Defect Detection Architecture: As shown in Fig. 8, the architecture of the proposed BAF-Detector is divided into three parts: feature extraction, region proposal (BAFPN-RPN), and classification and detection. First, ImageNet-pretrained ResNet101 [35] is employed as the backbone network to extract the features of the EL image. Second, the multilevel features will be passed to the proposed BAFPN-RPN module, which will generate many region proposals that may contain a defect. Third, each proposal generated at different scale levels is mapped to the corresponding level features of ResNet101, next the region of interest will resize the mapped features to a fixed-size vector. Finally, two fully connected layers is appended before two output layers: cls-score layer outputs classification scores of object classes attach a "background" class, bbox-pred layer outputs the predicted positions of the bounding-box for the corresponding object classes. In BAF-Detector, each predicted head of BAFPN-RPN can be optimized to regression by the following loss function: 缺陷检测架构：如图 8 所示，拟议 BAF-Detector 的架构分为三个部分：特征提取、区域建议（BAFPN-RPN）以及分类和检测。首先，采用经过 ImageNet 训练的 ResNet101 [35] 作为骨干网络来提取 EL 图像的特征。其次，将多级特征传递给 BAFPN-RPN 模块，该模块将生成许多可能包含缺陷的区域建议。第三，在不同尺度级别生成的每个建议都会映射到 ResNet101 的相应级别特征，接下来，感兴趣区域会将映射的特征调整为固定大小的向量。最后，在两个输出层之前附加了两个全连接层：cls-score 层输出 物体类别的分类分数，并附加一个 "背景 "类别；bbox-pred 层输出相应的 物体类别的边界框预测位置。在 BAF-Detector 中，BAFPN-RPN 的每个预测头可以通过以下损失函数进行优化回归：
Fig. 8. Architecture of the proposed BAFPN detector (BAF-Detector). 图 8.拟议的 BAFPN 检测器（BAF-Detector）的结构。
where is the index of an anchor box [29] in a minibatch and is the predicted probability of anchor box containing a defect. If the anchor box is predicted to contain a defect, the ground-truth label is 1 , otherwise is is a vector representing the four parameterized coordinates of the predicted bounding box, and is that of the ground-truth box associated with a defective anchor box. The term means the regression loss is activated only for defective anchor and is disabled otherwise . The outputs of the cls_score layer and bbox_pred layer consist of and , respectively. The classification loss is over two classes (defect or not defect). For the regression loss, we use where is the robust loss function (smooth L1) defined as follows: 其中， 是迷你批中锚点盒的索引[29]， 是锚点盒 包含缺陷的预测概率。如果预测锚点框包含缺陷，则地面实况标签 为 1 ，否则 为 是表示预测边界框四个参数化坐标的向量， 是与缺陷锚点框相关联的地面实况框的坐标。术语 表示回归损失仅对缺陷锚 激活，否则 禁用。cls_score 层和 bbox_pred 层的输出分别为 和 。分类损失 是两个类别（缺陷或非缺陷）的 。对于回归损失，我们使用 ，其中 是鲁棒损失函数（平滑 L1），定义如下：
The term means the regression loss is activated only for defective anchor boxes and is disabled otherwise ). Referring to Faster RCNN+FPN, the two terms are normalized by and , and weighted by a balancing parameter , thus both cls and reg terms are roughly equally weighted. 项表示回归损失仅在有缺陷的锚点盒 中激活，否则将禁用 ）。参照 Faster RCNN+FPN，这两个项通过 和 归一化，并通过平衡参数 加权，因此 cls 和 reg 项的权重大致相同。
For bounding box regression, the parameterizations of the four coordinates are defined as follows: 对于边界框回归，四个坐标的参数定义如下：
Note: , and Bc: The number of crack defect, finger interruption defect, and black core defect, respectively. 注： 和 Bc：分别为裂纹缺陷、断指缺陷和黑芯缺陷的数量。
studies, are presented. To understand and show the improvement directly, the visualization of similarity map is used as a powerful tool to support experimental results. 介绍。为了直接理解和展示改进效果，相似性图的可视化被用作支持实验结果的有力工具。
A. Dataset A.数据集
We evaluate the experimental results of our proposed BAFDetector on our PV cell EL image dataset. In this dataset, 2129 EL defective images and 1500 defect-free images with raw resolution of are used to evaluate the classification and detection effectiveness of our proposed BAF-Detector. Table II shows the raw dataset distribution of training data and testing data. First, the dataset is divided into two types: defective images and defect-free images, which are used to evaluate the classification performance of the proposed model. Second, the dataset is divided in details according to the categories of the defect. The reason why we classify defects within three main categories, namely crack, finger interruption, and black core defect, is that these three kinds of defects occur frequently, and we can build a balanced dataset distribution, which is the key point that the deep learning model can be trained to achieve good performance. We use EL technology [2] to visualize the internal defects of PV cells. 2129 defective images are selected from 150000 samples of PV cell images. Among them, crack, finger interruption, and black core defects are the most frequent ones. Other types of defect occur rarely, which will cause an unbalanced distribution of the dataset. Therefore, this article mainly classifies these three types of defects. 我们在光伏电池 EL 图像数据集上评估了我们提出的 BAFDetector 的实验结果。在该数据集中，我们使用原始分辨率为 的 2129 幅 EL 缺陷图像和 1500 幅无缺陷图像来评估我们提出的 BAF 检测器的分类和检测效果。表 II 显示了训练数据和测试数据的原始数据集分布。首先，数据集分为两类：有缺陷图像和无缺陷图像，用于评估所提出模型的分类性能。其次，根据缺陷类别对数据集进行详细划分。我们之所以将缺陷分为三大类，即裂纹、断指和黑芯缺陷，是因为这三种缺陷出现的频率较高，我们可以建立一个均衡的数据集分布，这也是深度学习模型可以训练出良好性能的关键点。我们使用 EL 技术[2]来可视化光伏电池的内部缺陷。从 15 万张光伏电池图像样本中选取了 2129 张缺陷图像。其中，裂纹、断指和黑芯缺陷出现频率最高。其他类型的缺陷很少出现，这将导致数据集分布不均衡。因此，本文主要对这三类缺陷进行分类。
For the ground truth of different defects, a dataset annotation tool (LabelImg) is used to label the EL image dataset. It just needs a rectangular box to tightly surround the defect and do not need too much expert experience. The rectangular box will reflect the specific location and class of the defect. Moreover, annotations are saved as XML files in PASCAL VOC format. The standard PASCAL VOC format can ensure the fairness comparison between different detectors. It is very important for the validation of the performance of our proposed model. 为了获得不同缺陷的基本事实，我们使用数据集标注工具（LabelImg）对 EL 图像数据集进行标注。它只需要一个矩形框来紧紧围绕缺陷，不需要太多专家经验。矩形框将反映缺陷的具体位置和类别。此外，注释以 PASCAL VOC 格式保存为 XML 文件。标准的 PASCAL VOC 格式可以确保不同检测器之间的公平比较。这对验证我们提出的模型的性能非常重要。
B. Evaluation Metrics B.评估指标
The classification of our model is evaluated by the precision , recall (R), and F-measure (F). Moreover, average precision (AP), mean AP (mAP), and mean intersection over union (MIoU) are applied to assess defect detection results. Parameters number and frames per second (FPS) are the metrics used to 我们通过精度 、召回率 (R) 和 F 测量 (F) 来评估模型的分类效果。此外，平均精度 (AP)、平均 AP (mAP) 和平均交集大于联合 (MIoU) 也用于评估缺陷检测结果。参数数和每秒帧数（FPS）是用于评估缺陷检测结果的指标。
TABLE III 表 III
HyPERPARameteRs During BAF-DeteCtor Training and TESting BAF-DeteCtor 培训和测试期间的水质参数
DECAY_STEP
DECAY_FACTOR
WEIGHT_DECAY
MOMENTUM
Training 培训
15000,30000
10
0.0001
0.9
IMG_SHORT_SIDE_LEN
IMG_MAX_LENGTH
BASE_ANCHOR_SIZE_LIST
BATCH_SIZE
600
1000
1
Testing 测试
SHOW_SCORE_THRSHOLD
NMS_IOU_THRESHOLD
asses the time efficiency. The aforesaid metrics are defined as 评估时间效率。上述指标定义如下
where and are the number of defect images, which are predicted to be correct or not; represents the number of nondefect, which is misclassified; DetectionResult is the defect detected box of the detector; GroundTruth is the defect annotation box. 其中， 和 是预测为正确或不正确的缺陷图像的数量； 代表被错误分类的非缺陷图像的数量；DetectionResult 是检测器的缺陷检测框；GroundTruth 是缺陷注释框。
C. Implementation Details C.实施细节
The experiments are conducted on a work station with a Intel Core i7-10 700 CPU and a NVIDIA GeForce RTX 2070 SUPER. The pretrained model on ImageNet is used to initialize the ResNet101, which can accelerate convergence of the network. The learning rate is set to 0.001 . The class number is set to 3 . Due to the limitation of the GPU memory, the batch size is set to 1 . The max iteration is fixed to 40000 which can ensure the fully loop through of the PV cell EL training data. In BAFPN-RPN, the stride of max pooling is 2. Moreover, a scale level is assigned with an anchor, which has three aspect ratios at each level. The anchors is defined to have areas of pixels on B2,B3,B4,B5,B6}, respectively [16], and anchors with different scales are responsible for predicting defects of different sizes. In the experiments, all input EL images are extended to three channels and resized to pixels. The detailed infor mation and hyperparameters of the BAF-Detector are presented in Table III, which can help the readers to better understand our method. 实验在配备英特尔酷睿 i7-10 700 CPU 和英伟达™（NVIDIA®）GeForce RTX 2070 超级显卡的工作站上进行。ResNet101 使用 ImageNet 上的预训练模型进行初始化，这可以加快网络的收敛速度。学习率设置为 0.001 。类数设置为 3。由于 GPU 内存的限制，批量大小设置为 1 。最大迭代次数固定为 40000 次，以确保光伏电池 EL 训练数据的完全循环。在 BAFPN-RPN 中，最大池化的步长为 2。 此外，一个刻度级别分配一个锚点，每个级别有三个长宽比 。锚点被定义为在 B2、B3、B4、B5、B6} 上分别有 像素的区域[16]，不同尺度的锚点负责预测不同大小的缺陷。在实验中，所有输入的 EL 图像都扩展到三个通道，并调整为 像素。表 III 列出了 BAF-Detector 的详细信息和超参数，有助于读者更好地理解我们的方法。
Moreover, in multihead cosine nonlocal attention module, factors , and are employed to balance the importance of the three inputs. For example, as shown in Fig. 8, the inputs of the second multihead cosine nonlocal attention module (B3) are , and . The simple method to determine , and is , which shows that the three inputs are equally important [36], [37]. As for , we refer to the fact that when performing multiscale feature summation in FPN [16], the balance value of each input is 0.5 , thus we also select 0.5 . 此外，在多头余弦非局部注意模块中，还使用了因子 和 来平衡三个输入的重要性。例如，如图 8 所示，第二个多头余弦非局部注意模块（B3）的输入为 和 。确定 和 的简单方法是 ，这表明三个输入同样重要 [36], [37]。至于 ，我们参考了 FPN [16] 中进行多尺度特征求和时，每个输入的平衡值为 0.5，因此我们也选择 0.5。
TABLE IV 表 IV
EXPERIMENTAL RESULTS OF DIFFERENT DETECTORS ON OUR PV CELL EL IMAGE DATASET 不同探测器在光伏电池 EL 图像数据集上的实验结果
The proposed BAF-Detector is compared with YOLOv3, Faster RCNN, and Faster RPAN-CNN in the classification and detection performance on the PV cell EL image dataset, which are presents in Table IV.重试错误原因
Classification Evaluation: In terms of the defective images classification results, the proposed BAF-Detector achieves a better performance than other detectors on each quantitative evaluation metric, such as precision ), recall ), and F-measure ). The high recall rate of the proposed BAF-Detector ensures that the defective PV cell is not easy to be missed during the intelligent manufacturing process, which is essential to the high-quality production of PV cells.重试错误原因
As shown in Fig. 9, the confusion matrix is reported to evaluate the classification performance of the PV cell. The confusion matrix is given for the three types of defects: crack, finger interruption, and black core. In confusion matrix, 11 crack defects are misclassified as defect-free, which accounts for of the total number of the crack defects. 13 finger interruption defects are misclassified as defect-free, which accounts for of the total number of finger interruption defects. Moreover, all black core defects are classified correctly. The proposed CNN model makes less prediction error, a small proportion of defects are misclassified as defect-free. It is not hard to see that BAFDetector achieves a good classification performance of PV cell defects.重试错误原因
Detection Evaluation: In terms of the proposed model in defect detection performance, mAP and MIoU are employed to evaluate the quantitative comparisons. Table IV shows the detection results of regression-based detector (YOLOv3) and region-based detectors (the others) with same training and testing EL image dataset. With embedding the proposed BAFPN block into RPN in Faster RCNN+FPN, the BAF-Detector outperforms other detectors in the defect detection effects重试错误原因
The curves of dot-product similarity and cosine similarity used in our proposed BAF-Detector are shown in Fig. 10. The area enclosed by the curve, the horizontal axis (recall), and the重试错误原因
Fig. 10. P/R curves of different similarity calculation methods for three types of defects.重试错误原因
vertical axis (precision) is equal to the value of the AP for each type of defect. The dotted line represents precision recall. The intersection of it and the curve represents the balance point (red dot). The larger the value of the balance point, the better the effect of the corresponding detection method. As can be seen from Fig. 10, comparing with dot-product similarity and cosine similarity used in BAF-detector, cosine similarity achieves better quantitative results.重试错误原因
Moreover, as can be seen from Fig. 10, the AP value of the black core defect is close to . This is due to the large scale and simple texture of the black core defect, which presents a black cluster area. The detection result of finger interruption defect is relatively good, due to the sharp contrast and the fixed shape. The crack defect is hard to be detected, because of various scales, different shapes, and the complex background disturbance.重试错误原因
The similarity map of the multihead cosine nonlocal attention module can be viewed as a feature visualization tool, which can help explain the effectiveness of the BAFPN. As shown in Fig. 8, B 3 and B4 belong to BAFPN, if the cosine similarity maps of B3 and B4 include the small defect feature, it illustrates that BAFPN is effective to boost the small defect feature transfer, and prevent the feature vanishment as the network deepens. Fig. 11 shows some intermediate and final detection results. As can be seen, the similarity maps of low layer B3 or deep layer B4 in BAFPN retain the informative features of multiscale defects during the network deepens. At the same time, the noise background features are suppressed. Thus, we can conclude that the BAFPN boosts the bottom-up feature transfer as the network deepens. It enables the BAF-Detector to better detect multiscale defects in EL images. Moreover, the contrast of the low-level similarity map in B3 layer is higher than that of the high-level similarity map in B4 layer, and the brightness is opposite, which shows that multihead cosine nonlocal attention achieves better performance in higher resolution features that contains much more textural and spatial information.重试错误原因
Fig. 11. Visualization of intermediate and final detection results. The first row is the input, the second row is the similarity map of B4 layer, the third row is the similarity map of B3 layer, and the fourth row is the output. The orange value represents the contrast and brightness of each similarity map.重试错误原因
Overall Evaluation: From aforementioned classification and detection evaluation of the proposed BAF-Detector, we can conclude that the proposed BAF-Detector outperforms other detectors in the EL image defect classification and detection performance. The reason is that the fusion strategy (BAFPN) can employ the proposed multihead cosine nonlocal attention module and the top-down bottom-up FPN to highlight target feature, suppress complex background feature, and better guide pyramidal feature fusion, which is very beneficial for multiscale defect classification and detection tasks under complex background interference in PV cell EL image dataset.重试错误原因
Time-Efficiency Evaluation: The results of FPS is the average of 1282 testing defective EL image, which is conducted on a work station with a GPU. As we can see from Table IV, the FPS of a detector is inversely proportional to the parameter number. Our BAF-Detector achieves 7.75 FPS. Although our method is not the fastest, but it outperforms other detectors in defect inspection accuracy that is essential to the industrial production.重试错误原因
Effect of Attention Module: To confirm the effectiveness of the proposed multihead cosine nonlocal attention module, the strategy of add or replace the attention module is employed for ablation studies. As illustrated in Table V, by comparing two similarity calculation methods of nonlocal (dot-product) and cosine nonlocal (cosine), it can be demonstrated that cosine similarity outperforms dot-product similarity in the PV cell defect inspection task. The visualization of similarity maps are shown in Fig. 6. For the second row of the comparisons, defect重试错误原因
TABLE V重试错误原因
Ablation Studies of The Proposed BAF-Detector on Our PV CeLL EL IMAGE DATASET WITH DIFFERENT COMPONENTS重试错误原因
Note: : Addition operation is used to replace the attention module. Mt: Middle two scale levels, attention modules are used in the middle two levels of FPN. : Not use attention module. : Use attention module 注： ：加法操作用于替换注意力模块。Mt：中间两级刻度，注意模块用于 FPN 的中间两级。 ：不使用注意模块。 ：使用注意模块
regions can be highlighted more clearly by cosine similarity map, and the background is more fully suppressed. Moreover, the performance of adding attention module is better than removing it. 通过余弦相似图，区域可以更清晰地突出，背景也被更充分地抑制。此外，添加注意力模块的效果优于去除注意力模块。
Effect of BAFPN: Ablation studies are employed to verify the effectiveness of the proposed BAFPN. The ablation experiments are evaluated by changing the structure of the FPN (top-down, top-down+bottom-up). The effect of the top-down bottom-up FPN with attention module (BAFPN) can be seen in the last two rows in Table V. By comparing the proposed BAFPN with other structures, we find that BAFPN achieves a better performance than the experimental results of the first four rows, which illustrates that the BAFPN block outperforms others in terms of multiscale defect detection. Moreover, as illustrated in the first three rows and the last three rows, FPN with top-down+bottom-up performs better than FPN with topdown under the condition of consistent attention modules. Take mAP column as an example, top-down+bottom-up architecture achieves , and improvement comparing with top-down architecture, respectively. It verifies that bidirectional multiscale feature fusion is better than a single direction. However, BAFPN has more parameters than original FPN, which slightly increases computational burdens. BAFPN 的效果：采用消融研究来验证所提议的 BAFPN 的有效性。通过改变 FPN 的结构（自上而下、自上而下+自下而上）对消融实验进行评估。通过将所提出的 BAFPN 与其他结构进行比较，我们发现 BAFPN 的性能优于前四行的实验结果，这说明 BAFPN 块在多尺度缺陷检测方面优于其他模块。此外，如前三行和后三行所示，在注意力模块一致的条件下，自上而下+自下而上的 FPN 性能优于自上而下的 FPN。以 mAP 列为例，"自上而下+ 自下而上 "结构与 "自上而下 "结构相比，分别实现了 和 的改进。这验证了双向多尺度特征融合优于单向多尺度特征融合。不过，BAFPN 比原始 FPN 多了 个参数，略微增加了计算负担。
V. CONCLUSION V.结论
In this article, a novel multihead cosine nonlocal attention module was proposed to highlight the defect feature and suppress the complex background feature. The novel attention module was also used to construct an efficient multiscale feature fusion block BAFPN, which combines with RPN in Faster RCNN+FPN to form a defect detection model BAF-Detector. The multiscale defects in PV cell EL image were effectively detected under the disturbance of the complex background. The proposed BAF-Detector outperformed other detectors in each quantitative metric, which demonstrated that our proposed deep learning model has certain advantages in defect inspection, and provided a practical solution for research and applications of PV cell defect detection 本文提出了一种新颖的多头余弦非局部注意力模块，以突出缺陷特征并抑制复杂的背景特征。该模块还被用于构建高效的多尺度特征融合模块 BAFPN，并与 Faster RCNN+FPN 中的 RPN 结合形成缺陷检测模型 BAF-Detector。在复杂背景的干扰下，光伏电池 EL 图像中的多尺度缺陷被有效检测出来。所提出的 BAF-Detector 在各项定量指标上都优于其他检测器，这表明我们提出的深度学习模型在缺陷检测方面具有一定的优势，为光伏电池缺陷检测的研究和应用提供了一种切实可行的解决方案。
There were also some limitations for our BAF-Detector. For example, the feature balance factors , and in attention module were set mutually, which takes time and efforts. In the future, adaptive methods will be researched to automatically determine these factors. 我们的 BAF-Detector 也有一些局限性。例如，注意力模块中的特征平衡因子 和 是相互设定的，这需要花费时间和精力。今后，我们将研究自动确定这些因素的自适应方法。
APPENDIX 附录
Here are some details for the intelligent defect detection system. First, the intelligent defect detection system needs to be grounded to prevent harm caused by current leakage, and the leakage circuit breaker is also employed to ensure the safe and efficient operation of the system. Second, it is necessary to ensure that the image acquisition conditions do not change, which is necessary to the normal and long-term operation of the proposed algorithm. Please refer to Su et al. [5] for the image acquisition conditions. 以下是智能缺陷检测系统的一些细节。首先，智能缺陷检测系统需要接地，以防止漏电流造成的危害，同时还要采用漏电断路器，以确保系统安全高效地运行。其次，需要确保图像采集条件不发生变化，这对所提算法的正常和长期运行是必要的。图像采集条件请参考 Su 等人的文章[5]。
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