## 2 Methods
### Root Cause Tracing Based on Adam Variational Inference Bayesian Neural Network
#### 2.2.3 Root Cause Tracing Based on Adam Variational Inference Bayesian Neural Network  
A. Analysis of underlying factors  
The factors influencing energy consumption can be categorized into three types: equipment factors, production factors, and operational factors. These factors are intertwined \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & \(x_{1}\) & \(x_{2}\) & \(x_{3}\) & \(x_{4}\) & \(x_{5}\) \\ \hline \(x_{1}\) & - & \(a_{12}\) & - & - & \(a_{15}\) \\ \(x_{2}\) & \(a_{21}\) & - & - & \(a_{24}\) & - \\ \(x_{3}\) & - & - & - & - & - \\ \(x_{4}\) & - & - & \(a_{43}\) & - & - \\ \(x_{5}\) & - & - & - & \(a_{54}\) & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Causal coefficient table (example). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & \(x_{1}\) & \(x_{2}\) & \(x_{3}\) & \(x_{4}\) & \(x_{5}\) \\ \hline \(x_{1}\) & - & \(a_{12}\) & - & - & \(a_{15}\) \\ \(x_{2}\) & \(a_{21}\) & - & - & \(a_{24}\) & - \\ \(x_{3}\) & - & - & - & - & - \\ \(x_{4}\) & - & - & \(a_{43}\) & - & - \\ \(x_{5}\) & - & - & - & \(a_{54}\) & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Example of weighted causal coefficient table. Figure 5: LSTM-based weighted Granger causality flow chart. (**a**) Training model. (**b**) Calculating weight. Figure 6: Cause and Effect Diagram (Example). and collectively determine energy utilization efficiency and consumption levels. Improving energy efficiency requires a systematic approach, focusing on technological upgrades in equipment, optimization of production processes, and improvements in operational management. Additionally, combining energy consumption data analysis with intelligent management systems can further uncover energy-saving potential, achieving an overall optimization effect. Equipment Factors: Equipment serves as the direct medium for energy consumption, and its performance and condition have a decisive impact on energy efficiency. Based on different professional classifications, equipment on the production line can be categorized into mechanical, hydraulic lubrication, electrical, water and gas, thermal, and specialized equipment. Due to differences in the design and operational characteristics of these equipment types, their energy consumption patterns vary. (1) Equipment Efficiency: The design level, technological advancement, and energy efficiency rating of equipment directly affect energy conversion and utilization efficiency. High-efficiency equipment typically reduces unnecessary energy losses. (2) Maintenance and Care: Wear, aging, or failure of equipment during long-term operation can lead to increased energy consumption. Regular maintenance, inspection, and upgrades can effectively lower energy use. (3) Equipment Compatibility: The compatibility between equipment and production requirements is also critical. For example, using equipment with capacities that are too large or too small can result in unnecessary energy waste. Production Factors: Production processes and process management determine the actual energy usage requirements. (1) Process Flow: The advancement, scientific nature, and rationality of the process flow directly affect energy consumption. Optimizing the process flow, reducing intermediate steps, or minimizing losses can effectively lower energy usage. (2) Production Scale: Large-scale production can reduce energy consumption per unit of product to some extent. However, excessive production beyond capacity may lead to additional energy consumption. (3) Product Quality Requirements: High-quality, high-precision products typically require more complex processes and equipment operations, which may result in higher energy consumption. Operational Factors: The operational level and management capabilities play a crucial role in the efficiency of equipment operation and the effectiveness of process execution. (1) Personnel Skills: The technical proficiency, training level, and familiarity with equipment of the operators directly impact energy efficiency.