Thermo-Mechanical Simulation and ANN-Based Prediction of Rolling Force and Torque in Two-Layer Copper–Aluminum Composite Panel

Thermo-Mechanical Simulation and ANN-Based Prediction of Rolling Force and Torque in Two-Layer Copper–Aluminum Composite Panel | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Thermo-Mechanical Simulation and ANN-Based Prediction of Rolling Force and Torque in Two-Layer Copper–Aluminum Composite Panel Alireza Jalili, Hamidreza Rezaei Ashtiani This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8495786/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this study, a hybrid modeling framework combining three-dimensional finite element (FE) simulation and artificial neural network (ANN) prediction is developed to analyze the asymmetric hot rolling behavior of a two-layer Cu/AA2030 composite panel. The FE model, implemented using the Abaqus/Explicit platform, couples thermal and mechanical fields to evaluate the effects of key process parameters including initial panel thickness, reduction ratio, rolling speed, and inlet temperature on rolling force and torque. The asymmetric configuration of the composite panel and the thermal-mechanical interaction between the rolls and panel are fully considered in the simulation. A validated FE dataset was subsequently employed to train a feed-forward back-propagation ANN using the Levenberg–Marquardt algorithm. The network architecture, consisting of four input neurons, two hidden layers, and two output neurons, was optimized to achieve minimum mean square error (MSE) and high correlation accuracy between predicted and simulated values. Results indicate that both rolling force and torque increase with greater thickness reduction and initial panel thickness, while higher rolling temperatures and rolling speeds reduce the required force and torque. The ANN model successfully predicts rolling force and torque with high accuracy, demonstrating strong generalization and computational efficiency. This integrated FE–ANN approach provides a reliable and time-effective method for optimizing process parameters in bimetallic panel rolling, reducing the need for extensive experimental trials and enabling improved control of rolling performance in copper–aluminum laminated composites. Asymmetric Hot Rolling Finite Element Simulation (FE) Artificial Neural Network (ANN) Rolling Force and Torque Prediction Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 1. Introduction Bimetallic composite materials are extensively utilized across various industries such as aerospace, automotive manufacturing, photovoltaic energy systems, electronic communication, power transmission, architectural decoration, and precision instrumentation. The Cu/Al clad panel is a type of composite material formed by bonding copper and aluminum through different fabrication processes. This combination integrates the superior properties of both metals offering the excellent electrical conductivity of copper along with the light weight and cost-effectiveness of aluminum. As a result, Cu/Al clad panels have found broad applications in numerous industrial and everyday contexts [ 1 – 3 ]. High-temperature deformation represents a critical stage in the manufacturing process. The behavior of materials under hot deformation is strongly affected not only by processing parameters such as temperature, strain rate, and applied strain but also by the steel’s chemical composition. Therefore, investigating and accurately modeling the hot deformation response is essential for optimizing forming processes through finite element simulations [ 4 , 5 ]. The study of the rolling process traces back to the foundational research of Orowan [ 6 ], who proposed a comprehensive theory extending the traditional slab method by accounting for the non-uniform plastic deformation of the panel and the elastic deformation of the rolls. In a study [ 7 ], the principal stress method is utilized to formulate a comprehensive mathematical model for predicting the rolling force during the asymmetric rolling process. The model integrates the equilibrium differential equations, yield criterion, geometric constraints, and boundary conditions to accurately determine the rolling pressure distribution. Furthermore, a detailed parametric analysis is conducted to examine the effects of key process variables on the rolling force, the neutral point position, and the extent of the cross-shear deformation zone, thereby providing a theoretical framework for optimizing the rolling process of Cu/Al clad panels. In a study [ 8 ], the hot roll bonding process of 7000-series aluminum alloy laminated materials was investigated using finite element numerical simulations, and the process parameters were validated experimentally through mechanical property testing and microstructure analysis. The study examined the effects of the intermediate layer, pass reduction ratio, rolling speed, and thickness ratio of the component layers on the deformation and overall behavior of the laminated materials. The results indicated that the inclusion of an intermediate layer and the use of a multi-pass rolling process could effectively prevent warping and delamination, while achieving successful metallurgical bonding between the layers. In some study [ 9 ], an analytical model for predicting the rolling force and thickness ratio of bimetallic composite plates has been proposed based on a novel hypothesis derived from Orowan’s [ 6 ] theory. In these investigations, the model was developed using the principal stress method in combination with the slab method, and its validity was assessed through both experimental testing and numerical simulations. The methodologies employed included the formulation of a mathematical model based on Orowan’s [ 6 ] unit pressure differential equation and the calculation of the average rolling force for each layer. Additionally, theoretical analysis, laboratory experiments, and finite element simulations using a reversible two-roller mill and ABAQUS software were implemented to further verify the model. P. Chandrasekar [ 10 ] fabricated aluminum matrix composites and observed that applying a chemical coating during the fabrication process can enhance the bonding strength of the resulting composites. M. Heydari Vini [ 11 ] produced 1050 aluminum/5083 aluminum composites using an accumulative roll bonding process. The study demonstrated that both the bonding strength and tensile ductility of the clad panels improved as the number of laminated layers increased, indicating that an appropriate increase in layer count can effectively enhance the overall bonding quality of the composite panels. Human limitations make it challenging to analyze the large-scale datasets associated with the properties of complex materials such as industrial steel. This challenge can be effectively addressed using machine learning techniques, particularly through the application of artificial neural networks (ANNs). Artificial neural networks (ANNs) offer an effective approach for predicting functional relationships without relying on pre-established physical laws. This methodology typically achieves very low computational error, though it necessitates a large experimental dataset for training. Liu et al [ 12 ]. demonstrated that an ANN-based model can accurately capture the hot flow behavior of 42CrMo steel, outperforming conventional Arrhenius-type models. Comparable levels of accuracy have been reported for other steels, including API 5CT-L80 [ 13 ], AISI 1045 [ 14 ], 9Cr-1Mo [ 15 ], 10Cr [ 16 ] and 40Mn [ 17 ]. In addition, K. Arun Babu et al. [ 18 ] developed a dynamic recrystallization model for super-austenitic stainless steel using an ANN framework. Nevertheless, these studies have focused on steels with fixed chemical compositions and have not leveraged the capability of ANNs to systematically evaluate how variations in alloying element concentrations influence hot deformation behavior. Yang et al. [ 19 ] developed a neural network-based approach for predicting roll force and torque, eliminating the need for physically-based or empirical models. To enhance predictive accuracy, they employed ensemble modeling techniques. In a related study, Lee and Choi [ 20 ] introduced an online adaptive neural network for rolling force control, addressing key aspects such as network architecture, selection of input parameters, debugging procedures, development platforms, and evaluation of test results. In this study, the hot rolling force and torque behavior of an asymmetric two-layer sandwich panel composed of 2030 aluminum alloy and pure copper was investigated using simulations in Abaqus/Explicit. Considering the asymmetry of the panel, a fully detailed geometric model of the rollers and the composite panel was developed. Key process parameters, including the initial panel temperature, layers thickness, thickness reduction in different sections, and roller rotational speed, were analyzed under various conditions to optimize simulation time and assess the influence of these factors on rolling behavior. Furthermore, a neural network model was developed to accurately predict rolling force and torque under diverse rolling conditions. The data required for training and validation of the neural network were generated through a three-dimensional finite element model. The results demonstrate that the neural network model exhibits high accuracy in predicting rolling force and torque, offering an effective and time-efficient alternative to conventional, labor-intensive experimental trials. 2. Mathematical Model 2.1. Thermal equations As an investigation of the hot rolling process, Performs heat transfer an important role in hot rolling, because due to the influence of the panel and roller under temperature fields and in order to consider the temperature distribution inside the panel, the thermal conductivity equations governing the panel and roller must have the characteristic thermo-physical values ​​and flow stress as a function of temperature; also, formulas and thermo-physical properties should be up-to-date in order to be able to correctly answer the investigation of convection currents and rolling conductivity and simulation conditions. Considering the temperature distribution equation in the roller, it is assumed that the heat conduction along the peripheral direction is insignificant compared to the bulk heat flow and the thermal conduction at the interface of the panel is the same as the lower part [ 21 ] thus: $$\:\frac{1}{r}\frac{\partial\:}{\partial\:r}\left(\:{k}_{r}\:r\:\frac{\partial\:T}{\partial\:r}\:\right)+\frac{\partial\:}{\partial\:z}\left(\:{k}_{r}\:\frac{\partial\:T}{\partial\:z}\:\right)={\rho\:}_{r}*{C}_{rp}\:\left(\:\:\frac{\partial\:T}{\partial\:t}\:\right)$$ 1 During the hot rolling process, the temperature in the panel is distributed according to the three-dimensional partial differential equation that governs the solution of the problem, where \(\:{\rho\:}_{r}\) is the density of the work roll, \(\:{C}_{rp}\) (j kg − 1 °C − 1 ) is the specific heat of the work roll, \(\:{k}_{r}\) (kW m − 1 °C − 1 ) is the thermal conductivity of the work roll, and this three-dimensional differential equation can be seen in Eq. ( 2 ) [ 21 ]: $$\:\frac{\partial\:}{\partial\:x}\left(\:{k}_{s}\:\frac{\partial\:T}{\partial\:x}\:\right)+\frac{\partial\:}{\partial\:y}\left(\:{k}_{s}\:\frac{\partial\:T}{\partial\:y}\:\right)+\frac{\partial\:}{\partial\:z}\left(\:{k}_{s}\:\frac{\partial\:T}{\partial\:z}\:\right)+\dot{q}={\rho\:}_{s}*{C}_{sp}\:\left(\:\:\frac{\partial\:T}{\partial\:t}\:\right)$$ 2 where \(\:{\rho\:}_{s}\) is the density of the rolled panel, \(\:{C}_{sp}\) (j kg − 1 °C − 1 ) is the specific heat of the rolled metal, \(\:{k}_{s}\) (kW m − 1 °C − 1 ) is the thermal conductivity of the rolled panel, in the partial differential Eq. ( 2 ), (x) represents the distance along the panel and the rolling direction, (y) represents the distance from the thickness, and the parameter (z) is the distance along the width of the panel, and \(\:\dot{q}\) (W.m − 3 ) is the amount of heat produced by the plastic work, and the subscripts r and s are respectively for It is a roller and panel that is used to generate heat from Eq. ( 3 ): $$\:\dot{q}=\stackrel{-}{\eta\:}*\stackrel{-}{\sigma\:}*\dot{\epsilon\:}$$ 3 In this equation, where \(\:\stackrel{-}{\sigma\:}\) (MPa) is the effective flow stress \(\:\dot{\epsilon\:}\) (s − 1 ) is the effective strain rate and \(\:\stackrel{-}{\eta\:}\) is the efficiency of conversion of deformation energy to heat; the latter is assumed to be 0.95 for aluminum alloys and for copper is 0.8, which is considered reasonable is the conversion fraction of plastic work into heat [ 22 ], To check the boundary heat transfer conditions between the panel and the roller, which is the heat flux by \(\:{q}_{strip}\) (W.m − 2 ) and the heat flux for the roller is \(\:{q}_{roll}\) (W.m − 2 ), and h (kW.m − 2 . \(\:^\circ\:\) C − 1 ) is the convection heat transfer coefficient, which is shown in Eq. ( 4 ). $$\:{q}_{strip}=-{q}_{roll}=h*\left({T}_{strip\:}-{T}_{roll}\right)$$ 4 2.2. Mechanical equations which is due to the distribution of surface flux, also \(\:{q}_{fric}\) (W.m − 2 ) is based on the sliding speed caused by the rolling speed, which leads to friction and in the areas that are along the arc of contact, it causes visible changes, and its contribution in the length of heat is small, but it can be considered and Eq. ( 5 ) explains it [ 23 ]: $$\:{q}_{fric}=\left|\tau\:*v\right|$$ 5 where \(\:\tau\:\) (MPa) is the shear stress and \(\:v\) (m.s − 1 ) is the sliding velocity. Since the heat lost from the panel is gained by the work roll in the roll gap, a simultaneous solution of the governing equations of both the panel and the work roll is required. also \(\:{q}_{fric}\) is generated from frictional sliding [ 24 ]. The effect of contact friction on the flow of metal can be effective, which should be considered when balancing the interaction between the metal. Also, the contact friction between the panel and the roller is solved using the Coulomb model, which is mostly used for forming processes where the friction effect is proportional. with the normal force in Eq. ( 6 ): $$\:{\tau\:}_{crit}\:=\:\mu\:*p$$ 6 where \(\:{\tau\:}_{crit}\) is the critical shear stress (MPa), \(\:\mu\:\) the coefficient of friction, and P (Pa) is the contact pressure. 3. Finite element model In this finite element model, a three-dimensional thermal-mechanical simulation process has been developed for data generation, with accurate validation under different types. Lagrangian-Eulerian (ALE) method rolling conditions as a formulation technique through Using the general-purpose FE business program ABAQUS™. In the model, thermal and mechanical interaction phenomena are considered. The yield stress entered in Abaqus software is associated with temperature, strain rate and strain. Simultaneous, Friction and deformation heat increase the temperature of the metal and the surface of the work roll. therefore, Thermal and mechanical models should be coupled together to simultaneously include the above-mentioned factor effects. It should also be mentioned that the simulation process considered in Abaqus software has a temperature and displacement couple solver which is explicitly involved in this process, so the main nature of the hot rolling process is temperature changes along with the displacement of the sandwich panel. Also, one of the reasons for using this solver is related to the difference in the temperature of the roller surface and the temperature of the composite panel. Finite element software for various analysis is used in a wide part of the industry. Due to the asymmetry of the problem conditions, the entire process has been modeled, also the geometry of the sandwich panel roller and panel has been assumed to be symmetrical in the width direction, but in the thickness direction, due to the lack of complete symmetry, it has been modeled. In the case of rollers, according to the heat transfer analysis between the roller surfaces and the sandwich panel, as well as Young's model, it is considered to be more rigid [ 25 ]. The modeling has been done in three dimensions. The problem has been solved in an explicit way, and since the hot rolling process is a thermodynamic process, it is necessary to use elements that can include the thermal effects of the process. The behavior of (C3D8RT) for this reason, from the six-sided elements that have the combination of displacement and heat effects, the panel is assumed to be thermos - viscoplastic. In addition, the re-mesh function of Abaqus software has been used along with Eulerian Lagrangian couple. Since the range of changes in temperature and strain rate in the rolling process is large, it is necessary to determine the plastic behavior of the panel as a function of temperature and strain rate. Considering that the rollers have a Young's modulus of 200 GPa [ 26 ], they are considered as a rigid body, and the composite panel in the initial thicknesses of 20 (10 mm copper and 10 mm AA), 24 (12 mm copper and 12 mm AA), 28 (14 mm copper and 14 mm AA) mm and in the initial temperatures of 400, 500, 600°C and the different rolling Speed (90,140,190 rpm) has been considered. the results of which can be seen. It has also been investigated in order to investigate the subject of force and torque required for rolling in different reductions. it was considered to be deformed. It is also worth mentioning that the total number of mesh considered for the sandwich panel is around ten thousand (10,000) elements and increasing this value to (15,000) and (20,000) does not change much in the output results and using This number of meshes can make the simulation time very long. In this article, the optimized value of this number was considered so that the simulation time is shorter and the solution does not face errors. Also, due to the fact that the roller is considered rigid, but considering the heat transfer between the surfaces of the rollers and the sandwich panel, an isothermal coupler has been used to bring the simulation process closer to the real hot rolling process. The mechanical and thermal properties of pure copper and aluminum alloy 2030 are considered in Abaqus as a function of temperature [ 7 , 9 , 25 , 27 ]. Figure 1 -a and 1 -b illustrate the positioning of the pure copper and 2030 aluminum alloy panels within the three-dimensional model. Table 1 Thermo-physical properties of Pure Copper [ 28 ]. Temperature (°C) Young's Modulus, E (GPa) Thermal Conductivity, k (W/m·K) Coefficient of Thermal Expansion, α (1/°C) Specific Heat, Cp (J/kg·K) 20 117 398 16.5 × 10⁻⁶ 385 100 110 390 16.5 × 10⁻⁶ 390 200 103 380 17.0 × 10⁻⁶ 395 300 95 370 17.2 × 10⁻⁶ 400 400 88 360 17.5 × 10⁻⁶ 405 500 82 350 17.8 × 10⁻⁶ 410 600 76 340 18.1 × 10⁻⁶ 415 700 70 330 18.4 × 10⁻⁶ 420 Table 2 Thermo-physical properties of AA2030 [ 28 ]. Temperature (°C) Young's Modulus, E (GPa) Thermal Conductivity, k (W/m·K) Coefficient of Thermal Expansion, α (1/°C) Specific Heat, Cp (J/kg·K) 20 73 210 23 × 10⁻⁶ 900 100 70 205 23.5 × 10⁻⁶ 910 200 6 200 24 × 10⁻⁶ 920 300 63 195 24.5 × 10⁻⁶ 930 400 59 190 25 × 10⁻⁶ 940 500 56 185 25.5 × 10⁻⁶ 950 600 52 180 26 × 10⁻⁶ 960 700 48 175 26.5 × 10⁻⁶ 970 4. Artificial neural network (ANN) The theoretical foundation of neural networks is derived from the architecture of the human brain and its capability to process vast amounts of information. Artificial neural networks (ANNs) are adaptive computational models capable of learning from data and generalizing acquired knowledge. They can be employed to establish complex mappings between inputs and outputs, providing insights into the practical behavior of the underlying phenomena [ 29 ]. A multi-layer neural network consists of an input layer, one or more hidden layers, and an output layer. The input layer receives experimental data, features, or measured indicators and serves as the entry point to the network. Hidden layers, positioned between the input and output layers, process the incoming signals and transmit the transformed information to the output layer, which then consolidates these signals to generate the final output vector. Each layer is composed of multiple processing units, or neurons, interconnected via adjustable synaptic weights. During the training phase, these weights are iteratively optimized commonly using the back-propagation algorithm by presenting the network with paired input-output samples that represent the underlying relationships to be learned. The output of each neuron is calculated through a weighted summation of its inputs followed by the application of a nonlinear activation function, as mathematically expressed in Eq. ( 7 ) [ 30 ]. $$\:{y}_{j}=f\left(\sum\:_{i=1}^{n}{w}_{ij}{x}_{i}+\:{b}_{j}\right)$$ 7 Where \(\:{x}_{i}\) is the inputs to the neuron, \(\:{w}_{ij}\) ​ is the corresponding synaptic weights, \(\:{b}_{j}\) ​ is the bias term, \(\:f\) is the activation function applied to the weighted sum, \(\:n\) is the number of inputs to the neuron. During the training phase, the neural network is provided with multiple sets of input-output pairs. An iterative optimization algorithm systematically updates the synaptic weights to ensure that the network’s predicted outputs \(\:{o}_{j}\) closely approximate the corresponding target outputs \(\:{d}_{j}\) for each input pattern. For a network with \(\:J\) total outputs, the training process seeks to minimize the discrepancy between predicted and desired values by reducing the mean squared error (MSE), as formulated in Eq. ( 8 ) [ 31 ]. This approach ensures that the network progressively learns the underlying relationships within the dataset, improving its predictive accuracy across all outputs. $$\:MSE=\:\frac{1}{J}\:\sum\:_{j=1}^{J}{({o}_{j}-{d}_{j})}^{2}$$ 8 The back-propagation algorithm is a widely adopted method for minimizing the mean squared error (MSE) by iteratively updating the connection weights within a neural network [ 32 ]. The learning procedure in this approach can be divided into three primary stages. Initially, the input dataset is fed into the network. Subsequently, using the randomly initialized weights and biases, along with the activation functions assigned to each neuron, the network propagates the signals forward, computing the output of every neuron layer by layer until the final output vector is generated. This systematic propagation ensures that the network’s response is determined for each input pattern, providing the foundation for subsequent weight adjustments during training. The training procedure of a neural network via the back-propagation algorithm consists of three sequential phases. In the initial phase, known as the feedforward stage, input data are propagated through the network, and the outputs of all neurons are computed layer by layer until the final output is obtained. During the subsequent phase, the discrepancy between the network’s predicted output and the desired target is quantified, and this error is systematically propagated backward through the network, allowing the computation of individual neuron errors; this is referred to as the back-propagation stage. In the final phase, the connection weights and biases are iteratively updated using a dedicated optimization algorithm to minimize the overall error. Each complete execution of these three phases constitutes a single training cycle, and the cycles are repeated continuously until a predefined stopping criterion is satisfied [ 24 ]. The neural network models for predicting rolling force and torque based on the input parameters are illustrated in Fig. 2 . To develop a robust and reliable neural network (NN) model, it is essential to have a sufficiently large and high-quality training dataset. The amount of data required depends on several factors, including the complexity of the process being modeled, the number of input variables, and the precision of the available process data. Typically, effective NN training requires hundreds or even thousands of data samples. Since finite element (FE) modeling involves intensive and time-consuming computations, generating training data through this method necessitates a carefully designed experimental framework. In this study, the training dataset was generated using the Design of Experiments (DOE) approach. Specifically, a three-level full factorial design, one of the most widely used Design of Experiments (DOE) techniques, was employed. In this design, the variable space is divided into three levels between the minimum and maximum values, resulting in 3ⁿ experimental combinations for n input variables. Given that four input parameters were considered in this study (n = 4), at least 81 data samples are required for training the neural network. However, to improve the accuracy and generalization capability of the ANN, a total of 243 data samples were generated using the validated finite element (FE) model. The factors and their corresponding levels used in this design are summarized in Table 3 . Table 3 Chosen experimental schedules for investigation of hot rolling simulation. Exp.no Inlet thick. (mm) Inlet panel temp. (°C) Reduction. (%) Roll Speed. (rpm) 1 20 500 30 90 2 20 500 35 90 3 20 500 40 90 4 24 400 40 140 5 24 500 40 140 6 24 600 40 140 7 28 500 30 190 8 28 500 35 190 9 28 500 40 190 10 20 400 30 90 11 24 400 30 90 12 28 400 30 90 13 20 400 40 140 14 20 500 40 190 15 20 600 40 90 16 24 500 35 90 17 24 500 35 90 18 24 400 35 90 19 24 500 35 140 20 24 600 35 190 In the present investigation, a customized computational framework was developed in MATLAB to implement the proposed Artificial Neural Network (ANN) model using the Back-Propagation Algorithm (BPA). Back-propagation based neural networks are among the most widely adopted approaches for nonlinear modeling due to their strong generalization capability and the availability of numerous well-established training schemes, such as gradient descent, quasi-Newton optimization, conjugate gradient, stochastic approximation, and Levenberg–Marquardt optimization methods [ 19 ]. In this study, the tangential sigmoid transfer function was employed for both the hidden and output layers, while the Levenberg–Marquardt algorithm was selected as the training function, owing to its superior convergence speed and efficiency in training medium-sized feedforward neural networks [ 33 ]. To prevent overfitting, the early-stopping technique was incorporated during the training process. In this approach, the available data are partitioned into two subsets: a training set, utilized for iterative adjustment of the network’s connection weights and biases, and a validation set, used to monitor the network’s generalization capability. During the training phase, both training and validation errors typically decrease simultaneously; however, once the network begins to overfit the training data, the validation error starts to rise. When this upward trend continues for a predefined number of epochs, the training is automatically terminated, and the optimal network parameters corresponding to the minimum validation error are preserved as the final trained model. Prior to feeding the datasets into the backpropagation (BP) network, it is essential to preprocess the input and output variables to ensure numerical stability and improve convergence performance. Accordingly, both the input and target data were normalized to a defined interval of [ 1 , 10 ] using the normalization procedure expressed in Eq. ( 9 ), enabling consistent scaling and enhancing the efficiency of the training process. $$\:{X}_{i}=\:0.1+0.8\left(\frac{{X-X}_{min}}{{X}_{max}{-X}_{min}}\right)$$ 9 where \(\:X\) represents the original dataset, \(\:{X}_{min}\) ​ and \(\:{X}_{max}\) denote the minimum and maximum values of \(\:X\) , respectively, and \(\:{X}_{i}\) ​ is the normalized value corresponding to each data point of \(\:X\) . The architecture of the artificial neural network and the functions employed in the final model are summarized in Table 4 . Table 4 The ANN architecture and functions. Network Feed-forward back propagation network Training function Levenberg–Marquardt Learning function Gradient descent with momentum weight & bias learning function Transfer function Tan sigmoid function Performance function Mean squared error Number of input layer unit 4 Number of hidden layers 2 Number of output layer units 2 5. Results and discussion 5.1. FEM Simulation Results In the asymmetric hot rolling process of a bimetallic panel, an AA2030 aluminum alloy and pure copper composite with a width of 40 mm was employed as the constituent materials. The specimen was rolled in all passes using rolls with a diameter of 160 mm. Figures 3 and Figs. 4 illustrate the variations of rolling force and rolling torque over time for different thickness reduction levels. As depicted in Fig. 3 -a, the amplitude of rolling force fluctuations within the steady-state region increases with the rise in thickness reduction. The initial thickness of the sandwich panel was considered to be 20 mm, with reduction ratios of 30%, 35%, and 40%, respectively. A similar trend is observed in Fig. 3 -b, where rolling torque oscillations also intensify as the reduction level increases. This phenomenon can be attributed to the changes in surface conditions particularly the contact friction within the roll panel interface which influence the distribution of interfacial shear stress and sliding behavior. As reported by Hum et al. [ 34 ], higher thickness reductions lead to increased forward slip and friction coefficients. Table 5 provides a comprehensive overview of the loading conditions and the parameters utilized in the simulation process. It is noteworthy that the roll diameter was maintained at 160 mm, and the convective heat transfer coefficient between the roll surface and the composite panel was assumed to be 40 kW/m²°C. With increasing thickness reduction, the rolling force in both layer increases. Since aluminum (AA2030) exhibits higher strength than copper at the rolling temperature, it bears a greater portion of the compressive load; consequently, the effective rolling force acting on the aluminum layer is higher than that on the copper layer. The rolling torque of each roll is proportional to the contact force and surface friction; therefore, the roll in contact with the aluminum layer experiences a higher torque. Table 5 Rolling force and torque under different reduction area rolling parameters. Exp.no Inlet thick. (mm) Inlet panel temp. (°C) Reduction. (%) Roll Speed. (rpm) 1 20 500 30 90 2 20 500 35 90 3 20 500 40 90 As expected, decreasing the rolling temperature necessitates higher rolling force and torque to deform the workpiece. Therefore, rolling the sandwich panel at lower temperatures requires increased levels of both rolling force and torque. However, since the sandwich panel is composed of two layers and exhibits an asymmetrical configuration, the rolling force and torque differ between the top and bottom rollers, resulting in asymmetry in both the rolling process and the simulation. In general, with increasing temperature, the plasticity of the sandwich panel improves, facilitating deformation. Once the material reaches its fluid-like state, the demand for excessive force and torque diminishes, and their values drop to lower, more favorable levels for the process. Figures 5 and 6 illustrate the variations in rolling force and torque under different temperature conditions. As evident from the graphs, both rolling force and torque decrease as the temperature increases, which can be attributed to the enhanced malleability of the sandwich panel at elevated temperatures. Table 6 provides a comprehensive overview of the loading conditions and the parameters utilized in the simulation process. It should be noted that the rolling rollers have a diameter of 160 mm, and the heat transfer coefficient between the roller surface and the composite panel surface is considered to be 60 kW/m²·°C. With the increase in temperature, the sandwich panel becomes more ductile and its plastic resistance decreases, leading to a reduction in the rolling force and torque required for both layers. Nevertheless, the aluminum layer consistently sustains higher force and torque compared to the copper layer. Table 6 Rolling force and torque under different temperature rolling parameters. Exp.no Inlet thick. (mm) Inlet panel temp. (°C) Reduction. (%) Roll Speed. (rpm) 1 24 400 40 90 2 24 500 40 90 3 24 600 40 90 Table 7 presents the rolling conditions considering the influence of different rotational speeds of the rollers on the variation of rolling force and torque over time. As the rolling speed increases, the amplitude of fluctuations in both rolling force and torque also increases. However, due to the shorter contact time between the sandwich panel and the rollers, the duration of these variations becomes more limited at higher speeds. Consequently, although the average force and torque may decrease, their instantaneous oscillations tend to intensify at higher rolling velocities. The simulation results obtained at rotational speeds of 90, 140, and 190 rpm indicate that increasing the rolling speed alters the magnitude and frequency of force and torque fluctuations. At higher speeds, the panel experiences partial sliding at the roll-panel interface, redistributing the shear stress over the contact surface. This directly affects the frictional and deformation behavior of the material during rolling. Figures 7 and Figs. 8 illustrate the time-dependent variations of rolling force and torque. As observed, the reduction in contact duration limits the range of force variations but simultaneously increases the vibration intensity of the system. Such intensified oscillations at higher speeds may promote panel distortion, crack initiation, and surface damage. Table 7 Rolling force and torque under different roller rotation speed rolling parameters. Exp.no Inlet thick. (mm) Inlet panel temp. (°C) Reduction. (%) Roll Speed. (rpm) 1 20 500 40 90 2 20 500 40 140 3 20 500 40 190 By increasing the initial thickness of the sandwich panel from 20 mm to 28 mm, the amount of plastic deformation and, consequently, the mechanical work required during rolling increases. This results in higher rolling force and rolling torque values. In other words, both force and torque exhibit a direct relationship with the initial panel thickness, as greater thickness leads to a larger volume of material being deformed within the roll bite region. In the numerical simulations, all other process parameters such as roll diameter (160 mm), rolling speed, and temperature were kept constant to isolate the effect of initial thickness on the rolling behavior. The variations of rolling force and torque with different initial thicknesses are illustrated in Fig. 9 and Fig. 10 . The input parameters and geometric conditions employed in the simulation are summarized in Table 8 . Moreover, the convective heat transfer coefficient between the roll surface and the composite panel was assumed to be 20 kW/m²·°C. Table 8 Rolling force and torque under different panel thickness rolling parameters. Exp.no Inlet thick. (mm) Inlet panel temp. (°C) Reduction. (%) Roll Speed. (rpm) 1 20 400 30 90 2 24 400 30 90 3 28 400 30 90 5.2. Neural Network Results The Artificial Neural Network (ANN) model developed in this study was employed to predict the roll force and roll torque based on the design data of the hot panel rolling process. The performance of the model on the training data is illustrated in Figs. 11 and 12 . The results indicate that the model exhibits high prediction accuracy and a good generalization capability toward the test data. The neural network analysis was carried out using MATLAB R2022. For the quantitative evaluation of the model performance, only the correlation coefficient (R) between the predicted and actual values was calculated, and the Best Fit line was plotted in the figures to visually demonstrate the degree of agreement between the model predictions and the experimental data. The neural network model is essentially a complex and nonlinear system consisting of numerous activation functions and interconnecting weights between neurons. To evaluate the compatibility of the developed model with the existing physical understanding of the rolling process, model response surfaces were employed. These surfaces were generated by varying two selected input parameters while keeping the remaining inputs fixed at their mean values. Such plots serve as an effective tool to assess the accuracy of the developed model based on the training data and to identify whether additional data may be required to further improve the training of the neural network. Some of the response surfaces obtained from the neural network model, illustrating the variation of roll force with respect to two selected input parameters, are presented in Figs. 13 and 14 . These plots were used to verify the validity of the developed model by comparing its behavior with the known physical trends of the rolling process. According to Fig. 13 , the reduction area and initial temperature are the most influential parameters affecting the roll force; as either parameter changes, the roll force also varies accordingly. Similarly, Fig. 14 shows that the reduction area and the initial thickness of the composite panel are among the key parameters influencing the roll force. In Fig. 13 -a, the rolling force corresponds to the upper roll, while Fig. 13 -b represents the lower roll under identical operating conditions (reduction area and temperature), where slight differences in force behavior can be observed. Likewise, Fig. 14 -a and Fig. 14 -b illustrate the rolling forces of the upper and lower rolls, respectively, under the conditions of reduction area and thickness. In this study, the effects of composite panel temperature, initial panel thickness, and cross-sectional reduction on the rolling force are investigated. To calculate the rolling force, the average force applied to the upper and lower rolls throughout the process is obtained and used to train the neural network. Figure 15 presents a comparison between the rolling force predicted by the neural network and that obtained from the finite element method. This figure illustrates the variation in the average rolling force with respect to changes in the initial panel thickness, demonstrating that the rolling force increases as the initial thickness increases. Figure 15 -a corresponds to the upper roll, while Fig. 15 -b represents the lower roll. Also In this study, the effect of increasing the initial temperature of the composite panel on the rolling force behavior is examined. As the panel temperature rises, the material becomes softer and its resistance to deformation decreases, leading to a noticeable reduction in the required rolling force. Figure 16 illustrates the variation of rolling force under different temperature conditions, demonstrating that elevating the panel temperature prior to the process plays a significant role in reducing the force applied to both the upper and lower rolls. This reduction is similarly observed for both rolls, as depicted in Figs. 16 -a and 16 -b. In this study, the effect of the reduction area on the rolling force was investigated. An increase in the reduction area subjects the panel to more severe deformation, thereby significantly raising the rolling force required to pass through the roll contact zone. Figure 17 illustrates the variation of rolling force for different reduction levels, showing that higher reduction percentages result in increased forces on both the upper and lower rolls. Moreover, a comparison of Figs. 17 -a and 17 -b indicates that the influence of increased reduction area is similar for both rolls, with the force increment pattern clearly observable in each case. In this section, the simultaneous variations of the upper and lower roller forces are examined. The corresponding plots allow for observing the patterns and correlations between the forces. The simulation results are compared with the predictions of the trained artificial neural network (ANN), showing that the ANN can accurately reproduce the simultaneous force variations. This analysis helps to better understand the impact of force differences on stress distribution. Finally, the combination of simulation data and ANN predictions enables the analysis of future trends and optimization of the rolling process. 6. Conclusions To simulate the rolling process of a composite sandwich panel composed of pure copper and aluminum alloy AA2030, a hybrid modeling approach combining finite element (FE) analysis and an artificial neural network (ANN) was developed. In this framework, data obtained from FE simulations were used to train the ANN, enabling efficient prediction of rolling force and rolling torque under various process conditions. The neural network generalizes the FE results and provides rapid predictions, thereby avoiding the high computational cost associated with performing full FE simulations for all scenarios. This study investigates the influence of key process parameters on rolling force and torque, including initial thickness, reduction ratio per rolling pass, initial panel temperature, and rolling speed, all of which directly affect the mechanical behavior and energy consumption during the rolling process. The effects of these parameters can be summarized as follows. Increasing the reduction ratio leads to a significant rise in rolling force and torque due to the higher level of plastic deformation required. Increasing the rolling temperature reduces the yield strength of the materials, resulting in lower rolling force and torque, which is consistent with hot rolling behavior. Higher rolling speeds reduce the contact time between the rolls and the panel, leading to a decrease in average rolling force, although excessively high speeds may induce dynamic vibrations and asymmetric deformation. Finally, increasing the initial panel thickness increases the rolling force and torque because of the greater mechanical work needed for deformation. Overall, the developed ANN successfully captures the complex nonlinear relationships between process parameters and rolling responses, enabling fast and accurate predictions that support process optimization, energy reduction, and minimized roll wear in copper–aluminum bimetallic rolling. Declarations Author Contribution H.R. conceived the original idea of the research and defined the overall scientific framework of the study. A.J. was responsible for developing the methodology, performing all numerical and finite element simulations, processing and analyzing the data, and generating all figures and graphical results. A.J. also wrote the original draft of the manuscript and integrated the results into their final form. Both authors discussed the results, contributed to the interpretation of the findings, reviewed the manuscript, and approved the final version for publication. Data Availability Yes, research data were generated in this study. References Ma Z, Zhao H, Liu C (2015) Critical fracture behavior of a Cu/Al composite laminate via the observation of scanning electron microscope. Mater Trans 56(6):813–818 Tian H et al (2018) Numerical simulations of the Cu/Al composite plate continuous cast-rolling process. Mater Res Express 5(12):126505 Sheng L et al (2011) Influence of heat treatment on interface of Cu/Al bimetal composite fabricated by cold rolling. Compos Part B: Eng 42(6):1468–1473 Teker E et al (2022) Hot deformation behavior and strain rate sensitivity of 33MnCrB5 boron steel using material constitutive equations. Trans Indian Inst Met 75(3):717–726 Renault C et al (2020) Microstructure and hot deformation behavior of FeMnAlCMo steel. J Mater Res Technol 9(3):4440–4449 Orowan E (1943) The calculation of roll pressure in hot and cold flat rolling. Proceedings of the Institution of Mechanical Engineers, 150(1): pp. 140–167 Chen S et al (2025) Research on Mathematical Model of Rolling Force for Asymmetrical Rolling of Cu/Al Clad Plate. Iran J Sci Technol Trans Mech Eng 49(1):329–348 Xu W, Xia C, Ni C (2024) Numerical Simulation and Experimental Verification of Hot Roll Bonding of 7000 Series Aluminum Alloy Laminated Materials. Metals 14(5):551 Che J et al (2025) Prediction Model Study of Rolling Force and Thickness Ratio of the Bimetallic Composite Plate. Chin J Mech Eng 38(1):1–13 Chandrasekar P, Nagaraju D (2022) Improvement of bonding strength at the interfaces in scrap Al alloy composites using electroless Ni-P coated SiC. Silicon 14(6):2941–2952 Heydari Vini M, Sedighi M (2018) Mechanical properties and bond strength of bimetallic AA1050/AA5083 laminates fabricated by warm-accumulative roll bonding. Can Metall Q 57(2):160–167 Liu H et al (2021) Deformation behavior and constitutive equation of 42crmo steel at high temperature. Metals 11(10):1614 Ahmadi H, Ashtiani HR, Heidari M (2020) A comparative study of phenomenological, physically-based and artificial neural network models to predict the Hot flow behavior of API 5CT-L80 steel. Mater Today Commun 25:101528 Murugesan M, Sajjad M, Jung DW (2019) Hybrid machine learning optimization approach to predict hot deformation behavior of medium carbon steel material. Metals 9(12):1315 Kumar S, Karmakar A, Nath SK (2021) Construction of hot deformation processing maps for 9Cr-1Mo steel through conventional and ANN approach. Mater Today Commun 26:101903 Shokry A et al (2019) Constitutive models for the prediction of the hot deformation behavior of the 10% Cr steel alloy. Materials 12(18):2873 Huang W, Lei L, Fang G (2021) Comparison between four flow stress models characterizing the constitutive behavior of hot deformation of 40Mn steel. J Mater Eng Perform 30(12):9149–9164 Babu KA et al (2021) Modeling and simulation of dynamic recrystallization in super austenitic stainless steel employing combined cellular automaton, artificial neural network and finite element method. Comput Mater Sci 195:110482 Yang Y, Linkens D, Talamantes-Silva J (2004) Roll load prediction—data collection, analysis and neural network modelling. J Mater Process Technol 152(3):304–315 Lee DM, Choi S (2004) Application of on-line adaptable neural network for the rolling force set-up of a plate mill. Eng Appl Artif Intell 17(5):557–565 Wang X, Yang Q, He A (2008) Calculation of thermal stress affecting strip flatness change during run-out table cooling in hot steel strip rolling. J Mater Process Technol 207:130–146 Kumar A, Samarasekera I, Hawbolt E (1992) Roll-bite deformation during the hot rolling of steel strip. J Mater Process Technol 30(1):91–114 Shahani A et al (2009) Prediction of influence parameters on the hot rolling process using finite element method and neural network. J Mater Process Technol 209(4):1920–1935 Shahani AR et al (2009) Prediction of influence parameters on the hot rolling process using finite element method and neural network. J Mater Process Technol 209(4):1920–1935 Ashtiani HR, Bisadi H, Adabjou M (2010) Modeling of Microstructural Evolution During the Hot Rolling of Aluminum Alloy. Int Rev Modelling Simulations 3(5):1129–1136 Ahmed H et al (2005) Modelling of microstructure evolution during hot rolling of AA5083 using an internal state variable approach integrated into an FE model. Mater Sci Engineering: A 390(1):278–290 Bagheripoor M, Bisadi H (2013) Application of artificial neural networks for the prediction of roll force and roll torque in hot strip rolling process. Appl Math Model 37(7):4593–4607 Manikanta JE et al (2025) A review on hybrid nanofluids: preparation methods, thermo physical properties and applications. Iran J Sci Technol Trans Mech Eng 49(1):67–79 Larkiola J et al (1998) The role of neural networks in the optimisation of rolling processes. J Mater Process Technol 80:16–23 Deng J et al (2005) Structural reliability analysis for implicit performance functions using artificial neural network. Struct Saf 27(1):25–48 Kazan R, Fırat M, Tiryaki AE (2009) Prediction of springback in wipe-bending process of sheet metal using neural network. Mater Design 30(2):418–423 Widrow B, Lehr MA (2002) 30 years of adaptive neural networks: perceptron, madaline, and backpropagation. Proceedings of the IEEE, 78(9): pp. 1415–1442 Hagan MT, Menhaj MB (1994) Training feedforward networks with the Marquardt algorithm. IEEE Trans Neural Networks 5(6):989–993 Hum B, Colquhoun H, Lenard J (1996) Measurements of friction during hot rolling of aluminum strips. J Mater Process Technol 60(1–4):331–338 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8495786","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":570274239,"identity":"4f58f1cf-2873-4067-b4a7-b5976b74d3a3","order_by":0,"name":"Alireza Jalili","email":"data:image/png;base64,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","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Alireza","middleName":"","lastName":"Jalili","suffix":""},{"id":570274240,"identity":"d3f6b602-7f5f-453e-b790-9b7255f1fa69","order_by":1,"name":"Hamidreza Rezaei Ashtiani","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Hamidreza","middleName":"Rezaei","lastName":"Ashtiani","suffix":""}],"badges":[],"createdAt":"2026-01-01 14:53:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8495786/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8495786/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99798848,"identity":"a33ddee3-f398-4e7a-a58e-4fb1f321693f","added_by":"auto","created_at":"2026-01-08 13:48:57","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5626347,"visible":true,"origin":"","legend":"","description":"","filename":"NewVesionofForceandTorque2PlyAlirezaJaliliManuscripte.docx","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/e5156e467927bafc4f6cc543.docx"},{"id":99799101,"identity":"e5deb005-194d-4da6-952c-aa67ead5dfdb","added_by":"auto","created_at":"2026-01-08 13:49:13","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4812,"visible":true,"origin":"","legend":"","description":"","filename":"1e8a7004d88944cda65d33285305306d.json","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/471ff08d95eb22f02e4fc2ca.json"},{"id":99799259,"identity":"4f0de97c-fc6f-4a78-8d92-e6de5bbbba52","added_by":"auto","created_at":"2026-01-08 13:49:23","extension":"xml","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":130239,"visible":true,"origin":"","legend":"","description":"","filename":"1e8a7004d88944cda65d33285305306d1enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/fa1552c6cfab7e2741aecac8.xml"},{"id":99780224,"identity":"7ddb103e-dcd7-4054-b794-4a9d02523dff","added_by":"auto","created_at":"2026-01-08 10:31:04","extension":"png","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":155378,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/77fadc542e22f4448495bc06.png"},{"id":99780230,"identity":"4dd5cc9b-8b39-4cb5-bff1-a400251973b2","added_by":"auto","created_at":"2026-01-08 10:31:04","extension":"jpeg","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":254453,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage10.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/a9bcd3f62b9c672997832a66.jpeg"},{"id":99780233,"identity":"caa25240-f089-4835-87ea-b04a757e803e","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"jpeg","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":394615,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage11.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/21f0fd7c5fbd598979541933.jpeg"},{"id":99798955,"identity":"5495b7ba-47d1-4f68-a9f1-42ab51e7b28e","added_by":"auto","created_at":"2026-01-08 13:49:05","extension":"jpeg","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":389459,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage12.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/0c9192010443d31a1307277b.jpeg"},{"id":99780239,"identity":"1e4f76c0-219f-43f8-a2b6-2e32de9d44db","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"jpeg","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":715785,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage13.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/b7ab0b61cb44b61001e348e0.jpeg"},{"id":99799237,"identity":"e4294b04-f931-48d7-8577-69baea03a307","added_by":"auto","created_at":"2026-01-08 13:49:22","extension":"jpeg","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":558154,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage14.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/208cba99d6433600e3d94aad.jpeg"},{"id":99799270,"identity":"7d77e673-9851-4942-905e-fbb373b3f97b","added_by":"auto","created_at":"2026-01-08 13:49:24","extension":"jpeg","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":388723,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage15.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/e11b5fd9102fb39a0fe6cab9.jpeg"},{"id":99798849,"identity":"17c959cc-d905-426d-b0cc-7d1b478e5a23","added_by":"auto","created_at":"2026-01-08 13:48:57","extension":"jpeg","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":370461,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage16.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/eaf1dc9ae5d6cd517c8aa7aa.jpeg"},{"id":99780241,"identity":"9e2504e1-ba9b-489b-8c2b-bbd7419b4750","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"jpeg","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":335575,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage17.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/18871fbbf04dfe146ebd375a.jpeg"},{"id":99780246,"identity":"9281c26c-6704-47ac-af2a-70dd33640a74","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"png","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":260828,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage18.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/8c2d5b5117f73326774a294c.png"},{"id":99798698,"identity":"a7edc077-b551-4888-99b3-6e63943b7937","added_by":"auto","created_at":"2026-01-08 13:48:48","extension":"png","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":271698,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/022acaccae3655b7877d3b3d.png"},{"id":99780251,"identity":"db77b0c6-ab88-4874-820f-e906d78b4952","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"jpeg","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":258392,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/580b335a58c1516c1b1443e6.jpeg"},{"id":99780248,"identity":"684bd372-aa99-4da1-b4ec-1a9970cf6a44","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"jpeg","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":263797,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/329de4acee97c751f4bc8cda.jpeg"},{"id":99780250,"identity":"d44054df-aa87-43cb-b347-c81807e55094","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"jpeg","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":308517,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/ac0da1078ea4ffe5923bdb02.jpeg"},{"id":99780255,"identity":"6a95bf73-779f-47bd-9f45-2311db184f63","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"jpeg","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":318599,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/6ceaeff6032f777701241abb.jpeg"},{"id":99780259,"identity":"919203a4-4c91-4e25-9ebd-ce79049286b7","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"jpeg","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":249655,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/fddf996ef42a3c7ccf6bb847.jpeg"},{"id":99798853,"identity":"fe8453cd-e559-449b-b83f-475563936339","added_by":"auto","created_at":"2026-01-08 13:48:57","extension":"jpeg","order_by":19,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":262128,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/4bc707de1f915729b61319ca.jpeg"},{"id":99798923,"identity":"a4c1a74f-201a-48b2-a805-45254460d7e5","added_by":"auto","created_at":"2026-01-08 13:49:02","extension":"jpeg","order_by":20,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":252849,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage9.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/9908dd0faa296d1288fffc70.jpeg"},{"id":99780253,"identity":"95bc37b9-0f7e-485a-aa82-8e8390e91120","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"png","order_by":21,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":24592,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/aa9e0f09c2900e96f83a694c.png"},{"id":99799016,"identity":"97b039d5-3007-4291-8c1f-cdf4d549cbd3","added_by":"auto","created_at":"2026-01-08 13:49:09","extension":"png","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":63039,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/a424082c63b7f6148d0f4d54.png"},{"id":99780257,"identity":"c2d87b4a-69e3-4695-8d62-496dee734963","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"png","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":62681,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/f5a84b0a57a5e99e2cf9e98a.png"},{"id":99780254,"identity":"dde92eba-e1ec-482b-80cf-bcc0d23312f8","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"png","order_by":24,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":62133,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/00b1563447311ae4e4770e05.png"},{"id":99780270,"identity":"5c84cc72-3e13-4963-9e8d-c34c081825fe","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"png","order_by":25,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":156554,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/8c783b7f14cd3cfb0e989f31.png"},{"id":99798867,"identity":"cf651254-be59-486d-95a2-737d52094bf5","added_by":"auto","created_at":"2026-01-08 13:48:58","extension":"png","order_by":26,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":153171,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/83f5d5862a7b514a40862681.png"},{"id":99780258,"identity":"0fcdf1e3-46a9-4940-9c40-3d825d6cd543","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"png","order_by":27,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":106387,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/79d387d5bfd84f10196b880f.png"},{"id":99780262,"identity":"1d54a6f6-9227-4b86-b1b8-428698fc626e","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"png","order_by":28,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":64452,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage16.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/75f46b78f9497365d9ececcc.png"},{"id":99780277,"identity":"e5a8ff45-3c45-477d-bc32-0cc9a5488528","added_by":"auto","created_at":"2026-01-08 10:31:06","extension":"png","order_by":29,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":92688,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage17.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/bafa3fb7f80fb928328c4024.png"},{"id":99780265,"identity":"958eabee-c2e9-45db-8d18-672f806f6817","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"png","order_by":30,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":32557,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage18.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/69e6316cd5cec13fff24094e.png"},{"id":99798731,"identity":"a8206402-0935-4b29-ad39-31550faa29c7","added_by":"auto","created_at":"2026-01-08 13:48:52","extension":"png","order_by":31,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":47232,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/f539da961ed3a112ee2af60d.png"},{"id":99798497,"identity":"323f05cc-03e3-494a-af47-9398f1a9f9ea","added_by":"auto","created_at":"2026-01-08 13:48:26","extension":"png","order_by":32,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":57659,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/f8a7456b365fc1a8389e0afb.png"},{"id":99798934,"identity":"ded7b8bd-be62-4a1b-a24b-e41939d43469","added_by":"auto","created_at":"2026-01-08 13:49:02","extension":"png","order_by":33,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":60341,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/c580340b90a2bc5c87892b5a.png"},{"id":99798944,"identity":"5e54c9df-9582-4bf1-8125-1865fbb47853","added_by":"auto","created_at":"2026-01-08 13:49:03","extension":"png","order_by":34,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":77699,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/38eb0983fb5b02282ce0729c.png"},{"id":99797939,"identity":"d82a99f8-103b-4842-bf80-bea44cdca0e5","added_by":"auto","created_at":"2026-01-08 13:46:56","extension":"png","order_by":35,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":79091,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/7793cf8ab06796f0833b2d96.png"},{"id":99780261,"identity":"7d1b4076-73ef-4f46-9ae6-4289abc1eb43","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"png","order_by":36,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":64216,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/9d71184a2435db9ff881f27b.png"},{"id":99797794,"identity":"8bcb3c9e-2c71-41e6-9dad-cfe1d4437f98","added_by":"auto","created_at":"2026-01-08 13:46:37","extension":"png","order_by":37,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":69262,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/55791c572d8048480b8202c6.png"},{"id":99780274,"identity":"a62e22ee-3816-4dbf-850a-88e50eef5039","added_by":"auto","created_at":"2026-01-08 10:31:06","extension":"png","order_by":38,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":59280,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/baeefb003cc3bf4ac991407f.png"},{"id":99799249,"identity":"432e2a79-70e7-4476-8491-c8fd7b411876","added_by":"auto","created_at":"2026-01-08 13:49:23","extension":"xml","order_by":39,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":129849,"visible":true,"origin":"","legend":"","description":"","filename":"1e8a7004d88944cda65d33285305306d1structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/c812eab2e96458c3ee690d50.xml"},{"id":99797772,"identity":"0b6240a5-4234-4d53-99fa-9a1b39df29b5","added_by":"auto","created_at":"2026-01-08 13:46:34","extension":"html","order_by":40,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":143352,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/3813ff848608ed5c95d45e7d.html"},{"id":99780219,"identity":"8b010810-54c2-43cc-b8e4-5397b32b323f","added_by":"auto","created_at":"2026-01-08 10:31:04","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":136182,"visible":true,"origin":"","legend":"\u003cp\u003ethe placement of pure copper and aluminum alloy 2030 a) 2D View and b) 3D View.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/c06a62532eaafd9c7a8f14c6.png"},{"id":99798547,"identity":"58692fd3-d64a-4a25-90eb-28d8fac07ca6","added_by":"auto","created_at":"2026-01-08 13:48:36","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":284058,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic illustration of the neural network structure.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/2ba7b7208dba00f7c0c71534.png"},{"id":99780220,"identity":"d9b42edb-9b56-48f8-b639-22b947b53410","added_by":"auto","created_at":"2026-01-08 10:31:04","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":138166,"visible":true,"origin":"","legend":"\u003cp\u003eThe effect of reduction area amount on the variations of a) top and b) bottom roll force.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/6c46863f24251455bae0bdb4.png"},{"id":99780223,"identity":"d337dac6-952b-4ade-b0b9-2f6523f02b43","added_by":"auto","created_at":"2026-01-08 10:31:04","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":153104,"visible":true,"origin":"","legend":"\u003cp\u003eThe effect of reduction area amount on the variations of a) top and b) bottom roll torque.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/194e7c4603c0d1968f9aa0fe.png"},{"id":99799531,"identity":"2cdbb966-00af-44b7-9633-fd1ca423c23f","added_by":"auto","created_at":"2026-01-08 13:49:43","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":153205,"visible":true,"origin":"","legend":"\u003cp\u003eThe effect of temperature amount on the variations of a) top and b) bottom roll force.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/e55d38e69f9ff82262d63b50.png"},{"id":99780228,"identity":"1b5dfc35-354d-4283-8054-516da50d73dc","added_by":"auto","created_at":"2026-01-08 10:31:04","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":180774,"visible":true,"origin":"","legend":"\u003cp\u003eThe effect of temperature amount on the variations of a) top and b) bottom roll torque.\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/6bd5b1b97557ec4e886a7db7.png"},{"id":99799294,"identity":"42b99f09-5a83-4714-97df-79c9bf082b3a","added_by":"auto","created_at":"2026-01-08 13:49:26","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":139767,"visible":true,"origin":"","legend":"\u003cp\u003eThe effect of roller rotation speed amount on the variations of a) top and b) bottom roll force.\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/2b14563a591dd173fdd3308e.png"},{"id":99798880,"identity":"4e1cfc79-9610-4dbf-9c1b-04c53d7d96f0","added_by":"auto","created_at":"2026-01-08 13:48:59","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":144047,"visible":true,"origin":"","legend":"\u003cp\u003eThe effect of roller rotation speed amount on the variations of a) top and b) bottom roll torque.\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/46a9bc1f5d642d303412541c.png"},{"id":99780234,"identity":"7dcca2fb-39dd-44ba-9d6a-508f96b8044a","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":118458,"visible":true,"origin":"","legend":"\u003cp\u003eThe effect of panel thickness amount on the variations of a) top and b) bottom roll force.\u003c/p\u003e","description":"","filename":"image9.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/5c0ffafdd7b21b7078f11b0e.png"},{"id":99799468,"identity":"3d04cb09-903d-43a5-9093-d10a8907ff84","added_by":"auto","created_at":"2026-01-08 13:49:37","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":122429,"visible":true,"origin":"","legend":"\u003cp\u003eThe effect of panel thickness amount on the variations of a) top and b) bottom roll torque.\u003c/p\u003e","description":"","filename":"image10.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/93d324d5c2a454a1668004c5.png"},{"id":99798950,"identity":"495f1df8-e403-4c5d-b4b0-3a7410ea5c1e","added_by":"auto","created_at":"2026-01-08 13:49:04","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":577589,"visible":true,"origin":"","legend":"\u003cp\u003ePerformance of the proposed ANN model during training for predicting of a) top and b) bottom roll force.\u003c/p\u003e","description":"","filename":"image11.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/c3b7dc1558b65a382a64a2ff.png"},{"id":99780237,"identity":"583c51ed-eb4a-4df5-bee2-68b24c196693","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":560416,"visible":true,"origin":"","legend":"\u003cp\u003ePerformance of the proposed ANN model during training for predicting of a) top and b) bottom roll torque.\u003c/p\u003e","description":"","filename":"image12.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/7c3bc5710c97aab82a579b13.png"},{"id":99780244,"identity":"f68c3eab-ed72-44a5-aa91-0796c4dca061","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":1581934,"visible":true,"origin":"","legend":"\u003cp\u003eEvolution of roll force vs. temperature and thickness reduction a) top roller and b) bottom roller.\u003c/p\u003e","description":"","filename":"image13.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/6485931bcbc6f55421b00455.png"},{"id":99780247,"identity":"aa35fc50-4c22-47c4-b554-d14da40733ef","added_by":"auto","created_at":"2026-01-08 10:31:05","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":1181198,"visible":true,"origin":"","legend":"\u003cp\u003eEvolution of roll force vs. thickness panel and thickness reduction a) top roller and b) bottom roller.\u003c/p\u003e","description":"","filename":"image14.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/dd8c9af3218b023dfb8974bc.png"},{"id":99798558,"identity":"725bf166-908e-4cfb-ae82-acdbbb230144","added_by":"auto","created_at":"2026-01-08 13:48:36","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":52086,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the average rolling force obtained from the finite element method and the neural network for varying initial panel thickness for a) top roller and b) bottom roller.\u003c/p\u003e","description":"","filename":"image15.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/f64ff6f5d54c53216a66d95f.png"},{"id":99798961,"identity":"d84dc3c2-e077-4f91-bfa4-2cd33e440d9a","added_by":"auto","created_at":"2026-01-08 13:49:06","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":54693,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the average rolling force obtained from the finite element method and the neural network for varying initial panel temperature for a) top roller and b) bottom roller.\u003c/p\u003e","description":"","filename":"image16.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/bfec85820f080119e40eeb3d.png"},{"id":99798918,"identity":"6957ffdf-6756-46f5-8240-1bc9109db9c9","added_by":"auto","created_at":"2026-01-08 13:49:01","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":41106,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the average rolling force obtained from the finite element method and the neural network for varying reduction area for a) top roller and b) bottom roller.\u003c/p\u003e","description":"","filename":"image17.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/86a06b2244653ad5e4958027.png"},{"id":99798435,"identity":"2381ef76-99fc-49a3-8afb-871d97b75b48","added_by":"auto","created_at":"2026-01-08 13:48:15","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":274035,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of hot rolling force–time data with ANN predictions and FEM showing 2.17% and 0.22% differences for top and bottom roller.\u003c/p\u003e","description":"","filename":"image18.png","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/98a716070f139c7641a85c15.png"},{"id":101206882,"identity":"011152e5-bc3d-4ef0-b748-9cf7e0dc12d5","added_by":"auto","created_at":"2026-01-27 09:56:55","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6078858,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8495786/v1/b836d52f-15cd-4410-8b1f-b1b830293133.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eThermo-Mechanical Simulation and ANN-Based Prediction of Rolling Force and Torque in Two-Layer Copper–Aluminum Composite Panel\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eBimetallic composite materials are extensively utilized across various industries such as aerospace, automotive manufacturing, photovoltaic energy systems, electronic communication, power transmission, architectural decoration, and precision instrumentation. The Cu/Al clad panel is a type of composite material formed by bonding copper and aluminum through different fabrication processes. This combination integrates the superior properties of both metals offering the excellent electrical conductivity of copper along with the light weight and cost-effectiveness of aluminum. As a result, Cu/Al clad panels have found broad applications in numerous industrial and everyday contexts [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. High-temperature deformation represents a critical stage in the manufacturing process. The behavior of materials under hot deformation is strongly affected not only by processing parameters such as temperature, strain rate, and applied strain but also by the steel\u0026rsquo;s chemical composition. Therefore, investigating and accurately modeling the hot deformation response is essential for optimizing forming processes through finite element simulations [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. The study of the rolling process traces back to the foundational research of Orowan [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], who proposed a comprehensive theory extending the traditional slab method by accounting for the non-uniform plastic deformation of the panel and the elastic deformation of the rolls. In a study [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], the principal stress method is utilized to formulate a comprehensive mathematical model for predicting the rolling force during the asymmetric rolling process. The model integrates the equilibrium differential equations, yield criterion, geometric constraints, and boundary conditions to accurately determine the rolling pressure distribution. Furthermore, a detailed parametric analysis is conducted to examine the effects of key process variables on the rolling force, the neutral point position, and the extent of the cross-shear deformation zone, thereby providing a theoretical framework for optimizing the rolling process of Cu/Al clad panels. In a study [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], the hot roll bonding process of 7000-series aluminum alloy laminated materials was investigated using finite element numerical simulations, and the process parameters were validated experimentally through mechanical property testing and microstructure analysis. The study examined the effects of the intermediate layer, pass reduction ratio, rolling speed, and thickness ratio of the component layers on the deformation and overall behavior of the laminated materials. The results indicated that the inclusion of an intermediate layer and the use of a multi-pass rolling process could effectively prevent warping and delamination, while achieving successful metallurgical bonding between the layers. In some study [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], an analytical model for predicting the rolling force and thickness ratio of bimetallic composite plates has been proposed based on a novel hypothesis derived from Orowan\u0026rsquo;s [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] theory. In these investigations, the model was developed using the principal stress method in combination with the slab method, and its validity was assessed through both experimental testing and numerical simulations. The methodologies employed included the formulation of a mathematical model based on Orowan\u0026rsquo;s [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] unit pressure differential equation and the calculation of the average rolling force for each layer. Additionally, theoretical analysis, laboratory experiments, and finite element simulations using a reversible two-roller mill and ABAQUS software were implemented to further verify the model. P. Chandrasekar [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] fabricated aluminum matrix composites and observed that applying a chemical coating during the fabrication process can enhance the bonding strength of the resulting composites. M. Heydari Vini [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] produced 1050 aluminum/5083 aluminum composites using an accumulative roll bonding process. The study demonstrated that both the bonding strength and tensile ductility of the clad panels improved as the number of laminated layers increased, indicating that an appropriate increase in layer count can effectively enhance the overall bonding quality of the composite panels. Human limitations make it challenging to analyze the large-scale datasets associated with the properties of complex materials such as industrial steel. This challenge can be effectively addressed using machine learning techniques, particularly through the application of artificial neural networks (ANNs). Artificial neural networks (ANNs) offer an effective approach for predicting functional relationships without relying on pre-established physical laws. This methodology typically achieves very low computational error, though it necessitates a large experimental dataset for training. Liu et al [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. demonstrated that an ANN-based model can accurately capture the hot flow behavior of 42CrMo steel, outperforming conventional Arrhenius-type models. Comparable levels of accuracy have been reported for other steels, including API 5CT-L80 [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], AISI 1045 [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], 9Cr-1Mo [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], 10Cr [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] and 40Mn [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. In addition, K. Arun Babu et al. [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] developed a dynamic recrystallization model for super-austenitic stainless steel using an ANN framework. Nevertheless, these studies have focused on steels with fixed chemical compositions and have not leveraged the capability of ANNs to systematically evaluate how variations in alloying element concentrations influence hot deformation behavior. Yang et al. [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] developed a neural network-based approach for predicting roll force and torque, eliminating the need for physically-based or empirical models. To enhance predictive accuracy, they employed ensemble modeling techniques. In a related study, Lee and Choi [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] introduced an online adaptive neural network for rolling force control, addressing key aspects such as network architecture, selection of input parameters, debugging procedures, development platforms, and evaluation of test results. In this study, the hot rolling force and torque behavior of an asymmetric two-layer sandwich panel composed of 2030 aluminum alloy and pure copper was investigated using simulations in Abaqus/Explicit. Considering the asymmetry of the panel, a fully detailed geometric model of the rollers and the composite panel was developed. Key process parameters, including the initial panel temperature, layers thickness, thickness reduction in different sections, and roller rotational speed, were analyzed under various conditions to optimize simulation time and assess the influence of these factors on rolling behavior. Furthermore, a neural network model was developed to accurately predict rolling force and torque under diverse rolling conditions. The data required for training and validation of the neural network were generated through a three-dimensional finite element model. The results demonstrate that the neural network model exhibits high accuracy in predicting rolling force and torque, offering an effective and time-efficient alternative to conventional, labor-intensive experimental trials.\u003c/p\u003e"},{"header":"2. Mathematical Model","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Thermal equations\u003c/h2\u003e \u003cp\u003eAs an investigation of the hot rolling process, Performs heat transfer an important role in hot rolling, because due to the influence of the panel and roller under temperature fields and in order to consider the temperature distribution inside the panel, the thermal conductivity equations governing the panel and roller must have the characteristic thermo-physical values ​​and flow stress as a function of temperature; also, formulas and thermo-physical properties should be up-to-date in order to be able to correctly answer the investigation of convection currents and rolling conductivity and simulation conditions. Considering the temperature distribution equation in the roller, it is assumed that the heat conduction along the peripheral direction is insignificant compared to the bulk heat flow and the thermal conduction at the interface of the panel is the same as the lower part [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] thus:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\frac{1}{r}\\frac{\\partial\\:}{\\partial\\:r}\\left(\\:{k}_{r}\\:r\\:\\frac{\\partial\\:T}{\\partial\\:r}\\:\\right)+\\frac{\\partial\\:}{\\partial\\:z}\\left(\\:{k}_{r}\\:\\frac{\\partial\\:T}{\\partial\\:z}\\:\\right)={\\rho\\:}_{r}*{C}_{rp}\\:\\left(\\:\\:\\frac{\\partial\\:T}{\\partial\\:t}\\:\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eDuring the hot rolling process, the temperature in the panel is distributed according to the three-dimensional partial differential equation that governs the solution of the problem, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\rho\\:}_{r}\\)\u003c/span\u003e\u003c/span\u003e is the density of the work roll, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{rp}\\)\u003c/span\u003e\u003c/span\u003e (j kg\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e \u0026deg;C\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) is the specific heat of the work roll, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{k}_{r}\\)\u003c/span\u003e\u003c/span\u003e (kW m\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e \u0026deg;C\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) is the thermal conductivity of the work roll, and this three-dimensional differential equation can be seen in Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\frac{\\partial\\:}{\\partial\\:x}\\left(\\:{k}_{s}\\:\\frac{\\partial\\:T}{\\partial\\:x}\\:\\right)+\\frac{\\partial\\:}{\\partial\\:y}\\left(\\:{k}_{s}\\:\\frac{\\partial\\:T}{\\partial\\:y}\\:\\right)+\\frac{\\partial\\:}{\\partial\\:z}\\left(\\:{k}_{s}\\:\\frac{\\partial\\:T}{\\partial\\:z}\\:\\right)+\\dot{q}={\\rho\\:}_{s}*{C}_{sp}\\:\\left(\\:\\:\\frac{\\partial\\:T}{\\partial\\:t}\\:\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\rho\\:}_{s}\\)\u003c/span\u003e\u003c/span\u003e is the density of the rolled panel, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{sp}\\)\u003c/span\u003e\u003c/span\u003e (j kg\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e \u0026deg;C\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) is the specific heat of the rolled metal, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{k}_{s}\\)\u003c/span\u003e\u003c/span\u003e (kW m\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e \u0026deg;C\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) is the thermal conductivity of the rolled panel, in the partial differential Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), (x) represents the distance along the panel and the rolling direction, (y) represents the distance from the thickness, and the parameter (z) is the distance along the width of the panel, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\dot{q}\\)\u003c/span\u003e\u003c/span\u003e (W.m\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e) is the amount of heat produced by the plastic work, and the subscripts r and s are respectively for It is a roller and panel that is used to generate heat from Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e):\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:\\dot{q}=\\stackrel{-}{\\eta\\:}*\\stackrel{-}{\\sigma\\:}*\\dot{\\epsilon\\:}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn this equation, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\stackrel{-}{\\sigma\\:}\\)\u003c/span\u003e\u003c/span\u003e (MPa) is the effective flow stress \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\dot{\\epsilon\\:}\\)\u003c/span\u003e\u003c/span\u003e (s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) is the effective strain rate and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\stackrel{-}{\\eta\\:}\\)\u003c/span\u003e\u003c/span\u003e is the efficiency of conversion of deformation energy to heat; the latter is assumed to be 0.95 for aluminum alloys and for copper is 0.8, which is considered reasonable is the conversion fraction of plastic work into heat [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], To check the boundary heat transfer conditions between the panel and the roller, which is the heat flux by \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{q}_{strip}\\)\u003c/span\u003e\u003c/span\u003e (W.m\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e) and the heat flux for the roller is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{q}_{roll}\\)\u003c/span\u003e\u003c/span\u003e (W.m\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e), and h (kW.m\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e.\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003eC\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) is the convection heat transfer coefficient, which is shown in Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{q}_{strip}=-{q}_{roll}=h*\\left({T}_{strip\\:}-{T}_{roll}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Mechanical equations\u003c/h2\u003e \u003cp\u003ewhich is due to the distribution of surface flux, also \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{q}_{fric}\\)\u003c/span\u003e\u003c/span\u003e (W.m\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e) is based on the sliding speed caused by the rolling speed, which leads to friction and in the areas that are along the arc of contact, it causes visible changes, and its contribution in the length of heat is small, but it can be considered and Eq.\u0026nbsp;(\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e) explains it [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{q}_{fric}=\\left|\\tau\\:*v\\right|$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\tau\\:\\)\u003c/span\u003e\u003c/span\u003e (MPa) is the shear stress and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:v\\)\u003c/span\u003e\u003c/span\u003e (m.s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) is the sliding velocity. Since the heat lost from the panel is gained by the work roll in the roll gap, a simultaneous solution of the governing equations of both the panel and the work roll is required. also \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{q}_{fric}\\)\u003c/span\u003e\u003c/span\u003e is generated from frictional sliding [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. The effect of contact friction on the flow of metal can be effective, which should be considered when balancing the interaction between the metal. Also, the contact friction between the panel and the roller is solved using the Coulomb model, which is mostly used for forming processes where the friction effect is proportional. with the normal force in Eq.\u0026nbsp;(\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e):\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{\\tau\\:}_{crit}\\:=\\:\\mu\\:*p$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\tau\\:}_{crit}\\)\u003c/span\u003e\u003c/span\u003e is the critical shear stress (MPa), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003e the coefficient of friction, and P (Pa) is the contact pressure.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Finite element model","content":"\u003cp\u003eIn this finite element model, a three-dimensional thermal-mechanical simulation process has been developed for data generation, with accurate validation under different types. Lagrangian-Eulerian (ALE) method rolling conditions as a formulation technique through Using the general-purpose FE business program ABAQUS\u0026trade;. In the model, thermal and mechanical interaction phenomena are considered. The yield stress entered in Abaqus software is associated with temperature, strain rate and strain. Simultaneous, Friction and deformation heat increase the temperature of the metal and the surface of the work roll. therefore, Thermal and mechanical models should be coupled together to simultaneously include the above-mentioned factor effects. It should also be mentioned that the simulation process considered in Abaqus software has a temperature and displacement couple solver which is explicitly involved in this process, so the main nature of the hot rolling process is temperature changes along with the displacement of the sandwich panel. Also, one of the reasons for using this solver is related to the difference in the temperature of the roller surface and the temperature of the composite panel. Finite element software for various analysis is used in a wide part of the industry. Due to the asymmetry of the problem conditions, the entire process has been modeled, also the geometry of the sandwich panel roller and panel has been assumed to be symmetrical in the width direction, but in the thickness direction, due to the lack of complete symmetry, it has been modeled. In the case of rollers, according to the heat transfer analysis between the roller surfaces and the sandwich panel, as well as Young's model, it is considered to be more rigid [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. The modeling has been done in three dimensions. The problem has been solved in an explicit way, and since the hot rolling process is a thermodynamic process, it is necessary to use elements that can include the thermal effects of the process. The behavior of (C3D8RT) for this reason, from the six-sided elements that have the combination of displacement and heat effects, the panel is assumed to be thermos - viscoplastic. In addition, the re-mesh function of Abaqus software has been used along with Eulerian Lagrangian couple. Since the range of changes in temperature and strain rate in the rolling process is large, it is necessary to determine the plastic behavior of the panel as a function of temperature and strain rate. Considering that the rollers have a Young's modulus of 200 GPa [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], they are considered as a rigid body, and the composite panel in the initial thicknesses of 20 (10 mm copper and 10 mm AA), 24 (12 mm copper and 12 mm AA), 28 (14 mm copper and 14 mm AA) mm and in the initial temperatures of 400, 500, 600\u0026deg;C and the different rolling Speed (90,140,190 rpm) has been considered. the results of which can be seen. It has also been investigated in order to investigate the subject of force and torque required for rolling in different reductions. it was considered to be deformed. It is also worth mentioning that the total number of mesh considered for the sandwich panel is around ten thousand (10,000) elements and increasing this value to (15,000) and (20,000) does not change much in the output results and using This number of meshes can make the simulation time very long. In this article, the optimized value of this number was considered so that the simulation time is shorter and the solution does not face errors. Also, due to the fact that the roller is considered rigid, but considering the heat transfer between the surfaces of the rollers and the sandwich panel, an isothermal coupler has been used to bring the simulation process closer to the real hot rolling process. The mechanical and thermal properties of pure copper and aluminum alloy 2030 are considered in Abaqus as a function of temperature [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Figure\u0026nbsp;\u0026lt;link rid=\"fig1\"\u0026gt;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u0026lt;/link\u0026gt;\u003c/span\u003e-a and \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e-b illustrate the positioning of the pure copper and 2030 aluminum alloy panels within the three-dimensional model.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThermo-physical properties of Pure Copper [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026times;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTemperature (\u0026deg;C)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eYoung's Modulus, E (GPa)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eThermal Conductivity, k (W/m\u0026middot;K)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eCoefficient of Thermal Expansion, α (1/\u0026deg;C)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eSpecific Heat, Cp (J/kg\u0026middot;K)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e117\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e398\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c4\"\u003e \u003cp\u003e16.5 \u0026times; 10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e385\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e110\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e390\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c4\"\u003e \u003cp\u003e16.5 \u0026times; 10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e390\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e103\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e380\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c4\"\u003e \u003cp\u003e17.0 \u0026times; 10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e395\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e370\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c4\"\u003e \u003cp\u003e17.2 \u0026times; 10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e360\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c4\"\u003e \u003cp\u003e17.5 \u0026times; 10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e405\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e350\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c4\"\u003e \u003cp\u003e17.8 \u0026times; 10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e410\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e340\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c4\"\u003e \u003cp\u003e18.1 \u0026times; 10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e415\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e700\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c4\"\u003e \u003cp\u003e18.4 \u0026times; 10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e420\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThermo-physical properties of AA2030 [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026times;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTemperature (\u0026deg;C)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eYoung's Modulus, E (GPa)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eThermal Conductivity, k (W/m\u0026middot;K)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eCoefficient of Thermal Expansion, α (1/\u0026deg;C)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eSpecific Heat, Cp (J/kg\u0026middot;K)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c4\"\u003e \u003cp\u003e23 \u0026times; 10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e900\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e205\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c4\"\u003e \u003cp\u003e23.5 \u0026times; 10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e910\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c4\"\u003e \u003cp\u003e24 \u0026times; 10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e920\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e195\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c4\"\u003e \u003cp\u003e24.5 \u0026times; 10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e930\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c4\"\u003e \u003cp\u003e25 \u0026times; 10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e940\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e185\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c4\"\u003e \u003cp\u003e25.5 \u0026times; 10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e950\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e180\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c4\"\u003e \u003cp\u003e26 \u0026times; 10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e960\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e700\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e175\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026times;\" colname=\"c4\"\u003e \u003cp\u003e26.5 \u0026times; 10⁻⁶\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e970\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4. Artificial neural network (ANN)","content":"\u003cp\u003eThe theoretical foundation of neural networks is derived from the architecture of the human brain and its capability to process vast amounts of information. Artificial neural networks (ANNs) are adaptive computational models capable of learning from data and generalizing acquired knowledge. They can be employed to establish complex mappings between inputs and outputs, providing insights into the practical behavior of the underlying phenomena [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. A multi-layer neural network consists of an input layer, one or more hidden layers, and an output layer. The input layer receives experimental data, features, or measured indicators and serves as the entry point to the network. Hidden layers, positioned between the input and output layers, process the incoming signals and transmit the transformed information to the output layer, which then consolidates these signals to generate the final output vector. Each layer is composed of multiple processing units, or neurons, interconnected via adjustable synaptic weights. During the training phase, these weights are iteratively optimized commonly using the back-propagation algorithm by presenting the network with paired input-output samples that represent the underlying relationships to be learned. The output of each neuron is calculated through a weighted summation of its inputs followed by the application of a nonlinear activation function, as mathematically expressed in Eq.\u0026nbsp;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e7\u003c/span\u003e) [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:{y}_{j}=f\\left(\\sum\\:_{i=1}^{n}{w}_{ij}{x}_{i}+\\:{b}_{j}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the inputs to the neuron, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{ij}\\)\u003c/span\u003e\u003c/span\u003e​ is the corresponding synaptic weights, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{b}_{j}\\)\u003c/span\u003e\u003c/span\u003e​ is the bias term, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:f\\)\u003c/span\u003e\u003c/span\u003e is the activation function applied to the weighted sum, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n\\)\u003c/span\u003e\u003c/span\u003e is the number of inputs to the neuron. During the training phase, the neural network is provided with multiple sets of input-output pairs. An iterative optimization algorithm systematically updates the synaptic weights to ensure that the network\u0026rsquo;s predicted outputs \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{o}_{j}\\)\u003c/span\u003e\u003c/span\u003e closely approximate the corresponding target outputs \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{d}_{j}\\)\u003c/span\u003e\u003c/span\u003e for each input pattern. For a network with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:J\\)\u003c/span\u003e\u003c/span\u003e total outputs, the training process seeks to minimize the discrepancy between predicted and desired values by reducing the mean squared error (MSE), as formulated in Eq.\u0026nbsp;(\u003cspan refid=\"Equ8\" class=\"InternalRef\"\u003e8\u003c/span\u003e) [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. This approach ensures that the network progressively learns the underlying relationships within the dataset, improving its predictive accuracy across all outputs.\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\:MSE=\\:\\frac{1}{J}\\:\\sum\\:_{j=1}^{J}{({o}_{j}-{d}_{j})}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe back-propagation algorithm is a widely adopted method for minimizing the mean squared error (MSE) by iteratively updating the connection weights within a neural network [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. The learning procedure in this approach can be divided into three primary stages. Initially, the input dataset is fed into the network. Subsequently, using the randomly initialized weights and biases, along with the activation functions assigned to each neuron, the network propagates the signals forward, computing the output of every neuron layer by layer until the final output vector is generated. This systematic propagation ensures that the network\u0026rsquo;s response is determined for each input pattern, providing the foundation for subsequent weight adjustments during training. The training procedure of a neural network via the back-propagation algorithm consists of three sequential phases. In the initial phase, known as the feedforward stage, input data are propagated through the network, and the outputs of all neurons are computed layer by layer until the final output is obtained. During the subsequent phase, the discrepancy between the network\u0026rsquo;s predicted output and the desired target is quantified, and this error is systematically propagated backward through the network, allowing the computation of individual neuron errors; this is referred to as the back-propagation stage. In the final phase, the connection weights and biases are iteratively updated using a dedicated optimization algorithm to minimize the overall error. Each complete execution of these three phases constitutes a single training cycle, and the cycles are repeated continuously until a predefined stopping criterion is satisfied [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. The neural network models for predicting rolling force and torque based on the input parameters are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo develop a robust and reliable neural network (NN) model, it is essential to have a sufficiently large and high-quality training dataset. The amount of data required depends on several factors, including the complexity of the process being modeled, the number of input variables, and the precision of the available process data. Typically, effective NN training requires hundreds or even thousands of data samples. Since finite element (FE) modeling involves intensive and time-consuming computations, generating training data through this method necessitates a carefully designed experimental framework. In this study, the training dataset was generated using the Design of Experiments (DOE) approach. Specifically, a three-level full factorial design, one of the most widely used Design of Experiments (DOE) techniques, was employed. In this design, the variable space is divided into three levels between the minimum and maximum values, resulting in 3ⁿ experimental combinations for n input variables. Given that four input parameters were considered in this study (n\u0026thinsp;=\u0026thinsp;4), at least 81 data samples are required for training the neural network. However, to improve the accuracy and generalization capability of the ANN, a total of 243 data samples were generated using the validated finite element (FE) model. The factors and their corresponding levels used in this design are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eChosen experimental schedules for investigation of hot rolling simulation.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp.no\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eInlet thick. (mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eInlet panel temp. (\u0026deg;C)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eReduction. (%)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eRoll Speed. (rpm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e190\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e190\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e190\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e190\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e190\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn the present investigation, a customized computational framework was developed in MATLAB to implement the proposed Artificial Neural Network (ANN) model using the Back-Propagation Algorithm (BPA). Back-propagation based neural networks are among the most widely adopted approaches for nonlinear modeling due to their strong generalization capability and the availability of numerous well-established training schemes, such as gradient descent, quasi-Newton optimization, conjugate gradient, stochastic approximation, and Levenberg\u0026ndash;Marquardt optimization methods [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. In this study, the tangential sigmoid transfer function was employed for both the hidden and output layers, while the Levenberg\u0026ndash;Marquardt algorithm was selected as the training function, owing to its superior convergence speed and efficiency in training medium-sized feedforward neural networks [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. To prevent overfitting, the early-stopping technique was incorporated during the training process. In this approach, the available data are partitioned into two subsets: a training set, utilized for iterative adjustment of the network\u0026rsquo;s connection weights and biases, and a validation set, used to monitor the network\u0026rsquo;s generalization capability. During the training phase, both training and validation errors typically decrease simultaneously; however, once the network begins to overfit the training data, the validation error starts to rise. When this upward trend continues for a predefined number of epochs, the training is automatically terminated, and the optimal network parameters corresponding to the minimum validation error are preserved as the final trained model. Prior to feeding the datasets into the backpropagation (BP) network, it is essential to preprocess the input and output variables to ensure numerical stability and improve convergence performance. Accordingly, both the input and target data were normalized to a defined interval of [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] using the normalization procedure expressed in Eq.\u0026nbsp;(\u003cspan refid=\"Equ9\" class=\"InternalRef\"\u003e9\u003c/span\u003e), enabling consistent scaling and enhancing the efficiency of the training process.\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$$\\:{X}_{i}=\\:0.1+0.8\\left(\\frac{{X-X}_{min}}{{X}_{max}{-X}_{min}}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:X\\)\u003c/span\u003e\u003c/span\u003e represents the original dataset, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{min}\\)\u003c/span\u003e\u003c/span\u003e​ and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{max}\\)\u003c/span\u003e\u003c/span\u003e denote the minimum and maximum values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:X\\)\u003c/span\u003e\u003c/span\u003e, respectively, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{i}\\)\u003c/span\u003e\u003c/span\u003e​ is the normalized value corresponding to each data point of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:X\\)\u003c/span\u003e\u003c/span\u003e. The architecture of the artificial neural network and the functions employed in the final model are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe ANN architecture and functions.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNetwork\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eFeed-forward back propagation network\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTraining function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLevenberg\u0026ndash;Marquardt\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLearning function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGradient descent with momentum weight \u0026amp; bias learning function\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTransfer function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTan sigmoid function\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePerformance function\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMean squared error\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumber of input layer unit\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumber of hidden layers\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumber of output layer units\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"5. Results and discussion","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e5.1. FEM Simulation Results\u003c/h2\u003e \u003cp\u003eIn the asymmetric hot rolling process of a bimetallic panel, an AA2030 aluminum alloy and pure copper composite with a width of 40 mm was employed as the constituent materials. The specimen was rolled in all passes using rolls with a diameter of 160 mm. Figures\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrate the variations of rolling force and rolling torque over time for different thickness reduction levels. As depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e-a, the amplitude of rolling force fluctuations within the steady-state region increases with the rise in thickness reduction. The initial thickness of the sandwich panel was considered to be 20 mm, with reduction ratios of 30%, 35%, and 40%, respectively. A similar trend is observed in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e-b, where rolling torque oscillations also intensify as the reduction level increases. This phenomenon can be attributed to the changes in surface conditions particularly the contact friction within the roll panel interface which influence the distribution of interfacial shear stress and sliding behavior. As reported by Hum et al. [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e], higher thickness reductions lead to increased forward slip and friction coefficients. Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e provides a comprehensive overview of the loading conditions and the parameters utilized in the simulation process. It is noteworthy that the roll diameter was maintained at 160 mm, and the convective heat transfer coefficient between the roll surface and the composite panel was assumed to be 40 kW/m\u0026sup2;\u0026deg;C. With increasing thickness reduction, the rolling force in both layer increases. Since aluminum (AA2030) exhibits higher strength than copper at the rolling temperature, it bears a greater portion of the compressive load; consequently, the effective rolling force acting on the aluminum layer is higher than that on the copper layer. The rolling torque of each roll is proportional to the contact force and surface friction; therefore, the roll in contact with the aluminum layer experiences a higher torque.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRolling force and torque under different reduction area rolling parameters.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp.no\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eInlet thick. (mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eInlet panel temp. (\u0026deg;C)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eReduction. (%)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eRoll Speed. (rpm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs expected, decreasing the rolling temperature necessitates higher rolling force and torque to deform the workpiece. Therefore, rolling the sandwich panel at lower temperatures requires increased levels of both rolling force and torque. However, since the sandwich panel is composed of two layers and exhibits an asymmetrical configuration, the rolling force and torque differ between the top and bottom rollers, resulting in asymmetry in both the rolling process and the simulation. In general, with increasing temperature, the plasticity of the sandwich panel improves, facilitating deformation. Once the material reaches its fluid-like state, the demand for excessive force and torque diminishes, and their values drop to lower, more favorable levels for the process. Figures\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e illustrate the variations in rolling force and torque under different temperature conditions. As evident from the graphs, both rolling force and torque decrease as the temperature increases, which can be attributed to the enhanced malleability of the sandwich panel at elevated temperatures. Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e provides a comprehensive overview of the loading conditions and the parameters utilized in the simulation process. It should be noted that the rolling rollers have a diameter of 160 mm, and the heat transfer coefficient between the roller surface and the composite panel surface is considered to be 60 kW/m\u0026sup2;\u0026middot;\u0026deg;C. With the increase in temperature, the sandwich panel becomes more ductile and its plastic resistance decreases, leading to a reduction in the rolling force and torque required for both layers. Nevertheless, the aluminum layer consistently sustains higher force and torque compared to the copper layer.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRolling force and torque under different temperature rolling parameters.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp.no\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eInlet thick. (mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eInlet panel temp. (\u0026deg;C)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eReduction. (%)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eRoll Speed. (rpm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e presents the rolling conditions considering the influence of different rotational speeds of the rollers on the variation of rolling force and torque over time. As the rolling speed increases, the amplitude of fluctuations in both rolling force and torque also increases. However, due to the shorter contact time between the sandwich panel and the rollers, the duration of these variations becomes more limited at higher speeds. Consequently, although the average force and torque may decrease, their instantaneous oscillations tend to intensify at higher rolling velocities. The simulation results obtained at rotational speeds of 90, 140, and 190 rpm indicate that increasing the rolling speed alters the magnitude and frequency of force and torque fluctuations. At higher speeds, the panel experiences partial sliding at the roll-panel interface, redistributing the shear stress over the contact surface. This directly affects the frictional and deformation behavior of the material during rolling. Figures\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e and Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e illustrate the time-dependent variations of rolling force and torque. As observed, the reduction in contact duration limits the range of force variations but simultaneously increases the vibration intensity of the system. Such intensified oscillations at higher speeds may promote panel distortion, crack initiation, and surface damage.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRolling force and torque under different roller rotation speed rolling parameters.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp.no\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eInlet thick. (mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eInlet panel temp. (\u0026deg;C)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eReduction. (%)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eRoll Speed. (rpm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e190\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eBy increasing the initial thickness of the sandwich panel from 20 mm to 28 mm, the amount of plastic deformation and, consequently, the mechanical work required during rolling increases. This results in higher rolling force and rolling torque values. In other words, both force and torque exhibit a direct relationship with the initial panel thickness, as greater thickness leads to a larger volume of material being deformed within the roll bite region. In the numerical simulations, all other process parameters such as roll diameter (160 mm), rolling speed, and temperature were kept constant to isolate the effect of initial thickness on the rolling behavior. The variations of rolling force and torque with different initial thicknesses are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e. The input parameters and geometric conditions employed in the simulation are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. Moreover, the convective heat transfer coefficient between the roll surface and the composite panel was assumed to be 20 kW/m\u0026sup2;\u0026middot;\u0026deg;C.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRolling force and torque under different panel thickness rolling parameters.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExp.no\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eInlet thick. (mm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eInlet panel temp. (\u0026deg;C)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eReduction. (%)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eRoll Speed. (rpm)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e5.2. Neural Network Results\u003c/h2\u003e \u003cp\u003eThe Artificial Neural Network (ANN) model developed in this study was employed to predict the roll force and roll torque based on the design data of the hot panel rolling process. The performance of the model on the training data is illustrated in Figs.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e and \u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e. The results indicate that the model exhibits high prediction accuracy and a good generalization capability toward the test data. The neural network analysis was carried out using MATLAB R2022. For the quantitative evaluation of the model performance, only the correlation coefficient (R) between the predicted and actual values was calculated, and the Best Fit line was plotted in the figures to visually demonstrate the degree of agreement between the model predictions and the experimental data.\u003c/p\u003e \u003cp\u003eThe neural network model is essentially a complex and nonlinear system consisting of numerous activation functions and interconnecting weights between neurons. To evaluate the compatibility of the developed model with the existing physical understanding of the rolling process, model response surfaces were employed. These surfaces were generated by varying two selected input parameters while keeping the remaining inputs fixed at their mean values. Such plots serve as an effective tool to assess the accuracy of the developed model based on the training data and to identify whether additional data may be required to further improve the training of the neural network. Some of the response surfaces obtained from the neural network model, illustrating the variation of roll force with respect to two selected input parameters, are presented in Figs.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e and \u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e. These plots were used to verify the validity of the developed model by comparing its behavior with the known physical trends of the rolling process. According to Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e, the reduction area and initial temperature are the most influential parameters affecting the roll force; as either parameter changes, the roll force also varies accordingly. Similarly, Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e shows that the reduction area and the initial thickness of the composite panel are among the key parameters influencing the roll force. In Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e-a, the rolling force corresponds to the upper roll, while Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e-b represents the lower roll under identical operating conditions (reduction area and temperature), where slight differences in force behavior can be observed. Likewise, Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e-a and Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e-b illustrate the rolling forces of the upper and lower rolls, respectively, under the conditions of reduction area and thickness.\u003c/p\u003e \u003cp\u003eIn this study, the effects of composite panel temperature, initial panel thickness, and cross-sectional reduction on the rolling force are investigated. To calculate the rolling force, the average force applied to the upper and lower rolls throughout the process is obtained and used to train the neural network. Figure\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e presents a comparison between the rolling force predicted by the neural network and that obtained from the finite element method. This figure illustrates the variation in the average rolling force with respect to changes in the initial panel thickness, demonstrating that the rolling force increases as the initial thickness increases. Figure\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e-a corresponds to the upper roll, while Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e-b represents the lower roll. Also In this study, the effect of increasing the initial temperature of the composite panel on the rolling force behavior is examined. As the panel temperature rises, the material becomes softer and its resistance to deformation decreases, leading to a noticeable reduction in the required rolling force. Figure\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003e illustrates the variation of rolling force under different temperature conditions, demonstrating that elevating the panel temperature prior to the process plays a significant role in reducing the force applied to both the upper and lower rolls. This reduction is similarly observed for both rolls, as depicted in Figs.\u0026nbsp;\u0026lt;link rid=\"fig16\"\u0026gt;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u0026lt;/link\u0026gt;\u003c/span\u003e-a and \u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003e-b. In this study, the effect of the reduction area on the rolling force was investigated. An increase in the reduction area subjects the panel to more severe deformation, thereby significantly raising the rolling force required to pass through the roll contact zone. Figure\u0026nbsp;\u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003e illustrates the variation of rolling force for different reduction levels, showing that higher reduction percentages result in increased forces on both the upper and lower rolls. Moreover, a comparison of Figs.\u0026nbsp;\u0026lt;link rid=\"fig17\"\u0026gt;\u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u0026lt;/link\u0026gt;\u003c/span\u003e-a and \u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003e-b indicates that the influence of increased reduction area is similar for both rolls, with the force increment pattern clearly observable in each case.\u003c/p\u003e\u003cp\u003eIn this section, the simultaneous variations of the upper and lower roller forces are examined. The corresponding plots allow for observing the patterns and correlations between the forces. The simulation results are compared with the predictions of the trained artificial neural network (ANN), showing that the ANN can accurately reproduce the simultaneous force variations. This analysis helps to better understand the impact of force differences on stress distribution. Finally, the combination of simulation data and ANN predictions enables the analysis of future trends and optimization of the rolling process.\u003c/p\u003e \u003c/div\u003e"},{"header":"6. Conclusions","content":"\u003cp\u003eTo simulate the rolling process of a composite sandwich panel composed of pure copper and aluminum alloy AA2030, a hybrid modeling approach combining finite element (FE) analysis and an artificial neural network (ANN) was developed. In this framework, data obtained from FE simulations were used to train the ANN, enabling efficient prediction of rolling force and rolling torque under various process conditions. The neural network generalizes the FE results and provides rapid predictions, thereby avoiding the high computational cost associated with performing full FE simulations for all scenarios. This study investigates the influence of key process parameters on rolling force and torque, including initial thickness, reduction ratio per rolling pass, initial panel temperature, and rolling speed, all of which directly affect the mechanical behavior and energy consumption during the rolling process. The effects of these parameters can be summarized as follows. Increasing the reduction ratio leads to a significant rise in rolling force and torque due to the higher level of plastic deformation required. Increasing the rolling temperature reduces the yield strength of the materials, resulting in lower rolling force and torque, which is consistent with hot rolling behavior. Higher rolling speeds reduce the contact time between the rolls and the panel, leading to a decrease in average rolling force, although excessively high speeds may induce dynamic vibrations and asymmetric deformation. Finally, increasing the initial panel thickness increases the rolling force and torque because of the greater mechanical work needed for deformation. Overall, the developed ANN successfully captures the complex nonlinear relationships between process parameters and rolling responses, enabling fast and accurate predictions that support process optimization, energy reduction, and minimized roll wear in copper\u0026ndash;aluminum bimetallic rolling.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eH.R. conceived the original idea of the research and defined the overall scientific framework of the study. A.J. was responsible for developing the methodology, performing all numerical and finite element simulations, processing and analyzing the data, and generating all figures and graphical results. A.J. also wrote the original draft of the manuscript and integrated the results into their final form. Both authors discussed the results, contributed to the interpretation of the findings, reviewed the manuscript, and approved the final version for publication.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eYes, research data were generated in this study.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eMa Z, Zhao H, Liu C (2015) Critical fracture behavior of a Cu/Al composite laminate via the observation of scanning electron microscope. Mater Trans 56(6):813\u0026ndash;818\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTian H et al (2018) Numerical simulations of the Cu/Al composite plate continuous cast-rolling process. Mater Res Express 5(12):126505\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSheng L et al (2011) Influence of heat treatment on interface of Cu/Al bimetal composite fabricated by cold rolling. Compos Part B: Eng 42(6):1468\u0026ndash;1473\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTeker E et al (2022) Hot deformation behavior and strain rate sensitivity of 33MnCrB5 boron steel using material constitutive equations. Trans Indian Inst Met 75(3):717\u0026ndash;726\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRenault C et al (2020) Microstructure and hot deformation behavior of FeMnAlCMo steel. J Mater Res Technol 9(3):4440\u0026ndash;4449\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOrowan E (1943) The calculation of roll pressure in hot and cold flat rolling. Proceedings of the Institution of Mechanical Engineers, 150(1): pp. 140\u0026ndash;167\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChen S et al (2025) Research on Mathematical Model of Rolling Force for Asymmetrical Rolling of Cu/Al Clad Plate. Iran J Sci Technol Trans Mech Eng 49(1):329\u0026ndash;348\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXu W, Xia C, Ni C (2024) Numerical Simulation and Experimental Verification of Hot Roll Bonding of 7000 Series Aluminum Alloy Laminated Materials. Metals 14(5):551\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChe J et al (2025) Prediction Model Study of Rolling Force and Thickness Ratio of the Bimetallic Composite Plate. Chin J Mech Eng 38(1):1\u0026ndash;13\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChandrasekar P, Nagaraju D (2022) Improvement of bonding strength at the interfaces in scrap Al alloy composites using electroless Ni-P coated SiC. Silicon 14(6):2941\u0026ndash;2952\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHeydari Vini M, Sedighi M (2018) Mechanical properties and bond strength of bimetallic AA1050/AA5083 laminates fabricated by warm-accumulative roll bonding. Can Metall Q 57(2):160\u0026ndash;167\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu H et al (2021) Deformation behavior and constitutive equation of 42crmo steel at high temperature. Metals 11(10):1614\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAhmadi H, Ashtiani HR, Heidari M (2020) A comparative study of phenomenological, physically-based and artificial neural network models to predict the Hot flow behavior of API 5CT-L80 steel. Mater Today Commun 25:101528\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMurugesan M, Sajjad M, Jung DW (2019) Hybrid machine learning optimization approach to predict hot deformation behavior of medium carbon steel material. Metals 9(12):1315\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKumar S, Karmakar A, Nath SK (2021) Construction of hot deformation processing maps for 9Cr-1Mo steel through conventional and ANN approach. Mater Today Commun 26:101903\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShokry A et al (2019) Constitutive models for the prediction of the hot deformation behavior of the 10% Cr steel alloy. Materials 12(18):2873\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHuang W, Lei L, Fang G (2021) Comparison between four flow stress models characterizing the constitutive behavior of hot deformation of 40Mn steel. J Mater Eng Perform 30(12):9149\u0026ndash;9164\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBabu KA et al (2021) Modeling and simulation of dynamic recrystallization in super austenitic stainless steel employing combined cellular automaton, artificial neural network and finite element method. Comput Mater Sci 195:110482\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYang Y, Linkens D, Talamantes-Silva J (2004) Roll load prediction\u0026mdash;data collection, analysis and neural network modelling. J Mater Process Technol 152(3):304\u0026ndash;315\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLee DM, Choi S (2004) Application of on-line adaptable neural network for the rolling force set-up of a plate mill. Eng Appl Artif Intell 17(5):557\u0026ndash;565\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang X, Yang Q, He A (2008) Calculation of thermal stress affecting strip flatness change during run-out table cooling in hot steel strip rolling. J Mater Process Technol 207:130\u0026ndash;146\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKumar A, Samarasekera I, Hawbolt E (1992) Roll-bite deformation during the hot rolling of steel strip. J Mater Process Technol 30(1):91\u0026ndash;114\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShahani A et al (2009) Prediction of influence parameters on the hot rolling process using finite element method and neural network. J Mater Process Technol 209(4):1920\u0026ndash;1935\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShahani AR et al (2009) Prediction of influence parameters on the hot rolling process using finite element method and neural network. J Mater Process Technol 209(4):1920\u0026ndash;1935\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAshtiani HR, Bisadi H, Adabjou M (2010) Modeling of Microstructural Evolution During the Hot Rolling of Aluminum Alloy. Int Rev Modelling Simulations 3(5):1129\u0026ndash;1136\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAhmed H et al (2005) Modelling of microstructure evolution during hot rolling of AA5083 using an internal state variable approach integrated into an FE model. Mater Sci Engineering: A 390(1):278\u0026ndash;290\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBagheripoor M, Bisadi H (2013) Application of artificial neural networks for the prediction of roll force and roll torque in hot strip rolling process. Appl Math Model 37(7):4593\u0026ndash;4607\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eManikanta JE et al (2025) A review on hybrid nanofluids: preparation methods, thermo physical properties and applications. Iran J Sci Technol Trans Mech Eng 49(1):67\u0026ndash;79\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLarkiola J et al (1998) The role of neural networks in the optimisation of rolling processes. J Mater Process Technol 80:16\u0026ndash;23\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDeng J et al (2005) Structural reliability analysis for implicit performance functions using artificial neural network. Struct Saf 27(1):25\u0026ndash;48\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKazan R, Fırat M, Tiryaki AE (2009) Prediction of springback in wipe-bending process of sheet metal using neural network. Mater Design 30(2):418\u0026ndash;423\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWidrow B, Lehr MA (2002) 30 years of adaptive neural networks: perceptron, madaline, and backpropagation. Proceedings of the IEEE, 78(9): pp. 1415\u0026ndash;1442\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHagan MT, Menhaj MB (1994) Training feedforward networks with the Marquardt algorithm. IEEE Trans Neural Networks 5(6):989\u0026ndash;993\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHum B, Colquhoun H, Lenard J (1996) Measurements of friction during hot rolling of aluminum strips. J Mater Process Technol 60(1\u0026ndash;4):331\u0026ndash;338\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Asymmetric Hot Rolling, Finite Element Simulation (FE), Artificial Neural Network (ANN), Rolling Force and Torque Prediction","lastPublishedDoi":"10.21203/rs.3.rs-8495786/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8495786/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this study, a hybrid modeling framework combining three-dimensional finite element (FE) simulation and artificial neural network (ANN) prediction is developed to analyze the asymmetric hot rolling behavior of a two-layer Cu/AA2030 composite panel. The FE model, implemented using the Abaqus/Explicit platform, couples thermal and mechanical fields to evaluate the effects of key process parameters including initial panel thickness, reduction ratio, rolling speed, and inlet temperature on rolling force and torque. The asymmetric configuration of the composite panel and the thermal-mechanical interaction between the rolls and panel are fully considered in the simulation. A validated FE dataset was subsequently employed to train a feed-forward back-propagation ANN using the Levenberg\u0026ndash;Marquardt algorithm. The network architecture, consisting of four input neurons, two hidden layers, and two output neurons, was optimized to achieve minimum mean square error (MSE) and high correlation accuracy between predicted and simulated values. Results indicate that both rolling force and torque increase with greater thickness reduction and initial panel thickness, while higher rolling temperatures and rolling speeds reduce the required force and torque. The ANN model successfully predicts rolling force and torque with high accuracy, demonstrating strong generalization and computational efficiency. This integrated FE\u0026ndash;ANN approach provides a reliable and time-effective method for optimizing process parameters in bimetallic panel rolling, reducing the need for extensive experimental trials and enabling improved control of rolling performance in copper\u0026ndash;aluminum laminated composites.\u003c/p\u003e","manuscriptTitle":"Thermo-Mechanical Simulation and ANN-Based Prediction of Rolling Force and Torque in Two-Layer Copper–Aluminum Composite Panel","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-08 10:30:55","doi":"10.21203/rs.3.rs-8495786/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"62b512ab-071c-49f3-8a3e-9a7c66bc3b11","owner":[],"postedDate":"January 8th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-01-27T07:12:08+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-08 10:30:55","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8495786","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8495786","identity":"rs-8495786","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}