# Neighborhood Rough Fuzzy Penetration Control Method with Variable Precision Based on GMAW
## 1 Introduction  
As an essential material joining technique, welding plays a highly significant role in industrial manufacturing, especially in automotive, aerospace, marine, and other widely used fields. Gas metal arc welding (GMAW) is widely used in industrial manufacturing operations because of its elevated welding efficiency and low cost. Welding is a typically complex process with extreme nonlinearity, time varying, interference, and multivariate coupling. In welding process control problems, the actual welding conditions and environment are continuously changing, which makes it difficult to summarize the welding experience and reproduce the excellent control results. Exploring intelligent methods for the control of penetration states is one of the main effective means. The rough set (RS) method is a mathematical tool used to deal with incomplete knowledge and fuzzy concepts [1]. Since rough set theory was proposed by [PERSON] [2] in 1982, it has been widely used in data mining, machine learning, and knowledge discovery. Several scholars have carried out effective studies based on rough set theory, joint fuzzy set theory, and other intelligent approaches. [PERSON] et al. [3] proposed a variable precision fuzzy neighborhood rough set (VPFNRS) model based on a neighborhood rough set, introduced fuzzy theory, gave fuzzy rule acquisition and decision-making theory, and successfully applied it in satellite power systems, which verified the feasibility and accuracy of this method for fault diagnosis. [PERSON] et al. [4] used rough set principles to extract uncertain information and combined it with machine learning technology for risk prediction. Many scholars have also applied rough sets in the field of welding. [PERSON] et al. [5] applied a rough set to the knowledge modeling of the pulse GTAW process of aluminum alloys. [PERSON] et al. [6] proposed a welding process modeling method based on variable precision rough sets inorder to improve modeling stability and model effectiveness over classical rough set. [PERSON] et al. [7] proposed a knowledge modeling method based on interval-valued fuzzy rough sets, which was effectively applied to predict welding deformation of Marine structures. [PERSON] et al. [8] applied rough set theory to the problem of welding defect identification and effectively identified selected welding defects. With the development of sensor technology, some characteristic information about the welding process can be easily obtained by the sensor. In welding, the penetration depth of the weld can reflect the quality of the welding [9], and the penetration depth of the weld is mainly affected by the welding process parameters (welding current, welding voltage, protective gas flow, wire feeding speed, etc.). The penetration depth cannot be measured directly but can only be obtained via prediction and estimation. [PERSON] et al. [10; 11] used acoustic sensors combined with neural network technology to predict the penetration state in the welding process, and by training a large number of data points, the prediction accuracy can reach 80%-90%. [PERSON] et al. [12; 13; 14] used vision sensors to obtain molten pool images and used deep learning and neural network technologies to predict and identify weld penetration depth, in which the two-dimensional image of the molten pool surface was taken as an influential feature input. In the course of experimental validation, the model developed by [PERSON] et al. [12] quantitatively predicted the penetration depth of tungsten gas shielded welding. The mean absolute error is 0.0596 mm, and R2 is 0.9974. [PERSON] et al. [13] used ViT-B/16 model ImageNet for pre-training, and the validation accuracy was successfully improved by 4.45%. The transfer learning results show that the ViT model achieves a test accuracy of 98.11%.