# 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
### Results for the Estimated Quantities of Interest  
At the current moment of the investigation, it is a problem to face the shortage of data for training deep learning models. It means that the framework is ready to provide data, but it takes time until there are enough data for training the neural network. Henceforth, we deal with cases in which data sources are scarce, and thus the simulation of data becomes a viable option. This shortage is a problem since the accuracy of a model is highly  
Figure 19: Neural network architecture. dependent on the size of the dataset when working with self-learning artificial intelligence. It is expected that other fields in machine learning study face a shortage of data. This can prevent researchers from obtaining conclusive results. A solution to the data shortage is to use synthetic training data when training a deep learning neural network. By using synthetic data, both the problem of data shortage and the labor intensity is reduced. Firstly, the data shortage problem will be eradicated since the data available through synthetic data are theoretically infinite. By having a theoretically infinite dataset, the researcher can simulate a dataset as large as they need it to be. Evaluating the machine learning algorithm is an essential part of successfully estimating the quantities of interest. The current model may yield satisfying results when evaluated using a metric, i.e., accuracy score, but may give poor results when evaluated against other metrics, such as logarithmic loss. For the current investigation, the most appropriate metrics are Normalized Root Mean Square Error (NRMSE), Mean Absolute Percentage Error (MAPE), and determination coefficient (R\({}^{2}\)). The NRMSE is a metric that indicates normalized error between 0 and 1. The MAPE is a metric that measures the percentage of error. The R\({}^{2}\) varies between 0 and 1 and expresses the variance of the estimated data explained for the linear model. The respective formulation for each metric is as follows:  
\[NRMSE(y,\hat{y})=\frac{\sqrt{\frac{1}{n_{samples}}\sum_{i=0}^{n_{samples}-1}{( y_{i}-\hat{y}_{i})^{2}}}}{std(\hat{y})} \tag{5}\]  
\[MAPE(y,\hat{y})=\frac{1}{n_{samples}}\sum_{i=0}^{n_{samples}-1}\frac{|y_{i}- \hat{y}_{i}|}{max(\epsilon,|y_{i}|)}*100 \tag{6}\]  
\[R^{2}(y,\hat{y})=1-\frac{\sum_{i=0}^{n_{samples}-1}{(y_{i}-\hat{y}_{i})^{2}}} {\sum_{i=0}^{n_{samples}-1}{(y_{i}-\overline{y})^{2}}} \tag{7}\]  
where \(y\) represents the actual data, \(\hat{y}\) the estimated data, \(\overline{y}\) is the mean, \(n_{samples}\) is the number of samples, std(\(\hat{y}\)) is population standard deviation of estimated data, and \(\epsilon\) is small positive number utilized to avoid an error result when \(y\) is zero. Table 3 presents the tension estimation results for some attempts choices of available features. Features are not easy to choose, and the results reveal that a method of choice beyond correlation is required. Additionally, the results highlight that the metric analysis is a good choice for choosing suitable features for successful quantities of interest estimation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Estimation** & **Features** & **NRMSE** & **MAPE** & **R\({}^{2}\)** \\ \hline T1 & A1, A2, A3, A4 & 0.0755 & 1.4559 & 0.9943 \\ \hline T2 & A1, A2, A3, A4 & 0.1057 & 1.7218 & 0.9888 \\ \hline T3 & A1, A2, A3, A4 & 0.0596 & 1.0897 & 0.9965 \\ \hline T4 & A1, A2, A3, A4 & 0.1234 & 2.7567 & 0.9848 \\ \hline T1 & X1, Y1, Z1, X2, \(\ldots\), \(ZA\) & 0.0912 & 1.8124 & 0.9917 \\ \hline T2 & X1, Y1, Z1, X2, \(\ldots\), \(ZA\) & 0.0736 & 1.4563 & 0.9946 \\ \hline T3 & X1, Y1, Z1, X2, \(\ldots\), \(ZA\) & 0.1516 & 3.3521 & 0.977 \\ \hline T4 & X1, Y1, Z1, X2, \(\ldots\), \(ZA\) & 0.1418 & 3.3136 & 0.9799 \\ \hline T1 & T2, T3, T4 & 0.0798 & 1.4903 & 0.9936 \\ \hline T2 & T1, T3, T4 & 0.1099 & 2.0871 & 0.9879 \\ \hline T3 & T1, T2, T4 & 0.1073 & 2.0099 & 0.9885 \\ \hline T4 & T1, T2, T3 & 0.077 & 1.558 & 0.9941 \\ \hline \hline \end{tabular}
\end{table}