Within the field of Non-Destructive Evaluation (NDE), specifically focusing on high-speed laser welding, there has been a notable increase in demand for automated monitoring during the process. This is largely due to the industry's desire to improve weld quality and simultaneously boost operational speed. Improving temporal resolution in defect identification is crucial for effective real-time surveillance. In response to this need, our study starts by analyzing structure-born and airborne ultrasound sensors. Then, we introduce a feature extraction method by combining conventional algorithms with the Wavelet Scattering Transform. Utilizing these extracted features, we employ machine learning techniques to identify and classify welding defects, more specifically simulated notches that represent butt joint gaps in laser welding. The primary objective of the utilized technique is to accurately detect and classify notches, with a particular focus on their varying sizes. In addition to standard laboratory setups, we also considered real-world industrial factors such as noise from cross-jets and other industrial ambient noises, leading to a more comprehensive evaluation. Furthermore, this research places a strong emphasis on ultrasound process monitoring due to its ability to probe deeper material layers and economic benefits in terms of data analysis. Competing techniques like X-ray methods face significant challenges, including high costs, safety issues, and limited penetration in certain welding situations. Moreover, camera-based approaches are restricted to surface-level analysis and are highly sensitive to external factors such as variable lighting and dust. On the contrary, ultrasonic techniques provide a comprehensive analysis of the welding process, focusing on its internal workings. After making use of all the advantages of this approach, our study achieved over 85% accuracy using signals as short as 1 ms. Combining the signal length and the defect sizes in our experiments, we reached a spatial resolution of 0.2mm in both axes (along and across the weld). Higher accuracies can be attained by using longer signals; for example, 95% accuracy with 10 ms signals and 99% accuracy with 50 ms signals. These findings show the potential to improve efficiency in the laser welding industry by depicting a reliable high resolution defect classification technique.