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Camber in hot-rolled plates significantly impacts product quality and rolling process stability, making accurate camber prediction crucial. However, it is challenging to measure asymmetric factors impacting camber in real production, hindering the ability of current models to predict and analyze the overall camber of rolled plates. This study proposes a method that combines asymmetric fluctuations of measurable variables with deep learning to predict camber. We developed a data analysis platform for plate processing and constructed a camber dataset using machine vision technology. During the modeling phase, a hot-rolled plate camber prediction model, BiLSTM-AM-Seq2Seq, was proposed, integrating a bidirectional long short-term memory network, an attention mechanism, and a sequence-to-sequence model. Additionally, an improved scheduled sampling method was also introduced to steer model training. Model performance was evaluated with real-world production data, demonstrating superior accuracy and stability. Specifically, the model achieved a mean absolute error of 12.29 mm and a root mean square error of 17.32 mm. Consequently, this model meets the demands of practical production and addresses the need for overall camber prediction of hot rolled plates. • Data-driven prediction model for overall camber shape of rolled plates is proposed. • Modeling using fluctuations of observable variables to address the absence of key asymmetric variables in real production. • Data analysis platform was developed and real data were used to demonstrate the superiority of the proposed model. [ABSTRACT FROM AUTHOR]

In the field of hot rolling big data, the presence of different steel types, specifications, and data heterogeneity poses significant challenges to the accuracy and stability of using single machine learning regression technology for prediction. Therefore, this study proposes a hot‐rolled strip crown prediction method that combines data clustering and fusion modeling. First, this article introduces a relevant mechanism for designing cluster strategies. The optimal clustering strategy is determined through comparative experiments using rolling process parameters, strip size, and main material components as the clustering features. Subsequently, the K‐Means++ algorithm is used to effectively cluster the training and testing datasets based on this strategy, generating multiple clusters for both datasets. Finally, this study establishes seven different training models to match the most suitable regression prediction model for each cluster, and matching between each cluster and the model is determined through rigorous testing. The evaluation of the fusion model shows an R2 value of 0.829 and a root mean square error value of 3.974. The experimental results show that the proposed method outperforms traditional methods in solving the challenges of multiclass classification and data heterogeneity, providing strong data support for the intelligent control of the hot‐rolled strip crown in the future. [ABSTRACT FROM AUTHOR]

Machine learning performs well in many problems. However, the tendency to generate predictions that violate theoretical knowledge makes it difficult to apply to practical processing. To resolve this situation, this paper combines domain knowledge with a data-driven model, proposes a theory-guided machine learning framework based on a parameter transfer strategy, and applies it to the width prediction of plates after multiple passes of hot rolling. The framework applies a swarm optimization algorithm to the original theoretical model and generates numerous highly-physical consistent samples. The established deep neural network (DNN) model is trained with simulated data, and the parameters are fine-tuned using a parameter transfer strategy combined with actual data to ensure excellent adaptation to the actual environment based on adequate learning of theoretical knowledge. In tests, the proposed model had the best overall prediction performance in this paper. Meanwhile, the developed model is consistent with the existing perception of rolling theory. This allows for the quick and reliable application of machine learning models in production. [Display omitted] • A novel theory-guided machine learning framework for width prediction of rolled plates. • Pre-training of the model using the data generated by the optimized theoretical model. • The proposed model has the best accuracy in both sufficient and less actual samples. • The variable influence of the proposed model is consistent with theoretical perceptions. [ABSTRACT FROM AUTHOR]

To obtain the transverse temperature distribution of running strips under C‐type edge induction heaters during the hot‐rolling process, a coupled electromagnetic–thermal finite‐element model is established using COMSOL, in which the electromagnetic and temperature distributions regularity with various process parameters are systematically obtained. It is shown in the results that the temperature increase is directly proportional to the frequency and current and inversely proportional to the thickness. Meanwhile, the edge temperature drop can be rapidly compensated for using an edge heater, but it also leads to the appearance of a "cat‐ear" high‐temperature zone at the edge; thus, the transverse temperature uniformity cannot be guaranteed. To improve the temperature uniformity of the running strip, a magnetic shield plate is designed to weaken the effect of the cat ear, and the effects of the size and installation position of the shielding plate on the temperature distribution are analyzed. The standard deviation and uniformity of the temperature are used to determine the uniformity of the transverse temperature, and the optimal parameter combination mode of the magnetic shielding amounts is obtained, which can provide a reference for optimizing the heating process at the edge of the strip under moving conditions. [ABSTRACT FROM AUTHOR]

In the hot strip process, the prediction of strip shape is a key factor to improve the quality of products. However, strip‐shape prediction models based on traditional machine learning algorithms with relatively simple network structures often rely on data preprocessing and feature selection. Herein, five strip‐shape prediction models are proposed by combining sparrow search algorithm (SSA), particle swarm optimization algorithm (PSO), extreme learning machine (ELM), and deep multilayer extreme learning machine (DELM). The prediction experiments show that the SSA‐DELM model has highest accuracy, and the determination coefficient (R2) of crown prediction and flatness prediction of SSA‐DELM model is 0.971 and 0.979. 100% of the samples have a prediction error of less than ±7 μm and ±7 IU. Furthermore, to solve the problem of concept drift affecting prediction accuracy in industrial processes, online optimization method is proposed. Especially, online sequential deep ELM model (OS‐DELM) optimized by SSA and guided by double window drift detection is proposed to fill the gap. Compared with other online optimization methods, the update time with this method can be reduced by up to 83.05% averagely, which is more suitable for online strip‐shape prediction in hot rolling process. [ABSTRACT FROM AUTHOR]

The strips with good flatness after finish rolling will have flatness defects such as edge wave after run-out table cooling. These defects are caused by the residual stress due to inhomogeneous thermal and microstructural behaviors during the cooling stage. The traditional residual stress control methods rely too much on experience, resulting in poor control effect and poor universality. Therefore, this study proposed two residual stress control methods based on model calculation: water flow central crown and center wave compensation control. The former is mainly based on controlling the uniformity of strip transverse temperature and microstructure. The latter is mainly controlled by mutual compensation of internal stresses. In this paper, the mathematical models of water flow central crown cooling and critical center wave compensation stress were established, respectively. Meanwhile, a post-buckling model of hot-rolled strip was established to calculate the aim flatness value at exit of finishing mill under critical compensation stress. Furthermore, a fully coupled finite element model based on temperature, phase transitions, and stress was developed and it was verified using experimental data. Finally, the above two residual stress control methods were realized in the finite element model. The results showed that the two methods can reduce the residual stress and improve the flatness, and the application of center wave compensation control is more effective. [ABSTRACT FROM AUTHOR]

Vertical rolling is an important technique used to control the width of continuous casting slabs in the hot-rolling field. Accurate prediction of vertical rolling force is a core point maintaining rolling-mill equipment. Owing to the limitation of the algorithm in use, the prediction accuracy of most vertical rolling force models based on the energy method can only reach more than 10%. Therefore, it is challenging to optimize the rolling-force model to improve prediction accuracy. An innovative approach for optimizing the calculation of vertical rolling force with a unified yield criterion is presented in this paper. First, the maximal width of a dog-bone region is determined by the slip-line method, and the dog-bone shape is described using a sine-function model. Second, the velocity and corresponding strain-rate fields satisfying kinematically admissible conditions are proposed to calculate the total power of the vertical rolling process. Finally, the analytical solution of the rolling force and the dog-bone-shape model is obtained by repeatedly optimizing the weighted coefficient b of intermediate principal shear stress on the yield criterion. Moreover, the effectiveness of the proposed mechanical model is verified by measured data in the strip hot-rolling field and other models' results. Results show that the prediction accuracy of the vertical rolling force model can be improved by optimizing the value of b. Then, the impacts of reduction rate, initial thickness, and friction factor on dog-bone shape size and vertical rolling force are discussed. [ABSTRACT FROM AUTHOR]

In the routine roll shifting mode, work rolls of the continuous variable crown (CVC) hot strip mill are always in repeated shifting positions, which affects the uniform wear of work rolls. As an available solution to the above problem, a new random shifting mode for CVC work rolls has been developed in this paper. According to the relationship between shifting position and bending force, the new CVC shifting mode shifts work rolls in a random pattern within the limits by randomly changing the bending force, so that the roll shifting is dispersed and the strip shape remains good. The Light Gradient Boosting Machine (LightGBM) algorithm is applied to build the prediction models of CVC shifting to accurately express the relationship between shifting position and bending force. Random search and Bayesian optimization are used to optimize the LightGBM models, respectively. By comparison, LightGBM with Bayesian optimization is recommended to predict roll shifting, which is more accurate and efficient than using random search. The new CVC shifting mode has been implemented by an off-line application in the 1780 mm hot rolling line. The results reveal that the proposed CVC shifting mode can well disperse roll shifting positions and accurately control strip shape. [ABSTRACT FROM AUTHOR]

Strip shape prediction is one of the most important technical to improve the quality of products in hot strip rolling process. In this paper, three hybrid models, including GA-MLP, MEA-MLP and PCA-MEA-MLP, are proposed for profile and flatness predictions by combining genetic algorithm (GA), mind evolutionary algorithm (MEA), principal component analysis (PCA) and multi-layer perceptron (MLP) neural networks. Mean absolute error (MAE), mean absolute percentage error, root mean squared error are adapted to evaluate the performance of the models. The results show that the data-driven model based on intelligent algorithm optimization neural networks can achieve good prediction of profile and flatness. Comparing with the hybrid GA-MLP model, the training speed of the hybrid MEA-MLP model is faster and the training time is greatly reduced. The model establishing with the input data after dimensionality reduction by PCA can reduce training time and become simple. The innovation of this paper is to propose a data-driven fast response model based on intelligent algorithm optimization neural network to replace the traditional mechanism model based on mathematical formula analysis to study complex, non-linear strip shape control in hot rolling process. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a prediction model for hot-rolled strip crown based on an artificial neural network (ANN) is presented. Considering the mean squared error (MSE) and correlation coefficient (R), production data of 10,133 coils collected from a hot rolling plant are used to establish models. A feed-forward neural network with one hidden layer, a non-dominated sorting genetic algorithm II (NSGA II) optimized ANN, and a deep neural network (DNN) are applied to evaluate the prediction performance. Parameter settings of the ANN and NSGA II including learning rate, hidden neurons, activation function and population size, and crossover probability, are investigated to acquire the optimal model. The structure of the DNN, including how many layers and units the network should contain, is also studied. Prediction performance comparisons of the ANN, NSGA II-ANN, and DNN are presented. Among the ANN, NSGA II-ANN and DNN, the results show that the DNN has the highest prediction accuracy. Root mean squared error (RMSE) of the proposed DNN is 2. 06 μ m , and 97.04% of the prediction data have an absolute error of less than 5 μ m. Through model response surfaces, effects of four key operating parameters are investigated. The results indicate that the proposed DNN with strong learning ability and generalization performance can be well applied to hot rolling production. Highlights • Three neural network based models are established based on a dataset from a hot-rolling line. • The proposed models used to predict strip crown can acquire high prediction precisions. • The best performed model precisely corresponds with the existing physical understandings. • Using the parameters obtained by the best performed model, strip crown is close to target values. [ABSTRACT FROM AUTHOR]

A parabolic velocity field is proposed to get the minimum required rolling force in hot rolling process, the equal area yield criterion is used to calculate the plastic deformation power, the collinear vector inner product method is used to get friction power, the analytical equation of strip rolling power functional is obtained, and the required rolling force was calculated by minimizing the power functional. Meanwhile, the location of neutral point, shape factor, and stress state coefficient are discussed. The accuracy of the proposed theoretical model is examined through comparing with the experimental measured ones and online measured ones, it shows good agreement, the relative error of rolling force is less than 9.1%, and the proposed model is considered to be effective in hot tandem rolling process. [ABSTRACT FROM AUTHOR]

Optimization of the schedule is an effective way to reduce energy consumption in hot strip manufacturing. The heating energy and the rolling energy contribute the vast majority of the energy consumption. In order to reduce the energy consumption for the whole process, an optimization method based on the multi-objective function was applied, and the heating energy and rolling energy were both taken into consideration during the function modeling. Meanwhile, process constraints and equipment limitations were taken as objective function boundary conditions, and the tapping temperature in the furnace exit and thickness of each pass were decision variables. Further, to obtain the optimal solution of the objective function, the differential evolution algorithm was used, finally, the optimal tapping temperature and the thickness were obtained successfully. Meanwhile, the validity of the calculated results was verified by comparing with the actual process in a hot rolling production line in Hebei province, the results indicated that with the proposed method, a more reasonable schedule were obtained; compared with the existing actual schedule of typical specification, the energy consumption can be reduced by about 1.5%. [ABSTRACT FROM AUTHOR]

• The symplectic approach is applied to solve the strip cross section temperature. • The mechanism of residual stress formation in hot strip rolling is studied by fiber rods model. • An analytical model for the coupling of temperature, crown and residual stress is established. • The strip critical exit crown ratio is obtained by using the residual stress analytical model. • Eliminating manifested and latent flatness defects by critical exit crown ratio of strip. Residual stress is introduced during hot-rolled strip production due to various factors, such as temperature distribution, crown change, and metal transverse flow. Excessive residual stress can cause flatness defects in the strip, while insufficient residual stress may result in deformation during subsequent cutting. To explore the mechanism of residual stress formation in hot-rolled strip and how to control it, an analytical model for the coupling of temperature, crown and residual stress is established. Firstly, based on the symplectic space Hamiltonian system, an analytical solution for the strip cross section temperature field in each inter-stand zone is obtained. Then the residual stress analytical model is derived based on the fiber rod model combined with the law of volume invariance, lateral metal flow function and high temperature stress relaxation phenomenon. Meanwhile, to verify the accuracy of the analytical model, a multi field coupled finite element model based on the measured data validation is established. The calculation results of the analytical model are in good agreement with the finite element model. Furthermore, the buckling model of strip in symplectic space Hamiltonian system is derived, and the critical buckling stress of different strip flatness defects is directly calculated. Finally, the residual stress analytical model is combined with critical buckling stress to calculate the critical exit crown ratio to keep the strip flat. [ABSTRACT FROM AUTHOR]

• Based on the fiber rods model, the formation mechanism of residual stress caused by temperature and phase transformation is studied. • An analytical model is established to calculate the residual stresses at different run-out table cooling stages. • Based on symplectic space Hamiltonian system, the mathematical relationship between residual stress and flatness is solved directly. • The edge wave defects in strip run-out table cooling process are calculated directly by using the analytical model. The residual stress formed in the run-out table cooling stage of hot-rolled strip has a great influence on flatness and subsequent cutting. Based on the fiber rods model, the formation mechanism of residual stress induced by incompatible deformation caused by temperature and phase transformation is studied in this paper. Meanwhile, the present study makes a first attempt to establishing the analytical model for calculating residual stresses at different run-out table cooling stages. Moreover, in order to further investigate the relationship between residual stress and flatness defects, a strip buckling model is introduced. The traditional buckling equilibrium equation of Lagrange system is introduced into the Hamiltonian system of symplectic space, and the mathematical relationship between residual stress and strip flatness is obtained directly without assuming stress and deflection function. Then the strip flatness is calculated by using this mathematical relationship and residual stress analytical model. Furthermore, to verify the accuracy of the analytical model, a multi-field coupled finite element model based on the validation of the measured data is established. Finally, the distribution of residual stress calculated by the analytical model and the finite element model is basically consistent. The analytical model calculated that the strip would have edge wave defects during run-out table cooling, which is highly consistent with the results of finite element model. [ABSTRACT FROM AUTHOR]

As one of the most critical variables in the hot rolling process, the accuracy of rolling force prediction is directly associated with production stability and product quality. Purely data-driven approaches, however, are severely constrained by the quantity and quality of data, posing challenges for further enhancing the accuracy of rolling force prediction. In this paper, a theory fusion deep neural network (DNN) modelling approach was proposed and applied to the prediction of rolling force during hot plate rolling. In terms of model establishment, the novel NN structure was designed in consideration of the rolling mechanism, and senior variable inputs were added at shallow locations in the network to reduce the loss of critical information. In terms of model training, the method of using rolling theory to guide the initialization of the model was proposed to enable the model to learn the theoretical features more completely in the pre-training phase. Finally, a method to optimize the overall structure of the model using the sparrow search algorithm (SSA) was proposed to ensure the best prediction performance. The model was tested with the data in the developed platform, and the results indicated that the proposed method achieves the best accuracy and stability in this paper, and the response relationship between model inputs and output was consistent with existing theoretical knowledge. Thus, the model can be trusted and flexibly applied to the actual manufacturing processes. [ABSTRACT FROM AUTHOR]

• A mathematical model of flatness defects accounting for lateral metal flow is proposed. • A 3D finite element model for the strip and work roll with variable roll contour was developed. • Rolling experiments in a hot rolling mill confirmed the accuracy of the simulation. • Influences of reduction rate and entry thickness of strip on flatness were investigated. • Coupling effect between crown ratio, lateral metal flow, and flatness was studied. Geometric dissimilarity between the thickness profile of the entry strip and the deformed roll gap is the main cause of flatness defects. However, the combination of the crown ratio and the lateral metal flow complicates the flatness defect mode, making it difficult to predict. A variety of rolled flatness defects may result, generally occurring as center waviness, edge waviness, M-mode waviness, and W-mode waviness. The effect of lateral metal flow on the flatness has rarely been considered or quantified in the traditional flatness model. To address this deficiency, an original mathematical model is proposed for computing the rolled flatness defects while accounting for lateral metal flow during the rolling process. The proposed analytical model was employed to compute the flatness deviations with and without lateral metal flow, and the flatness calculated results were compared with the numerical solutions provided by a three-dimensional finite element model. The influence of the lateral metal flow on the strip flatness distribution was clearly identified and explained. Finally, the effects of the reduction rate, entry thickness, and exit crown ratio on the flatness deviation and lateral metal flow are described and discussed. [ABSTRACT FROM AUTHOR]

• An analytical model of two-dimensional temperature field of strip in symplectic space Hamiltonian system is established. • Symplectic superposition method is used to deal with complex cooling boundary conditions. • Based on the basic equation, the analytical solution of two-dimensional unsteady temperature field is obtained by mathematical method. • Neglecting the latent heat of phase transformation in strip can lead to significant errors in temperature prediction. The cooling process of hot-rolled strip has an important influence on the mechanical and metallurgical properties of the final product. In particular, the uneven temperature of the hot-rolled strip in the run-out table cooling after rolling will lead to the formation of residual stress and eventually cause the flatness defects. Therefore, this study focused on the temperature distribution prediction of steel strips during run-out table cooling. For this purpose, an analytical model for calculating temperature distribution of strip width and thickness is presented. It is different from the traditional analytical models, this study introduces the two-dimensional heat conduction equation with an internal heat source under the traditional Lagrange system into the symplectic space Hamiltonian system to obtain the symplectic dual equations. Meanwhile, symplectic superposition method is used to deal with complex cooling boundary conditions. The symplectic analytical solution of the two-dimensional temperature field is calculated by strict derivation without any assumptions or predetermination of the solution forms. In order to verify the accuracy of the symplectic analytical solution, a temperature−phase transformation coupled finite element model for run-out table cooling of hot strip was established. Then the accuracy of the finite element model is verified by the measured data. Finally, it has been determined that the symplectic analytical solution exhibits a high degree of consistency with the computed results obtained from the finite element model. [ABSTRACT FROM AUTHOR]

[Display omitted] • Data-driven method is used for the first time to predict the effective length. • Machine vision is used to measure the effective length of rolled plates. • An improved optimization algorithm based on the BES is proposed, called IBES. • The IBES-XGBoost prediction model is proposed and the achieves the high accuracy. • The interval estimation of the effective length is made based on the point prediction. The prediction of the effective length of steel plates is essential for improving the yield. Due to the complexity of variables and the lack of measuring means, there are few efficient and accurate models for the prediction of effective length. In this paper, a novel data-driven model is proposed to predict the effective length of hot rolled plates. The dataset used for the problem is established using machine vision techniques. An improved bald eagle search algorithm is used to optimize extreme gradient boosting (IBES-XGBoost) for prediction. Based on the point prediction results, the effective length interval of plates is estimated by combining the kernel density estimation method (KDE), which effectively reduces the risk caused by errors. The main work was completed in Python programming language and the validation shows that the proposed model can obtain highly accurate point and interval prediction results, which can provide accurate data reference for billet design and plane shape control of plates. [ABSTRACT FROM AUTHOR]