# Regression Approach to a Novel Lateral Flatness Leveling System for Smart Manufacturing
## 1 Introduction  
The metal forming industry is considered the main part of mass production in the automotive, electronics, telecommunication, and construction industries. In the metal forming industry, sheet metal coil has been widely used in either metal stamping or laser cutting. In each coil, there are always different common symptoms of unleveling problems, as shown in Figure 1[1]. The five common symptoms are coil set, crossbow, twisted strip, center buckle, and a wavy edge of the coil. The most common symptom of an unleveled coil is coil set, which is caused by the way the sheet metal is stored and packaged with a surface-to-surface length differential [2]. Coil set can easily be leveled or flattened by a roller leveler with entrance and exit gap adjustment to the rolls. On the other hand, center buckle, wavy edge, and crossbow are lateral (width) lengthwise differences and require leveling in the lateral direction [3]. Due to the increase in sheet leveling quality demand in recent years, leveling in a lengthwise direction can no longer be sufficient for a much higher quality application. As a result, lateral leveling has become a crucial point for leveling quality to deliver high-quality products. In this paper, the research will be focused on the lateral leveling of coil sheet metal. The leveling process is achieved through a leveling machine, with a sheet metal coil feedthrough on the leveler with the alternating bending process. In recent years, smart manufacturing has been widely discussed for industrial applications due to the initiation of Industry 4.0, and one of the definitions has been defined to better predict and maintain production processes [4]. However, smart manufacturing has not been widely applied within the steel coil leveling process. The leveling process depends on the coil's thickness, width, tensile strength, yield strength, outer diameter, inner diameter, and the line speed of the production line. It is often through experienced machine operators with many yearsof experience together with trial-and-error techniques that the desired leveling quality is achieved through roll adjustments. During the leveling process, if the operator inputs unsuitable parameters, the whole leveling process of the strip will be required to reverse and restart, a process which is often around 5-10 m in length. Therefore, this manufacturing operation is considered time-consuming and may create much unusable waste sheet metal during the machine setup stage before becoming fully operational. The main advantage for this research is shortening this trial-and-error process. From the literature [5; 6; 7], most previous research has focused on investigation with the use of mechanical theories of the leveling mechanism of sheet metals. This method is commonly referred to as the model-driven approach. Apparently, there is limited research tackling the same issue through a data-driven approach based on machine learning techniques. However, with growing demands in smart manufacturing, it is desirable to integrate machine learning technologies into the steel coil processing industry to improve productivity and to offer reliable and repeatable results in leveling sheet metal coils. Residual stress caused by the manufacturing process was reported in the literature to be the key factor affecting the leveling quality of the sheet metal coils. Many published results regarding the residual stress were based on the solid mechanics model. [PERSON] et al. [8] investigated the evolution of the residual stress in multi-roll leveling, considering the curvature coupling between bendings of the sheet metal through the multi-roll. In their investigation, it was reported that multi-roll leveling could result in rolling residual stress while reducing the initial residual stress of the sheet.