This study thoroughly examines the detection of cracks and incomplete fusion in butt-welded steel plates. These defects, widely recognized as critical welding flaws, can significantly undermine the structural integrity and long-term reliability of metallic systems. To investigate this pressing issue, controlled and artificial defects, specifically cracks and incomplete fusion, were introduced during the experimental phase. These defects were systematically generated by inducing abrupt changes in the welding temperature and voltage during the welding process. Traditional approaches in this domain predominantly rely on ultrasonic waves and high-frequency sensors, which often entail high computational complexity and significant financial costs. In contrast, this study proposes an innovative method that utilizes the characteristics of elastic waves propagating through steel plates, presenting a more straightforward, accessible, and cost-efficient alternative. The proposed method incorporates data acquisition and analysis within a limited frequency range, which mitigates environmental influences and reduces computational demands, thereby facilitating the continuous monitoring of welded joints. The defect identification process involves analyzing the signal energy and higher-order statistical parameters, such as the third- and fourth-order statistical moments, to effectively differentiate between cracks and incomplete fusion. Experimental results indicated that in samples containing cracks, the ratios of signal energy, third-order statistical moments, and fourth-order statistical moments to those of defect-free samples increased by 125%, 394%, and 53%, respectively. Conversely, in samples with incomplete fusion, these ratios were found to be 76%, 28%, and 86%, respectively. These findings clearly underscore the efficiency, robustness, and accuracy of the proposed method for non-destructive testing of welding defects. The approach offers reduced computational complexity, making it a viable tool for practical industrial applications. Furthermore, the simplicity of this method and its capability for real-time monitoring highlight its great potential for integration into the continuous health monitoring of metallic structures. This approach offers a promising and practical alternative to conventional, more resource-intensive techniques for welded joint evaluation.