## 3 Results and Discussion
### Evaluation of Fire Heat Release Rate Prediction Performance
Figure 12b shows the results of the fire experiment involving corn oil in a Calphalon(r) pan. The MAE values for the YOLO-YCbCr and YOLO-seg models were 5.39 kW and 5.71 kW, respectively. The \(R^{2}\) values for the YOLO-YCbCr and YOLO-seg models were 0.65 and 0.61, respectively. Both models effectively followed the HRR variations; however, high fluctuations in the HRR values were observed in the fully developed stage at around 30 s. This inaccuracy was attributed to the light reflected from the pan handle in the dark experimental environment, which was mistakenly detected as flames, thereby resulting in an overestimated flame size. Compared with the solid-fuel fire experiments, the prediction performance was lower because of the smaller number of original video frames and the presence of light reflections. From the performance evaluation results, it was confirmed that the proposed method effectively predicted the HRR variations measured over time in the experiments, demonstrating the feasibility of image-based HRR prediction models. Despite differences in the flame segmentation characteristics of the YOLO-YCbCr and YOLO-seg models, their HRR prediction performances remained similar. The YOLO-YCbCr model, which has advantages such as relatively low learning cost, small model size, and fast inference time, is expected to have potential applications in fire-image-based real-time HRR prediction. Figure 11: HRR prediction results for the wood-crib fire experiments: (**a**) one wood crib and (**b**) four wood cribs. However, the HRR values predicted by the two models fluctuated significantly compared to the experimental values. This could be attributed to the limitations of the NIST fire experiment videos, which provided frames at 5 s intervals for solid-fuel fire experiments and at 3 s intervals for liquid-fuel fire experiments. A limited number of fire image frames could contain continuous and intermittent flames, randomly causing large fluctuations in the HRR. Thus, such a low frame rate could make it difficult to apply the average flame height greater than 50% flame occurrence probability to the Zukoski correlation [38; 39]. To confirm this, the HRR prediction was performed by applying the average flame height (AFH) definition specifically to the region near the peak HRR, where the NIST fire experiments provide a higher density of video frames (30 frames per second), and the magnitude of the HRR fluctuations and the prediction performance were evaluated. Figure 13 shows the prediction results of the HRR prediction models with the AFH definition for three representative fire videos: the one-box, one-wood-crib, and com oil in aluminum pan fire experiments. All results showed that applying the AFH calculation reduced the variation in the predicted HRR values, and the reduction in the coefficient of variation ranged from 3.6% to 26.1%. Moreover, applying the AFH calculation enhanced the HRR prediction performance, and the reduction rates in the MAE ranged from 9.1% to 70.2%. Although the evaluation was conducted over a limited time period, it was verified that applying the AFH calculation improved the prediction performance of fire-image-based HRR prediction models. Figure 12: HRR prediction results for the corn oil pool fire experiments: (**a**) aluminum pan and (**b**) Calphalon® pan. Additional HRR prediction analysis using a propane pool fire experiment video from the NIST database was conducted to analyze the effect of applying the AFH. This fire video dataset features a three-step HRR increase, with each quasi-steady stage providing a relatively sufficient number of image frames. Figure 14 shows the HRR prediction results for the propane pool fire experiment. As shown in Figure 14a, the HRR values predicted by the YOLO-YCbCr and YOLO-seg based HRR prediction models were highly fluctuated, with MAE of 11.9 kW and 10.1 kW, respectively.