## 3 Inclusion of Temperature in the DNN Model-Based Method  
### Foundations  
This section pursues two main objectives. The first is to utilize DNN algorithm architectures to predict the value of the theoretical exciter field current in a BSM, considering the effect of temperature on the machine, with temperature as an additional input. This approach aims to improve the results obtained in other research [18]. The results shown in this previous article are good because of the short-term tests in which the machine did not have time to warm up and the effect of temperature on the estimation of fault severity was not too high. However, in the current work it has been verified that if continuous monitoring of the BSM is to be carried out, the effect of the rotor temperature must be considered, as shown in Section 5.  
The second objective is to validate the feasibility of using the stator temperature in the model instead of the rotor temperature, since measuring rotor temperature in industrial BSMs is not possible.  
Figure 2: Simplified schema of a BSM under a self-excited topology.  
Based on the principles described in [18], the theoretical exciter field current (\(I_{fe,cal}\)) is estimated using a DNN model under healthy condition calculations. The inputs to this model are a combination of machine output voltage (\(U\)) and current (\(I\)) measurements that fully define a [\(U\), \(P\), \(Q\)] operating point. In addition to these inputs, the machine temperature measurement (\(\theta\)) will be included as an input in the present work, following the reasoning presented in Section 3. The comparison of \(I_{fe,cal}\) with the actual measured exciter field current (\(I_{fe,meta}\)) enables ITF severity (\(\alpha\)) estimation, as the ratio of faulty turns is directly related to the field current increase imposed by the automatic voltage regulator (AVR) with respect to the estimated current. Equation (2) shows the explicit calculation of the severity of the interturn fault in a BSM:  
\[\alpha\ [\%]=\frac{N_{Faultry}}{N_{total}}\cdot 100=\left(\frac{I_{fe,cal}}{I_{ fe,meta}}-1\right)\cdot 100 \tag{2}\]  
where \(N_{Faultry}\) is the number of equivalent faulty turns with \(R_{f}\) = 0 \(\Omega\), and \(N_{total}\) is the total number of turns.  
Figure 3 illustrates the simplified layout of the field winding ITF detection and severity estimation technique, with inclusion of the influence of temperature.  
The purposely developed DNN allows one to adaptively model the complex relationships among the mentioned variables through approximation of non-linear functions, with a reduced error. In accordance with the complexity of the problem, the DNN model is composed of four neurons in the input layer, one for each input variable (\(U\), \(P\), \(Q\), and \(\theta\)), and one output neuron which employs the sigmoid as the activation function. The developed DNN has two hidden layers, with their neurons using the rectified linear unit (ReLU) activation function, and was optimized for computational efficiency.  
To determine the optimal number of neurons in each hidden layer, the model was trained with all combinations of neurons ranging from 3 to 20 per layer, utilizing the backpropagation method. The backpropagation learning rate was set at 0.001, and the number of epochs was fixed at 40.000. The optimum configuration was selected by evaluating the trained DNNs based on the minimization of the mean square error (MSE) and the minimization of points with errors greater than 5%. The general form of the involved DNN architecture is presented in Figure 4.  
Figure 3: Simplified layout of the field winding ITF detection and severity estimation method, with inclusion of the influence of temperature.  
The main features of the development stages (data collection and processing, training with validation, and testing) are described in the following subsections.