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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]

Chatter is a major problem that restricts production efficiency and product quality in the cold rolling process at high speed. Although many research studies have focused on relating rolling parameters to mill stability, information about the roll-stack in the axial direction and the strip in the width direction have not yet been considered due to the limitations of modeling methods. This paper proposes a new finite element model for the Universal Crown Control mill (UCM mill) with an improved Timoshenko beam used to investigate the influence of flatness control actuators on the mill stability. A dynamic rolling force calculation formula coupled with a mixed lubrication model is obtained. Then, the structure–process coupling model is established to simulate the rolling process at both steady and unsteady states. The results show that the work roll bending (WRB) has the greatest impact on the critical speed, followed by the intermediate roll shifting (IRS) and the intermediate roll bending (IRB). During vibration, the distribution of the friction stress varies rapidly, and a negative forward slip appears, which exacerbates vibration. Furthermore, the analysis of the energy dissipation in the rolling interface illuminates the vibration mechanism. Therefore, this study contributes to mechanism improvement and chatter suppression in the cold rolling process. [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]

• 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]

During the slab sizing press (SP) process, the pressing force corresponds to the slab profile, which guides the production schedule design and the final profile control. To accomplish the prediction of pressing force for SP, an improved ensemble method based on chaotic Harris hawks optimizer (CHHO) and stacking is proposed. A mechanistic knowledge is introduced for feature selection that enhances the rationality of input features. Subsequently, 11 machine learning models are compared and 5 of them are selected as candidate learners for the stacking method. Based on the candidates learners, 8 stacking strategies are constructed, which the stacked model with extratree regressor, gradient boosted decision trees, and kernel ridge regression (KRR) as base‐learners and KRR as meta‐learner performs the best. The R2, MAE, mean square error, mean squared log error, and mean absolute percentage error for the test dataset are 0.9912, 0.0856, 0.0167, 0.0005, and 2.00%, respectively, and 95% of the prediction errors are less than 0.15 MN. Then, sensitivity analysis and predictive analysis based on Shapley Additive Explanations are performed to demonstrate the good alignment of the proposed model with physical reality. Furthermore, to cope with the complexity and uncertainty of the production process, the proposed CHHO‐stacking model and the kernel density estimation method are integrated to model the prediction interval. [ABSTRACT FROM AUTHOR]

Summary: This article studies the problem of data‐driven (DD) fault detection (FD) for linear systems. First, based on the DD realization of kernel representation, new residual generators are designed via a q‐step residual iteration method. Then, it is proved that the proposed residual generators guarantee the stability and L1 performance of the FD error systems, and the presented residual design method is more sensitive to faults than the existing ones constructed directly from available process data. Finally, two simulation examples are provided to verify the effectiveness and advantages of the designed method. [ABSTRACT FROM AUTHOR]

As an emerging technology in the production of electrical steel, edge‐drop control (EDC) caters to the increasing requirements for the overall shape quality of strips. Herein this review, the development of EDC theory, method, and control system used in the cold‐rolling process is summarized. Also, in this review, research on EDC theory is found to be based on the 3D plastic deformation model of the strip, considering the lateral metal flow. Further, an analytical model and a numerical calculation method are employed to establish an edge‐drop calculation model with high accuracy and speed. Next, taper‐work‐roll shifting (T‐WRS), a conventional EDC technology, is found to have been greatly improved in actual production. However, T‐WRS technology involves coupling problems in terms of edge drop and crown and flatness control. Finally, the closed‐loop EDC is found to depend on the online WRS of multiple stands. Particularly, the genetic law of strip thickness in the continuous rolling process and the edge‐drop regulation characteristics of each stand in the continuous rolling mill are significant aspects; thus, a reasonable roll‐shifting control strategy must be formulated. Based on the reviewed research, the development prospect of EDC is characterized. [ABSTRACT FROM AUTHOR]

The efficiency of the flatness actuator is the cornerstone of the strip steel flatness control system and is pivotal in maintaining the quality of the strip shape and microstructure properties in commercial strip steel. However, the fluctuation in the thermal crown of the work rolls during the cold rolling process significantly impacts strip flatness quality. Obtaining real-time updates on the thermal crown alterations of the work rolls presents notable difficulties. Hence, the actual efficiency of the flatness actuator measured in the cold rolling environment fails to consider the effects of the work rolls' thermal crown, undermining the control precision of strip shape. Exploring the mechanism through which the thermal crown of the work rolls influences strip shape is therefore crucial. This would allow for determining the efficiency of the flatness actuator, accounting for the work rolls' thermal crown. In this research, an innovative approach is utilized, where FEM is used to create a highly accurate model. This model encapsulates the temperature-stress-strain field. This model effectively elucidates the time-varying influence of the hot roll shape on the strip shape, enabling the derivation of a dynamic strip flatness actuator efficiency curve for work roll bending and other actuators in the nonstationary rolling process. In addition, it addresses common challenges encountered in strip shape control during tandem cold rolling, such as the roll change stage and acceleration/deceleration stage.> [ABSTRACT FROM AUTHOR]

The accurate prediction of strip crown is the precondition of the shape preset model in hot strip rolling. In this study, a new hybrid strip crown forecasting model is proposed in combination with extreme learning machine (ELM) and the industrial data. The production data of 1780 mm hot strip rolling are collected by the on-site data acquisition system to form dataset. Principal component analysis (PCA) is used to reduce the dimension of the input data for modeling samples. To improve the prediction accuracy of ELM, an improved PSO based on S-curve decreasing inertia weight (SDWPSO) is proposed to optimize the initial weights and biases of ELM. Finally, the optimal ELM model and simple production dataset are used to establish a strip crown prediction model of hot strip rolling named PCA-SDWPSO-ELM. The comprehensive performance of the proposed hybrid PCA-SDWPSO-ELM prediction model is evaluated by MAE, MAPE and RMSE. The superiority of the proposed model is also proved by comparing the prediction results with those of the other three comparison models. The research shows that the hybrid PCA-SDWPSO-ELM method can solve the problem of nonlinear and strong coupling in traditional engineering. It is suitable for parameter prediction and optimization in the iron and steel manufacturing industry, especially in the process of shape control in hot strip rolling. [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]

An accurate description of the metal flow behavior during wedge zone deformation is key to the stability of the endless strip production rolling process. To predict the flatness distribution based on the law of volume invariance, a flatness calculation model of the wedge zone during the flying gauge change (FGC) process was established by considering the metal transverse flow. Furthermore, the effect of different rolling parameters on the flow of metal in the wedge zone was investigated using a combination of this model with a 3D finite element model. In addition, the influences of the reduction rate, roll crown, and friction coefficient on the flatness and metal lateral flow were analyzed and discussed. Finally, the numerical results provided by the finite element model were compared with the computed results of the flatness distribution to illustrate the effectiveness and stability of the proposed model. [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]

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]

To investigate the edge drop control characteristics of the roll contour on the taper segment of a taper-work roll, a three-dimensional roll stack-strip-tension coupling model was established with the finite element method, and the simulation model was verified using experimental data. The effects of the taper-work roll shifting (T-WRS) for different contours on the edge drop, center crown, flatness, and nonuniformity of the rolling pressure field unevenness were studied. The results indicated that the thickness difference caused by the combination of the roll contour and the work roll shifting (WRS) effectively compensated for the edge drop caused by the elastic deformation of the roll was the main way for T-WRS to reduce edge drop. Increasing the height of the roll contour inserted into the strip could significantly improve the edge drop control ability. However, it would also lead to increasing the trend of M-mode waviness defects and increase the peak of rolling pressure and the unevenness of the contact pressure between the rolls. Therefore, a novel approach for the roll contour evaluation was proposed by constructing the multi-objective function of the taper-work roll shifting. With edge drop control as the primary goal, the optimal range and suitable range of the WRS for different roll contours were calculated for the first stand of the tandem cold mill. [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]

A dog‐bone profile is developed by inhomogeneous deformation of a slab, whose parameters can be used to describe the metal flow rule during the width reduction process by a sizing press. The accuracy of a dog‐bone profile is essential to ensure the high width precision of the roughing process. However, the existing equipment cannot satisfy the requirements of online measurement. To solve this problem, herein, a prediction model for dog‐bone parameters based on the finite‐element simulation and a neural network is presented. The finite‐element simulation can reproduce the field production process, revealing variations in the dog‐bone profile parameters. In addition, based on the simulation data, a neural network model is constructed to predict the dog‐profile parameters. By adjusting the hyperparameters, the prediction accuracy of the constructed deep neural network model with two hidden layers is improved. For the dog‐bone profile parameters, the mean squared error is less than 3 mm, the mean absolute percentage error is less than 2%, the maximum absolute percentage error is less than 9%, and the root mean squared error is less than 4 mm. Thus, an accurate prediction of the dog‐bone profile parameters is achieved, which can guide subsequent high‐precision width control. [ABSTRACT FROM AUTHOR]

Accurate calculation of the heat source in the roll gap during the cold rolling process is the basis for a well-designed coolant system, which is particularly important for reducing roll wear and improving the flatness quality of strip steel. Although many established numerical models have high precision when calculating the work roll temperature, complex modeling processes and large calculation times result in the inability to predict the work roll temperature quickly for the application of automatic control systems. Therefore, the authors developed a new analytical heat source model to calculate the axial temperature distribution of the work roll in the cold rolling process. First, according to the deformation characteristics of strip cold rolling, the deformation zone is divided into a plastic zone and two elastic zones, and the length of each deformation zone is calculated considering the effect of tension. Then, the friction heat generated in the elastic zone is calculated. Second, new exponential velocity and corresponding strain-rate fields satisfying kinematically admissible conditions are proposed to calculate the deformation heat and friction heat generated in the plastic zone. Finally, the work roll temperature prediction model is established by contemplating the heat source of the roll gap, emulsion heat transfer, air cooling, and contact heat transfer with the intermediate roll. By repeatedly optimizing the weighted coefficient d of intermediate principal shear stress on the yield criterion, the maximum error between the calculated results and the actual measured cold roll temperature data was reduced to 3.1%. The effects of the reduction ratio, rolling speed, and resistance to deformation on the deformation heat and friction heat are discussed, and the variation of temperature field of the work roll with time is analyzed quantitatively. [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]

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]

During the production of cold-rolled strips, the high-speed operation of rolling mills generates vibrations that significantly impact the production efficiency, the strip quality, and the rolling mill service life. Therefore, investigating the vibration characteristics of rolling mills is of paramount importance. Previous studies predominantly treated the rolls as point masses, overlooking variations in the vibrations along the lengths of the rolls. In this study, the working, intermediate, and backup rolls were regarded as continuous elastic bodies, and they were simplified as Timoshenko beams. The modal superposition method was used to solve the vertical vibration equations for the rolls of a six-high rolling mill; thus, the natural frequencies and modal shapes for the rolls were obtained for both free and forced vibrations. A finite-element model validation confirmed that the accuracy of the novel Timoshenko beam six-high rolling mill vibration model introduced in this paper is significantly higher than that of the traditional Euler beam model when the roller length-to-diameter ratio is relatively small. Further analysis based on this model indicates that the forced vibration of the rolls is primarily influenced by fluctuations in rolling force. The amplitude of forced vibration is affected by factors such as the friction coefficient in the deformation zone, rolling speed, and cumulative rolling distance of the work rolls. These findings provide a precise representation of the characteristics of forced vibrations in rolling mills and offer valuable theoretical insight to ensure stable rolling mill operation. [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]

The accuracy of flatness actuator efficiency (FAE) is a prerequisite to achieve high precision automatic flatness control. This study proposes an accurate acquisition approach of FAE based on the combination of simulation modeling and data‐driven modeling for flatness control of cold‐rolled strip. First, a 3D rolling feature space model is constructed according to the change interval of rolling process parameters based on rolling conditions. A 3D finite element simulation model is subsequently established to determine the prior value of actuator efficiency at each node in the feature space model. Then, to improve the accuracy of prior value, an online optimization model is developed by means of data‐driven mechanism. The sorting algorithm and the central limit theorem are introduced to filter the measured process data and calculate the variable weighting. The processed data are imported into the model to improve the fitting model. Finally, a linear output prediction model based on the trend extrapolation method is proposed to realize the accurate acquisition of FAE under any rolling conditions. The data analysis of the production process shows that the model is adaptive and accurate, which can realize high precision flatness control. [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]

To study the transverse temperature uniformity with transverse flux induction heating (TFIH) during endless strip production (ESP) rolling, a coupled electromagnetic-thermal finite element model of transverse flux induction heating is established. The initial temperature distribution at the TFIH inlet is taken into consideration, which is the basis of subsequent numerical studies. Magnetic screens are designed to weaken the influence of edge overheating, and the influence of magnetic shielding amounts on temperature uniformity is discussed. Moreover, an evaluation criterion is provided to determine the temperature uniformity. Furthermore, the effect of different shielding amounts on the edge temperature is studied. An ideal temperature distribution at the TFIH outlet is obtained based on a model combining various shielding amounts, and the temperature standard deviation of this method is 2.01% lower than the traditional arrangement of magnetic shielding amounts. Actual data are collected to verify the results of the proposed model. The temperature deviation between the middle and edge is approximately 12°C, and the temperature uniformity is enhanced with the optimized combination of magnetic shielding amounts. [ABSTRACT FROM AUTHOR]

Purpose: In the cold rolling process, friction coefficient, oil film thickness and other factors vary dramatically with the change in the rolling speed, which seriously affects the strip thickness deviation. This paper aims to improve the strip control precision with the forecast roll gap model based on CF-PSO-SVM approach in the rolling process. Design/methodology/approach: In this paper, a novel forecasting model of the roll gap based on support vector machine (SVM) optimized by particle swarm optimization with compression factor (CF-PSO) is proposed. Based on lots of online data, the roll gap models regressed by PSO-SVM, genetic algorithm (GA)-SVM and CF-PSO-SVM are obtained and verified through evaluating the performances with the decision coefficient (R2), mean absolute error and root mean square error. In addition, with the good forecasting performances of CF-PSO-SVM, a roll gap compensation model is studied. Findings: The results indicate that the proposed CF-PSO-SVM has excellent learning regression ability compared with other optimization algorithms. Meanwhile, a roll gap compensation model based on the rolling speed and plastic coefficient is obtained, which has been proved validated in product. Originality/value: In this paper, the SVM algorithm is combined with traditional rolling technology to solve the problems in actual production, which has great supporting significance for the improvement of production efficiency. [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]

• A validated nonlinear dynamic chatter model of universal crown mill is developed. • Effect of rolling processing parameters on stand stability is given for single stand. • An improved prediction criterion for the critical rolling speed of mill chatter is proposed. • Optimal design of friction and reduction for stands No.4 and No.5 are investigated. Tandem cold rolling mills are comprehensive dynamic systems coupling with structure and rolling technology. A frequent problem is mill chatter, often occurring when rolling hard, thin materials at high speed and affecting the quality of the strip. In this paper, a dynamic increment model for chatter in a Universal Crown Control mill (UCM mill) is proposed with the considering of strip hardening, elastic deformation of the work roll, non-linear friction, transfer delay of the strip, and dynamic coupling effect of tension between adjacent stands. Mathematically, this model is based on the Taylor series expansion of the Bland-Ford-Hill rolling force equation. The comparative results of both simulation and experimental data show that this chatter model has a high accuracy. A novel, time-varying stability criterion is proposed to evaluate mill stability. Further study is provided on the optimal friction coefficient and reduction ratio required to increase the critical rolling speed and vibration stability in a tandem cold rolling mill. This mathematical criterion is validated by comparing the actual rolling speed with the calculated critical rolling speed. The present work provides a more accurate prediction of mill chatter and a basis for optimal design of rolling conditions. [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]

Mill chatter in tandem cold rolling mill is a major rejection to the quality and production of the strips. In most mill vibration models, either the roll mass is usually limited to vibrate in vertical direction and vertical-horizontal directions, or the multiple rolls system is simplified to a single mass system. However, the torsional chatter is also a typical type of mill chatter, and the presence of intermediate roll and backup roll will affect the overall vibration of the mill structure system. In this paper, a newly cold rolling mill vibration model coupled with the dynamic rolling processing model and nonlinear vibration model is proposed with the consideration of dynamic coupling and nonlinear characteristics of the rolling process, multiroll equilibrium, and roll movement in both vertical-horizontal-torsional directions. By using Hopf bifurcation theorem and Routh–Hurwitz determinant, the existence of the Hopf bifurcation point of the mill vibration system and bifurcation characteristics are analyzed. At last, the influence of different rolling conditions on the stability of the coupled mill system is investigated, and these results can also be used to design an optimum rolling schedule and determine the appearance of mill chatter under certain rolling conditions. [ABSTRACT FROM AUTHOR]

Prediction and Online Optimization of Strip Shape in Hot Strip Rolling Process Using Sparrow Search Algorithm-Online Sequential-Deep Multilayer Extreme Learning Machine Algorithm The strip shape prediction model is proposed by combining a sparrow search algorithm (SSA) and a deep multilayer extreme learning machine (DELM). In article number 2200832, Jingguo Ding and co-workers show that rolling data in information space comes from rolling production lines in physical space. [Extracted from the article]

[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]

In the strip rolling process, conventional supervised methods cannot effectively address data with an imbalanced number of normal and faulty instances. In this paper, based on a deep belief network, a resampling method is combined with active learning (AL) to address imbalanced multiclass problems. The support vector machine-based synthetic minority oversampling technique was adapted to enrich the training data, whereas the true data distribution and model generalization were changed. A new selection strategy of AL is proposed that forms a function using uncertainty and diversity. AL uses an optimizing set that has a similar distribution with the whole dataset to calculate the informativeness of instances to optimize the model. Based on this step, the model study instances approach decision boundaries to promote performance. The proposed method is validated by five UCI benchmark datasets and strip rolling data, and experiments show that it outperforms conventional methods in tackling imbalanced multiclass problems. [ABSTRACT FROM AUTHOR]

A Correction to this paper has been published: https://doi.org/10.1007/s00170-021-07508-2 [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]