## 3 Overall Architecture of the Proposed Method
Therefore, the energy function of RBM is as follows:  
Figure 3:0  
where \(a_{i}\) and \(b_{j}\) are visible layer offsets and hidden layer offsets, respectively, and \(w_{ij}\) are the connection weights between the visible layer \(v_{i}\) and hidden layer \(h_{j}\). The joint probability distribution of visible layer \(v\) is as follows:  
Figure 3:1  
When the input signal of the visible layer is given, the activation conditions of each node of the hidden layer are independent; conversely, when the hidden layer condition is determined, the activation conditions of each node of the visible layer are also independent. Figure 3:2 Structure of the DBN model. Therefore, according to the above formula, when the input condition and visible layer \(v\) are known, the access probability of hidden layer \(h\) is as follows:  
Figure 3:3  
Similarly, when the output data of the hidden layer and the output unit vector \(h\) are known, the output probability of the visible layer \(v\) is as follows:  
Figure 3:4  
Taking the activation function Sigmoid function as an example, the activation probability of \(h\) and \(v\) is obtained as follows:  
Figure 3:5  
Figure 3:6  
The DBN network is obtained by stacking multiple RBMs and a BP layer. Then, the achieved network is pre-trained and adjusted accurately layer by layer. The unsupervised greedy learning algorithm and the contrast divergence algorithm are used to complete the pre-training layer by layer. Afterwards, the gradient descent algorithm is used to complete the accurate adjustment of the network. Considering the weak nonlinear regression ability of the DBN, this paper replaces the top structure of the DBN with SVR to strengthen the nonlinear regression ability and uses the data features extracted by the DBN as the prediction input of the SVR model. Additionally, the ACO is used to select the appropriate parameters for SVR, and the SVR algorithm is used to fine-tune the entire network. The structure of the proposed soft measurement model named DBN-ACO-SVR is shown in Figure 3:7  
Figure 3:8 The structure of the proposed soft measurement model. For the training set sample \(\{(x_{1},y_{1}),(x_{2},y_{2}),\cdots,(x_{m},y_{m})\}\) of the SVR model, we hope to obtain a regression model to make \(f(x)\) and \(y\) as close as possible. \(w\) and \(b\) are the regression parameters to be determined. Assuming that the deviation between \(f(x)\) and \(y\) can be tolerated up to \(\varepsilon\), the SVR problem is finally converted as shown in Equation (12):  
Figure 3:9  
where \(C\) is the regularization parameter and \(l_{e}\) is the insensitive loss function, as shown in Equation (13):  
\[l_{e}=\left\{ \begin{matrix}0&\text{if }|f(x)-y|<\varepsilon\\ |f(x)-y|-\varepsilon&\text{else}\end{matrix} \right. \tag{13}\]  
The final SVR solution is obtained as follows:  
\[f(x)=\sum_{i}^{m}(\alpha_{i}^{*}-\alpha_{i})x_{i}^{\text{T}}x+b \tag{14}\]  
Then, the kernel function is introduced:  
\[k\big{(}x_{i},x_{j}\big{)}=\varphi(x_{i})^{\text{T}}\varphi(x_{j}) \tag{15}\]  
In this manner, the SVR solution can be rewritten as follows:  
\[f(x)=\sum_{i}^{m}(\alpha_{i}^{*}-\alpha_{i})k\big{(}x_{i}^{\text{T}}x\big{)}+b \tag{16}\]