e(3)},\ \widetilde{m}_{II,e(3)},\ \widetilde{m}_{III,e(3)},\ \widetilde{m}_ {IV,e(3)}]=[0.006,\ 0.068,\ 0.133,\ 0.067]\). After normalization, the final BPA result after fusion is \([P_{I,e(3)},\ P_{II,e(3)},\ P_{III,e(3)},\ P_{IV,e(3)}]=[0.1,\ 0.2,\ 0.4,\ 0.3]\). The actual collapse level is Level III. As shown in Table 10, wrong conclusions are given by traditional D-S model. The reason is that the improved D-S model takes into account the importance and credibility, which allows \(e_{1}\) to correct \(e_{2}\) and \(e_{3}\). Through the above analysis, the traditional D-S model is highly sensitive to high conflict evidence when there is a high conflict of evidence, so its performance is poor. In contrast, the improved D-S model, which can be corrected for incorrect classifiers based on the importance rating and confidence of the correct classifier, has better fault tolerance. 2.