## 6 Case Validation
### Optimization of Equipment Safety Investment Plans for S Mining Enterprise Using Digital Twins
(1) Plan Formulation  
Assume that the actual safety investment cost for emergency equipment in January 2024 reaches CNY 4.25 million, exceeding the budgeted CNY 2.18 million, requiring adjustments to the plan. \(PE\) will feed real-time data back to \(DD\), after which the digital twin investment model will immediately adjust the investment plan, allocating some of the funds for next month to the current month's needs. \(Ss\) will then update the optimization model based on the results of the plan adjustments as follows:  
\[lnY=lnA+\alpha_{1}lnX_{1}+\alpha_{2}lnX_{2}+\alpha_{3}lnX_{3}+\alpha_{4}lnX_{ 4}+\alpha_{5}lnX_{5} \tag{13}\]  
\[ \begin{cases}4.37=lnA+\alpha_{1}5.53+\alpha_{2}5.02+\alpha_{3}5.35+\alpha_{4 }5.48+\alpha_{5}5.05\\ 4.28=lnA+\alpha_{1}5.61+\alpha_{2}5.18+\alpha_{3}5.38+\alpha_{4}5.50+\alpha_{5} 5.32\\ 4.19=lnA+\alpha_{1}5.71+\alpha_{2}5.32+\alpha_{3}5.49+\alpha_{4}5.63+\alpha_{5} 5.54\\ 4.08=lnA+\alpha_{1}5.74+\alpha_{2}5.40+\alpha_{3}5.56+\alpha_{4}5.69+\alpha_{5} 5.75\\ 4.05=lnA+\alpha_{1}5.81+\alpha_{2}5.35+\alpha_{3}5.62+\alpha_{4}5.80+\alpha_{5} 5.80\\ 3.88=lnA+\alpha_{1}5.86+\alpha_{2}5.45+\alpha_{3}5.69+\alpha_{4}5.87+\alpha_{5} 5.84\\ 3.81=lnA+\alpha_{1}5.89+\alpha_{2}5.68+\alpha_{3}5.96+\alpha_{4}5.92+\alpha_{5} 5.51\\ \end{cases}  \tag{14}\]  
Figure 14: Predicted accident losses for the mining enterprise in 2024. The optimization model is simulated and accident losses are predicted for this scheme, at which point the investment scheme is shown in Table 11.  
After completing the investment, it is necessary to update related parameters such as \(DD\), \(B_{V}\), and \(R_{V}\). (2) Comparison Between Digital Twins and Traditional Methods  
A comparison of the optimization scenarios of equipment safety investment under the traditional approach and the digital twin approach for January and February 2024 for enterprise S is shown in Table 12, for example. In January and February 2024, under the condition that the total investment of enterprise S remained unchanged, the digital twin's technology reduced the accident loss by CNY 104,600 compared to the traditional method, amounting to a reduction of 11.73%. The application of digital twins' technology allows the enterprise to adjust the investment plan more flexibly in actual operations, ensuring the efficiency and effectiveness of equipment safety investments. This consequently reduces the risk of accidents and enhances the overall safety level of the enterprise. In order to further validate the effectiveness of digital twin technology in reducing accident losses, a 95% confidence interval was calculated. According to the calculated results, the confidence interval for the reduction in accidental losses is [9.83, 11.09], which indicates that the reduction in accidental losses is statistically significant. And the Wilcoxon Signed Rank Test and Bootstrap method were used to further validate the effect of digital twin technique. The \(p\)-value of the Wilcoxon Signed Rank Test is less than 0.05, which indicates that digital twin technique has a significant effect in the reduction in accidental losses. The results of Bootstrap method show that the accidental loss reduction is not a chance phenomenon and has high robustness.