YOLOv8-A: Enhanced Lightweight Object Detection with Nonlinear Feature Fusion and Mathematical Optimization for Precision Small Target Detection in Industrial Silicon Melting Processes

Abstract The precise detection of small targets during the Czochralski process for monocrystalline silicon crystal growth is critical for ensuring high-quality production. However, conventional object detection models often face challenges such as inaccurate localization and high false-positive rates, particularly when detecting small protrusions in molten silicon images. To address these challenges, this study introduces an improved YOLOv8-based algorithm, YOLOv8-A, integrating nonlinear mathematical optimization techniques and advanced feature fusion strategies tailored for industrial applications. The proposed model incorporates a Bidirectional Feature Pyramid Network (BiFPN) to enhance multi-scale feature aggregation and a lightweight dynamic upsampling operator (DySample) based on nonlinear interpolation methods to refine feature quality. The nonlinear mathematical formulations incorporated in these components improve the model's ability to capture complex relationships within the data, reducing computational complexity while enhancing detection precision. Experimental validation demonstrates that YOLOv8-A achieves superior performance with a 98.2% mean average precision (mAP) and a 5.8% improvement in small target detection accuracy compared to traditional models. The results underscore the potential of YOLOv8-A as an efficient and robust solution for real-time quality control in silicon crystal growth processes, offering a novel approach to small target detection through mathematical modeling and nonlinear optimization.