A Study on Determining Weld Joint Hardening and a Quality Evaluation Algorithm for 9% Nickel Weld Joints Using the Dilution Ratio of the Base Material in Fiber Laser Welding

The demand for LNG-powered ships and related equipment is rapidly increasing among major domestic and foreign carriers due to the strengthened IMO regulations on the sulfur content of ship fuel oil. LNG operation in a cryogenic environment requires a storage tank and fuel supply system that uses steel with excellent brittleness and fatigue strength. A ship using LNG is very sensitive to explosion and fire. For this reason, 9% Ni is often used, because ships require high quality products with special materials and structural technologies that ensure operability at cryogenic temperatures. However, research to derive uniform welding quality is urgent because the deterioration of weld quality in the 9% Ni steel welding process is caused by high process difficulty and differences in welding quality depending on a welder’s skill set. This study proposes a method to guarantee a uniform quality of 9% Ni steel in a fiber laser welding process by categorizing weld joint hardness according to the dilution ratio of a base material and establishing a standard for quantitative evaluation.


Introduction
The International Maritime Organization (IMO) has applied a high standard to the sulfur content of ship fuel oil since January 2020, and has finally confirmed a plan to reduce the sulfur content of ship fuel oil from its current level of 3.5% to 0.5% in 2020. The IMO 2020 standards are legislated in each country around the world and the regulations are voluntarily applied to designated emission control areas with more stringent standards than other sea waters. Major domestic and foreign carriers are complying with the IMO's enhanced environmental regulations by considering the pros and cons of each alternative, such as installing a scrubber, using low-sulfur oil, or using LNG.
As eco-friendliness has become an international trend, a major energy transition is taking place around the world and the demand for liquefied natural gas (LNG) is increasing in the shipping sector as well. The bunkering industry, i.e., refueling LNG to LNG-powered ships, is also emerging worldwide. Equipment applied to an LNG propulsion ship can be broadly divided into the engine, fuel tank, fuel supply system, and fuel supply control system. A shipyard or a shipowner makes a packaged-type order, by which a tank or supply system can be directly installed onto a ship. However, a high-quality product with special materials and structural technologies for cryogenic operability is needed because As such, an analysis with various perspectives is required to clearly distinguish the specific conditions that can produce a similar bead shape compared to the intermittent variables, and it is necessary to identify the phenomenon that causes the structure of a weld joint to be hardened by matching the characteristics generated from the correlation between the partially divided shapes within a weld joint to the dilution ratio of a weld joint.
In 9% Ni steel, a higher dilution ratio of the base material results in lower strength. Therefore, excessive dilution of the base material should be avoided in order to secure the required strength. Although prior studies on the relationship between the dilution ratio and strength have found that the tensile strength does not change significantly even when there is a 10-20% change in the dilution ratio, it was reported that it may be lower than the API standard of 363 MPa due to the hardening of a weld joint if it is 25% or more [15,16].
Therefore, in this study, the dilution ratio formed in a weld joint was calculated for the fiber laser welding process applied to 9% Ni, a cryogenic steel, and the phenomenon in which a hardened weld joint is created compared to the heat-affected zone was identified in a procedure based on the calculated dilution ratio. Accordingly, this study tried to suggest a method of quantitatively evaluating the quality of a weld joint.

Experimental Works
The experiment was performed to determine the quality of a fiber laser weld joint of 9% Ni steel and to develop the optimal process parameters. A MIYACHI ML-6950A model (Amada Weld Tech Co. Ltd., Chiba, Japan) 5 kW fiber laser welding machine was used, and a YASKAWA's DX100 model (Yaskawa Electric Co., Kitakyushu, Japan) MOTOMAN was used to configure the entire system, as shown in Figure 1. As such, an analysis with various perspectives is required to clearly distinguish the specific conditions that can produce a similar bead shape compared to the intermittent variables, and it is necessary to identify the phenomenon that causes the structure of a weld joint to be hardened by matching the characteristics generated from the correlation between the partially divided shapes within a weld joint to the dilution ratio of a weld joint.
In 9% Ni steel, a higher dilution ratio of the base material results in lower strength. Therefore, excessive dilution of the base material should be avoided in order to secure the required strength. Although prior studies on the relationship between the dilution ratio and strength have found that the tensile strength does not change significantly even when there is a 10-20% change in the dilution ratio, it was reported that it may be lower than the API standard of 363 MPa due to the hardening of a weld joint if it is 25% or more [15,16].
Therefore, in this study, the dilution ratio formed in a weld joint was calculated for the fiber laser welding process applied to 9% Ni, a cryogenic steel, and the phenomenon in which a hardened weld joint is created compared to the heat-affected zone was identified in a procedure based on the calculated dilution ratio. Accordingly, this study tried to suggest a method of quantitatively evaluating the quality of a weld joint.

Experimental Works
The experiment was performed to determine the quality of a fiber laser weld joint of 9% Ni steel and to develop the optimal process parameters. A MIYACHI ML-6950A model (Amada Weld Tech Co. Ltd., Chiba, Japan) 5 kW fiber laser welding machine was used, and a YASKAWA's DX100 model (Yaskawa Electric Co., Kitakyushu, Japan) MOTOMAN was used to configure the entire system, as shown in Figure 1.
(a) The 5 kw fiber laser power source.
(b) Optical system and jig shape assembled in a six-axis robot. The test piece used in the welding test was used in a size of 150 mm (W) × 200 mm (H) × 15 mm (H) of 9% Ni steel. The specimen was cleaned with ethyl alcohol and sandpaper to prevent foreign substances such as rust, scale, oxide, etc. from causing welding defects on the surface of a specimen to be welded. The schematic diagram of a fiber laser welding process is shown in Figure 2. The chemical composition and mechanical properties of 9% Ni steel are shown in Tables 1 and 2, respectively. The test piece used in the welding test was used in a size of 150 mm (W) × 200 mm (H) × 15 mm (H) of 9% Ni steel. The specimen was cleaned with ethyl alcohol and sandpaper to prevent foreign substances such as rust, scale, oxide, etc. from causing welding defects on the surface of a specimen to be welded. The schematic diagram of a fiber laser welding process is shown in Figure 2. The chemical composition and mechanical properties of 9% Ni steel are shown in Tables 1 and 2, respectively.   Laser power, defocusing, and welding speed were selected as input variables because the fiber laser welding process applied in this experiment welds by generating a keyhole while delivering the high energy required for welding to the material surface. Weldability was analyzed by collecting mechanical properties such as the heat-affected zone and weld joint hardness [11]. Figure 3 shows a schematic diagram for the measurement of the penetration shape of the weld joint [17]. In this experiment, it is possible to estimate all the factor effects for the response of an output variable according to the change of an input variable, and the full factorial placement method (FFD) was applied to detect the correlation effect of higher orders. Full factorial design is a general Kn factorial design DOE with n factors and k levels, and experiments are designed at the combination of all factor levels. Therefore, Kn experiments should be performed even without repeated experiments. FFD forms a cube diagram of the experimental points in case of 3 factors and 2 levels, and the factor experiment by the factor arrangement method has the advantage that all factor effects can be estimated. The level and range of input variables (laser power, defocusing, welding speed) were chosen through preliminary experiments. A total of 18 experimental conditions were designed from 3 2 × 2 (3 laser powers, 3 defocusing and 2 welding speeds). Tables 3 and 4 show the   Laser power, defocusing, and welding speed were selected as input variables because the fiber laser welding process applied in this experiment welds by generating a keyhole while delivering the high energy required for welding to the material surface. Weldability was analyzed by collecting mechanical properties such as the heat-affected zone and weld joint hardness [11]. Figure 3 shows a schematic diagram for the measurement of the penetration shape of the weld joint [17].   Laser power, defocusing, and welding speed were selected as input variables because the fiber laser welding process applied in this experiment welds by generating a keyhole while delivering the high energy required for welding to the material surface. Weldability was analyzed by collecting mechanical properties such as the heat-affected zone and weld joint hardness [11]. Figure 3 shows a schematic diagram for the measurement of the penetration shape of the weld joint [17]. In this experiment, it is possible to estimate all the factor effects for the response of an output variable according to the change of an input variable, and the full factorial placement method (FFD) was applied to detect the correlation effect of higher orders. Full factorial design is a general Kn factorial design DOE with n factors and k levels, and experiments are designed at the combination of all factor levels. Therefore, Kn experiments should be performed even without repeated experiments. FFD forms a cube diagram of the experimental points in case of 3 factors and 2 levels, and the factor experiment by the factor arrangement method has the advantage that all factor effects can be estimated. The level and range of input variables (laser power, defocusing, welding speed) were chosen through preliminary experiments. A total of 18 experimental conditions were designed from 3 2 × 2 (3 laser powers, 3 defocusing and 2 welding speeds). Tables 3 and 4 show the In this experiment, it is possible to estimate all the factor effects for the response of an output variable according to the change of an input variable, and the full factorial placement method (FFD) was applied to detect the correlation effect of higher orders. Full factorial design is a general K n factorial design DOE with n factors and k levels, and experiments are designed at the combination of all factor levels. Therefore, K n experiments should be performed even without repeated experiments. FFD forms a cube diagram of the experimental points in case of 3 factors and 2 levels, and the factor experiment by the factor arrangement method has the advantage that all factor effects can be estimated. The level and range of input variables (laser power, defocusing, welding speed) were chosen through preliminary experiments. A total of 18 experimental conditions were designed from 3 2 × 2 (3 laser powers, 3 defocusing and 2 welding speeds). Tables 3 and 4 show the experimental variables, levels of the input variables, and the experimental conditions for a total of 18 trials, respectively.

Penetration Geometry
The BOP fiber laser welding of 9% Ni steel, a cryogenic steel, was performed correctly according to the welding process parameters. Based on the result of the experiment, it was confirmed that good penetration was formed in general, and there were no pores or defects in appearance. To properly represent the cross-sectional appearance of a specimen, a 90% ethanol plus 10% nitric solution was mixed and used to etch the cross-section. An optical microscope system was used to measure the penetration shape accurately. Table 5 shows the welding cross-section and penetration measurement results taken with a 10× optical microscope. experimental variables, levels of the input variables, and the experimental conditions for a total of 18 trials, respectively.

Penetration Geometry
The BOP fiber laser welding of 9% Ni steel, a cryogenic steel, was performed correctly according to the welding process parameters. Based on the result of the experiment, it was confirmed that good penetration was formed in general, and there were no pores or defects in appearance. To properly represent the cross-sectional appearance of a specimen, a 90% ethanol plus 10% nitric solution was mixed and used to etch the cross-section. An optical microscope system was used to measure the penetration shape accurately. Table 5 shows the welding cross-section and penetration measurement results taken with a 10× optical microscope. experimental variables, levels of the input variables, and the experimental conditions for a total of 18 trials, respectively.

Penetration Geometry
The BOP fiber laser welding of 9% Ni steel, a cryogenic steel, was performed correctly according to the welding process parameters. Based on the result of the experiment, it was confirmed that good penetration was formed in general, and there were no pores or defects in appearance. To properly represent the cross-sectional appearance of a specimen, a 90% ethanol plus 10% nitric solution was mixed and used to etch the cross-section. An optical microscope system was used to measure the penetration shape accurately. Table 5 shows the welding cross-section and penetration measurement results taken with a 10× optical microscope.

Weld Joint Hardness
A hardness test was performed to confirm the phenomenon of weld joint hardening caused by the change of internal strength and structure due to the difference in energy density of a laser keyhole when the fiber laser weld joint was solidified. For the hardness

Weld Joint Hardness
A hardness test was performed to confirm the phenomenon of weld joint hardening caused by the change of internal strength and structure due to the difference in energy density of a laser keyhole when the fiber laser weld joint was solidified. For the hardness test, the Vickers hardness test was performed on the upper and lower parts and the heataffected zone, where the change in internal strength occurs. The load used in the hardness test was 0.5 N and analysis was performed at 0.83 mm intervals so as not to affect the nearby hardness. The 6-point positions for measuring the hardness of the HAZ were used as the left and right positions divided into thirds between each boundary of the penetration, the HAZ, and the base material. The 243 HV value shown in Table 2 was used as the reference base material data to determine the hardness of the fiber laser welding. Figure 4 shows a schematic diagram of the hardness test for the weld joint of 9% Ni steel. Table 6 shows the results of the hardness test of the upper and lower parts of a weld joint and the heat-affected zone. The hardness test result means the average value measured at 5 points. The hardness (lower part) of a fiber laser weld joint has a value between 339.4 HV and 358.1 HV, which is higher than the 243 HV hardness that is standard for 9% Ni steel. Therefore, it is judged that sufficient weldability was obtained.

Weld Joint Hardness
A hardness test was performed to confirm the phenomenon of weld joint hardening caused by the change of internal strength and structure due to the difference in energy density of a laser keyhole when the fiber laser weld joint was solidified. For the hardness test, the Vickers hardness test was performed on the upper and lower parts and the heataffected zone, where the change in internal strength occurs. The load used in the hardness test was 0.5 N and analysis was performed at 0.83 mm intervals so as not to affect the nearby hardness. The 6-point positions for measuring the hardness of the HAZ were used as the left and right positions divided into thirds between each boundary of the penetration, the HAZ, and the base material. The 243 HV value shown in Table 2 was used as the reference base material data to determine the hardness of the fiber laser welding. Figure  4 shows a schematic diagram of the hardness test for the weld joint of 9% Ni steel. Table  6 shows the results of the hardness test of the upper and lower parts of a weld joint and the heat-affected zone. The hardness test result means the average value measured at 5 points. The hardness (lower part) of a fiber laser weld joint has a value between 339.4 HV and 358.1 HV, which is higher than the 243 HV hardness that is standard for 9% Ni steel. Therefore, it is judged that sufficient weldability was obtained.

Measurement of Weld Joint Dilution Ratio
Since the shape of weld joint penetration in a fiber laser welding process differs according to beam shape and energy density due to the power and defocusing, there is a high possibility of hardening due to changes in the chemical composition and internal strength of the weld joint. In the fiber laser welding process, a special welding process in which a welding wire is not consumed, the dilution ratio can be defined as the area of the upper and lower parts divided by the keyhole and laser diameters. Figure 5 shows a schematic diagram of the method used to calculate the weld joint dilution ratio of a fiber laser welding process, and Figure 6 shows a picture of the calculation of a weld joint dilution ratio using the area analysis tool in a system using an optical microscope. Table 7 shows the dilution ratio of the weld joint area according to the fiber laser welding process parameters. tals 2021, 11, x FOR PEER REVIEW ratio using the area analysis tool in a system using an optical microscope. Ta the dilution ratio of the weld joint area according to the fiber laser welding rameters.

Weld Joint Hardening according to Dilution Ratio
In 9% Ni steel, a higher dilution ratio of the base material causes a lower strength. Therefore, excessive dilution of a base material should be avoided to secure the required strength. Although the prior studies on the relationship between dilution ratio and strength have found that the tensile strength does not change significantly even when there is a 10-20% change in dilution ratio, it was reported that it may be lower than the API standard of 363 MPa due to the hardening of the weld joint if the dilution ratio is 25% or more [15,16]. In addition, even under different welding conditions, the level of hardening of the heat-affected zones is similar when the amount of heat input is the same. However, the electromagnetic force and the energy density of the beam are different, so the effect on bead formation is different. This leads to the disadvantage of the increased hardness of a weld joint compared to the heat-affected zone. To address the shortcomings of

Weld Joint Hardening according to Dilution Ratio
In 9% Ni steel, a higher dilution ratio of the base material causes a lower strength. Therefore, excessive dilution of a base material should be avoided to secure the required strength. Although the prior studies on the relationship between dilution ratio and strength have found that the tensile strength does not change significantly even when there is a 10-20% change in dilution ratio, it was reported that it may be lower than the API standard of 363 MPa due to the hardening of the weld joint if the dilution ratio is 25% or more [15,16]. In addition, even under different welding conditions, the level of hardening of the heat-affected zones is similar when the amount of heat input is the same. However, the electromagnetic force and the energy density of the beam are different, so the effect on bead formation is different. This leads to the disadvantage of the increased hardness of a weld joint compared to the heat-affected zone. To address the shortcomings of prior studies that established the characteristics of a welding process limited to the bead shape as described above, the correlation between the concepts of dilution and the strength of the weld joint was established.
Since the shape of the weld penetration in the fiber laser welding process differs from the beam shape and energy density due to the laser power and defocusing, the possibility of hardening due to changes in the chemical composition and proof strength of the weld is very high. Therefore, although it is different from the method of calculating the area of the welded part analyzed in the general flux-cored arc welding process, the characteristics of the welded part that are changed by the welding current, arc voltage, welding wire, etc. are considered similarly to those of fiber laser welding. Therefore, in this study, the dilution rate was defined as the upper and lower division areas by the keyhole and the laser diameter by confirming that it is possible to analyze the strength reduction characteristics for the dilution rate even in fiber laser welding.
Therefore, in this section, the dilution ratio formed in a weld joint is calculated for each welding process and process variable and a standard for the generation of a weld joint hardness compared to the heat-affected zone is established. According to the calculated dilution ratio, to set up a stable weld joint dilution ratio standard.
To analyze the correlation of hardness based on a dilution ratio that changes according to the penetration shape, a standard for hardening or scattering of the lower weld joint compared to the heat-affected zone was established. The difference and trend between the measured hardness of the heat-affected zone and the hardness of the lower weld joint were used to establish a standard dilution ratio that can avoid the hardening of a weld joint, as shown in Figure 7. As a result, the degree of hardness (difference between the hardness of the heat-affected zone and the hardness of the lower weld joint) of a fiber laser weld joint was found to be between 26.2 HV and 38.0 HV, and the difference in hardness of a weld joint was confirmed to be 26.2 HV or lower compared to the heat-affected zone when the dilution ratio of penetration was determined to be 17.7% or more. It was confirmed that the difference in hardness compared to the heat affected zone did not rise as the dilution ratio was increased. It is judged that this kind of hardening of a weld joint will make it difficult to secure quality against the brittle effect and durability.
are considered similarly to those of fiber laser welding. Therefore, in this study, the dilution rate was defined as the upper and lower division areas by the keyhole and the laser diameter by confirming that it is possible to analyze the strength reduction characteristics for the dilution rate even in fiber laser welding. Therefore, in this section, the dilution ratio formed in a weld joint is calculated for each welding process and process variable and a standard for the generation of a weld joint hardness compared to the heat-affected zone is established. According to the calculated dilution ratio, to set up a stable weld joint dilution ratio standard.
To analyze the correlation of hardness based on a dilution ratio that changes according to the penetration shape, a standard for hardening or scattering of the lower weld joint compared to the heat-affected zone was established. The difference and trend between the measured hardness of the heat-affected zone and the hardness of the lower weld joint were used to establish a standard dilution ratio that can avoid the hardening of a weld joint, as shown in Figure 7. As a result, the degree of hardness (difference between the hardness of the heat-affected zone and the hardness of the lower weld joint) of a fiber laser weld joint was found to be between 26.2 HV and 38.0 HV, and the difference in hardness of a weld joint was confirmed to be 26.2 HV or lower compared to the heat-affected zone when the dilution ratio of penetration was determined to be 17.7% or more. It was confirmed that the difference in hardness compared to the heat affected zone did not rise as the dilution ratio was increased. It is judged that this kind of hardening of a weld joint will make it difficult to secure quality against the brittle effect and durability. The standard 17.7% dilution ratio confirmed above is a standardized score, and can be used as an evaluation index for the process. When a high score is calculated, it means that a hardened structure of a weld joint was created. Therefore, the criteria for determining the hardening of a weld joint can be defined as shown in Table 8. These standardized The standard 17.7% dilution ratio confirmed above is a standardized score, and can be used as an evaluation index for the process. When a high score is calculated, it means that a hardened structure of a weld joint was created. Therefore, the criteria for determining the hardening of a weld joint can be defined as shown in Table 8. These standardized scores can be later applied as learning data to determine the increase in weld joint hardness and brittleness according to the penetration shape and dilution ratio, in part to prevent the generation of a hardened structure and deterioration of weld joint strength due to energy density of a 9% Ni steel weld joint in which this welding process was applied.

Discriminant Analysis
The system to determine the weld joint hardening in the fiber laser welding process of 9% Ni steel is a technique used to determine the affiliation of the input data by making a model using the collected data and entering it into developed group learning data [18][19][20].
For the weld joint hardening system developed in this study, a discriminant model was developed using the SVM (support vector machine) technique. Unlike neural networks, SVM is not a principle of minimizing the existing empirical risk, but an approximate implementation that minimizes the structural risk. It is difficult to generalize and it is easy to overfit the model to minimize the empirical risk used in the existing artificial neural network. On the other hand, SVM minimizes the upper limit of the expected risk by minimizing the structural risk, unlike minimizing the empirical risk that minimizes the error on the training data. In other words, the method of minimizing structural risk is based on a test error term whose range is determined by the sum of learning error ratios and a term dependent on the VC-dimension of the learning machine. By minimizing the sum of these two terms, it is possible to obtain better classification performance than the conventional pattern discriminant. In the problem of finding the hyperplane that maximizes margin in the two classes, where linear discrimination is possible based on the VC (Vapnik-Chervonenkis) theory and Equation (1), this study tried to determine the possibility of hardening of a weld joint in process [21].
where w is the weight vector, x is the input vector, and b is the reference value, and the SVM technique described above sequentially performs minimization of complex calculations in the QP (quadratic programming) process. The variables for learning in the weld joint hardening discrimination model are welding process variables (laser power, defocusing, welding speed), penetration shape (penetration width, penetration depth), upper and bottom hardness, heat affected zone hardness (HAZ hardness) and the dilution ratio. One hundred and eighty data points were entered with 10 multiple variables. For the groups to determine the hardening of a weld joint, the Regard Group was defined as 1 and the Regardless Group was defined as 0, to confirm the discrimination performance predicted by the SVM technique. Table 9 shows the learning data to discriminate the hardening of a weld joint and Table 10 and Figure 8 quantitatively show the group discrimination performance predicted by the data learned through the SVM technique.    Table 9 shows the learning data to discriminate the hardening of a weld joint and Table 10 and Figure 8 quantitatively show the group discrimination performance predicted by the data learned through the SVM technique.

Development of Mathematical Model Welding Factors
The response surface analysis method was used for analysis, as in the previous research [7]. The functional relationship between the input variables x 1 , x 2 , x 3 , · · · x k and the output variable y is expressed by Equation (2). Considering the predictive ability of linear and nonlinear models, Equation (3) is expressed as a second order regression model if it is assumed the predicted value of the output variable, i.e., the welding factor, has a linear relationship with an input variable.
Equation (3) can be arranged as Equation (4) by the least squares method: In this study, Equation (4) can be expanded as Equation (5) since the number of input variables is 3; that is, k = 3 .
To obtain relevant data through experiments, numerous trials and errors and economic losses may occur. To reduce such losses, a full factorial design was applied among the response surface analysis methods of the DOE method that well reflects the second order regression model, and the coefficients of each term were calculated using MINITAB.
The mathematical prediction models of penetration width, penetration depth, upper and bottom hardness, HAZ hardness and the dilution ratio developed using regression coefficients and Equation (5), can be expressed using Equations (6)-(11): To check the predictive ability of the developed mathematical prediction model, the graph showing the error range by comparing the average values of the measured welding factors for each experimental condition with the predicted welding factors, is shown in Figure 9. As shown in Table 11, the prediction model error range showed reliable results in general.
To check the predictive ability of the developed mathematical prediction model, the graph showing the error range by comparing the average values of the measured welding factors for each experimental condition with the predicted welding factors, is shown in Figure 9. As shown in Table 11, the prediction model error range showed reliable results in general.
In addition, the ANOVA (analysis of variable) results of the predictive model confirmed a high coefficient of determination of 96.3% at the maximum penetration depth and a minimum coefficient of determination of 71.1% at the upper hardness of the weld joint. This means that it is possible to make predictions using the coefficient of determination for the entire variation of welding factors and the interaction, when the independent influence of input variables affecting the regression model are simultaneously considered.

Optimization for the Welding Process of 9% Ni Steel
The MOO (multi-objective optimization) algorithm that was used in this study is a technique used to search for non-dominant solutions by mimicking the evolutionary process of an organism in an optimization problem with multiple objectives. This algorithm was used as in the previous research [7].
First of all, based on the mathematical definition of Pareto Domination as in Equation (12), the Pareto optimal set , and a set of non-dominant solutions , were created in a destination space. Genes belonging to the Pareto optimal set -that is, decision vectors-are randomly generated in as large a quantity as the number of populations in the decision space. A cluster with a high degree of non-dominance and the best fit is generated to calculate the crowding distance and an optimal solution set with a high cluster distance is judged to have more variety of solutions, at which point a multi-purpose optimal solution is derived [22][23][24]: In general, the multipurpose optimization problem can be described as a vector function ( ) that maps m parameters to n objectives. Here, is a decision vector, is a parameter space, is an objective vector, and is an objective space. Decision vector a is said to dominate decision vector . Also, it is written as < ( dominates ). Also, for an arbitrary decision vector , if no vector in the subset of the decision vectors dominates , it is said that the decision vector is non-dominated by . Based on the above theorem, the program schematic diagram of the MOO optimization method is shown in Figure 10 and MATLAB, a commercial numerical analysis program, was used to apply and modify the optimization method. To optimize the welding process variables when the hardening of a weld joint has occurred, the same 180 data in Table 9 and the variables and levels to drive the MOO optimization technique are shown in Table 12.  In addition, the ANOVA (analysis of variable) results of the predictive model confirmed a high coefficient of determination of 96.3% at the maximum penetration depth and a minimum coefficient of determination of 71.1% at the upper hardness of the weld joint. This means that it is possible to make predictions using the coefficient of determination for the entire variation of welding factors and the interaction, when the independent influence of input variables affecting the regression model are simultaneously considered.

Optimization for the Welding Process of 9% Ni Steel
The MOO (multi-objective optimization) algorithm that was used in this study is a technique used to search for non-dominant solutions by mimicking the evolutionary process of an organism in an optimization problem with multiple objectives. This algorithm was used as in the previous research [7].
First of all, based on the mathematical definition of Pareto Domination as in Equation (12), the Pareto optimal set P 0 , and a set of non-dominant solutions x i , were created in a destination space. Genes belonging to the Pareto optimal set P 0 -that is, decision vectorsare randomly generated in as large a quantity as the number of populations in the decision space. A cluster with a high degree of non-dominance and the best fit is generated to calculate the crowding distance and an optimal solution set with a high cluster distance is judged to have more variety of solutions, at which point a multi-purpose optimal solution is derived [22][23][24]: In general, the multipurpose optimization problem can be described as a vector function f (x) that maps m parameters to n objectives. Here, x is a decision vector, X is a parameter space, y is an objective vector, and Y is an objective space. Decision vector a is said to dominate decision vector b. Also, it is written as a < b (a dominates b). Also, for an arbitrary decision vector a, if no vector in the subset X of the decision vectors dominates a, it is said that the decision vector a is non-dominated by X. Based on the above theorem, the program schematic diagram of the MOO optimization method is shown in Figure 10 and MATLAB, a commercial numerical analysis program, was used to apply and modify the optimization method. To optimize the welding process variables when the hardening of a weld joint has occurred, the same 180 data in Table 9 and the variables and levels to drive the MOO optimization technique are shown in Table 12.  In the MOO technique, a range of fiber laser welding process parameters was chosen from the minimum [3 kW, −0.5 mm, 0.5 m/min] to the maximum [5 kW, +0.5 mm, 0.8 m/min]. The purpose of this study was to analyze a multi-purpose optimization problem that considers weld joint hardness as a criterion to evaluate the quality deterioration characteristics of a weld joint in 9% Ni steel. Therefore, Equations (13)-(15) represent the objective function ( ) of an arbitrary system having as a variable and the constraints and ranges required to optimize this function [25].
< 17.7 Test numbers 4 and 14 were selected to follow the MOO algorithm and Table 13 shows the welding process variables, expected welding factors, and discrimination results that were modified to satisfy the constraints according to the optimization procedure.  In the MOO technique, a range of fiber laser welding process parameters was chosen from the minimum [3 kW, −0.5 mm, 0.5 m/min] to the maximum [5 kW, +0.5 mm, 0.8 m/min]. The purpose of this study was to analyze a multi-purpose optimization problem that considers weld joint hardness as a criterion to evaluate the quality deterioration characteristics of a weld joint in 9% Ni steel. Therefore, Equations (13)- (15) represent the objective function f (x) of an arbitrary system having x as a variable and the constraints and ranges required to optimize this function [25].
Optimize f (L, D, S) (13) g(L, D, S) Test numbers 4 and 14 were selected to follow the MOO algorithm and Table 13 shows the welding process variables, expected welding factors, and discrimination results that were modified to satisfy the constraints according to the optimization procedure. The possibility of hardening of a weld joint and the effectiveness of optimizing the welding process for 9% Ni steel was confirmed by performing a comparative analysis with the hardening of a weld joint caused by the existing input variables, as seen in Figure 11. The X-axis represents the difference in hardness values between the HAZ and the bottom, and the Y-axis represents the dilution ratio. This graph was constructed to compare and examine whether the hardness of the bottom was close (∆HV = HV HAZ − HV bottom) to the hardness of the HAZ with the dilution ratio. Finally, it was confirmed that the two raw data points selected in the fiber laser welding process, satisfied the dilution ratio of 17.7% or less, which is the limiting condition for the hardening of a weld joint, and the quality degradation characteristics appearing in the previous process variables were resolved by the modified process variables.   The possibility of hardening of a weld joint and the effectiveness of optimizing the welding process for 9% Ni steel was confirmed by performing a comparative analysis with the hardening of a weld joint caused by the existing input variables, as seen in Figure 11. The X-axis represents the difference in hardness values between the HAZ and the bottom, and the Y-axis represents the dilution ratio. This graph was constructed to compare and examine whether the hardness of the bottom was close (ΔHV = HV HAZ − HV bottom) to the hardness of the HAZ with the dilution ratio. Finally, it was confirmed that the two raw data points selected in the fiber laser welding process, satisfied the dilution ratio of 17.7% or less, which is the limiting condition for the hardening of a weld joint, and the quality degradation characteristics appearing in the previous process variables were resolved by the modified process variables.

Conclusions
This study tried to optimize the welding process for 9% Ni steel, which is predominantly used in the LNG storage tank industry. After establishing the criteria for the hardening of a weld joint in the process, conducting learning in the discriminant function, and optimizing the process variables for hardening of a weld joint using the discriminant group, these conclusions were obtained: (1) The appropriate weldability of a weld joint was confirmed by measuring the penetration shape, mechanical strength, penetration area, etc. of a weld joint derived from the fiber laser welding test. It was found that the hardening of a weld joint depends on the energy density applied to the weld joint and the ratio of an area mixed with foreign substances after melting. In addition, when the weld joint hardening index is 17.7% or more, the group that needs to consider quality deterioration for weld joint hardening is classified. Thus, quality deterioration characteristics, according to the dilution ratio, were established. Figure 11. Weld joint hardening distributions using modified input parameters.

Conclusions
This study tried to optimize the welding process for 9% Ni steel, which is predominantly used in the LNG storage tank industry. After establishing the criteria for the hardening of a weld joint in the process, conducting learning in the discriminant function, and optimizing the process variables for hardening of a weld joint using the discriminant group, these conclusions were obtained: (1) The appropriate weldability of a weld joint was confirmed by measuring the penetration shape, mechanical strength, penetration area, etc. of a weld joint derived from the fiber laser welding test. It was found that the hardening of a weld joint depends on the energy density applied to the weld joint and the ratio of an area mixed with foreign substances after melting. In addition, when the weld joint hardening index is 17.7% or more, the group that needs to consider quality deterioration for weld joint hardening is classified. Thus, quality deterioration characteristics, according to the dilution ratio, were established. (2) To determine the weld joint hardening phenomena of 9% Ni steel caused by welding process variables, the quality deterioration characteristics were learned in the SVM technique and it was determined whether the group with quality deterioration could be accurately identified. As a result, it was confirmed that a group with the hardening of a weld joint was predicted 100% repeatedly. This result was used as a procedure to determine the deterioration of weld joint quality. (3) A response surface method mathematical prediction model was developed to apply an objective function to optimize the welding process variables where quality deterioration occurs. By entering the raw data of weld joint hardening into the optimization algorithm created by the objective function and constraint conditions, the quality degradation characteristics contained in the process variables were supplemented. (4) The predicted welding factors were calculated by entering the input variables supplemented for their quality degradation characteristics into the response surface mathematical model. By re-entering the corresponding output variables into the discrimination system, all the raw data where the hardening of a weld joint was expected, showed no quality deterioration. Funding: This study was conducted with the support of the Korea Institute of Industrial Technology as "The dynamic parameter control based smart welding system module development for the complete joint penetration weld (KITECH EH-21-0003)".

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest.