As mentioned earlier, when Al-Si coated hot stamping material (22MnB5) is heated above the Ac3 temperature, the specific color appears due to the formation of Al2O3 film and diffusion into the Al-Si coating layer of Fe in the material [12, 13]. Figure 4 represents the surface colors of the hot stamping material under various heating conditions ranging from 860 ℃ to 950 ℃ and 180 to 600 seconds by CIE-Lab. It is defined by the International Commission on Illumination (CIE) and consists of three coordinates: *L**, *a**, and *b**. The *L** coordinate represents the lightness of the color, where *L* = 0* represents black and *L* = 100* represents white [21]. The *a** coordinate represents the color's position between red and green, with positive values indicating red and negative values indicating green [20, 21]. The *b** coordinate represents the color's position between yellow and blue, with positive values indicating yellow and negative values indicating blue. The color difference will primarily be explained based on the *a** and *b** coordinates [13, 21]

As shown in Fig. 4, it can be observed that the color of the sheet changes towards reddish as the heating temperature and time increase. To analyze colors, it was generally intended to represent them as 2-dimensional arrays or matrices, with each component representing the point values of the data. The related mathematical expression can be represented as follows: If *X* is a dataset consisting of *p* data points and *q* dimensions; *X* can be represented as a p × q matrix [21].

\(X= \left[\begin{array}{ccc}{x}_{11}& \cdots & {x}_{1q}\\ ⋮& \ddots & ⋮\\ {x}_{p1}& \cdots & {x}_{pq}\end{array}\right]\) Eq. (4)

Each data point *x**{ij}* is represented by a color, and its value is determined by normalization and the color itself. In other words, the value of the data point *x**{ij}* can be normalized using the following formula [18–21]:

\(\widehat{{x}_{i,j} }=\frac{{x}_{ij}-min\left(X\right)}{man\left(X\right)-min\left(X\right)}\)Eq. (5)

Where, *min(X)* represents the minimum value of *X*, *max(X)* represents the maximum value of *X*, and \(\widehat{{x}_{i,j} }\)is the normalized value of *x**{ij}*. Each data point *x**{ij}* can be indicated as the color in the following method [18–21].

\(color\left({x}_{i,j}\right)=C (\widehat{{x}_{i,j})}\) Eq. (6)

The *color(x**i,j**)* represents the color corresponding to *x**{ij}*, and this color representation allows for visualization through data point values [18–21]. The colors resulting from variations in hot stamping heating temperature and time were represented as a CIE-Lab based color map. Figure 5 (a) shows the color changes obtained from experiments conducted at heating times of 180 to 600 seconds and the heating temperature of 950 ℃, represented by the intensity of CIE-Lab. It can be observed that as the heating time increases, the *a** coordinate of CIE-Lab moves from negative to positive values, while the *b** coordinate changes from negative to positive values. The *L** coordinate indicates the distribution of 35 ~ 44. Figure 5 (b) represents the color changes observed in experiments conducted at the heating time of 300 seconds and heating temperatures ranging from 860 to 950 ℃, represented by the intensity of CIE-Lab. It is noticed that the trend with increasing temperature is quite different from that observed with varying heating times. As the temperature increases, the *a** coordinate changes from positive to negative, while the *b** coordinate changes from positive to negative as well. The *L** coordinate is observed to have a distribution of 35 ~ 44. These relationships are expressed using Eq. (6); and each *L*a*b** coordinate is quantified according to the heating temperature and time, as seen in Fig. 6. It is observed that the *L** and *a** coordinates mainly react to changes in the heating temperature, while the *L** and *b** coordinates are mainly affected by changes in the heating time. However, it can be observed that the *a** coordinate is mainly affected by the heating temperature and the *b** coordinate is mainly affected by the heating time when excluding the *L** coordinate, which has a similar variation range obtained from the experimental results.

Based on the color difference by CIE-Lab, the aim was to predict the heating temperature and time, as well as the inter-diffusion layer thickness that affects weldability and hydrogen uptake that affects hydrogen embrittlement, using the color of the part image and the training algorithm.

### 1) Analysis of color difference by hot stamping conditions

To evaluate the surface color of hot stamping sheets, which have undergone the specific manufacturing process, the colorimeter, and the NN model were utilized, and their results were compared. CIE-Lab standard was employed to analyze the color of the hot stamping sheets, resulting in the average NN model and colorimeter results being found to be similar. Based on this, the NN model was used to predict the hot stamping heating conditions of 880 ℃ for 300 seconds for (a), 930 ℃ for 300 seconds for (b), and 960 ℃ for 300 seconds for (c), as represented in Fig. 7. To validate this consistency across a wider range, the results were analyzed in the CIE-Lab range of -10 to + 10. As shown in Fig. 8, it was confirmed that the statistical R2 trend between the obtained colors and the predicted values by the NN model was about 0.99 or higher. While the colorimeter has the disadvantage of only analyzing the color in the limited local area, making real-time analysis difficult, the NN model has the advantage of being able to analyze a wide range of colors in real-time using only image information. By integrating this image-based color analysis technology with hot stamping manufacturing technology, it is expected that hot stamping manufacturing monitoring and real-time analysis can be performed.

### 2) Inter-diffusion layer thickness prediction using color analysis

Evaluation of resistance spot welding characteristics has to be performed for the application of hot stamping vehicle parts. The Al-Si coated 22MnB5 material changes the coating layer depending on the heating temperature and time; typically there were 4 layers in the Al-Si coating [22]. In particular, the inter-diffusion layer is formed at the boundary between the Al-Si coating and the Fe substrate, and it is known that it is advantageous for resistance spot welding to have a thickness of 15 µm or less [22, 23]. Also, depending on the heating conditions, voids are created and grown inside the inter-diffusion layer and on the surface of the coating layer, which increases resistance and affects spot welding characteristics [22–24]. Figure 9 shows optical microscopy analysis of cross-sections of coating layers after 300 seconds and 600 seconds at the heating condition of 950 ℃; (a) is after 300 seconds and (b) is after 600 seconds. In the cross-section heated for 300 seconds, the inter-diffusion layer of about 11.3 µm was formed, while in the cross-section heated for 600 seconds, the thickness of the inter-diffusion layer was about 19.15 µm and many voids were created on the surface.

As heating time increases, the thickness of the inter-diffusion layer increases, and voids increase, resulting in the deterioration of resistance spot welding characteristics [22]. To predict the inter-diffusion layer thickness that affects resistance spot welding characteristics, the present study aims to verify the FeAl intermetallic formation model [23, 24]. To predict the inter-diffusion layer thickness, the diffusion principle of phase transformation in solids was considered to predict the overall coating thickness and the thickness of each layer of the coating generated by each phase [23].

\(IDY=G\sqrt{t}\) Eq. (7)

In this Eq. (7), *IDY* denotes the layer thickness, *t* represents the soaking time, and *G* stands for the growth rate in units of µm/s2. It is also noteworthy that the growth rate, *G*, can be described by *G = G**0**exp(-Q/RT)*, where *G**0* is a constant, *Q* is the apparent activation energy, *T* is the soaking temperature measured in Kelvin, and *R* is the gas constant [23]. Furthermore, because the inter-diffusion layer comprises α-Fe and FeAl intermetallic, the model considering the properties of each phase is necessary [23, 24].

\(IDY=\left[{G}_{\alpha -Fe} exp\left(\frac{{Q}_{\alpha -Fe}}{RT}\right)+{G}_{FeAl} exp\left(\frac{{Q}_{FeAl}}{RT}\right)\right]\sqrt{t}\) Eq. (8)

The values were calculated using *Q**α-Fe* of 182 KJ/mol and *Q**FeAl* of 250 KJ/mol [23], and the required temperature *(T)* and time *(t)* were determined by applying the results obtained from image analysis based on the NN model. To predict the inter-diffusion layer based on the aforementioned models, the center pillar component with the initial Al-Si coating weight of approximately 85 g/m2 was used, as represented in Fig. 10.

The flat surface color was analyzed with the NN model, which predicted CIE-Lab values of -0.76 for *a** coordinate and − 7.75 for *b** coordinate, allowing for the prediction of the heating temperature of 970 ℃ and the time of 260 seconds. This was consistent with the real hot stamping heating conditions. Furthermore, applying the obtained temperature *(T)* and time *(t)* to Eq. (8) allowed for the inter-diffusion layer thickness analytical, which was predicted to be approximately 11.3 µm. This was found to be similar to the experimental thickness of the inter-diffusion layer obtained from the vehicle part, which was 11.8 µm, as shown in Fig. 11. The models and approach presented suggest that it is possible to predict the inter-diffusion layer thickness that affects the resistance spot welding characteristics using only image color analysis without specimen extraction.

### 3) Hydrogen uptake prediction by using color analysis

The Al-Si coated 22MnB5 material may undergo a process of brittleness due to the absorption of hydrogen when it is heated to achieve a higher strength [23–25]. The reason behind this is the diffusion of hydrogen into the austenite microstructure during the heating phase [24, 25]. After the phase transformation, the hydrogen is temporarily held within the internal microstructure, unable to exit through the Al-Si surface coating at room temperature until a sudden fracture takes place under residual or additional stress [25–29]. To avert the issue of hydrogen embrittlement, it is critical either to avert the absorption of hydrogen or to integrate processes that will eliminate the absorbed hydrogen [25]. In order to study these characteristics beforehand, the absorption of hydrogen was anticipated using the neural network-based image color analysis [24–27].

To predict hydrogen absorption, the well-known constant surface concentration diffusion model can be adopted [24]. This model can be used to analyze one-dimensional diffusion. Assuming that hydrogen is available for diffusion within the furnace, it is possible to calculate hydrogen absorption over time and distance [24–25].

\(\frac{{C}_{s}-C(x,t)}{{C}_{s}-{C}_{0}}=erf\left(\frac{x}{2\sqrt{Dt}}\right)\) Eq. (9)

Here, *C**0* represents the initial constant hydrogen concentration, *x* denotes the distance from the source of hydrogen, *T* is the heating temperature and *t* is the heating time [24–26]. In this case, the heating time is assumed as 1/3 of the total heating time, as the time spent at the austenite phase is significant. The diffusion coefficient *D* is used (*D = D**0**exp(-W/RT)*, where *D**0* is 4.4×10− 7 m/s2, *W* is the apparent activation energy of 37 KJ/mol) at high temperatures [26–35]. Additionally, taking into account that hydrogen diffuses for both sides of the 22MnB5 sheet, *x* is set to half of the sheet thickness, which is 1.6mm. The temperature *(T)* and time *(t)* required for Eq. (9) was obtained from the color distribution in Fig. 10, as mentioned earlier. To analyze the diffusible hydrogen, the model validation was evaluated using the thermal desorption analysis (TDA) analysis [31, 32]. TDA analysis was conducted by heating the sheet at approximately 20 ℃/min in the nitrogen atmosphere and analyzing the hydrogen desorption from the sheet in ppm/s units [31–35]. Figure 12 represents the hydrogen uptake of approximately 0.47 ppm based on the experimental center pillar vehicle part. With utilizing the diffusion model assuming the surface concentration within the heating process, it was determined that the value was approximately 0.58 ppm by using the diffusion model. These approach methods can also be achieved using extended constitutive models, such as hydrogen-assisted damage and others [31–33].

By employing the NN-based image color analysis, it was possible to predict the hot stamping heating temperature and time using only the color information obtained from vehicle part images, and its accuracy was considered to be high. In future work, hot stamping part performance will be investigated using finite element analysis in conjunction with constitutive models.