## 3 Experiments
### Training Environment and Evaluation Indicators  
The training process of the proposed model runs under the Windows 10 operating system and PyTorch framework. The software environment for the experiment is CUDA11.1, CUDNN8.0.4 and Python 3.7. The hardware condition of the experiment is to have a CPU of Intel Core i9-13900 K with a basic frequency of 3.0 GHz, equipped with 32 Gb RAM, and the GPU is NVIDIA GeForce RTX 4090 24 Gb. The initial parameters of the experimental device are shown in Table 2.  
Figure 8: Preprocessing for adding various types of noise. Figure 7: Data set after data enhancement. In order to measure the performance improvement of the improved algorithm compared with the original algorithm, several evaluation indicators are as follows. Recall rate (R) is the ratio of the predicted correct target among all of the targets marked as correct. The mathematical calculation expression is as follows:  
\[\text{Recall}\ =\frac{\text{TP}}{\text{TP}\ +\ \text{FN}} \tag{8}\]  
where TP in the above two formulas represents the number of positive examples of correct prediction, FP represents the number of negative examples of wrong prediction, FN represents the number of positive examples of wrong prediction, and TN represents the number of negative examples of correct prediction. Average precision (AP) is an important indicator to measure the advantages and disadvantages of the trained network model in a single category. Its mathematical calculation expression is as follows:  
\[\text{AP}\ =\int_{0}^{1}\text{P(R)dR} \tag{9}\]  
The mean average precision (mAP) is an important indicator to measure the average quality of the trained network model in each category. mAP is the average value of AP in all categories. Its mathematical calculation expression is as follows:  
\[\text{mAP}\ =\frac{\sum_{i=1}^{\text{N}}\text{AP}_{i}}{\text{N}} \tag{10}\]  
Intersection-over-union (IoU) refers to the ratio of the area of the intersection part of the prediction box and the real box to the area of the union part of the prediction box and the real box. The mathematical calculation expression of IoU is as follows:  
\[\text{IoU}\ =\frac{\text{S}_{\text{overlap}}}{\text{S}_{\text{union}}} \tag{11}\]  
Frames per second (FPS) refers to the measure of how quickly an imaging device, such as a computer, TV, or video game console, can produce unique consecutive images called frames. High FPS often results in smoother and more realistic motion. The mathematical calculation expression of FPS is as follows:  
\[\text{FPS}\ =\frac{1}{\text{T}} \tag{12}\]  
where T represents the time taken to detect a frame. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter Name** & **Symbol** & **Numeric Value** \\ \hline Initial learning rate & Ir0 & 0.01 \\ Cycle learning rate & Irf & 0.2 \\ momentum & Momentum & 0.937 \\ Optimizer weight decay & Weight\_decay & 0.0005 \\ Warm-up training rounds & Warmup\_epochs & 3.0 \\ Preheat training momentum & Warmup\_momentum & 0.8 \\ The Box loss gain & Warmup\_bias\_lr & 0.05 \\ The cls loss gain & cls & 0.5 \\ cls BCELoss positive weight & cls\_pw & 1.0 \\ The obj loss gain & Obj & 1.0 \\ obj BCELoss positive weight & obj\_pw & 1.0 \\ The iou training threshold value & iou\_t & 0.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Initial training parameters. Confidence (Conf) in object detection is a metric that indicates the degree of belief in the existence and class of an object in a bounding box predicted by the model. The confidence is calculated using the following formula:  
\[\text{Conf}\;=(1.0-gr)+gr\cdot\text{CIoU} \tag{13}\]  
where \(gr\) represents a parameter known as the label smoothing coefficient, which helps to reduce overfitting. Complete Intersection over Union (CIoU) is the Complete Intersection over Union score between the predicted bounding box and the ground truth box. When \(gr\) equals 1, the confidence score is equal to the CIoU score.