# Analysis of Flame Evolution Generated from Methyl Laurate Droplet Using Deep Learning
## 2 Materials and Methods
### Droplet Combustion Testing
Changes over time in the diameter of the droplets and the visualization of the flame were analyzed using an object detection and segmentation technique that utilized the YOLOv9 deep learning algorithm. To track the changes in droplet diameter, the seg  
Figure 1: Illustration of experimental design. mentation area of the droplet was utilized to compute the equivalent area. The equivalent diameter was then determined by applying the circular area formula described in Equation (1). \[D=2\sqrt{\frac{A}{\pi}} \tag{1}\]  
\[A=\frac{N}{\alpha^{2}} \tag{2}\]  
In this formula, \(A\) represents the droplet area based on automatic segmentation (mm\({}^{2}\)), \(N\) denotes the number of pixels, \(D\) signifies the droplet's equivalent diameter (mm), and \(\alpha\) stands for the spatial resolution (pixels/mm). The common progression of the flame was assessed by counting the number of pixels along a straight line from the base of the non-luminous flame zone to the flame tip. The flame height was calculated by dividing the pixel count by the spatial resolution of the camera (\(\alpha=37\) pixels/mm). The experiment was conducted ten times for both the droplet and the flame. The ignition delay time is the time between positioning the heater under the droplet and the time a flame appears on the droplet. The burning lifetime is the length of the burning time, namely from the time the flame appears until the fire goes out. These two parameters are obtained from recorded data of the combustion process, which is then studied by a computer that has been trained with a deep learning algorithm. The average burning rate is obtained from the burning lifetime divided by the initial diameter of the droplet. The burning rate graph is obtained from the evolution of the square of the droplet diameter (indicating the surface area of the droplet) over time, which is normalized by the square of the initial diameter. The experimental setup and data acquisition processes were carefully designed to minimize errors, but potential sources of uncertainty were identified and addressed as follows:  
* Thermocouple Accuracy: Temperature measurements were acquired using a Type R thermocouple (Pt-Pt/Rh, 200 \(\upmu\)m diameter) with a maximum error of \(\pm\)2.5 \({}^{\circ}\)C. To account for this uncertainty, the temperature profiles were averaged over ten repeated trials, and the standard deviation was calculated to ensure statistical reliability. The thermocouple's response time (100 ms) was also considered to avoid temporal misalignment with the combustion process. The thermocouple's measurement error aligns with ASTM E230 standards for Type R thermocouples, ensuring compliance with industrial calibration protocols [38]. * Image Resolution and Segmentation Accuracy: The Nikon D5300 camera (60 fps, 40 mm macro lens, Nikon Corporation, Tokyo, Japan) provided a spatial resolution of 37 pixels/mm. However, minor variations in image quality (e.g., motion blur during rapid flame evolution) could affect segmentation accuracy. To mitigate this, the YOLOv9 model was trained on 1500 annotated images (80% training, 20% testing) with diverse lighting and droplet/flame conditions. The model achieved a mean average precision (mAP) of 0.974 for flame segmentation and 0.921 for droplet segmentation, as validated by the intersection over union (IoU) thresholds (Table 3). Post-processing techniques, including morphological operations, were applied to refine the segmentation boundaries. * Environmental Factors: The combustion chamber was isolated from ambient airflow, but minor fluctuations in room temperature (\(\pm\)1 \({}^{\circ}\)C) and residual air currents could introduce variability. To minimize these effects, experiments were conducted in a climate-controlled laboratory, and baseline measurements were recorded before each trial. The ignition delay time and burning lifetime were normalized against control conditions to isolate pressure-independent effects.