Prediction of the Form of a Hardened Metal Workpiece during the Straightening Process

Abstract

In industry, metal workpieces are often heat-treated to improve their mechanical properties, which leads to unwanted deformations and changes in their geometry. Due to their high hardness (60 HRC or more), conventional bending and rolling straightening approaches are not effective, as a failure of the material occurs. The aim of the research was to develop a predictive model that predicts the change in the form of a hardened workpiece as a function of the arbitrary set of strikes that deform the surface plastically. A large-scale laboratory experiment was carried out in which a database of 3063 samples was prepared, based on the controlled application of plastic deformations on the surface of the workpiece and high-resolution capture of the workpiece geometry. The different types of input data, describing, on the one hand, the performed plastic surface deformations on the workpieces, and on the other hand the point cloud of the workpiece geometry, were combined appropriately into a form that is a suitable input for a U-Net convolutional neural network. The U-Net model’s performance was investigated using three statistical indicators. These indicators were: relative absolute error (RAE), root mean squared error (RMSE), and relative squared error (RSE). The results showed that the model had excellent prediction performance, with the mean values of RMSE less than 0.013, RAE less than 0.05, and RSE less than 0.004 on test data. Based on the results, we concluded that the proposed model could be a useful tool for designing an optimal straightening strategy for high-hardness metal workpieces. Our results will open the doors to implementing digital sustainability techniques, since more efficient handling will result in fewer subsequent heat treatments and shorter handling times. An important goal of digital sustainability is to reduce electricity consumption in production, which this approach will certainly do.

1. Introduction

Heat treatment of steel is a widely used process in industry to increase the hardness of metal workpieces. During the hardening process, residual stresses occur in the workpieces which cannot be controlled effectively. Heat treatment results in high-hardness workpieces, which are often deformed geometrically. To achieve the desired functionality of hardened workpieces, the need for straightening is very common. Due to the high hardness achieved, conventional bending and rolling handling approaches are not effective because they lead to material failure. To this end, reheat treatment, with the aim of improving the geometry of the workpiece, is often used in practice, which is time consuming, of limited effectiveness, and has a significant negative ecological footprint [1]. However, during the process of additional heat treatment, a lot of energy is also consumed. This is an opportunity to use manufacturing systems to reduce energy consumption and contribute to sustainability in the steel industry. The second approach used is manual straightening of hardened workpieces by applying surface deformations to the workpiece. Such straightening can only be carried out effectively by an experienced worker. At the same time, such straightening is far from optimal, as the straightening process relies on the informal knowledge of the worker—his experience and feelings. It is also exhausting and has a significant negative impact on the health of the worker.

The process itself is harmful to workers carrying out the straightening. In addition, it is also harmful to the environment. It was stated that heat treatment is used to correct the geometry. This is performed if the workpieces cannot be straightened using the conventional straightening process. Heat treatment of steel requires high temperatures which must be maintained for a long time. This means that the heat treatment of steels is very energy demanding. The steel industry is one of the most energy-intensive sectors [2,3]. Results of this research will lead to more efficient, faster, and less energy-consuming straightening of workpieces, which will contribute towards sustainability in the steel industry.

In industry, metal workpieces are heat-treated to improve their mechanical properties. These mechanical properties of metal workpieces include strength, hardness, ductility, toughness, and resistance to material fatigue [4]. Metal workpieces are often deformed geometrically by heat treatments such as inelastic deformation, quenching, welding, and casting. This results in local deformations of the material, which cause residual stresses [5]. Most commonly, workpieces are deformed geometrically due to three causes. The first cause is residual stress. The second cause is the stresses due to the different expansions of the individual crystal structures in the material, which also leads to different volumes of the crystal structures, which is the third cause [6,7]. In the context of this research, we will focus on flat metal workpieces, which can be deformed in width and length due to heat treatment [8]. However, there are also combinations of the above deformations.

Straightness measurement methods are essential because information about the geometry of the workpiece is needed before straightening. The first flatness measurement methods that appeared were contact methods [8]. These could also include coordinate table measurement. Measurement methods also appeared that determined flatness by superimposing on a flat surface [9]. Later, non-contact ultrasonic measurement methods emerged to detect the thickness and textures of sheet metal [10]. Other methods are based on optical triangulations [11]; for example, the detection of a form with a CCD camera and the projection of a laser beam [12,13]. A 3D reconstruction of the surface can be made with such methods. Three-dimensional scanners are often used for geometric measurements. With this technology, a complete 3D model of the workpiece can be obtained where all geometry features are visible [14].

The straightening of metal workpieces with high hardness (around 60 HRC) and toughness is a very demanding process. For such high-hardness materials, the classical and established material straightening approaches of bending and rolling are not effective as material failure occurs [11,15,16]. One option is to straighten the workpiece by a process that combines heating and bending of the workpiece. In this study, the workpiece is clamped at one end and a magnet is placed at the other end to generate a straightening force. A laser is used to heat the bending point [17,18]. This method is only suitable for thinner workpieces. It also introduces additional heat into the workpiece, which has a negative effect on the material’s structure [19] and even reduces the hardness. Rolling [20,21] and bending [15,22] methods are also presented in the literature. These methods are not suitable for workpieces with high strength and hardness because the small difference between yield stress and tensile strength leads to rapid failure of the material. High-hardness workpieces can also be straightened with a gas torch. Such straightening is carried out by experienced straighteners, who use a hand torch to heat the workpiece at a specific point. Such straightening requires the handler to have considerable experience and informal knowledge. There is also a known method for the straightening of low ductile materials, which works on the principle of striking the surface of the workpiece [23]. Such processes can be used to straighten hardened shafts, and the straightening process is carried out manually or automatically by a straightening machine. The straightening mechanism uses strikes, which create plastic deformations that expand the material locally, leading to the straightening of the shafts themselves [24,25].

Predictive analysis combines various statistical techniques, such as predictive modeling, data mining, and machine learning. The aim of these techniques is to analyze already known data to extract upcoming, unknown data [26,27]. Many scientific contributions in this field are related to Industry 4.0 [28]. With modern industry and the presence of the Internet of Things (IoT), there is a huge number of sensors and, consequently, data [29,30,31]. The use of artificial intelligence methods to process large amounts of data efficiently is often invoked [32]. Predictive analytics is also used in mechanical manufacturing. In one study, predictive analysis was applied to the grinding process to optimize the grinding parameters with the aim of preventing overheating of the workpiece surface [33]. Another example of predictive analysis in machining is fine milling, where the cutting force is predicted for the best milling results [34,35]. Predictive analysis has also been applied to renewable energy. It involves the development of a concept and a control platform in a modern automation system. Artificial neural networks have also been used [36]. Predictive analysis, together with artificial intelligence methods such as neural networks and deep learning, is a key focus area of smart factories. Such systems can process large amounts of data and operate in real time [37,38].

The approach proposed in this paper is novel as there are no studies in the available scientific and technical literature and patent databases where researchers have proposed a methodology for machine-assisted straightening of high-hardness metal workpieces. In the existing research, researchers have focused a lot on bending and rolling, which is not effective for handling high-hardness metal workpieces as there is a high probability of material failure. The aim of this research was to develop a predictive model that will allow the prediction of the change in the form of a hardened workpiece after the introduction of surface deformations applied during the straightening process. To this end, an extensive laboratory experiment was carried out in which controlled strikes were deliberately introduced on the workpieces. The form of the top surface of the workpieces was scanned to determine the change in the form of the workpiece in relation to the strikes. The captured experimental data, combined with the intended strikes, was used to train and test a deep neural network to predict the change in workpiece form with the input strikes. Such a predictive model is a prerequisite for the future development of machine-based straightening of high-hardness metal workpieces.

This paper contributes to scientific knowledge and novelty in the following aspects:

• Conducting a large-scale laboratory experiment to produce a large database of data that provide material for in-depth analyses in the field of straightening of high-hardness metal workpieces.
• Development of an accurate AI model to predict the form changes of hardened workpieces when surface deformations are applied using a modified U-Net convolutional neural network architecture.
• Analysis of the influence of the input data (describing the form of the workpiece) resolution on the performance of the prediction model.
• Combining mixed data into a form suitable for input into a U-Net convolutional neural network.
• Presentation of the proposed methodology.

The paper is divided into four sections. In the introduction section, the state-of-the- art is presented where it is established that a predictive model for the handling of hardened workpieces does not yet exist. The research process is explained in the following chapter. In Section 2.3 we discuss that an experiment was carried out in which strikes were performed on high-hardness workpieces. The forms of the workpieces after each strike were captured to show the change in form caused by the strike. The mechanism of the form change is also presented and supported by a real example. Section 2.4 describes how the form prediction model was built. This involves preprocessing the data to make them suitable for neural network learning. This is followed by a description of the modified U-Net neural network, which predicted the form of the workpieces according to the strikes. Finally, the results of neural network learning are presented with the RAE, RMSE, and RSE parameters. The paper ends with the conclusions, where a brief commentary is given on the excellent neural network prediction results.

2. Materials and Methods

2.1. Research Framework

Figure 1 shows how the research was conducted. In the first phase, a large-scale laboratory experiment was carried out where a database of 3063 samples was prepared based on the controlled input of workpiece surface deformations and high-resolution capture of the workpiece geometry. The collected data were divided into 85% data for model learning, 10% for validation, and 5% for testing. This was followed by the model learning phase, where data preprocessing and training were performed of the U-Net convolutional neural network. In the last phase, the developed predictive model was tested using 5% of the data that were not included in the AI model learning phase.

2.2. Straightening Hardened Workpieces by Applying Surface Deformations

Throughout this article, the term “strike” will be used and its explanation is described below. Surface impaction is one of the methods used for handling low-ductile materials [23]. By applying a strike to the surface of the workpiece, a plastic deformation occurs at the point of the strike. In this region, forces are applied parallel and perpendicular to the surface. This leads to stretching of the area, and, consequently, to flattening of the workpiece (Figure 2) [39]. Due to the complexity of the straightening with surface deformation, currently such straightening can only be performed manually, where the process is carried out by an experienced expert with acquired informal knowledge [9]. Each strike means a deterioration of the mechanical properties of the workpiece, so the aim is to carry out such straightening with the fewest number of strikes possible [40].

The method of straightening was validated by an experiment. Figure 3a shows the change in form of the workpiece after the 1 strike. Observing the color map, just 1 strike caused form changes large enough to be detected with our 3D scanning equipment. From the measurement marks on the workpiece, the location of the strike is convex by 0.02 mm and the workpiece was lowered by 0.02 mm at the ends. Additional strikes were added in Figure 3b. It can be seen that the center bulges out even more, but, at the same time, from the blue color on the edges, it can be seen how the orientation of the punch affects the change in the form of the workpiece. Namely, the workpiece has bent parallel to the orientation of the strike.

2.3. Experiment

2.3.1. Samples

The experiment was limited to tool steel 1.2379 (DIN X155CrVMo12-1), a cold-working steel with a high carbon and chromium content. It is used for applications where good wear resistance is required, such as punching tools and thread rolling. It is also used for cutting tools, woodworking, and is suitable for molds in plastic casting. The chemical composition of 1.2379 tool steel is in

Table 1. Chemical composition of DIN X155CrVMo12-1 steel in percent.

C	Si	Mn	Cr	Mo	Ni	V	W	Other
1.53	0.35	0.40	12.00	1.00	-	0.85	-	-

. The workpiece size was chosen based on a 24 × 200 × 5 mm workpiece size, which is used commonly in the knife industry. To find out how the workpiece behaved with other width/length ratios, an intermediate dimension and a 1:1 aspect ratio were chosen. The workpieces used in the experiment were the ones shown in

Table 2. Workpiece sizes.

Workpiece Variants	Workpiece Dimensions (Height–Width–Length) in mm	Number of Physical Workpieces	Number of Applied Strikes per Workpiece	Number of 3D Scans or Acquired STL Files per Workpiece	Total Number of 3D Scans
Variant 1	5–24–200	3	10	11	219
Variant 2	5–90–200	3	24	25
Variant 3	5–200–200	3	36	37

. Three pieces were used for each type of workpiece [24 × 200, 90 × 200, and 200 × 200].

Workpieces made of 1.2379 steel (DIN X155CrVMo12-1) were hardened in a vacuum furnace. Quenching was started by heating from room temperature to an austenitizing temperature, which took approximately 5 h. The residence time at the austenitizing temperature of 1040 °C was 10 min. The samples were then cooled to 30 °C in a vacuum oven using nitrogen gas, after which the workpieces were removed from the oven. This was followed by tempering in an atmospheric furnace heated electrically by coils. The furnace was already heated to the tempering temperature when the workpieces were loaded into it. The tempering at 525 °C lasted 300 min. After the tempering process, the samples were removed from the oven and cooled in still air. The heat treatment described above resulted in a hardness of 60 HRC.

2.3.2. Experimental Setup

For the purpose of the experiment, a device was designed that allows the controlled application of surface deformations to the workpieces (Figure 4). The device was divided into mechanical, sensing, and software parts. The 3D scanner for capturing the form of the workpiece was a separate part.

The mechanical part works on the pendulum principle and consists of the following components:

• Table (Figure 4-1). Its function is to provide a fixed base on which all other equipment is mounted.
• The base plate (Figure 4-2) provides a fixed base for the strike on the workpiece. The dimensions of the plate are 505 × 1005 × 25 mm, made of 1.1730 steel. Foam is placed between the table and the base plate to attenuate unwanted sounds and forces that would interfere with the experiment. A stopper and a trigger are also mounted on the plate, which are necessary for the application of the strikes.
• The bearing support plate (Figure 4-3) ensures that the hammer hits the workpiece in a precise position. The bearing plate is made of 4 mm thick structural steel and is adjustable in height. The angle at which the hammer will strike the workpiece can be adjusted by varying the height. The bearings on the bearing plate, together with the axle, provide a stable pivot for the hammer. A position encoder is mounted on the axle.
• The hammer (Figure 4-4) consists of a striking hammer, a handle, and a clamp. A lever connects the pivot and the clamp. The position of the clamping can be changed; thus, the force of the strike can be varied. The strike hammer was designed primarily for manual use. Figure 5a shows a strike hammer with a hard tip inserted. Figure 5b shows the dimensions of the tip of the hammer used to create surface plastic deformations.

The force generated by the hammer when it collides with the workpiece is 70.8 kN. The force was calculated from the average strike acceleration (a = 8736 m/s²) measured with a PCB 353B03 sensor (PCB Piezotronics Inc., Depew, NY, USA) mounted on the hammer handle, and the mass of the hammer measured at the tip of the hammer in the horizontal position (m = 8104 kg).

• The trigger (Figure 4-5), as the name suggests, causes the hammer to fall. It consists of a clamp and a threaded rod. On the threaded rod is a nut with a bolt that holds the pendulum at a certain height. The position of the nut changes the height of the pendulum. It is used by lifting the pendulum manually and inserting the nut pin into the pendulum. When ready, pull the threaded rod to dislodge the pin and the pendulum falls onto the workpiece.
• The stopper (Figure 4-6) stops the hammer so that it hits the workpiece only once. When the hammer and workpiece strike, the hammer rebounds a certain distance. If the hammer is not stopped at this point, the hammer will fall again on the workpiece from a smaller distance. It will rebound several times. This could spoil the results of the experiment, so multiple rebounds are prevented by a stopper, which, after the rebound of the hammer at strike, holds the hammer so that it does not fall on the workpiece again.
• A position encoder (Figure 4-7) from RLS with 360 pulses per revolution is mounted on the axis of the pendulum. Its signals are used to trigger the data acquisition of the experiment. The position and velocity of the hammer can also be calculated.

The experiment is guided by a program developed in the LabView software environment. The program is responsible for generating the orientation and strike location, as well as for capturing and storing the data.

Each workpiece must be measured before and after each strike to detect changes in form. The 3D scanner used was a GOM ATOS Core 200 3D scanner (GOM Metrology, Braunschweig, Germany). The measurements were performed by placing the 3D scanner on a stand oriented vertically towards the rotary scanning table (Figure 6). The workpiece was placed on the rotary scanning table, which holds the workpiece magnetically, and has the option to adjust the inclination and rotation of the plate itself. The workpiece is sprayed with a scanning spray before data acquisition to prevent glaring. The scanning table has the reference points necessary for the assembly of the captured scanner data.

2.3.3. Performing the Experiment

The experiment was carried out by applying strikes to workpieces at predetermined locations. The strike location and orientation were chosen randomly each time. Before and after each strike, 3D scanning was performed to obtain data on the change in form of the workpiece. Three different workpiece sizes were used, as listed in Table 2. Figure 7, Figure 8 and Figure 9 below show where the strike positions were on the workpiece. The number of strike positions was determined according to the size of the workpiece. Thus, the smallest workpiece (24 × 200 mm) had 10 strike positions, the middle workpiece (90 × 200 mm) had 24 strike positions, and the largest workpiece (200 × 200 mm) had 36 strike positions. The strikes were applied to the workpieces on 1 face only.

The experiment was carried out with the following steps until all strikes were performed:

• Three-dimensional scanning of the workpiece to capture the form of the workpiece before strike.
• Positioning of the workpiece using a dedicated template, ensuring that the strike was performed at the position and orientation specified by the software.
• Execution of the strike.
• Three-dimensional scanning of the workpiece to capture the form of the workpiece after the strike. The scanned workpiece file is saved with a name generated by the software.

2.4. Model Building

2.4.1. Data Preprocessing

Create workpiece 2D form representations based on 3D scans. From each of the 219 STL files, we extracted the point cloud data (x, y, and z coordinates) and neglected the connection between points in an STL file. An empty matrix of arbitrary size was prepared (e.g., 18 rows and 29 columns). It served as an input into the Artificial Neural Network once populated with values representing the upper surface topology of the workpiece. The same matrix form was used to build representations for every workpiece variant. We were interested only in the upper surface of the workpieces. It follows that points on the sides need to be discarded. Points were kept that were on the interval [0.04 × length, 0.96 × length] in the x-direction and [0.04 × width, 0.96 × width] in the y-direction. Let us define a few variables of a point cloud after cutting off the edges:

• L_max = the max value of the x-coordinates in a point cloud.
• L_min = the min value of the x-coordinates in a point cloud.
• W_max = the max value of the y-coordinates in a point cloud.
• W_min = the min value of the y-coordinates in a point cloud.

The value for each matrix cell was calculated next. A matrix with m rows and n columns (e.g., m = 18, n = 29) separated the point cloud data into m × n sections. Each section was (L_max − L_min)/n long and (W_max − W_min)/m wide. We calculated the mean value of z-coordinates of points that fitted inside every section. This is the value that gets stored in the corresponding cell of the matrix. This procedure resulted in a matrix of size m × n, where each of its cells represents the z-coordinate (height) of the upper surface of the workpiece. Lastly, we scaled data in the matrix. Their values were remapped onto the interval [0, 1]. The value 0 was assigned to the minimum matrix value and 1 to the maximum.

Merging the data to build inputs for the NN. The training samples (NN inputs) were constructed as a matrix that contains the upper surface topology information of a workpiece with 3 extra columns appended. The information regarding planned or not-yet-applied strikes is decoded here. The first extra column contains the x-coordinate of the strike location, the second the y-coordinate, and the last contains the information about the strike orientation (0°, 45°, 90°, or 135°). Figure 10 shows an example of an NN input. Our objective was that the model would be able to predict the changed, new geometry of a workpiece after applying the planned strikes.

Training sample construction. During the experiment, we collected data on every strike position, orientation, and the order in which they were executed. To get as many training samples as possible, we considered all possible combinations of strikes that could be applied on each workpiece. A training sample can be constructed as follows: let us take the 2D topology representation of a workpiece that already has a certain number of strikes (N_init) applied and decide that we want a model to predict its form after we apply the next strike. However, the model should also predict a new form if we apply the next 2 (or 3, and so on, up to N_ps) strikes. This way, we get additional training samples. The number of strikes that can still be applied to the workpiece (N_s) depends on the total number of strikes (N_ps) a certain workpiece can have. The quantity of training samples (S) that one can obtain from a specific workpiece variant was calculated in Equation (4).

Number of strikes that are already on a workpiece:

$$N_{init}=\left[0,N_{ps}-1\right],N_{init}\in \mathbb{N}$$

(1)

Number of strikes that can still be applied to the workpiece:

$$N_s=\left[N_{init}+1,N_{ps}\right],N_s\in \mathbb{N}$$

(2)

Total number of strikes a workpiece can have:

$$N_{ps}=\left[10,24,36\right]$$

(3)

Number of all possible training samples per workpiece:

$$S=\frac{N_{ps}\cdot \left(N_{ps}+1\right)}{2}$$

(4)

Number of training samples for workpiece variant 1 is calculated using Equation (5):

$$S\left(N_{ps}=10\right)=\frac{N_{ps}\cdot \left(N_{ps}+1\right)}{2}=\frac{10\cdot 11}{2}=55$$

(5)

Number of training samples for workpiece variant 2 is calculated using Equation (6):

$$S\left(N_{ps}=24\right)=\frac{N_{ps}\cdot \left(N_{ps}+1\right)}{2}=\frac{24\cdot 25}{2}=300$$

(6)

Number of training samples for workpiece variant 3 is calculated using Equation (7):

$$S\left(N_{ps}=36\right)=\frac{N_{ps}\cdot \left(N_{ps}+1\right)}{2}=\frac{36\cdot 37}{2}=666$$

(7)

Table 3. Training sample creation. On a workpiece of variant 1 there are 10 possible initial configurations (from 0 to 9 strikes already applied). Each dot represents a separate sample, where all strikes up to it are planned. This means that 55 samples can be obtained for a workpiece with 10 possible strikes.

						$N_s$
$N_{init}$		1	2	3	4	5	6	7	8	9	10
entry 2	0	∙	∙	∙	∙	∙	∙	∙	∙	∙	∙
	1		∙	∙	∙	∙	∙	∙	∙	∙	∙
	2			∙	∙	∙	∙	∙	∙	∙	∙
	3				∙	∙	∙	∙	∙	∙	∙
	4					∙	∙	∙	∙	∙	∙
	5						∙	∙	∙	∙	∙
	6							∙	∙	∙	∙
	7								∙	∙	∙
	8									∙	∙
	9										∙

depicts how training samples were selected, taking as an example a workpiece of the first variant. Considering a workpiece form representation that already contains 3 strikes, we can construct 7 possible outcomes (we can still make strikes from 4 to 10 and instruct the model to predict new forms for each case).

The total number of created samples (N_total) was calculated as the sum of all possible samples per every workpiece variant, multiplied by 3 (we had 3 workpieces per each variant). The result was calculated by Equation (8):

$$\begin{gathered} N_{total}=\left(S\left(N_{ps}=10\right)+S\left(N_{ps}=24\right)+S\left(N_{ps}=36\right)\right)\cdot 3 \\ {N}_{total}=\left(55+300+666\right)\cdot 3=3063 \end{gathered}$$

(8)

2.4.2. U-Net Convolutional Neural Network

The U-Net convolutional network was designed primarily for segmentation [41]. Since both the inputs and outputs to the deep neural network in this case are matrices of dimension NxM, the existing architecture of the U-Net neural network was modified to be suitable for image-to-image regression. The number of filters in the last convolutional layer of the neural network was set to 1, making the output data format identical to the input data format.

The U-Net network structure is based on the encoder-decoder convolution and deconvolution operations. The encoder-decoder-based model was modified by adding a skip-connection so that the upper and lower portions of the structure are connected directly. Each subsequent layer was connected directly to the layer that preceded the current layer. The purpose of the convolution process was to extract the image features and compress the image (the contraction path), encouraging propagation of only relevant information. The contracting path consisted of the repeated application of 2 3 × 3 convolutions, each followed by an ReLU and a 2 × 2 max pooling operation with stride 2. The task of the deconvolution process (the expansive path) was to up-sample the image size to achieve the original resolution. The expansive path included an upsampling of the feature map, a 2 × 2 convolution, a concatenation with the corresponding cropped feature map from the contracting path, and 2 3 × 3 convolutions with ReLU activation. The U-Net network used in this study was set up with 3 layers of convolution and 3 layers of deconvolution; the network structure is shown in Figure 11. The network had a total of 11 convolutional layers, 2 max-pooling and dropout layers, 2 transposed convolutional layers, and 2 depth concatenation layers. The input in each layer of the generative network structure included the output of the previous layer and the corresponding convolution layer, so that the generated image retained as much information as possible from the original image.

Training parameters. The initial layer took as an input the 2D matrix representation of the surface topology of the workpiece with encoded “planned” strikes (i.e., a grayscale image). No normalization was applied to the input data. Training used 85% of all data, leaving 10% for validation during training and 5% for testing of the model’s performance after training was completed. We trained the network using the Adam (adaptive moment estimation) solver, which combines the advantages of the adaptive gradient algorithm (AdaGrad) and the root mean square propagation (RMSProp) solver. The initial learning rate was set to 0.001. During training, the validation step was executed on every 50th epoch. We trained our model for 200,000 iterations, or 5000 epochs. The mini batch size consisted of 64 training samples.

2.5. Performance Indicators

The computational confirmation of the constructed non-linear model was tested using standard statistical tests, such as relative absolute error (RAE), root mean square error (RMSE), and relative standard error (RSE). These commonly used parameters can be calculated as follows [42,43]:

$$RAE=\frac{{{\displaystyle \sum }}_{i=1}^n\left|y_i-{\widehat{y}}_i\right|}{{{\displaystyle \sum }}_{i=1}^n\left|y_i-\overline{y}\right|}where\overline{y}=\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n{y}_i,$$

(9)

$$RMSE=\sqrt{\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2},$$

(10)

$$RSE=\frac{{{\displaystyle \sum }}_{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}{{{\displaystyle \sum }}_{i=1}^n{\left(y_i-\overline{y}\right)}^2}where\overline{y}=\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n{y}_i,$$

(11)

• $y_i:actualvalueoftheithobservation$;
• ${\widehat{y}}_i:predictedvalueoftheithobservation$;
• $\overline{y}:meanofactualvalues$;
• $n:numberofobservations$.

3. Results and Discussion

The metrics observed during training were training loss, training RMSE, validation loss, and validation RMSE. The 2D form representation of the workpieces based on 3D scans is described in subchapter 2.4.1. Based on this, seven models of specific input size were tested, namely, 9 × 5, 29 × 18, 41 × 24, 61 × 40, 81 × 56, 125 × 80, and 253 × 128. The training process and convergence of metrics for an artificial neural network with input size of 5 × 9 are shown in Figure 12. The scale used in the Figure was logarithmic for clearer presentation of the training procedure.

After training of the neural network was completed, we utilized 5% of our data (153 samples) to evaluate the model’s actual performance on new, previously unseen cases. Each input sample was sent into the model, which provided us with an output. This prediction was the same size as the input, but we were interested only in the model’s prediction of the workpiece form representation, so the last three columns (reserved for strikes- to-be-applied data) were not considered when carrying out the calculation of RAE, RMSE, and RSE. These performance metrics were calculated using only values that considered the form representation of the workpiece. We evaluated every model of specific input size in the same manner. An overall performance indicator for each input resolution was constructed in two ways: as a median of all testing samples, shown in Figure 13, and as their mean value, depicted in Figure 14.

In RAE, the worst performing network error (input size of 253 × 128) was still lower than 0.4, and the best (9 × 5) achieved the incredible result of only 0.05 error. Similar observations can be made on the other two performance metrics, where the best model was again of input size 9 × 5, yielding errors of 0.0129 and 0.004 for RMSE and RSE, respectively.

To visualize and test the trained neural network, we prepared an input of a second workpiece variant (5–90–200 mm) with the intent to apply 24 strikes. The initial state of the workpiece was strikeless. Prepared input was used on the model, which made a prediction of the new workpiece form after all strikes had been applied. This sample was selected from the test set and was not used during training. Figure 15 shows the initial state of the workpiece, with its 2D matrix representation of size 5 × 9 on the left and the final state of the workpiece after application of the strikes. On the bottom right corner there is a comparison between an actual form representation of the scanned workpiece and the AI-predicted form representation. This visualization is a stark statement of the model’s performance. The workpiece scans in the upper half of the image were elongated along the z-axis to expose and enhance topology features. The dark shade of pixels indicates low relative surface positions, and pixels with a brighter shade represent high points on the surface of a workpiece.

4. Conclusions

In this paper, a model was proposed to predict the form/geometry changes of hardened metal workpieces depending on the introduced surface plastic deformations. The approach employed a modified U-Net convolutional neural network architecture that allowed multiple-input multiple-output regression. A method was proposed to combine mixed data into a form suitable for input into a convolutional neural network. To learn and test the deep neural network, a large-scale laboratory experiment was designed and executed to analyze the influence of surface plastic deformation on the form change of high-hardness (around 60 HRC) metal workpieces. The influence was analyzed of the resolution of the input data describing the form of the workpiece on the performance of the developed predictive model.

The main conclusions of the survey are:

• By applying surface plastic deformations, it is possible to influence the form of high-hardness metal workpieces without breaking the material.
• The location and orientation of the applied plastic surface deformation affects the form change of a high-hardness metal workpiece.
• By adapting the architecture of the U-Net convolutional neural network, which was used originally for segmentation, multiple-input multiple-output regression can be implemented efficiently.
• A fine neural network can be used to predict the form changes of high-hardness metal workpieces very efficiently, depending on the previous form of the workpiece, the number and sequence of introduced surface plastic deformations, and the location and rotation of the introduced surface deformations. The U-Net model’s performance was investigated using relative absolute error (RAE), root mean squared error (RMSE), and relative squared error (RSE). The results showed that the model had excellent prediction performance, with the mean values of RMSE less than 0.013, RAE less than 0.05, and RSE less than 0.004 for testing data.
• The resolution of the input data describing the form of the workpiece affects the performance of the prediction model. A lower resolution of the input data ensures a higher accuracy of the predictive model. For the design of the handling process, a resolution of 9 × 5 is sufficient for the size of the workpieces used in the study, while, at the same time, providing the best accuracy of the prediction model.

The research also makes an important contribution to sustainability. The presented model for predicting the form of a hardened workpiece in a straightening process implements digital sustainability, and this has not been achieved before. The methodology will help in the following areas of sustainable production:

• The negative impact on the environment will be reduced as less energy will be consumed and therefore fewer natural resources will be used.
• There will be better working conditions for employees with higher job satisfaction and less absence due to illness. Health and safety of workers currently performing manual straightening work will be improved. Workers will be less burdened with strenuous and monotonous work (repetitive motion leads to injuries).
• There will be less waste in production because the process will be more controlled and less dependent on the human factor or human assistance to achieve even better handling results.
• Less energy will be consumed as there will be fewer subsequent heat treatments due to straightening errors.
• The productivity of the straightening process will be increased as it can be performed faster.

Future research is needed to develop a system that uses the predictive model presented in this paper to design an optimal or near-optimal handling strategy for high-hardness metal workpieces. Using multi-criteria optimization, it will be possible to search for solutions that will provide optimum flatness of the hardened metal workpiece with a minimum number of plastic surface deformations. Such solutions will allow the automation of the handling process of high-hardness metal workpieces.