# An Adaptive Process Monitoring Method Based on an Improved ADALINE Neural Network
## 3 Adaptive Process Monitoring Approach
### Control Limit Adaptive Model
#### 3.3.2 Adaptive Control Model for Control Limits  
After establishing the initial control limit for point control based on the status information, we need to further establish an adaptive update model to achieve the adaptive dynamic adjustment of the control limit and gradually use the process status information of the product to establish a \"control channel\" to further improve the quality level of the product and improve the control accuracy of the control limits. Control accuracy refers to the fluctuation range of the product quality. One of the calculation methods is shown in Equation (8):  
\[G=\frac{\sum\limits_{i=n-k}^{n}g_{i}}{100k}\times 100\%, \tag{8}\]  
\(G\) is the control accuracy of the process control limit, \(n\) represents the total number of machining cycles, and \(K\) is the step size. \(g_{i}\) is the quality score of the processed product in the \(i\)-th cycle, and \(g_{i}\) is summed to obtain the control accuracy.  
At the same time, to ensure the effectiveness of monitoring, the concept of control success rate is introduced, and the calculation method is Equation (9):  
\[R=\frac{TT+FF}{T+F}, \tag{9}\]  
\(T\) is the total number of normal data cycles, and \(F\) is the total number of fault data cycles. \(TT\) is the number of products that are normal, and the control limit is determined as normal. \(FF\) is the number of product faults, and the control limit is determined as abnormal.  
For the update of the control limit based on the ADALINE neural network, the schematic structure of the model is shown in Figure 6. In Figure 6, the blue part is the main body of the model. The update control limit consists of two parts. One part is \(L(n-1)\), which is the control limit determined in the previous cycle. When \(n=1\), the control limit is the initial control limit \(L(0)=L_{OLD}\). The other part is the real-time status data \(L_{NEW}\). The weights are multiplied between the two parts to complete the update of the control limit. The initial weights \(w\) is given based on production experience. The gray part is the adjustment strategy for the dynamic adjustment of the control limit. When the control success rate \(R\) does not meet the requirements, the ADALINE neural network is used to adjust the weights \(w\) in the process to achieve automatic update of the process control limit and meet the requirements.  
When combining the algorithm topology in Figure 1 with the ADALINE neural network in the model, \(x_{1}\) is the control limit of the previous cycle, \(x_{2}\) is the real-time data collected during the latest cycle, \(y\) is designed to be the actual calculated control success rate, and \(r\) is set to the expected control success rate for the machining process. Through the ADALINE neural network model, the weight \(w\) is continuously adjusted so that \(r\) is continuously close to the actual output \(y\), and then the obtained \(w\) is used to complete the update of the control limit. The calculation method for updating the control limit is shown in Equation (10):  
\[L=\begin{cases}L(n)=\omega L(n-1)+(1-\omega)L_{NEW}&n=1,2,3,4,...\\ \hskip 56.905512 ptL(0)=L_{OLD}&n=0\end{cases}, \tag{10}\]  
If the design requirements are met, the current updated control limits \(L(n)\) will be output. The purple part is the control limit accuracy training part. When the control limit accuracy does not meet the design requirements, the blue and gray parts are repeated to iteratively update the control limit and reduce the fluctuation range of the upper and lower control limits. Otherwise, the training control limit is output.