## 1 Introduction  
Functions such as light-weighting and corrosion resistance are being strengthened, whereas construction convenience must be considered when connecting pipes such as water or gas pipes. In particular, it is difficult to apply welding and fastening methods using screws because pipes used as water pipes are thin. Therefore, a crimping joint method using a pressure jig is applied when connecting water pipes. A crimping joint with dual ring points, which is a type of crimping joint, is shown in Figure 1. The joints on the ends of the two pipes to be connected are compressed when a metal ring for preventing vibration and deflection and a watertight rubber ring are inserted between the joints and the connecting pipe. When the material of the metal ring inside the joint is stainless steel, it is known as the stainless ring (SR) joint, as shown in Figure 0(a). The commercial crimping joint with dual ring points contains a metal ring and a rubber ring adjacent to it Figure 0(b); hence, the two rings can be compressed using a relatively small pressing tool in a single attempt. Although such a structure affords the light-weighting of the tool or high work efficiency, the rubber ring might penetrate into the dented part of the metal ring after the compression,as shown in Figure 1c. Consequently, leaked water due to the lowered water-tightness accumulates in the gap between the fitted pipe and SR-joint, resulting in corrosion. In addition, a conventional SR-joint cannot respond to the recently reinforced seismic design of structures owing to problems such as the separation of rubber rings or rotation of metal rings when vibrations occur because of earthquakes. A new SR-joint shape that separates the metal and rubber rings must be developed for improvement. [PERSON] et al. [1] conducted structural analysis of the crimping tool in the crimping state as a preliminary preparation stage for the technology development of the SR-joint. However, there is a limitation that the analysis of various parameters affecting pipe compression is insufficient, and actual verification has not been performed. Although empirical design is being conducted by observing the pipe joint and the cut surface at the field, the behavior of the metal and rubber rings inside the pipe is not well understood when the SR-joint is compressed. Therefore, it is difficult to develop and apply a new SR-joint that separates the metal and rubber rings. Various studies have been conducted to derive an optimal design method using finite element analysis to solve problems encountered in such an empirical design. [PERSON] et al. [2] investigated the mechanical deformation between pipes during the field joining of a bent sandwich pipe. [PERSON] et al. [3] analyzed the load for a 180\({}^{\circ}\) pipe bending using three-dimensional (3D) finite element analysis considering geometric nonlinearity. In addition, [PERSON] et al. [4] performed a contact analysis of wedge-type pipe joints, whereas [PERSON] et al. [5] developed plastic deformation and permanent crimping methods for pipes using pressing tools based on finite element analysis. [PERSON] et al. [6] predicted the wear life of the CrN coating layer on a press tool for stamping an ultra-high-strength steel sheet through a design of experiment. [PERSON] et al. [7] applied a design of experiment to analyze the performance of the internal fin shape of a microchannel heat sink and then optimized the shape. Regression analysis has been performed to obtain the optimal design of a product, as in the aforementioned studies; however, studies using artificial intelligence have increased recently to further improve the accuracy of prediction models. [PERSON] et al. [8] used finite element analysis in addition to machine learning to develop a model for predicting the surface deflection of rectangular drawing products. [PERSON] et al.