# Root Cause Tracing Using Equipment Process Accuracy Evaluation for Looper in Hot Rolling
## 3 Root-Cause-Tracing Algorithm
### Construction of Root-Cause-Tracing Algorithm
In this way, we only need to solve each coefficient \(p_{i}\) in the system of equations to determine the contribution of each influencing factor. Since each equation is nonlinear and cannot be directly solved, the equation-solving problem of the above equations is transformed into an optimization problem. \[\min \sum_{k=1}^{m}|f(\Delta x_{k_{1}}\ldots\Delta x_{k_{n}})-\sum_{i=1 }^{n}p_{i}\Delta x_{ki}+o(\Delta x_{ki})| \tag{27}\] \[x=\frac{\sum_{i=1}^{n}s_{i}}{n} \tag{20}\]0  
Then, the particle swarm optimization (PSO) algorithm is used [28] to solve each \(p_{i}\). Finally, the weight coefficients are sorted to find the final cause. We end up with Algorithm 1. The idea of the algorithm is as follows: first preprocess the data, turn it into manageable data. Then, use the BP neural network to fit the functional relationship between the various looper factors and the score; afterwards, construct a system of equations and convert it into an optimization problem with constraints, and solve it using PSO. Finally, the root-cause-tracing results are given. ```
1:Give the data processing formula: \(x=g(s)\) calculate the feature average, \(\Delta x=h(x)\) calculate the feature deviation, \(\Delta x^{{}^{\prime}}=s(\Delta x)\) to perform data normalization. Specify the standard score of the looper \(y_{\text{std}}=80\). 2:Based on the database, give the number of data that needs to be processed \(L\). 3:for\(\lambda=0:L\)do
4: Loop \(x=g(s)\rightarrow\Delta x=h(x)\rightarrow\Delta x^{{}^{\prime}}=s(x),\Delta y =y-y_{\text{std}}\). 5:endfor
6:Take the \(\Delta y\) as the output, \(\Delta x^{{}^{\prime}}\) as the input, and use the BP neural network to fit the function \(f\). 7:Load new data and get the looper's EPAE score \(y^{{}^{\prime}}\). When \(y^{{}^{\prime}}<y_{\text{std}}\), do the following. 8:Search for historical steel coils with scores similar to the new sample. 9:Use new sample data and historical steel coil data to construct a system of equations, and utilize the PSO algorithm to solve the weight parameters. 10:Sort the factors by weight and give the final result. ```  
**Algorithm 1** Root-cause-tracing algorithm  
At present, most steel industries have mature detection systems, and various variables during the hot rolling process can be measured in real time. Therefore, it is only necessary to train the BP neural network using previous data and input the measured fault data to calculate the result. Therefore, the EPAE score of each product can be calculated in real time, and these data can be used for training the BP neural network. Therefore, the root-cause-traceability algorithm can be seamlessly integrated with existing control and monitoring systems in industrial environments without the need for additional equipment. In addition, there is no need to consider the compatibility of different data sources or architectures, as this algorithm only uses the basic data measured by sensors, and even if the data source changes, it does not affect the basic characteristics of the data. This algorithm can adapt to dynamic production environments: when there are local changes in operating conditions or the equipment configuration in the production environment, such as replacement of some data collection equipment, the neural network only needs to be retrained with new data. If there are significant structural changes, such as changes in the hot rolling process, it is necessary to modify the corresponding EPAE model and retrain the neural network. Due to the fact that each part of the root-cause-tracing algorithm can be designed and trained separately, the low coupling of the algorithm ensures its effectiveness in constantly changing scenarios.