## 1 Introduction  
Gas metal arc welding (GMAW) is a crucial process that is extensively employed in various industries, including automotive, heavy equipment, and shipbuilding. The weld quality directly impacts the integrity, durability, and safety of the fabricated components. Traditional methods to assess the quality of weld joints involve destructive testing, such as confirming weld shape [1, 2, 3, 4] and evaluating mechanical properties through tensile testing [4, 5, 6] and fatigue testing [7, 8, 9, 10]. However, these methods only facilitate a partial inspection of the weld joints and indirectly represent the welding quality of the overall structure [11, 12]. Consequently, there is a significant need for research on non-destructive testing methods to predict welding quality, with preliminary studies indicating potential in this area. Prior studies have primarily focused on predicting weld bead shape [13; 14; 15; 16] and mechanical properties [17; 18; 19] using statistical analysis considering various welding conditions. Additionally, artificial neural networks (ANNs) have been employed to predict the morphology [13; 14; 15] and mechanical properties [18; 19; 20] of weld joints in response to changes in welding conditions. Additionally, various methods such as fuzzy logic, neuro-fuzzy, image processing, D-S evidence, and physical models have been used to predict welding quality [21]. Due to the challenges associated with incorporating disturbances into GMAW processes, recent studies have explored ANN-based prediction of welding quality using diverse sensor-based data [20; 21; 22; 23]. GMAW is widely used in heavy equipment component manufacturing and shipbuilding industries for fabricating thick welding structures, and components produced through multi-pass welds in butt joints are prevalent. In such butt joints, the penetration of the root weld is a crucial factor determining the welding quality of the plate structure. Efforts are being made to predict the penetration condition and shape of the back-bead in such weld joints. [PERSON] et al. [24] reported on a deep learning-based prediction of the penetration state in gas tungsten arc welding (GTAW). Two vision cameras simultaneously captured images of the molten pool from the top and shape of the back-bead. Using the captured images, a convolutional neural network (CNN) model was trained with the tip images as input data and the penetration states as labels. The residual neural network and transfer learning methods were employed, resulting in a final prediction accuracy of 96.35% for penetration classification. [PERSON] et al. [25] proposed a support vector regression model to predict the width of a back-bead extending through the surface of the molten pool in GTAW. The characteristic parameters were acquired from the surface of the molten pool by using a three-dimensional (3D) vision sensor. The prediction performance was evaluated in terms of the root-mean-square error and squared correlation coefficient, which were determined to be 0.421 and 0.798, respectively, indicating a high predictive accuracy. [PERSON] et al. [26] proposed a model for collecting molten pool images by using vision sensors in GMAW; they further validated confirmed the variation trend of the penetration prediction based on a deep learning network. The model demonstrated remarkable predictive performance with penetration depth errors of less than 0.09 mm across various welding parameters and working conditions. In previous studies, images of welding states captured by vision systems were used as input data to ANN models for predicting the penetration state and shape of the back-beads. The use of a vision system to directly observe the molten pool provides the advantage of real-time prediction by leveraging it as input data. Despite the effectiveness of using vision systems for real-time prediction, they are expensive and increase the complexity of welding systems. Therefore, measuring current and voltage during welding presents a more practical method for assessing weld quality in GMAW.