# An IoT-Based System for Monitoring the Health of Guyed Towers in Overhead Power Lines
## 5 Evaluation of the Tower Parameters for Machine Learning Estimation Model
### The Machine Learning Predictive Model  
A Feedforward Neural Network (FFNN) was chosen to solve the regression problem, which is to estimate the position of the tower displacement or cable tension in an analytical model designed for the initial experiments of the structural monitoring system. The FNN contains all neurons in a layer directly connected to all neurons in the next layer. The information flow starts at the input layer and goes in the same direction until the output layer. The neural network architecture is composed of the input layer, the next layers are two hidden layers and the output layer. Figure 19 shows the neural network architecture used in the experiments. The number of neurons defined in the input layer is the number of features used to estimate the parameters. The hidden layers have 64 neurons each, and the \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **X** & **Y** & **T1** & **T2** & **T3** & **T4** & **A1** & **A2** & **A3** & **A4** \\ \hline
**X** & 1.000 & 0.002 & 0.703 & \(-\)0.701 & 0.702 & \(-\)0.704 & \(-\)0.697 & 0.696 & \(-\)0.696 & 0.698 \\ \hline
**Y** & 0.002 & 1.000 & 0.705 & 0.703 & \(-\)0.702 & \(-\)0.704 & \(-\)0.699 & \(-\)0.698 & 0.697 & 0.698 \\ \hline
**T1** & 0.703 & 0.705 & 1.000 & 0.010 & 0.005 & \(-\)0.978 & \(-\)0.986 & 0.006 & 0.011 & 0.976 \\ \hline
**T2** & \(-\)0.701 & 0.703 & 0.010 & 1.000 & \(-\)0.977 & 0.005 & 0.006 & \(-\)0.987 & 0.975 & 0.012 \\ \hline
**T3** & 0.702 & \(-\)0.702 & 0.005 & \(-\)0.977 & 1.000 & 0.007 & 0.012 & 0.975 & \(-\)0.986 & 0.009 \\ \hline
**T4** & \(-\)0.704 & \(-\)0.704 & \(-\)0.978 & 0.005 & 0.007 & 1.000 & 0.976 & 0.010 & 0.008 & \(-\)0.986 \\ \hline
**A1** & \(-\)0.697 & \(-\)0.699 & \(-\)0.986 & 0.006 & 0.012 & 0.976 & 1.000 & \(-\)0.022 & \(-\)0.028 & \(-\)0.947 \\ \hline
**A2** & 0.696 & \(-\)0.698 & 0.006 & \(-\)0.987 & 0.975 & 0.010 & \(-\)0.022 & 1.000 & \(-\)0.948 & \(-\)0.027 \\ \hline
**A3** & \(-\)0.696 & 0.697 & 0.011 & 0.975 & \(-\)0.986 & 0.008 & \(-\)0.028 & \(-\)0.948 & 1.000 & \(-\)0.024 \\ \hline
**A4** & 0.698 & 0.698 & 0.976 & 0.012 & 0.009 & \(-\)0.986 & \(-\)0.947 & \(-\)0.027 & \(-\)0.024 & 1.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Correlation between dataset variables. Figure 17: Relationship between **(a)** A1 and A4, **(b)** A2 and A3  
Figure 18: Relationship between **(a)** T1 and T4, **(b)** T2 and T3 output layer has 2 neurons for X Y estimation and 1 neuron for cable traction. The hidden layer activation function is the Rectified Linear Unit (_ReLU_). The data used in the FFNN training process were 10,000 records obtained from the analytical model. The features considered in model were the position, angles information, cable traction, but the model can be retained for considered new features of monitoring system, e.g., temperature and wind information. The features with weak to very strong correlation coefficients were chosen for the estimation of the parameters because they present a strong linear relationship between the features, facilitating the adjustment of the model in the training process. However, in some experiments, some features with smaller correlation coefficients were inserted for evaluating the data fusion with moderate to very strong correlation. The parameter estimation is considered a regression problem where we want to find the tension of the cables and the displacement of the X and Y axes from the initial position. We used a combination of features obtained from the simulations of the analytical model from the previous section. From the total amount of data samples, 80% are for neural network training, while the remaining 20% are for testing the estimation. Before using data for training the neural network, it is vital to scale the samples to change the range of the values. This is because many machine learning algorithms perform better or converge faster when the features are relatively similar.