## 2 Materials and Methods
### ANN Analysis  
Once the superiority of the Fibonacci blade profile was verified through CFD, the next step is to analyze the effect of other parameters. In a previous work [22], it was verified that the optimum number of blades is 2 and the optimum separation gap is 0. The same conclusion was obtained by other authors [17; 31; 32; 33]. Nevertheless, the optimum aspect ratio, overlap, and twist angle are not clear, and there is no consensus in the scientific literature. Further on, the determination of the most appropriate combination of these parameters is a complex issue. The reason is that a huge number of combinations are possible and the relation between these parameters and the power is not a simple task. As mentioned above, in order to analyze a high number of combinations, an ANN is proposed in the present work. Three input variables were established: the aspect ratio, overlap, and twist angle. It is worth mentioning that it is common to provide the overlap as the overlap/chord length ratio, i.e., O/C. Regarding the output variables, in this case, only one variable is needed, the maximum power coefficient, C\({}_{\text{Pmax}}\). For instance, regarding the base case with AR = 1, O/C = 0, and TA = 0, the maximum power coefficient is the maximum value of the graph  
Figure 6: Comparison between the Fibonacci and original Savonius blade profiles; (**a**) C\({}_{\text{P}}\) against TSR; (**b**) C\({}_{\text{T}}\) against TSR. Figure 7: Performance of Fibonacci and original Savonius blade profiles along a rotor cycle; (**a**) C\({}_{\text{P0}}\); (**b**) C\({}_{\text{T0}}\). shown in Figure 6a, which corresponds to 0.2465. According to this, the ANN used for the present work will perform as a \"black box\" in which the three inputs are provided and the output is returned, as shown in Figure 8.  
ANNs are structures that imitate human intuition. An ANN is capable of simulating the human brain and is able to process information and provide the corresponding predictions. The human brain uses neurons to process data. Figure 9 shows the structure of biological neurons. The data are transferred from synapses to the axon through electrochemical media called neurotransmitters. The human brain contains approximately 100 billion interconnected neurons [34]. The information in the brain propagates via electrochemical media known as neurotransmitters and is transferred along the neurons. The artificial neural network imitates this configuration. The principle of operation of ANNs is based on interconnected nodes that can process information. Two main advantages are provided by ANNs:  
* Capacity to learn from existing data and thus the ability to provide a prediction from multivariable relationships between process parameters. * Capacity to treat complex relationships between dependent and independent variables with high accuracy. In the present work, the software Matlab 2021 was employed. The learning between the inputs and outputs of an ANN is performed through a mathematical training process that minimizes errors and provides an optimal prediction. The neurons of the ANN are organized into three layers: input, hidden, and output--Figure 10. The input layer corresponds to the independent variables; in this particular work, the aspect ratio, overlap/chord length ratio, and twist angle. On the other hand, the output layers correspond to the dependent variable; in this particular work, \(\text{C}_{\text{Pmax}}\). The effect of the input to the cell refers to weights. There is no exact rule to define the number of hidden layers and hidden nodes, and several methods to determine them can be found in the literature. Generally, a single hidden layer is recommended for most problems, and the multi-layered structure is only recommended for complex problems [35; 36; 37; 38] since adding hidden layers may cause memorizing instead of generalizing [39]. Each input node has an assigned weight and transfer functions related to the nodes. Figure 8: ANN structure for the present work.