## 6 Case Validation  
Currently, coal mine S primarily relies on historical investment plans and personnel experience for equipment safety investments. This approach is susceptible to subjective biases and lacks scientific guidance. To address these issues, a method based on digital twin technology for optimizing coal mine equipment safety investments and predicting accident losses has been introduced. This method aims to guide the enterprise towards scientific management of equipment safety investments. The digital twin safety investment optimization model is illustrated in Figure 6.  
In this model, Physical Equipment (_PE_) represents represents the actual safety investment equipment of the enterprise, and the safety resource investment for these equipment covers the investment in safe transportation facilities, emergency response facilities, safe extraction facilities, safe ventilation facilities, and safety education. The virtual model (_VE_)  
Figure 6: Digital twin optimization model for coal mine equipment safety investment in S enterprise. is composed of three core components: \(P_{V},\ B_{V},\text{ and }R_{V}\). The \(P_{V}\) segment is responsible for establishing a detailed indicator structure for coal mine safety investments. This structure not only serves as a concrete representation of \(VE\) but also lays a solid foundation for subsequent safety investment optimization and accident loss prediction. The \(B_{V}\) segment employs buffer operator techniques to meticulously preprocess data and integrates with C-D production functions to collaboratively establish a refined model for optimizing equipment safety investments. The \(R_{V}\) segment relies on advanced BP neural network algorithms to conduct in-depth analysis and unveil underlying patterns between safety investments and accident losses, ultimately constructing an efficient and accurate model for predicting safety investment-related accident losses. Following the issuance of safety investment tasks by enterprises, the equipment safety investment optimization model generates alternative safety investment scenarios through simulation (future scenario simulation, \(FS\)). Subsequently, the accident loss prediction model simulates (future scenario simulation, \(FS\)) to forecast accident losses after implementing alternative scenarios. If the predicted accident losses are lower than historical losses, the scenario is considered preliminarily validated. If the predicted accident losses exceed expectations, decision-makers will examine whether the total investment exceeds the maximum investment limit for safety economic benefits. If not exceeding, the investment plan will be re-optimized and re-validated; if exceeded, adjustments will be made to the total investment and new scenarios will be generated for optimization and validation. Ultimately, the results of the optimized plan and accident loss predictions will be presented in \(Ss\) in the form of data and tables, for reference and decision-making by stakeholders. Decision-makers assess the need for adjustments to the plan (\(BS\)) based on the results of optimization and validation. If adjustments are necessary, the plan will be re-optimized and re-validated based on modification suggestions. After completing adjustments, the plan is implemented as required. Throughout the entire safety investment process, required data and simulation-derived data are stored in \"Data (\(DD\))\", driving the entire investment process. Connections between various components are facilitated by \(CN\) to ensure the flow of data and information. Upon completion of the entire safety investment implementation process, \(DD\) conducts an analysis and summary of the entire process, and updates \(D_{K}\), \(B_{V}\), and \(R_{V}\).