## 4 Experimental Results and Analysis  
Grey correlation analysis was conducted using data obtained from industrial sites. The correlation analysis method was used to analyze the temperature and casting speed variables that are closely related to the tail diameter. The correlation between the two comparison sequences and the tail diameter is shown in Figure 8.  
As shown in Figure 8, the temperature, pulling speed, tail length, and mass increment have a high correlation with the tail diameter in the tail process. The mean correlation coefficients of the temperature, pulling speed, tail length, and mass increment are 0.4896, 0.3606, 0.3588, and 0.3452, respectively. The growth process data of 300 mm monocrystalline silicon were obtained for the Czochralski furnace of the Crystal Growth Equipment and System Integration National & Local Joint Engineering Research Center. These data were used to validate the soft measurement method. According to experience, the delay time of the temperature is  
Figure 8: The correlation between the two comparison sequences and the tail diameter. about 10-13 min, and the delay time of the pulling speed is less than 1 min. The pre-set values of the temperature delaying order \(n\), the pulling speed delaying order \(m\), and the maximum delaying time all need to be satisfied. The data-sampling frequency is 0.2 Hz, so let \(n=100,m=20\). Taking the delaying order identification of temperature as an example, the inputs of the neural network in the MIV algorithm are \([T(k-301),T(k-302),\cdots,T(k-400)]\), and the number of neurons in the hidden layer is \(\sqrt{N_{i}+N_{o}}+a\), where \(N_{i}\) is the number of inputs and \(N_{o}\) is the number of outputs. \(a\) is between 1 and 10, so let \(a=10\). The Levenberg-Marquardt algorithm is used to obtain the relationship between the delaying order of the temperature and pulling speed and the absolute value of the MIV after 1000 iterations. The relationship diagram is shown in Figure 9.  
The delaying order maximum MIV counterparts of the effect of the temperature and pulling speed on the crystal diameter were \(T(k-346)\) and \(V(k-12)\). In order to prevent the omission of other input items, the final selection of the temperature input item was \(T(k-345),T(k-346),T(k-347)\) and the pulling speed input item was \(V(k-11),V(k-12),V(k-13)\). After the delaying order of the temperature was obtained, the DBN-ACO-SVR network was constructed. The network model can be expressed by Formula (17):  
\[ \begin{array}{c}D(k)=F(T(k-345),T(k-346),T(k-347),\\ V(k-11),V(k-12),V(k-13),L(k),M(k))\end{array}  \tag{17}\]  
From the above formula, the number of input nodes in the network was 8, and the number of output nodes was 1. We determined the number of layers and nodes of the DBN through continuous experimental verification. The number of network layers of the DBN was set as four layers, and the number of RBMs was two. The number of nodes in each layer was selected as 8-20-6-1. The learning rate was set as 0.02, and the activation function was selected as Sigmoid. The error results of each RBM iteration and prediction error results of the DBN iteration are shown in Figure 10.  
ACO is used to select the optimal parameter of SVR and apply it to soft sensing models. The results of the iterative optimization after processing 200 iterations are shown in Figure 11. We substituted the optimal parameter of the SVR algorithm obtained from the ACO algorithm into the DBN model to obtain a new soft measurement model, DBN-ACO-SVR, and predict the crystal tail diameter using this model. Figure 9: Delaying order and the \(\left|MIV\right|\) curve of the pulling speed and temperature. This paper proposes a soft measurement method for the tail diameter of the DBN-ACO-SVR model. The training dataset of the verification conclusion in this paper includes two kinds of datasets. In the first dataset, the basic processing parameters are the same, and the control processing parameters are different.