## 3 Method
### Method Detailed Description
#### 3.2.3 First Instance Classification
The final classification of each ensemble (Committee Classification Technique) considers both the ensemble inducers estimates and the performance metrics of each inducer. A particular case of this committee classification technique corresponds to the majority voting, where the performance metric of the inducers will only be taken into account to select the best performance inducer if each ET inducer provides a different classification. The inducers performance metrics correspond to true-positives (TP), false-positives (FP), true-negatives (TN), false-negatives (FN), precision (PCS), recall (RCA), F1-score (F1), and accuracy (ACC). Table 3 summarizes all of them according to a confusion matrix \(C_{n,n}\), true values represented by columns, predict values by rows, and \(n\) is the number of rows and columns, respectively. These equations and definitions also can be found in [12; 13; 24]. At the end of the committee classification, it will be associated with a single system state classification per ensemble triad. Each ensemble triad is defined in performance metrics such as the inducer's metrics according to Table 3. If ensemble triad performance is below a minimum threshold, then the state classification associated with the ET is considered as under suspect, which means that ET was not able to make a consistent decision. Finally, taking into consideration all ensemble triads, it is possible to create a vector that can express overall ET classification performance for each possible system state. This vector is represented by \(\overrightarrow{d}^{s+1}\), where \(s\) is the total system possible states. The first \(s\) elements of this vector correspond to \begin{table}
\begin{tabular}{c c} \hline \hline
**Metric** & **Equation** \\ \hline TP & \(TP_{i}=C_{i,j}\) \\ TN & \(TN_{i}=\sum_{i=1}^{n}\sum_{j=1}^{n}C_{i,j}-\sum_{j=1}^{n}C_{i,j\
eq i}-\sum_{j =1}^{n}C_{j,j\
eq j}\) \\ FP & \(FP_{i}=\sum_{j=1}^{n}C_{i,j\
eq i}\) \\ FN & \(FN_{i}=\sum_{j=1}^{n}C_{j,i}\
eq j\) \\ PCS & \(PCS_{i}=\frac{TP_{i}TP_{i}}{TP+TP}\) \\ RCA & \(RCA_{i}=\frac{TP_{i}}{TP+FN}\) \\ F1 & \(F1_{i}=\frac{PCS_{i}RCGA}{PCS_{i}+RCTA}\) \\ ACC & \(ACC=\frac{TP+TN}{TP+TN+FP+FN}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Machine Learning algorithms performance metrics. the percentage of ensemble triads that classified the system state corresponding to the vector element. The element \(s+1\) corresponds to the percentage of triads that were not able to make a consistent decision (undefined state), according to the criteria defined previously. All triad decisions have the same influence, and they have counted as votes for each state n such a manner that lack of decisions take count. The votes received by each state are held in \(\sigma_{i}\), while \(\xi\) holds the total number of no-decisions. Thus, the vector elements from \(y_{1}\) to \(y_{s}\) (inclusive) are the respective state votes proportion, while the element \(y_{s+1}\) is the undefined state votes proportion. \[\overrightarrow{d}^{s+1}=\{y_{1},y_{2},...,y_{s},y_{s+1}\}\ \mid\ \Sigma_{i=1}^{s+1}y_{i}=1,\ \ 0\leq y_{i}\leq 1 \tag{3}\] \[y_{i}=\left\{ \begin{array}{ll}\frac{\sigma_{i}}{N}&\text{for} \ \ \ i\leq s\\ \frac{\xi}{N}&\text{for}\ \ \ i=s+1\end{array} \right.\]  
Activity 5--Residues Estimation Based on Physical Models  
The ensemble learning classification performed on Activity 4 of GADHA receives as inputs all features extracted from Activities 2 and 3, and classify system state, estimating what is the most probable state among a finite and enumerable list of possible system states. Residues estimation is made by comparing real system state values with expected values of each system state estimated by the respective physical model. This comparison is made straightforwardly, subtracting one value from the other. Physical models are typically achieved through dynamic equations and state variables, but can also be represented in different ways, using, for instance, lookup tables.