# Root Cause Tracing Using Equipment Process Accuracy Evaluation for Looper in Hot Rolling
## 4 Experimental Results and Analysis  
Taking the monthly production data of finishing rolling loopers of the 2250 mm hot tandem rolling production line as the experimental data. In fact, we used 19,418 training data, which is the monthly output of the steel plant, each datum is further divided into 21 aspects. Therefore, we firmly consider the root-cause-tracing algorithm can handle large datasets or more complex production scenarios. And when scalability challenges arise, such as the addition of sensors in industrial sites, the dimensionality of measurement data increases. Only slight changes are needed to some parameters of the neural network and PSO, and the basic theory of the algorithm will not change. Using the relevant factors of the loopers (material factors, equipment factors, control factors) as model inputs, the data were first analyzed by preprocessing operation, after which the average value of each factor was calculated as the feature value. Some groups with better looper scores are selected as standards for comparison, the deviations between the characteristic values of each sample and the standard values are calculated, and a dimensionless operation is performed on the deviations. The relationship between the eigenvalues and the looper EPAE score \(f\) is fitted through the BP neural network. Finally, a system of equations is established and solved using the PSO algorithm. The contribution of each factor to the low looper EPAE score is obtained based on the weight. Finally, by sorting each factor according to its contribution, root cause tracing can be achieved. As an intelligent search algorithm, the particle swarm optimization algorithm has the advantages of fast convergence speed and simple parameters in solving nonlinear problems. The particles in the algorithm adjust their search direction by memorizing the optimal position, as shown in Figure 7.  
The particle's velocity \(v_{i}^{d}\) and position \(x_{i}^{d}\) are updated through the following formula to find the optimal solution to the objective function:  
\[ \begin{split} v_{i}^{d}(k+1)=& w\times v_{i}^{d}(k)+c_{1} \times\text{rand}_{1}^{d}\times\left(\text{pBest}_{i}^{d}-x_{i}^{d}(k)\right)\\ &+c_{2}\times\text{rand}_{2}^{d}\times\left(\text{gBest}_{i}^{d}-x _{i}^{d}(k)\right)\\ & x_{i}^{d}(k+1)=x_{i}^{d}(k)+v_{i}^{d}(k+1)\end{split}  \tag{28}\]  
Figure 6: Self-parameters and looper scoring. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Input layer node & 21 \\ \hline Middle layer node & 7 \\ \hline Output layer node & 2 \\ \hline Activation function & Sigmoid function \\ \hline Error back-propagation & Derivative of sigmoid function \\ \hline Threshold & 0 \\ \hline Loss function & Mean square error function \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Neural network parameter settings. Figure 7: PSO algorithm. where \(i\) is the particle number, \(d\) is the particle dimension, \(k\) is the iterations, \(w\) is the weight inertia, \(c_{1}\) and \(c_{2}\) are the acceleration coefficients (also called learning factors), \(\text{rand}_{i}^{d}\) and \(\text{rand}_{2}^{d}\) are random numbers on two \([0,1]\), and \(\text{pBest}_{i}^{d}\) and \(\text{gBest}_{i}^{d}\) represent the optimal positions for individuals and groups, respectively. The various parameter settings of the particle swarm algorithm are as shown in Table 6.  
Several groups of question samples are selected with similar looper EPAE scores, and a series of operations is performed on the data of related factors, such as feature extraction, feature deviation calculation, and dimensionality reduction. The results are shown in Figure 8. The characteristic deviation of Figure 8 is processed by Equations (20) and (21) in the root-cause-tracing algorithm. The larger the value, the greater the impact of this factor on the looper failure. Using several similar loop data of EPAE in Figure 8, an equation system is established, like Equation (26), and iteratively solved using the PSO algorithm.