## 1 Introduction  
Ships are larger than regular transport structures, and thus their manufacturing process is more complex. Shipbuilding consists of multiple processes of assembling numerous members, materials, and equipment. This process starts with the design stage. The design stage proceeds in order of the initial, basic, detail, and production design. Steel plates are procured and processed after the design stage. The fabricated steel plates are used as members of the hull after the piece assembly process of attaching reinforcements to the inner structure of the hull and the sub-block assembly process of attaching frames to the outer plates of the hull. Then, the hull structure is assembled through the block assembly process. The ship is finally completed through the process of pre-outfitting, erection, and painting the outer plates of the hull. Welding technologies are widely used in the production and assembly of ships. Steel hull welding is a complicated thermo-mechanical treatment process, because deformation and shrinkage of the materials are caused by the heat during the welding process. For this reason, skilled technicians spend a great deal of time and expense on the manual improvement process. Sometimes the deformation and shrinkage accumulate during the actual assembly stage, leading to situations where the gaps are too large to be welded in the block assembly stage. As it takes a lot of time through simulations to calculate the shrinkage and deformation caused by welding large structures such as hull structures, several simple analysis methods have been developed over the years. It is necessary to calculate the deformation and shrinkage due to welding in the manufacturing stages quickly through simulations in advance. Based on the calculated welding deformation and shrinkage, this study aims to satisfy the allowable tolerances by offsetting the deformation and shrinkage in each assembly stage by providing accurate margins in the manufacturing stage. In general, three methods are used to calculate weld deformation. The first is an experimental elasticity method, the second is a numerical method, and the third method is the equivalent load method. The development of these welding deformation methodologies is summarized in Table 1.  
The elasticity method involves a simple welding experiment by changing the welding conditions and the dimensions of the work piece. After that, the factors affecting the welding deformation are summarized and the welding deformation is expressed using the equation for these factors. [PERSON] et al. performed a study to obtain an analytical solution based on an elastic theory by applying strain to the initial state [1]. The numerical method, a thermal elasto-plastic analysis method, involves a simulation of all the physical phenomena relevant to the welding process that is as close to reality as possible. A numerical analysis is applied to the precise simulation of the welding process to determine the thermal, structural, and metallurgical phenomena. [PERSON] et al. applied the finite element method to the analysis of in-plane residual stresses in two-dimensional structures [2]. However, this requires a huge amount of computational time. The equivalent load method extracts the characteristics of welding distortion and converts the sources of distortion into equivalent loads. This method can only be used to estimate the welding distortion of complicated structures in a very short time. The experimental-based equivalent load method was proposed by [PERSON] et al. and derived a moment equation that gave the same angular deformation as the experimental estimate [3]. [PERSON] et al. calculated equivalent load by arranging a correlation between angular deformation and heat input [4]. [PERSON] et al. conducted an experiment to find the equivalent loads for the angular deformation and longitudinal bending of fillet welding [5]. The inherent strain method is the most suitable method for calculating the welding deformation and shrinkage in large structures such as hulls [6].