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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.

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

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.

This article is concerned with the problem of event-triggered (ET) fault detection (FD) observer design for Takagi–Sugeno (T–S) fuzzy systems. The nonlinear systems considered are presented as T–S models, and the system outputs are selected as the premise variables (PV) of T–S models. New types of observers, namely, switched fuzzy FD observers, are designed, which are switched at different triggering instants based on the online asynchronous premise reconstruction (APR) method. By employing new triggering instants-dependent Lyapunov functions (LFs) established via the idea of event interval partitioning, it is proved that the proposed FD observers can guarantee the stability and desired performance of the systems. Finally, a simulation example is applied to show that the proposed FD scheme can achieve better FD results than the existing design methods.

The accurate prediction of strip crown is the precondition of the shape pre-set model in hot strip rolling. In this study, a new data-driven model of strip crown based on extreme learning machine (ELM) optimized by S-curve decreasing inertia weight PSO (SDWPSO) algorithm and industrial data is proposed. In order to simplify the model structure and save modeling time, principal component analysis (PCA) is used to reduce the dimension of the input data for modeling samples. The comprehensive performance of the proposed hybrid PCA-SDWPSO-ELM prediction model is evaluated by several error indexes. The superiority of the proposed model is also proved by comparing the prediction results with other three comparison models. The research shows that the hybrid PCA-SDWPSO-ELM method can solve the problem of nonlinear and strong coupling in the traditional engineering. It is suitable for the parameters prediction and optimization of the iron and steel manufacturing industry, especially in the process of shape control in hot strip rolling.

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.

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.

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 in calculating the work roll temperature, complex modeling processes and large calculation times result in the inability to predict work roll temperature quickly for the application of automatic control systems. Therefore, the authors develop 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 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 is reduced to 3.1%. Then, 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.

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.

This paper established a model based on an ensemble method to predict strip crown using 230,000 coils of data obtained from a hot rolling line. Before modeling, a specific method was proposed to reduce noise and remove outliers, and a new dataset of 5657 samples was generated. Parameter tuning considering mean squared error (MSE) was carried out to establish three machine learning models including support vector machine (SVC), regression tree (RT), and random forest (RF). Determination coefficient (R2), mean absolute error (MAE) and root mean squared error (RMSE) were used as indicators to evaluate the prediction of models. Results showed that the RF had the best performance with the highest R2 of 0.707, as well as the lowest RMSE of 5.66 μm. Moreover, an additional method that repeated the three models 100 times was developed, and box plots were used to visualize the distribution of R2, MAE and RMSE. RF can correct for decision trees to reduce overfitting to their training set, improving the generalization, and in this paper, the trained RF which had stable performance is considered as the most recommended model. After that, for RF, rankings of rolling process variable were validated to make a comparison with the existing physical understanding.

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.

Funding Information: This work was supported by the National Natural Science Foundation of China (Grant Nos. 52074085 and U21A20117 ), the Fundamental Research Funds for the Central Universities (Grant No. N2004010 ), and the LiaoNing Revitalization Talents Program ( XLYC1907065 ). Publisher Copyright: © 2022 Elsevier B.V. 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.

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.

An approach to analyzing three-dimensional vertical rolling is presented on the basis of energy method. The double parabola function model is applied to describe dog bone shape in the deformed region between the vertical rolls. The DSF (dual stream function) method is utilized to obtain three-dimensional velocity and strain rate fields. The values of dog bone shape dimensions and roll force are obtained when the total power functional achieves minimum, which is received according to double parabola model, velocity field, and the first variational principle. The validity of the proposed approach is discussed by contradistinguishing the present predictions with other models’ results and measured data in a hot strip plant in miscellaneous rolling conditions. Moreover, the impacts of different rolling conditions on the dog bone shape and stress state coefficient are researched, respectively.