# Detection and Optimization of Photovoltaic Arrays' Tilt Angles Using Remote Sensing Data
## 3 Results  
To the authors' knowledge, there is no publicly available VHR dataset annotating individual modules. Hence, initially, a training dataset was generated from publicly available VHR satellite imagery over Slovenia provided by Google (Airbus, CNES/Airbus, Maxar Technologies, 2024). This dataset comprises 105 satellite images with a resolution of 512 \(\times\) 512 pixels, where modules were annotated utilizing the presented unsupervised method with manual corrections to obtain ground truth data. Moreover, the datasetunderwent simple augmentations through 90\({}^{\circ}\), 180\({}^{\circ}\), and 270\({}^{\circ}\) rotations and horizontal and vertical flips, which enhanced the dataset size to 1260 images. Subsequently, the augmented dataset was split using a 4:1:1 rule into learning, validation, and testing sets. Various semantic segmentation methods were evaluated for the automatic detection of individual 2D modules using methods based on U-shaped deep learning architectures with different encoder backbones, as shown in Table 1. The encoder backbones' weights were pretrained on ImageNet [53], where, for the encoder backbone, the traditional ResNet-18 encoder [54] was used. For newer methods [37; 38; 39], the Swin vision Transformer [55] was also considered, as well as EfficientNet-b5 and SE-ResNeXt50, which reported good results for the whole PV system/array detection in a recent work [25]. Table 1 also provides ablation analysis when using detection complemented with FOM and without, where the results were superior when FOM [21] was applied at the end. The choice of suitable hyperparameters was performed by using a grid search approach. Each model was trained for 200 epochs with early stop if no improvements were observed within 20 epochs, using the Adam optimizer with a weight decay of 0.00025, an initial learning rate of 0.001, and an adaptive learning rate scheduler using Cosine Annealing with warm restarts (\(T_{0}=25\) and \(\eta_{\min}=0.00001\)). The loss function was set as the joint loss of SoftCrossEntropy and Dice loss functions [39]. The performance of each model was assessed using the average intersection-over-union (IoU) and the harmonic mean of precision and recall (F1). In addition, the computational complexity of each model was evaluated using GFLOPS metrics [G] and its size based on the number of parameters in millions [M]. Each model was run 5 times using 5-fold cross-validation in order to ensure higher robustness of the results. An example visual prediction error of module detection using the best model FT-UnetFormer (with SwinTransformer encoder backbone) based on a fully Transformer network is shown in Figure 5, where the model can overpredict in case of false positives like skylights or underpredict due to the non-homogeneous color of the modules. Furthermore, Figure 6 shows the training and validation F1 score and loss per epoch, respectively. The model can reach an above 0.8 F1 score after 15 epochs, which hits a granularity level of approximating an array, but not an individual module, for which more epochs of training were required.