## 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
For example, improper operation can lead to malfunctioning equipment, resulting in unnecessary energy waste. (2) Operating Standards: Strict adherence to operating procedures can minimize energy losses caused by incorrect operations or arbitrary adjustments of parameters. (3) Monitoring and Management: A lack of real-time energy consumption monitoring and analysis tools may prevent timely identification and adjustment of issues. For example, improper peak energy usage management can lead to avoidable wastage. Qualifications should cover both theoretical knowledge and practical skills, such as understanding the nuances of the machinery, safety protocols, and troubleshooting techniques. Standards should include inspection routines, criteria for acceptance/rejection, and specific metrics for evaluating the quality of the output. Standardization of processes reduces variability and ensures that all staff follow best practices. Monitoring tools, such as Supervisory Control and Data Acquisition (SCADA) systems, can be used to track operational performance in real-time. For example, in the case of gas consumption, the equipment-related factors, production-related factors, and operational factors are shown in Tables 3-5, respectively. B. Bayesian neural network construction  
Bayesian Inference is a statistical inference method that updates beliefs or probability distributions about parameters using Bayes Theorem [29]. It can be expressed as  
\[ \begin{split}\Pr(A)=\sum_{i=1}^{n}\Pr(B_{i})\Pr(A|B_{i}),\\ \Pr(B_{i}|A)=\frac{\Pr(B_{i})\Pr(A|B_{i})}{\sum_{j=1}^{n}\Pr \left(B_{j}\right)\Pr(A|B_{j})},\end{split}  \tag{23}\]  
where \(\Pr(A)\) represents the prior probability of event \(A\) occurring and \(P(A|B_{i})\) represents the conditional probability of event \(A\) occurring given that event \(B_{i}\) has occurred. Using this formula, we can compute the posterior probability of the target based on the prior probability and the new evidence. Applying this to root cause analysis, let event \(A\) represent a fault occurring in variable \(X\) and let event \(B_{i}\) represent the occurrence of an anomaly in factor \(z_{i}\). Then,m \(\Pr(B_{i}|A)\) represents the probability that the anomaly in factor \(z_{i}\) caused the fault in variable \(X\). This method is only applicable in limited cases, where both event \(A\) and event \(B_{i}\) are finite. However, the weighted Granger causality analysis proposed earlier involves contin \begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Factor** & **Description** \\ \hline
1 & Deviation in Furnace Time & The difference between the actual furnace time and the lower limit of the process-required furnace time, averaged \\
2 & Hot Air Ventilation Volume & Total time during which the hot air vent is open \\
3 & Air–Fuel Ratio & The ratio approaches the theoretical optimal air–fuel ratio \\
4 & Furnace Exit Temperature & Proportion of slab data with an exit temperature \(\geq\) 1190 °C \\
5 & Steel Exit Temperature & Average difference between actual steel exit temperature and the theoretical lower limit of steel exit temperature \\
6 & \(\cdots\) & \(\cdots\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Production-related factors (gas consumption). \begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Factor** & **Description** \\ \hline
1 & Steam Recovery Volume & The daily steam recovery volume \\
2 & Flue Gas Temperature & Temperature of the flue gas after the heat exchanger, increasing air temperature to avoid heat loss \\
3 & Heat Loss & Heat loss per unit of time \\
4 & Furnace Refractory Loss & Temperature control of the furnace wall within the required range \\
5 & Furnace Surface Temperature & Measured temperature of the heating furnace surface \\
6 & \(\cdots\) & \(\cdots\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Equipment-related factors (gas consumption).