46 Advances in Production Engineering & Management ISSN 1854-6250 Volume 19 | Number 1 | March 2024 | pp 46–64 Journal home: apem-journal.org https://doi.org/10.14743/apem2024.1.492 Original scientific paper Predicting the deep drawing process of TRIP steel grades using multilayer perceptron artificial neural networks Sevšek, L. a , Vilkovský, S. b , Majerníková, J. b , Pepelnjak, T. a,* a Forming Laboratory, Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia b Department of Technologies, Materials and Computer Aided Production, Technical University of Košice, Košice, Slovakia A B S T R A C T A R T I C L E I N F O TRIP (Transformation Induced Plasticity) steels belong to the group of ad- vanced high-strength steels. Their main advantage is their excellent strength combined with high ductility, which makes them ideal for deep drawing pro- cesses. The forming of TRIP steels in the deep drawing process enables the pro- duction of a thin-walled final product with superior mechanical properties. For this reason, this study presents comprehensive research into the deep drawing of cylindrical cups made from TRIP steel. The research focuses on three main aspects of the deep drawing process, namely the sheet metal thinning, the max- imum force value and the ear height as a result of the anisotropic material be- haviour. Artificial neural networks (ANNs) were built to predict all the men- tioned output parameters of the part or the process itself. The ANNs were trained using data obtained from a sufficient number of simulations based on the finite element method (FEM). The ANN models were developed based on variable material properties, including anisotropic parameters, blank holding force, blank diameter, and friction coefficient. A good agreement between sim- ulation, ANN and experimental results is evident. Keywords: Forming; Deep drawing; TRIP steel; Artificial neural network (ANN); Finite element methods (FEM); Modelling; Simulation *Corresponding author: Tomaz.Pepelnjak@fs.uni-lj.si (Pepelnjak, T.) Article history: Received 25 March 2024 Revised 24 April 2024 Accepted 26 April 2024 Content from this work may be used under the terms of the Creative Commons Attribution 4.0 International Li- cence (CC BY 4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1. Introduction The development of materials for vehicle production faces the challenge of solving diverse and often conflicting requirements. These include the need to reduce vehicle weight while providing high levels of weldability, formability, joinability, and sufficient stiffness or mechanical strength to increase the safety of passengers. In addition, it is important to optimize the simple installation of components, maintain surface resistance in demanding conditions, and preserve aesthetic properties. In today's automotive environment, meeting fuel efficiency and environmental stand- ards within economic constraints is critical [1-3]. Cost reduction can be considered one of the main interests for companies in the modern era [4]. Different advanced forming methods have been developed to make custom made goods at a reasonable price [5]. Given these complex re- quirements, the choice of materials plays a key role in shaping the car's structure. High-strength steels (HSS) have demonstrated the ability to strike a balance between cost-effectiveness, weight consideration and favourable mechanical properties [6, 7]. Predicting the deep drawing process of TRIP steel grades using multilayer perceptron artificial neural networks Advances in Production Engineering & Management 19(1) 2024 47 Current research is focused on advanced high-strength steels (AHSS) and ultra-high-strength steels (UHSS), mainly composed of martensitic steels. The AHSS category includes two-phase steels and TRIP (Transformation Induced Plasticity) steels. These groups of materials exhibit me- chanical properties that meet stringent environmental standards and customer requirements while remaining economically affordable for manufacturers [1-3]. 1.1 Fundamentals of TRIP steels TRIP steels hold significant appeal for the automotive industry in constructing the body-in-white due to their enhanced mechanical properties, formability, and exceptional energy absorption dur- ing a crash [8]. The microstructure of TRIP comprises distinct phases, including ferrite, austenite, martensite, and bainite, contributing to the high performance of the steel [9]. The TRIP effect, em- ployed to improve formability and strength, is rooted in a lattice transformation. The face-centred cubic (fcc) austenite transforms, without diffusion, into either the body-centred cubic (bcc) mar- tensite (α-martensite) or a hexagonal martensite phase (β-martensite). The bcc crystal phase is more stable, and the hexagonal phase transitions to bcc depending on the conditions [10, 11]. These diverse phases are not only beneficial for forming processes but also play a crucial role in the crash behaviour of components. However, as mechanical properties are directly linked to mi- crostructural evolution, local stress and strain conditions impact both forming and failure behav- iour. Therefore, understanding the interaction among microstructure, stress and strain condi- tions, and the occurrence of failure is essential [12]. 1.2 Fundamentals of deep drawing Deep drawing is a sheet metal forming process which are used to plastically deform the sheet metal into the desired shape of the final product [13]. The deep drawing process, widely utilized across industries, involves forming sheet metal for a variety of applications. Its uses span from crafting automotive components, products in the arms industry, and aerospace parts to forming tubes for medication and perfume, pots, pans, and various kitchen appliances. This method relies on forming production parts with either simple or intricate designs through substantial plastic deformation [14, 15]. Throughout the deep drawing process, potential defects may arise, such as surface scratches, wrinkling of walls and flanges, tearing, and earing [16, 17]. The effectiveness of the deep drawing process is heavily dependent on material properties, geometric considerations, and technological parameters. Key material factors encompass elasticity, plasticity, and anisot- ropy. Additionally, significant roles are played by parameters like punch velocity, blank holding pressure, and lubrication. The radius of the punch and die, blank thickness, and the clearance be- tween the punch and die also contribute to the process. Incorrectly defining these parameters can result in common defects of the deep drawing process [18, 19]. Earing, a distinctive defect marked by the development of a wavy edge at the open end of the cup, is a notable issue in the deep drawing process. Numerous recent studies have addressed ear- ing defects [20, 21]. Colgan and Monaghan [22] explored key parameters in the deep drawing pro- cess, including punch and die radii, punch velocity, friction, and draw depth. Using ANOVA soft- ware, they calculated the percentage contributions of each factor. Interestingly, punch velocity emerged as the fourth most crucial parameter, particularly impacting wall thickness deviation. Seth et al. [23] investigated the formability of steel sheets subjected to high-velocity impact from an electromagnetically launched punch at speeds of 50 and 220 m/s. Their experiments involved five different steel specimens with varying thicknesses, revealing failure strains ranging from 30 % to 50 %. Notably, the study observed that higher forming velocities correlate with increased form- ability. Huang et al. [24] examined the influence of blank thickness and fracture thickness on form- ing limits. Fracture strain, derived from a uniaxial tension test, served as the fracture criterion. The assumption was made that the blank fractures when its thickness reaches the fracture thick- ness in any section. The study involved the analysis of square cup drawing and elliptical hole flang- ing. Chalal et al. [25] determined forming limit diagrams using different localization criteria, such as the criterion based on the maximum second-time derivative of thickness strain, the criterion based on the ratio of equivalent plastic strain increment, the maximum punch force criterion, and the loss of ellipticity. ABAQUS/Explicit tool was employed for their analysis [25]. Gusel et al. [26] Sevšek, Vilkovský, Majerníková, Pepelnjak 48 Advances in Production Engineering & Management 19(1) 2024 focused on the forming of high-strength steel sheets (DP780 and DP1180HD) by deep drawing. The influence of yield stress, tensile strength, blank holder force and punch speed on the output parameter of cup height was evaluated [26]. The fracture problems during deep drawing were successfully predicted using genetic modelling. 1.3 Simulation using finite element method Simulations allow the prediction of crucial outcomes within the system or process itself, using the computer environment. A correctly created simulation model of a forming process enables fast and reliable prediction of key output parameters. A small discrepancy between experimental and simulation results shows the general correctness of the set simulation model. Simulations were carried out as part of this study to predict three key output parameters of the deep drawing pro- cess of TRIP steel. A sufficient number of simulations with different input parameter values and corresponding output results were used as the basis for building an artificial neural network (ANN) for each target output parameter. The simulations based on the finite element method (FEM) were carried out in the ABAQUS simulation environment. The material properties, the ge- ometric properties of the blank and the tools as well as the kinematics of the deep drawing process were simulated. FEM simulations can be carried out with different calculation methods, finite el- ement types and in different simulation environments [27]. The FEM simulation of the deep draw- ing process can be very time-consuming [28]. The use of the explicit calculation method provides acceptable accuracy with faster calculation compared to the implicit method [29]. For this reason, the explicit method was chosen for all 50 simulations in the study presented here. The study by Vrh et al. [30] focused on the constitutive modelling of anisotropic plates and the prediction of the earing for the round cup drawing using the FEM method. Shell finite elements with reduced integration were used in the ABAQUS/Explicit simulation environment [30]. Bandy- opadhyay et al. [31] evaluated the limiting drawing ratio (LDR) of tailor welded blanks using a deep drawing test. FEM models of the deep drawing process considered the anisotropy of the sheets and the inhomogeneous properties in the welded zone of the tailor welded blanks [31]. The simulations were performed with the nonlinear solver Lsdyna-971 using shell elements [31] The study by Dwivedi and Agnihotri [32] focused on testing different materials for deep drawing of cylindrical cups without using a blank holder. The ANSYS 14.0 simulation environment was used to determine the limit drawing ratio [32]. Magnesium alloys develop a crystallographic texture and plastic anisotropy during rolling, resulting in ear formation during deep drawing of such sheets [33]. This was investigated in the study by Walde and Riedel [33], who performed FEM simulations of the deep drawing process in ABAQUS/Explicit environment using C3D8R solid brick elements with four elements across the sheet thickness. It was found that the earing pattern depends on the initial texture and on the development of the texture during the forming process under investigation [33]. In the study by Engler and Aretz [34], S4R shell elements with reduced integration were used in the ABAQUS simulation environment for the FEM simulation of the deep drawing process of various anisotropic aluminium alloys. In the study by Luyen et al. [35], FEM simulations of the deep drawing of cold-rolled carbon steel were carried out in the ABAQUS simulation environment. The simulations were used to determine the fracture heights of cylindrical cups and were vali- dated with experimental results [35]. Another aim of the simulations and experiments in the study by Luyen et al. [35] was to investigate the effects of the blank holder force, the punch radius and the drawing ratio on the fracture height. Simulations and experiments showed that increasing the blank holder force reduces the fracture height and increasing the punch radius increases the frac- ture height [35]. Jayahari et al. [36] investigated the formability of austenitic stainless steel 304 at different temperatures under warm conditions during the deep drawing process of a cylindrical cup. The explicit FEM analysis was performed in the LS-DYNA program for forming at room tem- perature and other temperatures up to 150°C [36]. Shell elements were used for the blank and the tools, as this results in a shorter calculation time [36]. Shell finite elements were also used in the study presented here. Predicting the deep drawing process of TRIP steel grades using multilayer perceptron artificial neural networks Advances in Production Engineering & Management 19(1) 2024 49 1.4 Fundamentals of neural networks Artificial intelligence can contribute to sustainable manufacturing [37]. With advances in manu- facturing intelligence, information technology is part of the automated production technologies that are the main contributors to industrial change today [38]. Artificial intelligence models used in the field of metal forming use process parameters as input parameters and forming results as output parameters [37]. One special branch of such models are neural network models, which are expressed by a nonlinear function of the weighted sum of inputs [37]. Artificial neural network (ANN) is a set of neurons and connections between them with adjustable weights [39]. Commonly used type of ANNs are the multi-layer neural networks, which consist of an input layer, one or more hidden layers, and an output layer [39, 40]. Neurons of each layer are connected to each other by connection links with adjustable weights [39]. These weights are adjusted during the training process of the neural network, commonly through the backpropagation algorithm, where the input-output example patterns are presented to the neural networks [39]. The main advantage of ANNs is the data-driven self-adaptive capabilities that allow ANNs to adapt to the data they have been trained on [41]. A basic structure of ANN is presented in Fig. 1. Fig. 1 Basic structure of ANN [39] In order to teach the neural network, sufficient amount of data is needed. The data can either be provided by experiments or by simulations, including finite element method [39]. A large enough number of FEM simulations was also performed in here-presented study with a goal to provide data points on which the neural network is trained. One of the advantages of using ANN model is easy construction of said model on provided input and output data values with the goal of accurately predicting process dynamics [42]. Machine learning, deep learning, artificial intelligence and more specifically artificial neural networks are being used in many fields, including state of tools, defect detection, forming pro- cesses and material science [43-46]. In the study by Czinege and Harangozo [46], experimental data from tensile tests and Nakazima tests were used as input data for the ANN. The ANN models allowed estimation of points of the forming limit curve [46]. ANN models gave high correlation coefficient between predicted and measured values, which was better compared to capabilities of other linear and non-linear models [46]. Multi-layer perceptron (MLP) artificial neural networks are good for classification and for regression, which is also one of the reasons for being used in the study by Czinege and Harangozo [46]. MLP ANN requires a proper selection of the number of hidden layers and data splitting into training set, test set and validation set [46, 47]. In order to predict the flow curves of ZAM100 magnesium alloy sheets under hot-forming conditions as a function of process parameters, El Mehtedi et al. [48] developed an empirical model based on ANNs. ANN model predicted the flow stress as a function of strain, strain rate and temperature [48]. The ANN from the study by El Mehtedi et al. [48] had 6 input parameters and one output of equivalent stress, and it also had two hidden layers with 6 neurons each. The back-propagation training and validation of the multi-layer feed forward ANN was performed using MATLAB soft- ware [48]. Great capabilities of the set model were proven with excellent fitting between experi- mental and predicted curves [48]. For the reason of evaluating the prediction capabilities, the cor- relation coefficient (R) was considered, which compares predicted values and experimentally pro- duced data [48]. The model for predicting flow curves requires a sufficient number of experiments to obtain the necessary data on which it can be trained, which is expensive and time-consuming Sevšek, Vilkovský, Majerníková, Pepelnjak 50 Advances in Production Engineering & Management 19(1) 2024 [48]. ANN models are often used also in the field of metal forming. In the study by Gondo and Arai [37] an ANN was developed for metal spinning using tool-path parameters, the size of the blank, size of the tools and the height and the thickness of the part. In the study by Xia et al. [45] multi- layer feed-forward perceptron ANN models with back-propagation were used to investigate the influence of rolling parameters on the rolling force, rolling power, and slip of tandem cold rolling. Different ANN architectures had been tested and the ANN configuration of one hidden layer with 9 neurons provided the best results [45]. In the study by Kazan et al. [39] a prediction model using ANN was developed in the field of wipe-bending. The training of the ANN model was done on the data provided by FEM simulations [39]. In the study by Sivasankaran et al. [42] a feed forward back-propagation neural network was presented for predicting and avoiding surface failure, in- cluding wrinkling, during pure aluminium sheet drawing through a conical die. The neural net- work had two hidden layers with different numbers of neurons for different grades of aluminium sheets tasted [42]. The study by Babu et al. [49] focused on developing an expert system using ANN to predict the deep drawing behaviour of welded blanks made of steel grade and aluminium alloy. FEM code is used for forming simulation and data generation for ANN training [49]. ANNs with one hidden layer with 6 neurons, 6 neurons on the input layer and one neuron on the output layer are used for four different output parameters, including depth of drawing [49]. In the study by Ma- noochehri and Kolahan [50] an ANN was developed based on FEM results in the case of deep drawing, where important process parameters as inputs and process characteristics as outputs were considered. FEM models were verified with experimental tests using same parameter val- ues, including stainless steel 304 (AISI 304) with 0.5 mm thickness with its mechanical properties and anisotropic coefficients [50]. In the study by Manoochehri and Kolahan [50] ABAQUS/Explicit software was used to develop FEM models of the deep drawing process, where the depth of draw- ing was 30 mm. The input parameters considered were blank holder force, punch radius, die ra- dius, friction coefficient between punch and blank as well as die and blank, while the output pa- rameter was minimum sheet thickness after forming [50]. An ANN with two hidden layers was developed in MATLAB software [50]. 2. Material and methods 2.1 Used materials TRIP steels prove highly effective in manufacturing automotive components that undergo signifi- cant work hardening during crash deformation and necessitate substantial energy absorption. Additionally, these steels are particularly well-suited for forming intricate and challenging to form parts due to their exceptional formability and hardening characteristics. In the experimental re- search, a double-sided galvanized steel sheet TRIP RAK40/70 Z100MBO with a thickness of 0.75 mm was utilized. To determine the mechanical properties, a uniaxial tensile test was conducted on the TIRAtest2300 machine (Fig. 2) according to the STN EN ISO 6892-1:2020 standard. During the examination, 5 test samples were assessed in three directions: 0°, 45°, and 90° degrees with respect to the rolling direction (see Fig. 3). The mechanical properties obtained using uniaxial tensile test are displayed in Table 1. The chemical composition of the experimental material TRIP RAK40/70 Z100MBO is shown in Table 2. Table 1 Mechanical properties of TRIP RAK40/70 Z100MBO Table 2 Chemical composition of TRIP RAK40/70 Z100MBO wt. % C Mn Si P S Al Nb Ti V Mo Cr 0.204 1.683 0.199 0.018 - 1.731 0.004 0.009 0.004 0.008 0.055 RD (°) Rp0,2 (MPa) Rm (MPa) A80 (%) r (-) rm (-) Δr (-) n (-) 0 435 764 29 0.702 0.834 -0.100 0.298 45 443 763 29 0.884 0.294 90 449 764 31 0.867 0.279 Predicting the deep drawing process of TRIP steel grades using multilayer perceptron artificial neural networks Advances in Production Engineering & Management 19(1) 2024 51 Fig. 2 TIRAtest2300 testing machine Fig. 3 Samples after uniaxial tensile test: a) in the RD direction 0°; b) in the RD direction 45°; c) in the RD direction 90° 2.2 Deep drawing test Deep drawing is a sheet metal forming technique where a sheet metal blank is radially drawn into a forming die by mechanical energy. This process is notably influenced by material properties, as well as geometric and technological parameters. Key material parameters include elasticity, plas- ticity, and anisotropy. Moreover, parameters like punch velocity, blank holding force, and lubrica- tion are crucial, besides the radius of the punch and die, the thickness of the blank, and the clear- ance between the punch and die. Improperly defining these parameters can lead to defects such as surface scratches, wrinkling, and tearing due to excessive thinning. The paper focuses on ana- lysing how various technological and material parameters affect the key characteristics of the product and its forming process. These characteristics include deep-drawing force, earing, and thinning. In the experimental research, three circular blanks with a diameter of 95 mm were cut from the sheet metal strip, from which cylindrical cups with a flat bottom were subsequently drawn on an experimental deep drawing tool (Fig. 4a) with the parameters shown in Fig. 4b. In the deep drawing test, oil was used as a lubricant to reduce the coefficient of friction. The holding force was set to 18000 N. During the deep drawing process, it is essential to comprehend the maximum deep drawing force and the impact of input parameters on its magnitude. This understanding is fundamental for selecting the appropriate machine with the designated force. To measure the force during our experiment, we employed a load cell integrated into the forming press. During the deep drawing test, the load cell recorded and transmitted force data to a connected data acquisition system. The force was monitored and recorded throughout the entire process of deep drawing. Sevšek, Vilkovský, Majerníková, Pepelnjak 52 Advances in Production Engineering & Management 19(1) 2024 Fig. 4 a) Experimental deep drawing tool, b) parameters of the tool, where: Dp (punch diameter) = 50 mm, Dd (die diameter) = 52.4 mm, Rp (punch radius) = 5 mm, Rd (die radius) = 5.5 mm Furthermore, we focused on understanding the influence of the parameters on earing, charac- terized by the development of a wavy edge at the open end of the cup. In this paper, earing was assessed as the difference between the highest (H max) and lowest (H min) measured heights on the cups, as defined by Eq. 1, where ΔH represents ear height. Δ 𝐻𝐻 = 𝐻𝐻 𝑚𝑚𝑚𝑚 𝑚𝑚 − 𝐻𝐻 𝑚𝑚 𝑚𝑚𝑚𝑚 (1) According to the value of ∆ r, it is possible to determine the susceptibility of the sheet to the formation of ears during deep drawing. Ears are formed in the directions of the sheet where the value of the coefficient of normal anisotropy r is maximum, if: • ∆r > 0 ears will form in the directions of 0° and 90° to the rolling direction, • ∆r = 0 ears will not form, • ∆r < 0 ears will form in the direction of 45°. The height of the ears (Fig. 5a) was measured with a sliding calliper at eight locations on the cups (Fig. 5b). Subsequently, according to Eq. 1, the maximum difference in the height of the cups was calculated. We also focused on the thinning of the sheet, which was expressed by the t min value, which represented the lowest measured value of the sheet thickness after forming. Thinning of the blank typically occurs at the transition point from the cylindrical part to the bottom of the blank. Exces- sive thinning in these areas can lead to the formation of cracks. The thinning itself is affected by the initial thickness of the sheet metal and by the diameter of the tool. When assessing the impact of these parameters on thinning, it is crucial not to overlook the material parameters. After measuring the heights, the experimental cups were cut in half, allowing us to measure the thickness of the cups and obtain the values of thinning across the cross-section. The thinning of the sheet was measured using an optical microscope (Fig. 6a) at the transition point between the cylindrical part and the bottom of the cup as shown in Fig. 6b. Fig. 5 a) Ear height on the cup, b) Measurement of ear heights on the cup Predicting the deep drawing process of TRIP steel grades using multilayer perceptron artificial neural networks Advances in Production Engineering & Management 19(1) 2024 53 Fig. 6 a) Microscope used for thickness measurement, b) thickness measurement points 2.3 Finite element method setup The simulation of the deep drawing process was performed using the ABAQUS simulation soft- ware environment, utilizing the explicit method. The CAD model of the drawing tool used in the simulation had identical dimensions to the experimental tool (see Fig. 4b). The blank model was given the characteristics of TRIP steel, which were acquired through the uniaxial tensile test (see Table 1). The material density was 7850 kg/m 3 , the Young's modulus was 210,000 MPa, and the Poisson ratio was 0.33. During the simulations, the Hollomon approximation was used to describe the flow curve of the material. The sheet material was considered anisotropic using yield criteria according to Hill. The simulation time for the explicit simulation method was set to 0.5 seconds. According to the finite element method, the simulation of technological processes requires the meshing of the entire set of 3D objects (rigid as well as deformable models) with finite elements. For all rigid bodies (punch, die, and blank holder), R3D4 quadrilateral shell finite elements and R3D3 transition triangle elements were used. In terms of workpiece meshing, concentric mapped quadrilateral finite elements S4R were chosen for the outer section, while a freely meshed combi- nation of quadrilateral finite elements (S4R) and triangular finite elements (S3) was utilized for the central part. Since the size of the blank was one of the parameters that was regularly changed in each sim- ulation, the number of elements was different in each simulation. Table 3 shows the number and types of elements used in simulations for every 3D model used in simulations. Fig. 7 shows the mesh of the blank used in the simulation. Table 3 Number and types of elements used in simulations Object Number of elements Type of element Punch 1634 R3D4, R3D3 Die 4200 R3D4 Blank Holder 2040 R3D4, R3D3 Blank varied S4R, S3 Fig. 7 Mesh of blank CAD model Sevšek, Vilkovský, Majerníková, Pepelnjak 54 Advances in Production Engineering & Management 19(1) 2024 The procedure involved conducting 50 simulations in which 8 independent input parameters were randomly varied. These parameters include blank diameter (D 0), blank holding force (F bh), friction coefficient (f), material constant (C), hardening exponent (n), and normal anisotropy co- efficient values (r) in the 0°, 45°, and 90° directions. Additionally, one dependent parameter, the yield strength (R p). Table 4 displays the range of input parameters within which values were ran- domly selected for individual simulations. Values from these intervals were selected randomly for each simulation using the random function in Microsoft Excel. Table 5 shows the values of the input parameters used in the simulations. Table 4 Range of input parameters used in simulations Table 5 Randomly selected input values used in individual simulations Simulation number D0 (mm) Fbh (N) f (-) Rp (MPa) C (MPa) n (-) r0 (-) r45 (-) r90 (-) 1 88.4 17778 0.11 491 1512 0.23 0.93 0.74 0.89 2 96.9 18078 0.15 308 1038 0.28 0.64 0.8 0.65 3 100.4 19788 0.07 418 1372 0.27 0.63 0.62 0.75 4 90.6 18082 0.19 308 1112 0.3 0.99 0.7 0.72 ….. … … … … … … … … … 50 87.8 16560 0.1 385 1076 0.23 0.92 0.69 0.95 2.4 Artificial neural network With the aim of making predictions of forming force value, sheet metal thinning and ear height for the deep drawing process and product, artificial neural networks (ANNs) had been set up. For this study, a separate ANN was set up for every output parameter that considered all 9 input parame- ters. In order to allow faster training of the neural network and good regression of the results, multilayer perceptron artificial neural networks (MLP ANN) had been used. This is an ANN model that used backpropagation learning algorithm. The basis of MLP ANN remains the same, meaning transformation of input values into output values or predictions. To better understand the process of MLP ANN, Eq. 2 shows the basic function, where y is the output value, x is the input value, w are weights and b are biases. 𝑦𝑦 = 𝑓𝑓 ( 𝑛𝑛𝑛𝑛 𝑛𝑛 ) = 𝑓𝑓 � � 𝑤𝑤 𝑚𝑚 𝑥𝑥 + 𝑏𝑏 𝑚𝑚 𝑚𝑚 = 1 � (2) The basis for training an ANN is a sufficient number of data points, which was in our case pro- vided by 50 finite element method simulations with different values of input parameter values and their corresponding values of output parameters of forming force, minimum sheet thickness and ear height. To set up the architecture for all three ANNs of three different output parameters, data had to be divided into subsets for training and for testing. A preliminary investigation showed that the best possible division of the data is 90 % for training and the rest for testing, meaning 45 points are used for training and five points out of 50 are used for testing. Once the lengthy process of training is complete, the set ANNs can be used for prediction pur- poses. All three ANNs of three considered output parameters are based on the feed-forward mul- tilayer perceptron (MLP) and are thus divided into layers. On every layer there is at least one neuron. The layers present within an MLP ANN are the input, output and at least one hidden layer. On the input layer there are as many neurons as there are input parameters, which in the case of Parameter Minimal value Maximal value D0 (mm) 86 102 Fbh (N) 16000 20000 f (-) 0.05 0.20 Rp (MPa) 300 700 C (MPa) 900 1800 n (-) 0.2 0.35 r0 (-) 0.6 1 r45 (-) 0.6 1 r90 (-) 0.6 1 Predicting the deep drawing process of TRIP steel grades using multilayer perceptron artificial neural networks Advances in Production Engineering & Management 19(1) 2024 55 our study is equal to 9. In the case of our study there is only one neuron on the output layer of all three neural networks which corresponds to one output parameter of either forming force value, minimum sheet thickness or ear height. Within the preliminary study the number of hidden layers was set to five for every neural network and their corresponding output parameter. The same is true for the number of neurons on these five hidden layers, where 60 neurons had been chosen for all five hidden layers for all three neural networks. The configuration of hidden layers and corresponding number of neurons can be written as (60, 60, 60, 60, 60). Within the neural network the value leaving a specific neuron is affected by the weight and the bias value before entering a specific neuron of the next layer. An important role is played by the activation function which removes certain values and maps modified remaining values. Many dif- ferent activation functions had been tested in a preliminary study and a decision had been made to use sigmoid or logistic activation function on the neurons of the hidden layers and linear or identity activation function to be used on the output layer of all three set ANNs within this study. Eq. 3 represents sigmoid and Eq. 4 the linear activation function. Additionally, Adaptive Moment Estimation (ADAM) solver type had been used in MATLAB program environment, used for train- ing of the ANNs and for predictions made used trained ANNs. Initial learning rate value was cho- sen to be 0.1 for all set ANNs and the value of the learning rate remained constant throughout the neural network training process. L2 regularisation was used, and its value chosen as 0.001 for all ANNs within the study. The essential hyperparameter values for all three ANNs are written in Table 6. For a better understanding of the ANN configurations for this study, Fig. 8 shows a sche- matic presentation of all the neurons within input, output and hidden layers. With all the chosen values of hyperparameters that define the ANN architecture, the training of three different ANNs of all three tested output parameters has been carried out. 𝑓𝑓 ( 𝑥𝑥 ) = 1 1 + 𝑛𝑛 − 𝑚𝑚 (3) 𝑓𝑓 ( 𝑥𝑥 ) = 𝑥𝑥 (4) Table 6 Hyperparameters chosen for three ANNs within the study for the corresponding output parameters of forming force, minimum sheet thickness and ear height Hidden layer sizes Activation function Solver Initial learning rate Learning rate type L2 (60 60 60 60 60) Sigmoid ADAM 0.100 Constant 0.001 Fig. 8 Schematic representation of the ANNs used within here presented study; input layer with 9 neurons of the 9 tested input parameters, 5 hidden layers with 60 neurons each and an output layer with one neuron for one output parameter within a single ANN. 3. Results and discussion As part of the deep drawing test, three cups with a flat bottom were drawn out of circular blanks with a diameter of 95 mm. Three parameters were examined: deep drawing force, minimal thick- ness, and ear height. Fig. 9 shows cups from TRIP RAK40/70. Sevšek, Vilkovský, Majerníková, Pepelnjak 56 Advances in Production Engineering & Management 19(1) 2024 Fig. 9 Cups made of TRIP RAK40/70 steel after deep drawing test Within the framework of the experiment deep drawing forces with values of 84315 N for cup 1, 84490 N for cup 2 and 84490 N for cup 3 were measured. These values were measured by sub- tracting the holding force from the maximum force measured. The plot of the forces is shown in Fig. 10. Fig. 10 The course of measured force during the experiment of deep drawing The measured values of the ear heights in the eight measured directions are shown in Table 7. The ΔH value (the difference between the maximum and minimum ear height) was calculated for each cup, and the average value was subsequently determined. As shown in Table 7, the most significant disparity in the measured heights occurred at cup 3, where the discrepancy between the maximum and minimum height reached 1.31 mm. The arith- metic average for the parameter ΔH was calculated to be 1.23 mm. The sheet thickness after the deep drawing test was measured at five points along the cross- section of the cups at the transition from the cylindrical part to the bottom of the cups. The exam- ined sheet thicknesses after the deep drawing tests are shown in Table 8. From the measured thicknesses, the smallest obtained value (t min) was evaluated. From the value t min, the arithmetic average was calculated within the three cups. Fig. 11 shows the measurement of sheet metal thick- ness at the bottom radius of the second cup. Table 7 Ear height values of the cups in eight directions along with the calculated ΔH value Cup number H0 (mm) H45 (mm) H90 (mm) H135 (mm) H180 (mm) H225 (mm) H270 (mm) H315 (mm) ΔH (mm) 1 33.61 34.11 33.07 33.17 32.93 33.25 32.86 33.84 1.25 2 32.95 33.96 33.58 34.09 33.22 33.58 32.98 33.65 1.14 3 33.65 34.52 33.67 34.02 33.53 33.95 34.02 34.84 1.31 avg. ΔH (mm) 1.23 Predicting the deep drawing process of TRIP steel grades using multilayer perceptron artificial neural networks Advances in Production Engineering & Management 19(1) 2024 57 Fig. 11 Measurement of thinning at the bottom radius of the test cup Table 8 Minimal thickness values of the cups in five measured points along with the tmin value A deep drawing test simulation was performed with same parameter values as the performed experiments. The explicit method in the ABAQUS simulation program was used. The maximum deep drawing force, thinning value, and ear heights were measured in eight directions, from which the ΔH value was calculated using Eq. 1. Fig. 12 shows the cup shape after the performed simulation. The results of the 50 simulations present the influence of 9 input parameters on the three mon- itored outputs, which are the maximum deep drawing force, minimum sheet thickness and earing. The results of 50 simulations in which the input parameters were randomly selected (see Table 5) from the interval of values (see Table 4) are shown in Table 9. As we can see, changing the 9 input parameters monitored significantly affects the observed output parameters. Fig. 12 Result of the simulation of deep drawing test using ABAQUS Cup number tA (mm) tB (mm) tC (mm) tD (mm) tE (mm) tmin (mm) 1 0.65 0.64 0.64 0.64 0.67 0.64 2 0.71 0.67 0.67 0.68 0.68 0.67 3 0.65 0.62 0.62 0.62 0.65 0.62 avg. tmin (mm) 0.64 Sevšek, Vilkovský, Majerníková, Pepelnjak 58 Advances in Production Engineering & Management 19(1) 2024 Table 9 Results of 50 simulations carried out in ABAQUS simulation software Simulation number Fmax (N) tmin (mm) Hmax (mm) Hmin (mm) 𝚫𝚫 𝑯𝑯 (mm) 1 77814 0.713 27.32 26.41 0.91 2 63907 0.641 35.26 33.92 1.34 3 84826 0.653 37.11 36.52 0.59 4 62045 0.672 30.01 28.79 1.22 ….. … … … … … 50 54482 0.713 26.34 25.07 1.27 With all the chosen values of hyperparameters that define the ANN architecture, the training of three different ANNs of all three tested output parameters has been carried out. Trained neural networks allow for predictions to be carried out. Figs. 13, 14 and 15 show diagrams comparing original output values provided by simulations and predicted values using trained ANNs that were provided by using the same input parameter values. If the predictions perfectly matched the orig- inal values, then a straight line would be seen on the diagrams. But as we can see, a slight discrep- ancy is evident. To further understand the predictive capabilities of all three ANNs two coefficients were calculated, namely correlation coefficient R and coefficient of determination R 2 . Using the MATLAB program environment, the value for R squared was calculated automatically at the end of the ANN training process. R 2 value (Table 10) was calculated with the use of Eq. 5, where sim- ulation output parameter values y i are compared to ANN predicted values 𝑦𝑦 � 𝑚𝑚 . For the predicted values using ANN, same input parameter values were used as in the case of the FEM simulations. To better understand the predictive capabilities of ANNs and to show the general correctness of the simulations performed, Fig. 16, Fig. 17 and Fig. 18 show a comparison of the values obtained with an experimental method, an explicit simulation and a neural network using the same input parameters (see Table 11). Table 10 Evaluation of set ANNs for three different output parameters using R and R 2 Output parameter R R 2 Forming force 0.975 0.949 Sheet metal thickness 0.953 0.907 Ear height 0.926 0.844 Fig. 13 Comparison of simulation results and predicted values by ANN for the output parameter of forming force value Predicting the deep drawing process of TRIP steel grades using multilayer perceptron artificial neural networks Advances in Production Engineering & Management 19(1) 2024 59 Fig. 14 Comparison of simulation results and predicted values by ANN for the output parameter of minimum sheet thickness Fig. 15 Comparison of simulation results and predicted values by ANN for the output parameter of ear height Table 11 Parameters used in the experiment, explicit simulation and ANN with results shown in Figs. 16 to 18 D0 (mm) Fbh (N) f (-) Rp (MPa) C (MPa) n (-) r0 (-) r45 (-) r90 (-) 95 18000 0.1 422.3 1488 0.28 0.702 0.884 0.867 Sevšek, Vilkovský, Majerníková, Pepelnjak 60 Advances in Production Engineering & Management 19(1) 2024 Fig. 16 Comparison of measured and calculated maximal deep drawing force values Fig. 17 Comparison of measured and calculated tmin values Fig. 18 Comparison of measured and calculated ΔH values 4. Conclusion Optimisation of the deep drawing process is crucial due to its wide application in the automotive industry. Constantly increasing requirements for reducing emissions force designers to utilize high-strength materials, resulting in a reduction in the weight of structures. The demands on the industry are constantly growing, leading to the development of new methods for optimizing the deep drawing process. Artificial intelligence plays a pivotal role in this, with its increasingly fre- quent integration into technological processes. Thanks to constant improvement in this field, the output parameters of deep drawing can be predicted. In this study, ANN was used to predict the output parameters, the results of which were compared with experimental values and simulation using the explicit integration method. The paper has focused on the analysis of various technological and material parameters that influence the key properties of the forming process. The results of the experiment demonstrate the potential for employing various methods and their integration to predict selected output pa- rameters, such as evaluating the maximum deep drawing force, thinning and earing expressed Predicting the deep drawing process of TRIP steel grades using multilayer perceptron artificial neural networks Advances in Production Engineering & Management 19(1) 2024 61 through the difference between the maximum and minimum yield height. In the experimental part of the research, a deep-drawing tool with defined geometry was used. Double-sided galvanized steel sheet TRIP RAK40/70 was chosen as the test material. TRIP steels represent a material that combines exceptional forming properties with strength. In the simulations, eight independent input parameters and one dependent input parameter, which was the yield strength (R p), were randomly varied. Independent input parameters include blank diameter (D 0), blank holding force (F bh), coefficient of friction (f), material constant (C), strain hardening exponent (n) and normal anisotropy coefficient values (r) at 0°, 45°, and 90° di- rections. The experiment proved the correctness of the simulation of the deep drawing process for the prediction of the selected output parameters, considering the variability of the use of pos- sible input parameters that affect the forming process. In order to predict the selected output pa- rameters, artificial neural networks were developed. Each output parameter was modeled by its own dedicated ANN, considering all nine input parameters for this study. In order to provide a sufficient amount of data to train the ANNs, a sufficient number of simulations had to be carried out. Running a simulation took between one to two hours, which is a lengthy process. The training of the ANNs and the predictions with the trained ANNs were performed on a computer with an Intel Core i7-1065G7 processor with 3.6 GHz and 16 GB RAM. The training of the ANNs took sev- eral minutes, while the prediction process took less than one second after the input values of all input parameters were provided to the ANN. As can be seen from Table 10, the prediction of the maximum deep drawing force using ANN achieved the best results within all evaluated parameters with a value of R 2 = 0.949. When enter- ing the input parameters, which were identical to the performed experiment, the prediction using ANN reached the maximum deep drawing force of 88792 N. During the simulation, it was meas- ured as 82911 N compared to the deep drawing force of 84315 N during the experiment. The same values of the input parameters used in the experiment and in the simulation and provided to the ANN are listed in Table 11. One of the main difficulties in the deep drawing process lies in optimizing the thinning as it can lead to reduced mechanical strength in the final product. If the thinning reaches a critical value, it can lead to failure. As part of the experiments, thinning was evaluated on three cups. The meas- ured minimal thickness (t min) reached the value of 0.64 mm for cup 1, 0.67 mm for cup 2 and 0.62 for cup 3. When comparing the arithmetic mean of these three values, we register a difference of 0.047 mm compared to the results from the simulation using the explicit method. In all three ex- perimental cups, a smaller wall thickness value was measured compared to the simulation, where t min reached a value of 0.693 mm using same input parameter values listed in Table 11. When com- paring original output values provided by 50 simulations and predicted values using trained ANNs that were provided same 50 sets of input parameter values, R 2 of 0.907 was calculated. The trained ANN predicted a minimum thickness of 0.696 mm when entering exact values of the experiment listed in Table 11. The most significant discrepancy in predicting the output parameters was measured in the case of ear height, evaluated using the ΔH parameter. When comparing the dif- ference in maximum and minimum cup height, the deviation between simulation and experi- mental results was found to be 0.21 mm for the same input parameter values. ANN showed supe- rior performance in this regard, with the difference narrowing to 0.04 mm. The calculated R 2 value for the ANN was 0.844 when comparing 50 results from simulations and predictions made with trained ANN using same input parameter values. With this value of R 2 parameter, we can state that this value was influenced by the manual measurement of heights after the experiments and sim- ulations, that were utilized to train the ANN. The conducted research provides a strong foundation for the continued utilization of the Finite Element Method and Artificial Neural Network techniques in the field of predicting the critical output parameters of deep drawing such as maximal deep drawing force, thinning and earing. With the aim of predicting the crucial output parameter values of the deep drawing process and providing additional control of the process itself, our future work will focus on the following: Sevšek, Vilkovský, Majerníková, Pepelnjak 62 Advances in Production Engineering & Management 19(1) 2024 • Analysis of different tool geometry for the production of a cylindrical cup with a smaller inner diameter. Experiments, simulations and ANNs will be set for the use of a smaller tool and compared with the results obtained with the tool in the study presented here. • Analysis of different steel grades and their performance during the deep drawing process. Further extension of the predictive capabilities of ANN models for more extensive material parameter ranges. • Analysis of deep drawing of more complex part shapes. Experiments and simulations for different tool and thus part shapes would enable the development of more flexible ANN models that would allow the prediction of important deep drawing output parameters for a larger number of selected part shapes. Acknowledgement This paper was written with the financial support of the granting agency APVV within the project solution APVV-21- 0418 and support from the Slovenian Research Agency ARIS (research core funding No. P2-0248). References: [1] Spišák, E., Majerníková, J. (2014). A study of thickness change of spherical cup made from TRIP steel after hydrau- lic bulge test, Key Engineering Materials, Vol. 635, 157-160, doi: 10.4028/www.scientific.net/KEM.635.157. [2] Lai, M., Brun, R. (2007). 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