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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]

The control precision of thickness and tension is a crucial indicator for evaluating a tandem cold rolling control system. However, the control mode for field application cannot meet the actual quality requirements. Therefore, a distributed model predictive control (DMPC) strategy combined with neighborhood optimization is proposed to decrease the strip thickness deviation and tension change in this paper. First, a cold rolling model describing the relationship among the process parameters is established for the multi-stand cold rolling system. Then, according to the neighborhood optimization theory, the state evolution equation of the output system on each stand is derived. Furthermore, through proper consideration of the input and state information during optimization, optimal control variables are obtained using the proposed performance index to improve the system performance. A series of simulations were carried out with actual rolling data to analyze and validate the capability of the designed control system. The statistical data show that as roll speed disturbance occurs, the thickness and tension deviations can be controlled within respective ranges of 6 × 10 − 5 mm and 0.012 kN with the DMPC control strategy. In addition, each scan cycle calculation only takes 0.0085 s in such a strategy. Compared with the conventional control method, the thickness and tension DMPC control system provides excellent performance and can effectively enhance the strip product quality. • A state space model of thickness and tension is established with considering all the stands of cold rolling process. • A novel distributed model predictive control strategy based on Neighborhood Optimization is designed for the system. • Compared with other control strategies, the proposed DMPC strategy has excellent control performance. [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]

The flatness control system of cold-rolled strip is characterized by nonlinearity, strong coupling, and multivariable features. Theoretical models of flatness derived from physical mechanisms of the rolling process are intricate. This complexity makes it challenging to establish an accurate control model. Reinforcement learning (RL) is a machine learning method that uses an intelligent agent to learn from data interacting with its environment. In this study, considering the large quantity of historical data generated by the strip steel control system, we used the RL method to analyze the data offline in order to train a data-driven controller. We combined it with ensemble learning to propose a novel method for flatness control based on ensemble deep reinforcement learning (EDRL). Initially, we constructed a state space model for the cold-rolled flatness utilizing historical production data. This model served as the environment for offline RL training. We present an EDRL-based flatness control method that incorporates the principles of ensemble learning. Ensemble learning amalgamates multiple individual models to achieve superior performances. In the online simulation of rolling production, the EDRL-controlled flatness value was less than 5 (I-Unit) IU from the target flatness value, exceeding the performance of the proportional–integral (PI) controller. The proposed method surpassed the conventional approach in terms of both robustness and its capability to regulate flatness. • An EDRL control strategy is proposed for the cold rolling flatness control problem. • The integration strategy effectively improves the convergence speed of flatness. • The proposed control strategy outperforms state-of-the-art PI controllers. • The proposed integrated strategy exhibits robust stability in industrial scenarios. [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 symplectic analytical approach is proposed to study the thermal-metallurgical coupling problems. • The symplectic analytical solution of three-dimensional temperature field is derived directly. • An alternating algorithm is designed to realize the nonlinear thermal-metallurgical coupling calculation. • The symplectic approach considers both quantization mechanism and computational efficiency. • The temperature and microstructure evolution during the coil cooling process are precisely calculated. The cooling process of hot-rolled coil directly affects the mechanical and metallurgical properties of the final product. The non-uniform behavior of temperature and microstructure can easily result in sufficient residual stress to induce subsequent cutting deformation. Therefore, the focus of this study is to analyze the thermal-metallurgical coupling problem during the cooling process of hot-rolled coil. Unlike before, a symplectic analytical approach is proposed to calculate the temperature and microstructure evolution of hot-rolled coil. Firstly, the hot-rolled coil is discretized to convert the three-dimensional heat transfer problem in cylindrical coordinate system to cartesian coordinate system. Then, the traditional heat transfer model is introduced into the symplectic Hamiltonian system and the symplectic superposition method is employed to handle complex cooling boundary conditions. The symplectic analytical solution of the three-dimensional temperature field is obtained through rigorous derivation without any assumptions or predetermined solution forms. Meanwhile, an alternating algorithm is designed between the heat transfer model and the phase transformation dynamics model to realize the coupling process. Moreover, a high-precision finite element model verified by the measured data is established. The symplectic analytical solution of coil temperature and microstructure during the cooling process is in good agreement with the finite element solution. Finally, the symplectic approach has been proven to enable quantitative mathematical analysis of the coupling mechanism of thermal-metallurgical processes. [ABSTRACT FROM AUTHOR]

• Adjustments of flatness actuators can be determined through overall modeling. • The improved interior penalty function method is efficient for global optimization. • Optimal allocation of actuator adjustments can be achieved between sub-systems. • Double-layer optimization based control strategy can achieve optimal flatness control. The flatness control system consists of two subsystems. One is the feedback control subsystem which is used to implement the closed-loop flatness control. Another is usually referred to as feedforward control subsystem in the field of strip flatness control. To realize the cooperative control of roll bending between two subsystems, a feedforward-–feedback coordination control strategy based on double-layer optimization is proposed to obtain the optimal adjustments of actuators. Firstly, a global optimization model of actuator adjustment is established by the overall modeling, and an improved interior penalty function method is developed and utilized to solve this model subsequently. On this basis, an optimal allocation model is proposed to achieve a global optimal allocation of actuator adjustments between feedforward control and feedback control. Numerical experiments and applications show that this new control strategy and the corresponding models are effective in the flatness control process of cold rolling mill. [ABSTRACT FROM AUTHOR]

• A dynamic velocity field for speed variation conditions is proposed. • A hybrid model combining data-driven and theoretical models is established. • MI improves the accuracy of prediction and reduces the computing time. • LR adjustment enhances the stability of initial network and the convergence speed. • Some parameters of uncertain physical relationship with rolling force are studied. The variations in thickness at the head and tail significantly impact the product quality in tandem cold rolling. Improving rolling force calculation accuracy under speed-up and speed-down conditions is essential to enhance thickness control. This paper proposes a sequential coupled model combining data-driven and theoretical models to predict rolling force under speed variation conditions. To enhance accuracy and overcome the limitations of traditional velocity field, a linear cross-section dynamic velocity field taking into account the effects of roll gap changes on the deformation zone is established. Moreover, a long short-term memory (LSTM) network is constructed to capture sequential information from production data and compensate for changes in friction state caused by speed variation and roughness attenuation in the theoretical model. 12 coils, totaling 12,000 samples, are selected from the process data acquisition system (PDA) and utilized as the dataset after normalization. Mutual information (MI) theory is employed for feature selection to improve the prediction accuracy and reduce the computing consumption. Learning rate (LR) adjustment is applied to enhance the stability of initial network and the convergence speed. Compared to evaluated models, the proposed model has relative error within ±2.5 %, R2 of it is 0.9935 and the prediction time is only around 2.5 ms. The results suggest that the proposed model demonstrates the most favorable overall performance. Additionally, some key rolling parameters whose physical relationship with rolling force remains uncertain are investigated. [Display omitted] [ABSTRACT FROM AUTHOR]

With the increasing demands on strip product quality, conventional control methods cannot break the cold rolling production bottleneck The development of advanced control algorithms provides theoretical support for the improvement of strip accuracy and product stability of the tandem cold rolling process. Considering the complex characteristics of the system, a distributed model predictive control (DMPC) strategy based on the Nash equilibrium is proposed in this study. A state space model including the rolling process with constraints is established. To improve the calculation speed, a Laguerre function is integrated in the control strategy, so as to reduce the parameter dimension. The DMPC online optimal control strategy based on the Nash equilibrium is proposed to solve the problem between the constrained multivariable complex system and online rolling optimization. Its performance and effectiveness are demonstrated through a series of experiments based on rolling data from industry. • A state space model of thickness and tension during rolling process is established. • A DMPC strategy based on Nash Equilibrium is designed for the rolling system. • The DMPC strategy of the whole rolling system shows excellent control performance. [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]

Mill chatter is a major restriction in the high-speed rolling of high-strength and thin strips. To maintain mill stability, the friction coefficient must be kept within a certain range. Unfortunately, there is no model to calculate the lower limit of the friction. In this paper, a new model is developed to capture the minimum friction coefficient. This model is proposed based on mixed lubrication theory and monotonicity analysis in the friction curve. The verification results showed that the established model could accurately predict the minimum friction and the friction balance in tandem rolling mills. The model was utilized to design the optimal rolling conditions to expand the stability range of the friction and improve mill vibration stability. [Display omitted] • A mathematical model is proposed to predict the lower limit friction coefficient. • The model is proposed by monotonicity analysis based on mixed lubrication theory. • The model is validated to be accurate by previous literature and actual rolling test. • The optimization of the rolling condition is designed to increase mill vibration rolling stability. [ABSTRACT FROM AUTHOR]

The friction characteristics of rolling interface play a considerable role in rolling stability. In this work, vertical vibration speed is introduced into the Kármán equation. An unsteady lubrication model considering entraining and squeezing effect is proposed. Additionally, a dynamic chatter model is developed by coupling the improved rolling force and unsteady lubrication model. The verification results at the micro- and macro-scales indicate that this chatter model has high accuracy. The effects of main process parameters, such as reduction, back tension and viscosity, on the mill stability were analyzed. Moreover, the changes in parameters and tribological characteristics due to unstable rolling process were investigated. The work concludes that the rapid change of lubrication state and friction stress result in vibration intensification. Image 1 • Developed rolling force model considering vertical vibration speed is proposed. • Friction model that reflects lubrication state during unsteady rolling is obtained. • Natural frequency of the system slightly decreases with rolling speed increasing. • Lubrication state changes tremendously with time during unsteady rolling. • The decrease of average friction power leads to vibration more easily. [ABSTRACT FROM AUTHOR]