## 5 Proposed Methodology  
The methodology of this study introduces a novel and robust approach to enhance the classification performance for surface defect detection, consisting of five distinct yet interconnected stages. Figure 2 shows the representation of the proposed approach. The  
Figure 1: Dataset samples of classified shapes with defects: (**a**) pitted surface, (**b**) crazing, (**c**) scratches, (**d**) patches, (**e**) non-defect [21]. innovative aspect of the approach begins with the pre-processing of raw images, where a unique method is employed. Unlike traditional image pre-processing techniques, this study applies a spectrogram algorithm to time series signals derived from images that contain surface defects. This step transforms 2D image data into a 1D stack by utilizing pixel values, enabling the extraction of spectrogram images. This novel transformation provides a powerful representation of pixel variations in defect regions, enhancing the model's ability to capture subtle details crucial for classification. In the second stage, the processed spectrogram images are used to train a newly designed architecture known as the Parallel Attention-Residual CNN (PARC) model. Figure 3 shows the layer connections of the PARC model. The innovation in this model lies in its dual use of attention and residual mechanisms within a customized CNN framework, operating in parallel. Attention mechanisms focus on emphasizing critical areas within the image, while residual connections allow the preservation of feature information from earlier layers by passing it forward to subsequent layers. This synergy ensures that vital details, which may have otherwise been diminished or lost in deep layers, are retained and utilized, thus improving the learning capability of the network. While state-of-the-art architectures such as Swin Transformer, EfficientNetV2, and YOLOv7 have demonstrated remarkable performance across a variety of vision tasks, they are primarily designed as general-purpose models and often involve high computational costs and large parameter counts. In contrast, the proposed PARC (Parallel Attention and Residual Convolution)  
Figure 2: The framework of the proposed methodology. model is specifically tailored for steel surface defect recognition, focusing on enhancing subtle and fine-grained texture variations that are commonly present in such industrial inspection tasks. The parallel integration of attention and residual mechanisms in PARC enables it to capture both local defect features and global structural information more effectively, without significantly increasing the computational complexity. Compared to Transformer-based models like Swin Transformer, which require large datasets and extensive training resources to generalize well, PARC achieves a competitive or superior accuracy with a lightweight and task-optimized architecture. Furthermore, unlike YOLOv7, which is object-detection-focused and might exhibit overkill or be less efficient for fine-grained classification tasks, PARC offers a better balance between precision, speed, and model complexity. Its compact design makes it more suitable for real-time deployment in edge environments commonly found in industrial inspection systems. Detailed layer information of the PARC model is given in Table 1 in the Appendix A section. The third stage focuses on feature extraction from the fully connected (FC) layers of the PARC model, where deep features are drawn from both the activations and the processed input data. This stage sets the foundation for the next key novelty: instead of relying solely on the softmax classifier typically employed in CNN models, the extracted features are evaluated using a range of highly effective classification algorithms. This offers a fresh perspective on model training, allowing for a more versatile comparison of classifiers. In the fourth stage, an efficient feature selection algorithm called INCA is applied.