# Analysis of Flame Evolution Generated from Methyl Laurate Droplet Using Deep Learning
## 3 Results and Discussion
### Automatic Segmentation of Flame and Droplet  
Automatic segmentation of droplets and flames is vital in fields like combustion research and fluid dynamics due to its ability to accurately delineate complex shapes in real-time. It improves process control, such as optimizing fuel combustion, and it enables the extraction of critical quantitative data, including size, velocity, and temperature distribution [57]. This reduces human error and bias, allowing for consistent analysis. Furthermore, segmentation integrates seamlessly with machine learning models for predictive analysis, aiding in pattern recognition and anomaly detection. The training sequences of YOLOv9 in this research involve several stages, as follows:  
1. Set up environment: Installing necessary dependencies and configuring the GPU. 2. Prepare the dataset: Gather 1500 images of the flame and droplets each, with annotated images and the related segment shape positioned around the objects of interest along with the class labels. 3. Download pretrained weights: Using pretrained weights for transfer learning allows a YOLOv9 model, already trained on a large dataset, to quickly adapt and improve its accuracy on a custom dataset. 4. Modify configuration files: Tune the hyperparameters into the configuration files. Change the settings, including batch size, learning rate, and input image dimensions (Table 2). 5. Set hyperparameters: Adjust learning rate and batch size. 6. Start training: Initiate the training procedure with the prepared dataset. The model acquires the ability to detect objects by reducing detection errors through optimization. 7. Evaluate the model: Validating data using metrics like mAP. 8. Fine-tuning: This step is not mandatory and is only applied if needed. Figure 4: Flame visualization of methyl laurate. Figure 5: Droplet visualization of methyl laurate. Save the best model. * 10. Perform inference: Apply the trained model to a new dataset. This study employs mean average precision (mAP) as a metric for measuring indicators within a range from 0 to 1. mAP is an essential metric for assessing the effectiveness of models in object detection and segmentation [46]. In particular, mAP 0.5:0.95 calculates the average precision across various intersection over union (IoU) thresholds from 0 to 1, offering a detailed assessment of the model's accuracy in detecting and segmenting objects at varying degrees of overlap. Figure 6 illustrates the mAP 0.5:0.95 values for flame and droplet detection and segmentation across 100 epochs. The graph demonstrates the model's incremental learning and performance enhancement throughout the training process, which assists in identifying trends, evaluating training efficacy, and directing model optimization [58]. The mAP curves demonstrate the model's robustness against segmentation errors, with convergence achieved after 100 epochs. Table 3 provides an overview of the test results using the mAP dataset. In YOLOv9, mAP is utilized as a measure for assessing the precision of object detection and segmen  
Figure 6: Curves of mAP (mean average precision) during the training of YOLOv9 with the dataset: (**a**) flame, (**b**) droplet. tation, which may fluctuate when the model is presented with novel scenarios involving flames and droplets. Precision (P) measures the accuracy of detected objects, representing the proportion of correct detections among all predicted detections. High precision indicates that the model effectively minimizes false positives. Recall (R), on the other hand, assesses the model's ability to recognize all instances of objects within an image, reflecting its capacity to minimize false negatives. Figure 7 illustrates the capabilities of the YOLOv9 model in real-time object detection and segmentation. In the first image, the model accurately identifies a droplet with a confidence score of 0.95, while in the second image, it detects a flame with a confidence score of 0.96. The model's dependence on supervised learning may pose difficulties in recognizing unfamiliar objects or regions.