###### Abstract  
The imaging detection of ultrasonic guided waves in plates using arc sparse arrays is highly significant for weld scattering conditions. A novel approach for detecting welded plate structures using the left rank of ultrasonic guided waves in arc sparse arrays was proposed. The relationship between the receiving matrix and the left rank was analyzed, along with the connection between the arc sparse array with the left rank and the receiving aperture. The imaging mechanism of the ultrasonic guided waves in arc sparse arrays with left rank under weld scattering conditions was investigated. The results of imaging experiments demonstrated a downward trend in the gray and background gray of the multi-frame images. As the left rank reaches approximately 64% of the full rank, the slope of the image gray and background gray decreases gradually, leading to the appearance of an inflection point. With an increasing signal-to-noise ratio curve, the imaging improved during the multi-frame imaging process of ultrasonic guided waves for the arc sparse arrays with left rank under weld scattering conditions. This research showed that the multi-frame imaging of ultrasonic guided waves in welded structural plates using arc sparse arrays with left rank effectively characterized scattering information with millimeter-scale wavelength size. The experimental results validated the feasibility of the theoretical analysis. This research provides a crucial foundation for the further exploration and application of the multi-frame imaging detection of ultrasonic guided waves using irregular arrays in welded structural plates. arc sparse array with left rank; weld structural; ultrasonic guided waves in plates; multi-frame imaging detection 202420241489811 10.3390/appl/1498981 10.  
guided waves are highly suitable for inspecting waveguide structures. However, when ultrasonic guided waves propagate in bounded media such as welded structural plates and pipelines, their behavior is influenced by the structure and size of the medium. This leads to the presence of multiple modes and different sound velocities corresponding to these modes. Consequently, the wave velocity of the sound wave becomes highly dependent on the frequency, resulting in changes in wave velocity with frequency. At a specific frequency, multiple modes coexist, resulting in the multimodal phenomenon of ultrasonic guided waves [7]. Guided wave imaging poses a significant challenge due to various factors such as the selection and analysis of ultrasonic guided wave modes, the transmission and reception of guided wave signals, and the scattering of defects [8; 9; 10]. To enhance the effectiveness of detection, ultrasonic guided wave imaging detection utilizes the propagation characteristics of ultrasonic media and utilizes reflected or transmitted sound waves as carriers of information. In the case of the imaging detection of ultrasonic guided wave arrays in plates, particularly in butt structural plates with weld defect scatterers, the defect reflection echo becomes scattered or superimposed, resulting in a significant attenuation of acoustic energy and compromising the imaging quality. Furthermore, there exist differences and connections between different frame sequence images corresponding to changes in the aperture during imaging [11]. Ultrasonic array imaging detection commonly involves various array forms, including regular arrays and irregular arrays [12; 13]. Regular ultrasonic guided wave arrays encompass linear arrays [14; 15; 16], arc arrays [17], ring arrays [18; 19; 20], and more, depending on the detection conditions and methods. Irregular ultrasonic guided wave arrays, on the other hand, consist of dispersed arrays [16; 21]. In the research and application of ultrasonic guided wave imaging detection using these different array types, there is a wealth of imaging data available from both the transmitting and receiving apertures.