## 2 Predictive Model
### Regression-Based Methods  
In general, the use of regression techniques consists of numerical prediction, i.e., a methodology to generate a mathematical function or model to predict missing or new numerical data values; but it also covers the identification of distribution trends based on the available data. For the latter, the support vector machine (SVM) has been widely used since a regression function is found from the training dataset. Among the available research works, SVMs have been presented in the literature as one of the most promising methods to diagnose faults in power transformers [57]. [PERSON] et al. [58] and [PERSON] et al. [59] implement SVM-based strategies to establish the classification of faults in power transformers by using the gases available from the DGA. Both works present an interesting performance comparison among different methods. In [58], five artificial intelligence methods are presented. It is found that the SVM is the most effective and fastest method, obtaining an accuracy of 100% and a training time less than 1s, NN (92.76% accuracy and 81s training time), expert system (89.34% accuracy and training time no mentioned), FL (92.32% accuracy and 82s training time), and combined NN and expert system (93.54% accuracy and 44s training time). In [59], the classification accuracy of FL (86.7%), multi-layer perceptron (80%), radial basis function (86.7%), and SVM (90%) is presented. In a similar venue, SVMs are also explored for the detection and localization of faults in transmission lines, where [PERSON] and [PERSON] [60] and [PERSON] et al. [61] conclude that the SVMs are a highly accurate method for these tasks. [PERSON] et al. [62] present a SVM-based methodology for data-based line trip fault prediction in power systems, where long-term memory networks are used to capture time series characteristics from multiple sources in large systems. The accuracy of the line trip fault prediction can reach about 97%. SVMs have been also employed in the diagnosis of induction motors, e.g., [PERSON] and [PERSON] [63] carry out a comparative investigation to predict mechanical and electrical faults in induction motors from the analysis of vibration and current signals and the use of multiclass SVM methods. [PERSON] et al. [64] propose a method based on the robust local linear embedding algorithm and an SVM for the diagnosis the gear fault from an experimental setup composed by a motor, a torque transducer/encoder, and a dynamometer. The diagnosis of fault severity in the stator winding of induction motors using SVM in regression mode is presented by [PERSON] et al. [65]. In their research, they analyze the current signals for  
\begin{table}
\begin{tabular}{c l l l l} \hline \hline \multicolumn{1}{c}{**Classification Methods**} & \multicolumn{1}{c}{**Equipment Under test**} & \multicolumn{2}{c}{ \begin{tabular}{c} **Physical Variable Used as** \\ **Information Source** \\ \end{tabular}  } \\ \hline \multirow{3}{*}{ \begin{tabular}{c} Decision tree: C4.5 algorithm [39; 40; 42] \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} Transformer \\ Monoblock \\ centrifugal pump \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} Data from DGA \\ Current \\ Vibration \\ \end{tabular}  } \\  & Decision trees: J4s algorithm, best first algorithm, random forest algorithm, functional algorithm, and linear model algorithm (a comparison) [43] & & & \\  & Fault tree analysis [44] & & \\  & Fault tree analysis [44] & & \\  & Fault tree analysis and Bayesian networks [45] & & \\  & & aircraft engines & \\ \hline \multirow{3}{*}{ \begin{tabular}{c} Bayesian non-linear state estimation technique \\ (detection based on a threshold value) [46] \\ Tree-structured fault dependence kernel [47] \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} Chiller plant \\ Building cooling system \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} Pressure \\ Temperature \\ \end{tabular}  } \\  & & \\ \hline \multirow{3}{*}{