Algorithm 1 Approach for load recognition based on the Analysis of Variance F-test with SelectKBest and the model optimization of the gradient-boosting machines

Input:  Generated dataset ($\mathbf{D}$), proportion of training data (p.train), proportion of test data (p.test), initial number of components ($\eta$), threshold ($\xi$), number of folds (K), set of J candidates for the values of the maximum depth hyperparameter of the chosen model/GBM: $\{h_1^{\left(\mathrm{GBM},k\right)},h_2^{\left(\mathrm{GBM},k\right)},\dots ,h_J^{\left(\mathrm{GBM},k\right)}\}$ = ${\left\{h_i^{\left(\mathrm{GBM},k\right)}\right\}}_{i=1}^J$. Output:  Type of load in operation   1:First step: Divide the $\mathbf{D}$ database between ${\mathbf{D}}_{(\mathrm{p}.\mathrm{train})}$ training set and the ${\mathbf{D}}_{(\mathrm{p}.\mathrm{test})}$ test set.   2:Second step: Employ the ANOVA with SelectKBest using ${\mathbf{D}}_{(\mathrm{p}.\mathrm{train})}$ and $\eta$ initial number of features. In the sequel, obtain the selected data ${\mathbf{D}}_{(\mathrm{p}.\mathrm{train},\mathrm{ANOVA})}^{\left(\eta \right)}$.   3:Third step: Compute the covariance matrix ${\mathbf{C}}_{\left(\mathrm{ANOVA}\right)}$ from ${\mathbf{D}}_{(\mathrm{p}.\mathrm{train},\mathrm{ANOVA})}^{\left(\eta \right)}$. We calculate the covariance matrix based on Lemes et al. [12].   4:Fourth step: Obtain the eigenvalues ${\gamma }_i$ via ${\mathbf{C}}_{\left(\mathrm{ANOVA}\right)}=\mathbf{\Lambda }·\mathbf{\Gamma }·{\mathbf{\Lambda }}^{-1}$, in wich $\mathbf{\Lambda }$ is the eigenvector matrix and $\mathbf{\Gamma }$ is the diagonal matrix, i.e., $diag({\gamma }_1,{\gamma }_2,\dots ,{\gamma }_{\eta })$.   5:Fifth step: Sort the eigenvalues in descending order: ${\gamma }_1\ge {\gamma }_2\ge {\gamma }_3\ge \dots \ge {\gamma }_{\eta }$   6:Sixth step: Discover the optimal number of features (k) through CEV:     Generate the variable k and set its value to zero     Compute CEVr=${\sum }_{j=1}^r{\displaystyle \frac{{\gamma }_j}{{\sum }_{i=1}^{\eta }{\gamma }_i}}$         if CEVr≥$\xi$             k ← number of r-th feature         end if   7:Seventh step: Employ the ANOVA with SelectKBest, according to k features, to obtain the new selected data for the training set, i.e., the ${\mathbf{D}}_{(\mathrm{p}.\mathrm{train},\mathrm{ANOVA})}^{\left(k\right)}$.   8:Eighth step: Employ the possible values for the hyperparameters for each k, i.e., ${\left\{h_i^{\left(\mathrm{GBM},k\right)}\right\}}_{i=1}^J$   9:Ninth step: Apply GS with K-CV     Divide ${\mathbf{D}}_{(\mathrm{p}.\mathrm{train},\mathrm{ANOVA})}^{\left(k\right)}$ in K folds     Train the model on each K fold     Calculate accuracy     Measure average accuracy     Assign the average accuracy to the current possible values for the hyperparameters     Adopt the hyperparameter with the highest average accuracy achieved: $h_{\mathrm{optimal}}^{\left(\mathrm{GBM},k\right)}$ 10:Tenth step: Train the chosen GBM with $h_{\mathrm{optimal}}^{\left(\mathrm{GBM},k\right)}$ 11:Eleventh step: Testing the optimized model: GBM using ${\mathbf{D}}_{(\mathrm{p}.\mathrm{test},\mathrm{ANOVA})}^{\left(k\right)}$ return Type of load in operation