A Study on Predicting Joint Quality Using Self Piercing Riveting Process Signals

Jaehun Kim; Jooyong Cheon; Jongjin Baek; Kiman Bae; Changwook Ji

doi:10.5781/JWJ.2024.42.6.9

Abstract

This study investigates the prediction of joint quality in self-piercing riveting (SPR) using process signals. As the use of lightweight materials such as aluminum and carbon fiber reinforced polymer (CFRP) increases in the automotive industry, ensuring joint integrity has become critical. Two material combinations were analyzed: CFRP with aluminum vibration damping sheets and galvanized steel (SGACEN) with aluminum vibration damping sheets. Force and Displacement signals were monitored during the SPR process, and their correlation with maximum tensile load was evaluated. The results showed that brittle fracture, occurring vertically during the piercing of CFRP, had a significant impact on joint strength, while the gap between the rivet head and the sheet played a crucial role in determining joint strength in SGACEN-based joints. Various regression models were developed to predict joint quality, and machine learning models such as Randomforest and XGBoost were found to be more suitable than linear regression for use in different material combinations. Both the XGBoost and Randomforest models demonstrated similar accuracy in predicting joint performance, proving their reliability as real-time monitoring solutions for SPR joints.

Key words: Self piercing riveting, Aluminum vibration damping sheet, CFRP, Force-displacement curve, Machine learning, Quality prediction

1. Introduction

The automotive industry is currently undergoing a period of change, with environmental regulations and demands for sustainable solutions¹⁾. Strict regulations to reduce greenhouse gas (GHG) emissions, especially carbon dioxide (CO²), are in place, with the European Union, Corporate Average Fuel Economy (CAFE) standards in the United States, and policies aimed at carbon neutrality by 2050 in various countries, including Japan and China²⁾. These regulations are aimed not only at reducing emissions during vehicle operation, but also at reducing emissions throughout the production, use, and disposal of vehicles. In response to these regulations, the automotive industry is focusing on the development of vehicles with environmentally friendly power systems, such as electric vehicles (EVs), hybrid electric vehicles (HEVs), and hydrogen fuel cell vehicles (FCVs), which play an important role in meeting carbon dioxide reduction targets, especially since EVs produce no direct emissions while driving³^,⁴⁾. For environmentally friendly vehicles, body lightweighting is essential for longer range and improved energy efficiency, and since EVs use heavy batteries as their primary power source, overall vehicle weight increases. Lightweighting is therefore a key factor in improving range and battery efficiency, and it also has a positive impact on safety and energy efficiency by improving a vehicle’s acceleration and braking performance⁵^,⁶⁾. A variety of advanced materials are used to lighten the weight of green vehicles, with aluminum being widely used in automotive bodies and components because it is much lighter than traditional steel while still providing sufficient strength. Aluminum is mainly applied to body frames and suspension parts, and its light weight and corrosion resistance make it an essential material for various vehicles. In addition, since electric vehicles do not have internal combustion engines and therefore have low engine noise, the vibration inside the vehicle is prominent, so aluminum vibration damping materials with vibration damping properties are increasingly applied to automotive parts to mitigate vibrations caused by road surface and aerodynamic forces. In addition, Carbon Fiber Reinforced Polymer (CFRP) is mainly used in high-performance vehicles and electric vehicles due to its superior specific strength compared to steel and aluminum, and much research is being conducted to apply it to various parts. As the combination of dissimilar materials such as aluminum, steel, and CFRP increases, conventional fusion joining techniques such as resistance spot welding, seam welding, and projection welding are showing limitations in joining materials with different thermal and physical properties. As a result, mechanical fastening technology is gaining attention as an alternative, and self-piercing riveting (SPR) is a technology that can join dissimilar materials without pre-drilling and heating, and is currently widely used in automotive body assembly⁷^-⁹⁾. It is particularly suitable for body structures using lightweight materials and is advantageous for joining different thicknesses and materials. However, SPR technology has technical limitations depending on the strength and thickness of the material, and in particular, in the case of CFRP, the strength of the joint is greatly affected by the bonding conditions due to fiber fracture caused by piercing during the piercing process. In addition, in the case of aluminum vibration isolation materials, two layers of plates are bonded with a viscoelastic adhesive polymer, making it more difficult to secure bond strength than aluminum plates of the same thickness¹⁰⁾. Lightweight materials are made of various types of materials and manufacturing processes, and when joining dissimilar materials, it is key to ensure sound joint quality and evaluate the quality of the joint due to the different characteristics of the materials. Currently, on the shop floor, to evaluate the characteristics of the joint, the joint is removed from the part and subjected to destructive tests such as joint cross-sectional inspection, peel test, and tensile test to evaluate the quality of the joint. These evaluation methods are difficult to respond to immediately on the shop floor, so there is a need for a method that can judge quality in real time on site. Recently, with the development of Al and Internet of Things (loT) technologies, quality assurance in production lines has become an important research topic, The technology to control various process variables and monitor various signals such as pressure force, displacement, acoustic emission, and ultrasound generated in the process to determine quality has become an important research topic¹¹^-¹³⁾. Kam¹⁴⁾ et al. evaluated the mechanical fastening properties of ultra-high strength steel plate and aluminum vibration isolation plate, and C. Shao¹⁵⁾ et al. studied the low frequency vibration-assisted self piercing riveting (LV-SPR) technology that utilizes the vibration effect to soften the metal at room temperature and reduce the interfacial friction in order to prevent CFRP fracture during rivet piercing due to the brittleness of CFRP material in the combination of CFRP and ultra-high strength steel plate. In addition, R. Haque¹⁶⁾ et al. categorized the SPR process into three stages: sheet bending, piercing, and flaring using real time force and displacement signals obtained in real time through SPR process monitoring, H. Zhao¹⁷⁾ et al. implemented the SPR process in simulation and used it to predict the rivet joint quality. However, due to the different process characteristics of various material combinations depending on the application of new materials, there is a lack of research on the analysis of bonding characteristics for each material combination, in particular, in the case of CFRP, which has high strength but brittleness, and vibration isolation plates, which are sandwich structures formed using adhesives, there is a lack of consideration of bonding characteristics because each material has its own characteristics. In addition, various machine learning and deep learning models are being developed, it is necessary to consider process monitoring signals to make quality judgments using them and research to secure quality prediction accuracy.

Therefore, in order to develop a real-time quality monitoring and prediction system for the SPR bonding process of dissimilar materials, this study compared the bonding characteristics under different pressing force conditions during the SPR bonding of dissimilar material combination steel/aluminum zinc and CFRP/aluminum zinc materials, the correlation between the bonding characteristics and process monitoring signals was analyzed using the press force and displacement monitoring data collected under each condition. We also proposed a method to predict splicing quality using regression and deep learning models and validated the model.

2. Experiment Method

In this study, aluminum vibration isolation plate, galvanized steel plate (SGACEN), and carbon fiber reinforced plastic (CFRP) were used, the mechanical properties and thickness of each plate are shown in Table 1. The aluminum vibration isolation plate consists of two 0.9 mm thick sheets of Al5052-O bonded by viscoelastic adhesive, the CFRP utilizes 1 ply of Woven prepreg on the outer surface, the remainder is laminated with 8 ply UD prepregs arranged in orthogonal directions. For the experimental material combinations, CFRP, which has high brittleness, and SGACEN, which is difficult to use as a bottom plate due to its thin thickness, were selected as the top plate, and two combinations were selected as CFRP/aluminum vibration isolation plate and SGACEN/aluminum vibration isolation plate. For each combination, the basic specifications of the die and rivet were kept the same, but the rivet length was adjusted according to the sheet thickness, and the press force condition was set according to the mechanical properties of the material, which are shown in Table 2. The die used in the experiment is a DZ type with a 2 mm high protrusion (Pip) at the center, as shown in Fig. 1, which is designed to be 0.25 mm higher than the die body. The rivets have a head diameter of 7.8 mm and a rivet diameter of 5.3 mm with Almac coating and a hardness of approximately 450- 510 HV. The experimental equipment used was a Rivset hydraulic SPR machine from Bollhoff. It is capable of pressurizing up to 78 kN and can monitor pressurization forces and displacements in real time. The joint quality prediction in this study is based on the maximum tensile load, which is the most important factor in determining the quality of the SPR process, to evaluate the joint quality under different pressurization conditions, for each material combination, experiments were conducted by increasing the pressurization force in six steps of 5 kN from the lower limit condition considering interlock formation, minimum thickness of the remaining bottom plate, rivet head height, etc. The specimens for measuring the maximum tensile load were made in three replicates for each condition, and the specimens were made according to KS B ISO14273 as shown in Fig. 2. In addition, to evaluate the quality of the joints according to the joint combination and pressurization force conditions, the joints were cut and various dimensions such as interlock and head height were measured under an optical microscope, and defects such as cracks and buckling of the joints were observed. The measurement basis of the joint cross-sectional dimension is based on the interlock because the Al vibration damping plate is applied to the lower plate, the interlock distance was measured by assuming that the entire Al vibration damping plate with two sheets bonded by adhesive is a single sheet. The head height was measured as the degree of protrusion or depression of the rivet head relative to the upper sheet, and the Bottom Thickness was measured as the thickness of the thinnest part of the bottom sheet. To develop a quality assessment algorithm, Pearson correlation coefficient (R) was used to analyze the correlation between the maximum tensile load and the Force and Displacement signals,and based on this, independent variables were selected, and a quality prediction regression equation was derived through regression analysis. Furthermore, to more accurately model complex non-linear relationships, the study applied machine learning algorithms such as Random Forest and XGBoost, which perform ensemble learning by generating multiple decision trees.

Table 1

Mechanical properties and thickness of the material

Material	Thickness	Ultimate tensile strength (MPa)
Al vibration damping sheet - Al5052 O	1.81 mm	188
SGACEN	0.7 mm	270
CFRP	1.8 mm	0° : 982 90° :860

Table 2

Joining parameters for different material combinations

Combination	Upper sheet	Bottom sheet	Joining condition
Combination	Upper sheet	Bottom sheet	Die	Rivet	Force (kN)
I	CFRP	Vibration damping sheet - Al5052 O	DZ type	C type (Rivet length : 6 mm)	30 ~ 55
II	SGACEN	Vibration damping sheet - Al5052 O	DZ type	C type (Rivet length : 5 mm)	35 ~ 60

Fig. 1

Geometry and sizes of the rivet and die(dimensions in mm)

Fig. 2

Shape and dimensions of the Self piercing riveting specimen

3. Result and Discussion

3.1 Comparison of SPR Process Joining Characteristics According to Material Combinations

The joining characteristics of two different material combinations for the SPR process were analyzed. Fig. 3 is a graph of the maximum tensile load as the joining pressure increases. For combination 1, the maximum tensile load was found to be between approximately 2600 N and 2900 N. As the joining pressure increased, the maximum tensile load also increased, but at joining pressures above 40 kN, the maximum tensile load converged to about 2900 N. This means that further increasing the joining pressure does not significantly improve the maximum tensile load of the joint. The standard deviation of the maximum tensile load at each joining pressure condition was on average 51.993 N at 35 kN and 102.87 N at 40-55 kN, showing about a twofold difference and this is thought to be due to the change in fracture mode as the joining pressure increased. Analysis of the fracture modes showed that at 30 kN joining pressure, rivet pullout was the main fracture mode, and at 35 kN, mostly rivet pullout occurred with some bearing failure observed¹⁸⁾. At joining pressures of 40 kN and above, bearing failure became the main fracture mode, indicating improved rivet retention and material interaction at higher joining pressures. For combination 2, the maximum tensile load ranged from about 2200 N to 2900 N, showing a continuous increase with increasing joining pressure. Particularly at 60 kN joining pressure, there was a sharp increase in maximum tensile load, indicating significant improvement in joint strength at high joining pressures. In this case, the standard deviation of the maximum tensile load ranged from 15.18 N to 67.92 N, with an average of 35.55 N, showing more consistent maximum tensile load performance compared to combination 1. At both 35 kN and 60 kN joining pressures, upper sheet tearing occurred, indicating that the joint failure mechanism is dominated by the properties of the upper sheet material. Also, as the joining pressure increased, the rivet legs became more firmly fixed in the bottom sheet, reducing the possibility of rivet pullout and demonstrating superior mechanical bonding at higher joining pressures. Combination 1 showed a rapid convergence of the maximum tensile load and bearing fracture as the dominant failure mode at high joint pressures, while combination 2 showed a continuous trend of increasing maximum tensile load with increasing joint pressures, but with different degrees of top plate tearing. To analyze the cross-section of the joint, the center of the joint was cut and polished with a precision cutter and observed under an optical microscope. The results are shown in Fig. 4, which compares the characteristics of combination 1 and combination 2 at each bond pressure condition. For combination 1, the rivet head height tended to decrease with increasing joint pressurization force, with the rivet head height changing from +0.55 mm at 30 kN to -0.25 mm at 55 kN. This means that the rivet penetrates deeper into the material as the joining pressure increases. The interlock value increased with increasing joint pressure, from 0.32 mm to 0.47 mm on average from side to side. Also, the residual thickness of the bottom plate is similar for all conditions, showing that the deformation is concentrated around the rivets and top plate. The cross-sectional defects show that at 30 kN and 45 kN, CFRP fiber fracture occurred in the shoulder region where the rivet head meets the top plate, and at 55 kN, fiber fracture was observed not only in the shoulder region but also in the vertical direction from the center of the plate¹⁹⁾. At 55 kN of joint pressure, buckling of the rivet legs occurred, causing the rivet to lose balance and become unstable. The reason for the higher interlock value of 55 kN than that of 45 kN, which showed the highest tensile load, is considered to be due to the increased fracture of the CFRP fiber as the joint pressure increases and the change in failure mode due to the buckling of the rivet. For combination 2, the rivet head height also decreased with increasing joint compression force, from +0.14 mm at 35 kN to -0.33 mm at 60 kN. This indicates that the penetration of the rivet improved with increasing joint pressure, similar to combination 1. The interlock values were higher compared to Combination 1, ranging from 0.82 mm to 0.98 mm on average from side to side, and tended to increase steadily with increasing joint pressure. This means that combination 2 forms a stronger mechanical bond in the lower plate than combination 1. The residual thickness of the bottom plate was similar for all joining pressure conditions, indicating that the deformation occurred mainly around the rivets in the top plate²⁰⁾. The largest gap between the rivet head and the top plate was observed at the relatively low joining pressure condition of 40 KN, and gradually decreased with increasing joining pressure until it was not observed at 60 kN. This shows that the joint is optimally formed at 60 kN. After measuring the maximum tensile load, the fracture surface was observed under an optical microscope to analyze the fracture mechanism, and the results are shown in Fig. 5. For combination 1, at joint pressures of 30 kN to 35 kN, the shear stress caused the bottom plate to bend, resulting in a rivet pull-out failure mode, where the rivet leg pulls out of the bottom plate. This is believed to be due to insufficient interlocking between the bottom plate and the rivet, which failed to withstand the shear load and caused the rivet to separate. Increasing the joint pressurization force above 40 kN caused bearing failure, and the interlock increased with increasing joint pressurization force, resulting in the largest bending deformation of the bottom plate at 45 kN, where the maximum tensile load was observed Under conditions above 50 kN, not only cracks in the shoulders of the top plate, CFRP, but also cracks running vertically inside the plate reduced the clamping force, making it easier for the bearing failure of the top plate to occur²¹⁾. In particular, at 55 kN, buckling of the rivet legs occurred, and the left-right balance of the rivets was not consistent, which is considered to be a factor that reduced the strength of the joint. In combination 2, the tearing by ductile fracture of the upper plate gradually increased as the joint pressurization force increased, while the rivet leg dislodging phenomenon decreased as the lower plate bent. This means that the higher the bonding pressure, the stronger the mechanical bond with the top plate. The degree to which the rivet is holding the top plate together is stronger as the joint pressure increases, as can be seen from the cross-sectional observations, because the gap between the rivet head and the top plate decreases as the joint pressure increases. In particular, at 60 kN, the gap between the rivet and the top sheet was completely eliminated, optimizing the joint, which resulted in almost no rivet pull-out. In conclusion, it was found that the mechanism by which the top plate is pierced and interlocked to the bottom plate is different depending on the properties of the top plate, which significantly affects the mechanical properties and failure mode of the joint. Since the characteristics of the joint vary depending on the material combination, quality judgment and prediction techniques in the SPR process require analysis from various perspectives. In the next chapter, the SPR process mechanism is considered by comparing the curves of pressure and displacement monitored in real time.

Fig. 3

Effect of joining force on maximum tensile load in self-piercing riveted joints : (a) Combination Ⅰ, (b) Combination Ⅱ

Fig. 4

Cross-section of SPR joint under different joining force (a) : Combination 1, (b) : Combination 2

Fig 5

Failure Modes of SPR Joints in lap-shear testing for dissimilar material combinations: (a) : Combination 1, (b) : Combination 2

3.2 Analysis of SPR Process Real-time Monitoring Data and Correlation with Maximum Tensile Load

Fig. 6 shows the Force-Displacement graphs according to the joining pressure for each material combination. In the SPR process, Force and Displacement signals are broadly divided into three stages: bending, where the rivet first contacts the upper sheet and begins to deform; piercing, where the rivet penetrates the upper sheet and reaches the lower sheet; and flaring, where the rivet legs expand to form a mechanical joint¹⁶⁾. These monitoring signals can be used to detect abnormal conditions occurring during the process. Abnormal patterns appear in the Force-Displacement curve when the rivet fails to properly penetrate the upper plate or properly join with the lower plate. Additionally, the shape of the curve varies depending on joining conditions, material properties, and combinations, which can be analyzed to evaluate joining quality²²^,²³⁾. Examining the Force-Displacement graph of combination 1 in Fig. 6(a), as the joining pressure condition increases, there is no clear trend in the behavior of the pressure curve in the section where the upper sheet is pierced, and the piercing section and rivet flaring section are not clearly distinguished. This is thought to be due to brittle fracture occurring due to the high strength and low ductility of CFRP, resulting in non-uniform piercing. In Fig. 6(b), which shows the Force-Displacement graph of combination 2, the pressure increases similarly in all conditions as displacement increases in the section where the upper sheet is pierced. This is because the upper sheet, SGACEN, has low tensile strength and high ductility, resulting in ductile fracture and uniform deformation of the upper sheet during this process. Therefore, the piercing section and rivet flaring section are clearly distinguished, and the pressure increases rapidly in the rivet flaring section. This trend shows that the mechanical fastening process of the joint is more stable than in combination Comparing the Force-Displacement graphs of combination 1 and combination 2 under the same joining pressure condition (40 kN) in Fig. 6(c), the amount of displacement change in the piercing section is similar, but the pressure formed shows a significant difference. The upper sheet of combination 1, CFRP, forms high pressure even at short displacements due to its high strength and low ductility. In contrast, the upper sheet of combination 2, SGACEN, has low strength and high ductility, causing the pressure to increase gradually at larger displacements. After the piercing section, rivet flaring starts earlier in combination 2, and the extent of displacement increase is larger. This indicates that due to the high ductility of SGACEN, the upper sheet deforms more significantly during the rivet flaring process, resulting in a more stable formation of the joint. The results of these analyses show that the mechanical properties of the top plate have a significant impact on the force-displacement behavior, and while CFRP with brittle fracture has no significant effect on rivet flaring, SGACEN with ductile fracture has a positive effect on rivet flaring, which can improve the performance of the joint. Fig. 7 shows the method of selecting factors to analyze the correlation with maximum tensile load using time-dependent graphs of Displacement and Force. As the joining pressure condition increased, the joining process time tended to increase, with the lowest 30 kN condition measuring about 220 ms and the highest 60 kN condition measuring about 238 ms. Since the joining time varies for each condition, the start of the joining time was set to 0% and the end to 100%, and four sections were uniformly divided by 25% to include the piercing and rivet flaring sections. When compared to the Displacement-Force curve, 0~25% represents the section where the rivet touches the sheet surface and the sheet is bent, 25~50% is the section where the rivet pierces the upper sheet, 50~75% is the section where some piercing and rivet flaring occur simultaneously, and 75~100% is the section where rivet flaring is formed. To analyze the impact on maximum tensile load for each section, a total of 24 factors were derived by calculating the average, maximum, and standard deviation for each section. For combination 1, calculations were made from 30 kN to 55 kN, and for combination 2, from 35 kN to 60 kN, with six conditions for each combination calculated in the same way to derive respective values. These factors derived for each section can be used as important information in understanding the correlation with maximum tensile load, and through this, directions for predicting and improving joint quality can be suggested. Table 3 shows the correlation coefficients between the variables of Displacement and Force and the maximum tensile load for material combinations 1 and 2. Analyzing the combined results of the two material combinations through Pearson correlation analysis, no correlation coefficient exceeding an absolute value of 0.5 was found, whether positive or negative. This is thought to be due to the different trends in Force-Displacement graphs observed in material combinations 1 and 2. When each material combination was analyzed separately, the correlation coefficient was high. First, when analyzing only material combination 1, the variable with the highest correlation to the maximum tensile load is X18, which is a standard deviation in the 25-50% range. It can be seen that all variables of displacement and compressive force were higher on average in this section, and that the piercing of the top plate had the greatest impact on the maximum tensile load of the joint. Analyzing only material combination 2, the variables with the highest correlation with the maximum tensile load are X1 and X3: mean value and standard deviation in the 0-25% range. The 0-25% and 75-100% bands, where the correlation values are higher on average, suggest that the initial bending of the rivet against the top sheet and the flaring of the rivet have the greatest impact on the maximum tensile load of the joint. The factors of material combination 2 showed generally higher correlation values than those of material combination 1. This is thought to be due to the linear increase in maximum tensile load with increasing joining pressure in material combination 2, and the small and consistent standard deviation of maximum tensile load.

Fig. 6

Influence of joining force on force-displacement response in self-piercing riveted joints: (a) Combination 1, (b) Combination 2, (c) Comparison under same joining force conditions

Fig 7

Range-based selection of factors for correlation analysis in displacement-force curves (Combination 1 - joining force 40 kN)

Table 3

Correlation coefficients of displacement and force parameters with maximum tensile load for material combinations

Material Combination : I, II
Range(%)	Displacement			Force
Range(%)	AVG	Max	STD	AVG	Max	STD
0~25	X1	X2	X3	X13	X14	X15
0~25	0.232	0.454	0.432	0.075	0.317	0.419
25~50	X4	X5	X6	X16	X17	X18
25~50	0.270	0.178	-0.426	0.395	0.354	0.414
50~75	X7	X8	X9	X19	X20	X21
50~75	0.273	0.286	0.284	0.354	0.378	0.344
75~100	X10	X11	X12	X22	X23	X24
75~100	0.317	0.336	0.452	0.368	0.361	0.287
Material Combination : I
Range(%)	Displacement			Force
Range(%)	AVG	Max	STD	AVG	Max	STD
0~25	X1	X2	X3	X13	X14	X15
0~25	0.641	0.628	0.568	0.677	0.661	0.611
25~50	X4	X5	X6	X16	X17	X18
25~50	0.716	0.742	0.692	0.709	0.733	0.761
50~75	X7	X8	X9	X19	X20	X21
50~75	0.685	0.664	-0.084	0.697	0.684	0.315
75~100	X10	X11	X12	X22	X23	X24
75~100	0.678	0.674	0.526	0.691	0.695	0.743
Material Combination : II
Range(%)	Displacement			Force
Range(%)	AVG	Max	STD	AVG	Max	STD
0~25	X1	X2	X3	X13	X14	X15
0~25	0.976	0.949	0.976	0.921	0.921	0.932
25~50	X4	X5	X6	X16	X17	X18
25~50	0.867	0.848	-0.591	0.868	0.824	0.806
50~75	X7	X8	X9	X19	X20	X21
50~75	0.855	0.861	0.682	0.860	0.894	0.874
75~100	X10	X11	X12	X22	X23	X24
75~100	0.894	0.907	0.906	0.898	0.892	0.875

3.3 Quality Prediction Model Derived from Displacement and Force Signals

Table 4 shows the results of deriving a quality prediction model based on Displacement and Force signals using material combinations. When material combinations 1 and 2 were combined, it was not possible to derive a regression equation due to the low correlation value, so a regression equation was derived for each material combination, and 10 variables with high correlation were used. The backward elimination method was used to remove the variables with the highest P-value one by one, so that only significant variables with a P-value less than 0.1 remained in the model²⁴^,²⁵⁾. First, for Material Combination 1, the variables finally selected were X16 and X17, both of which are based on data from the 0-25% interval. The regression equation using these two variables showed a coefficient of determination (R²) of 0.643, with an adjusted R² value of 7.074. This secures a certain level of reliability for quality prediction, but shows relatively low accuracy compared to other models. Additionally, the Root Mean Square Error (RMSE) was 94.147 N, indicating the prediction error range of the regression equation for quality prediction in material combination 1. For material combination 1, it can be confirmed that the displacement and load changes in the 0-25% interval, where the upper plate is pierced, had the greatest impact on the quality of the joint. On the other hand, for material combination 2, Displacement and Force data from the 0-25% and 75-100% intervals were used to predict the maximum tensile load. The variables that were finally selected were X1, X2, X3, X11, X13, X14, and X22, with a total of seven variables included in the regression, and the resulting coefficient of determination was 0.997, which is a very high correlation. The adjusted R² value was 1.051, indicating that the prediction model’s accuracy is excellent. The Root Mean Square Error was 17.831 N, demonstrating that the model derived from material combination 2 has a relatively low error range. For material combination 2, we can see that the data played an important role not only in the bending region (0-25%), but also in the rivet flaring region (75-100%). Fig. 8 shows the results of using the regression model to predict the maximum tensile load for each material combination. The predicted maximum tensile load values were analyzed by comparing them with actual data obtained through tensile shear tests, and were visualized in graphs based on this. Graph (a) shows the results from regression model 2 for material combination 1, while graph (b) shows the results from regression model 2 for material combination 2. For material combination 1, the prediction results of regression model 2 showed an average error of 69.36 N, with an error rate of about 2.45%. This indicates that the difference between predicted and actual measured values is not relatively large, implying that the model’s performance was appropriately implemented. However, errors may occur in some data, which could be due to nonlinear behavior of the material or subtle differences in measurement environments. In contrast, for material combination 2, regression model 2 showed more precise prediction performance. In this case, the average error was very low at 11.44 N, and the error rate was also very small at 0.47%. These results demonstrate that the prediction model for material combination 2 can more accurately predict the maximum tensile load. The regression model for material combination 2 showed superior performance in that it could more consistently predict load changes according to material characteristic variations. Overall, the results derived through regression model 2 for both material combinations showed good agreement with actual measured values, but the prediction performance of the model was particularly superior for material combination 2. This is believed to be due to the smaller deviation in maximum tensile load and higher data consistency in material combination 2, resulting in better model prediction performance. As the existing method using linear regression equations had limitations in simultaneously explaining both material combinations, this study utilized two machine learning models, Random- Forest and XGBoost, to effectively reflect more complex data interactions for predicting the maximum tensile load of SPR joints²⁶^,²⁷⁾. RandomForest uses a bagging technique to independently train multiple decision trees and combine their results for final prediction, while XGBoost uses a boosting technique to sequentially train multiple decision trees, improving performance by assigning more weight to incorrectly predicted samples from previous trees. Both models were trained using 30 decision trees, with 24 out of 36 total data points used for training and 12 for validation. Looking at the prediction results of the RandomForest model in Fig. 9, the Root Mean Square Error (RMSE) was 95.983 N, the error rate was 2.92%, and the coefficient of determination was 0.855. RandomForest has the advantage of well reflecting interactions between variables and is effective in handling complex nonlinear relationships caused by multiple variables. However, it has the disadvantages of complex model interpretation and potentially slow learning speed due to combining multiple decision trees. On the other hand, the XGBoost model showed slightly lower prediction performance than the RandomForest model, with a Root Mean Square Error of 100.59 N, an error rate of 3.27%, and a coefficient of determination of 0.859. As can be seen from the comparison of the two models, both provide high prediction accuracy and, in particular, were able to integrate the two material combinations into a single model. Both models showed suitable performance for predicting SPR joint quality, with Random- Forest recording slightly higher performance. The importance of variables contributing to the predictions of the two models, RandomForest and XG- Boost, was compared using SHAP (SHapley Additive exPlanations) values and is shown in Fig. 10. While both models are decision tree-based ensemble models, they are trained and predicted differently, so it is valid to utilize SHAP analysis to clearly understand the contribution of each trait. SHAP visualizes how much each feature contributes to the prediction, allowing for a clear understanding of each variable’s influence beyond simple performance evaluation.

Table 4

Regression coefficients and model performance for material combinations

Material Combination : I
Model No.	Value	Entered factors											R²	Adjust R²	Root MSE
Model No.	Value	Constant	X4	X5	X6	X16	X17	X18	X19	X22	X23	X24	R²	Adjust R²	Root MSE
1	Estimate	2780.554	1206.210	-198.686	-2665.090	-0.570	0.627	-0.289	-0.406	0.328	-0.069	-0.911	0.758	5.113	113.407
1	P-value	0.1322	0.5112	0.8951	0.2942	0.4839	0.4992	0.8088	0.2998	0.6452	0.8995	0.5442	0.758	5.113	113.407
2	Estimate	2833.475				-0.209	0.136						0.643	7.074	94.147
2	P-value	<0.0001				0.053	0.028						0.643	7.074	94.147
Material Combination : II
Model No.	Value	Entered factors											R²	Adjust R²	Root MSE
Model No.	Value	Constant	X1	X2	X3	X10	X11	X12	X13	X14	X15	X22	R²	Adjust R²	Root MSE
1	Estimate	-2402.458	5121.072	-1884.299	8318.833	-166.649	-190.518	261.341	0.283	0.454	-0.320	-0.043	0.997	1.045	19.924
1	P-value	0.114	0.002	0.003	0.009	0.849	0.817	0.797	0.484	0.152	0.659	0.007	0.997	1.045	19.924
2	Estimate	-2525.088	4959.821	-1812.435	8450.096		-319.508		0.448	0.288		-0.039	0.997	1.051	17.831
2	P-value	0.045	0.000	< 0.0001	< 0.0001		0.047		0.026	0.002		0.001	0.997	1.051	17.831

Fig. 8

Measured and predicted maximum tensile load by regression models (a) : Combination 1 / Model 2, (b) : Combination 2 / Model 2

Fig. 9

Measured and predicted maximum tensile load by machine learning models : (a) RandomForest Model, (b) XGBoost Model

Fig. 10

Feature importance based on SHAP-value : (a) RandomForest Model, (b) XGBoost Model

First, in the results of the RandomForest model, the variable with the highest SHAP value was X6. This means that the X6 variable played the most important role in the model’s predictions. The next most important variables are X9, X3, X23, and X12, with X6 having a very high SHAP value compared to the other variables, indicating that the RandomForest model is highly dependent on X6. In the XGBoost model, X6 was also identified as the most important variable, with X1, X2, X15, and X4 forming other important variables. The XGBoost model relies heavily on X6 variables, as does RandomForest, and we can see that X6 plays a key role in both models. In the linear regression model, the X6 variable was not significant and was not used, but it emerged as a very important variable in the tree-based model. This is likely because the X6 variable, with standard deviation values in the 25-50% range, has a non-linear pattern, and the tree-based ensemble model effectively learned this complex pattern. Therefore, the X6 variable is judged to play a crucial role in classifying and predicting each material combination.

4. Conclusion

This study analyzed the quality of joints in various material combinations in the SPR process and predicted the mechanical properties and quality of joints using real-time process signals (Force, Displacement). In particular, it compared the CFRP/aluminum damping plate combination and the SGACEN/aluminum damping plate combination, analyzing the joining characteristics and fracture modes of each material combination.

In combination 1, the brittle fracture occurring perpendicular to the CFRP during piercing significantly affected the joint strength, resulting in high variability in the maximum tensile load of the joint. In contrast, for combination 2, the gap between the rivet head and the plate played a crucial role in joint strength, with increasing joining pressure reducing this gap and forming a stable mechanical bond. The analysis of joining characteristics for each material combination confirmed that the mechanical properties of the upper plate significantly influence the joint’s mechanical properties and fracture mode, as the piercing of the upper plate and interlocking with the lower plate occur differently depending on the mechanical characteristics of the upper plate.

Analysis of real-time process signals showed that in combination 1, high pressure occurred at small displacements due to the brittle nature of the upper plate, with an unclear boundary between the piercing and flaring zones. In contrast, combination 2 showed a uniform increase in displacement and pressure due to the ductility of the upper plate, with a clear boundary between the piercing and flaring zones. Correlation analysis revealed no clear correlation when analyzing both combinations simultaneously, but high correlation coefficients were observed when analyzing each material combination separately.

A model was developed to predict joint quality based on Displacement and Force signals. As the correlation with maximum tensile load did not show linearity when using both material combinations, separate regression models were constructed for combinations 1 and 2, both showing high predictive performance. To more accurately model the complex nonlinear relationship, we used tree-based machine learning models such as RandomForest and XGBoost to build a model that could explain both combinations simultaneously, and both models had high predictive performance, and each performed similarly to the results of building a linear regression model. Notably, SHAP analysis confirmed that the standard deviation variable in the 25-50% range played an important role in both models. This is believed to be due to this variable’s non-linear characteristics, effectively classifying the two material combinations in tree-based models.