## 5 Proposed Method  
In the previous section, several supervised learning algorithms used in fault diagnosis showed the benefit of machine learning in improving diagnostic results in terms of time. This section describes the Extra Trees algorithm as a model capable of detecting and classifying faults in PV systems.  
The Extra Trees or Extreme Model Randomized Trees is a supervised learning algorithm from the Ensemble Learning family of algorithms. This algorithm was first proposed and implemented in 2006 in a paper entitled Extremely random tree by [PERSON] et al. [128]. The model is widely used for both regression and classification problems. The Extra Trees (ET) model uses a set of decision trees to randomly construct a group of unpruned decision trees to reduce the risk of overfitting [130]. The construction of the Extra Trees algorithm is similar to the Random Forest (RF) algorithm which is a tree-like combination of multiple trees [131]. However, the difference between the two algorithms is that the ET model uses the entire training sample to train each tree instead of a Bootstrap sample used by the RF model. Also, the selection of division points is conducted randomly unlike the RF model which uses an optimal distribution. The ET model execution procedure is based on the analysis of the training dataset (S) and three important hyperparameters [130]:  
* The number of trees (M) to train based on the number of training samples S
* The number of attributes (K) to be randomly selected and used in each node for each trained ensemble tree
* The minimum number of samples/instances (\(N_{min}\)) needed to split a node of each trained ensemble tree  
After training the trees, the algorithm makes its final prediction based on test data through majority voting for classification or by calculating the arithmetic mean for regression [38]. The Extra Trees or Extremely Randomized Trees model is widely used in various fields, including health [39; 129; 132], economy [38], transportation [129], and telecommunications [41; 42; 43]. For instance, in medicine, the Extra Trees model has been proposed to detect and classify cancer as malignant or benign tumors. The obtained results indicate an accuracy of 99.27% [40]. [PERSON] et al. proposed the Extra Trees model to detect faults in a wireless sensor network. The results demonstrate superior performance compared to other machine learning algorithms in the literature, such as artificial neural networks, support vector machines (SVM), Random Forest, and decision trees [43]. [PERSON] et al. utilized the Extra Trees algorithm to predict short-term traffic flow in a non-stationary environment. The obtained result showed higher precision compared to existing methods [133]. To the best of our knowledge, this algorithm has not been proposed before in the context of photovoltaic fault diagnosis. Additionally, the Extra Trees algorithm exhibits high precision, lower computational complexity, and variance compared to other models such as decision trees, support vector machines, artificial neural network (ANN), Random Forest, and decision trees [40]. This is an opportunity to propose the Extra Trees model as an effective algorithm that addresses the inadequacies of other models, such as decision trees, the AdaBoost model, SVM, DT, KNN, and FKNN [133]. The execution algorithm for the Extra Trees model is presented in Figure 19.