## 2 Methodology
### Improved D-\(S\) Evidence Fusion Collapse Risk Assessment  
In the identification framework of \(\Theta\), an evidence can be expressed as Equation (9) [28]. In the formula, \(\theta\) is any real proposition in \(P(\Theta)\). The meaning of (\(\theta\),\(P_{\theta,j}\)) is that the probability mass of the evidence \(e_{j}\) pointing to proposition \(\theta\) is \(P_{\theta,j}\). \[e_{j}=\left\{\theta,p_{\theta,j}\right\}|\forall\theta\subseteq\Theta,\sum_{ \theta\subseteq\Theta}p_{\theta,j}=1\right\} \tag{9}\]  
In the formula, \(e_{j}\) is evidence, and \"\(j\) = 3\" represents three sources of evidence, which are advanced geological forecast data, instrument monitoring data and field inspection data. The identification framework \(\Theta\) = (I, II, III, IV), which represents the risk levels are I, II, III and IV, respectively. Improved D-S theory in this study combines credibility \(r_{j}\) (\(0\leq r_{j}\leq 1\)) and importance \(t_{j}\) (\(0\leq t_{j}\leq 1\)). Generally speaking, credibility is an objective existence, indicating the ability of \(e_{j}\) to evaluate correctly compared with other evidence, and importance can be subjectively determined according to the information source of the generated evidence which reflects the relative importance of \(e_{j}\) compared with other evidence in the combination of pieces of evidence. Firstly, the value of credibility needs to be obtained. At present, the measurement methods of uncertainty include conflict measurement and confusion measurement [29; 30]. Aggregated uncertainty is used to calculate the confidence level of each evidence learned from the probabilistic classification model, as shown in Equation (10). In the formula, \(P_{\theta,i}\) is the trust of focus element \(\theta_{i}\), and \(n\) is the total number of focus elements, which is 4 in this study. \[r_{j}=1+\frac{\sum_{\theta\in\Theta}p_{\theta,j}\log_{2}p_{\theta,j}}{\log_{2 }n} \tag{10}\]In the formula, \(r_{j}\) is the degree of trust. \(n\) is the total number of focal elements, which is 4 in this paper, indicating the number of risk levels in the identification framework. \(P_{\Theta,j}\) denotes the basic probability distribution value (BPA) corresponding to the risk level. Secondly, the value of importance needs to be calculated. In the environment of model learning and verification, the importance rating is directly determined by its contribution to the accuracy of the model. Minimum class-wise F1-score can limit the contribution of low-quality evidence. So, the importance of each evidence is set to min{class-wise F1-scores} in the probability classifier, which combines precision and recall, as shown in Equation (11). \[\left\{ \begin{array}{l}t_{j}=\min\Bigl{\{}\frac{P_{j}\cdot S_{j}}{P_{j}+S_{j} }\Bigr{\}}\\ \text{P}_{j}=\frac{TP_{j}}{TP_{j}+\text{FP}_{j}}\\ \text{S}_{j}=\frac{TP_{j}}{TP_{j}+\text{FN}_{i}}\end{array} \right. \tag{11}\]  
In the formula, \(t_{j}\) denotes the importance. \(TP_{i}\) means that both the true value and the predicted value are Positive. \(FP_{i}\) indicates that the true value is negative but the predicted value is positive. \(FN_{i}\) indicates that the true value is positive but the predicted value is negative. Finally, in order to obtain non-high-conflict evidence, the original BPA needs to be adjusted by credibility and importance to obtain BPA used for evidence fusion. The adjusted evidence is fused in pairs, and the overall evidence fusion result is obtained after normalization, as shown in Equation (12). \[\left\{ \begin{array}{l}p_{i,e(3)}=\frac{\widetilde{m}_{i,e(3)}}{\sum\limits_ {i\in\{i,\{i,j,j\}\}}\widetilde{m}_{i,e(3)}}\\ \widetilde{m}_{i,e(3)}=(1-r_{3})\widetilde{m}_{i,e(2)}+(1-r_{2})(1-r_{1}) \widetilde{m}_{i,3}+\widetilde{m}_{i,e(2)}\widetilde{m}_{i,3}\\ \widetilde{m}_{i,e(2)}=(1-r_{2})\widetilde{m}_{i,1}+(1-r_{1})\widetilde{m}_{ i,2}+\widetilde{m}_{i,1}\widetilde{m}_{i,2}\\ \widetilde{m}_{i,j}=\frac{t_{j}t_{j}}{1+t_{j}-r_{j}}\end{array} \right.