Digital twins are an emerging technology that can be harnessed for the digitalization of the industry. Steel industry systems contain a large number of electro-hydraulic components as proportional valves. An input–output model for a water proportional cartridge valve was derived from physical modeling based on fluid mechanics, dynamics, and electrical principles. The valve is a two-stage valve with two two/two-way water proportional valves as the pilot stage and a marginally stable poppet-type cartridge valve as the main valve. To our knowledge, this is the first time that an input–output model was derived for a two-stage proportional cartridge valve with a marginally stable main valve. The orifice equation, which is based on Bernoulli principles, was approximated by a polynomial, which made the parameter estimation easier and modeling possible without measuring the pressure of the varying control volume, in contrast with previous studies of similar types of valves situated in the pilot stage part of the valve. This work complements previous studies of similar types of valves in two ways: (1) data were collected when the valve was operating in a closed loop and (2) data were collected when the valve was part of a press mill machine in a steel manufacturing plant. Model parameters were identified from data from these operating conditions. The parameters of the input–output model were estimated by convex optimization with physical constraints to overcome the problems caused by poor system excitation. For comparison, a simple linear model was derived and the least squares method was used for the parameter estimation. A thorough estimation of the parameters’ relative errors is presented. The model contains five parameters related to the design parameters of the valve. The modeled position output was in good agreement with experimental data for the training and test data. The model can be used for the real-time monitoring of the valve’s status by the model parameters. One of the model parameters varied linearly with the production cycles. Thus, the aging of the valve can be monitored.

In the present work, a digital twin of a radial-axial ring rolling machine was built by modelling the time series of the positions of the tools and control signals rather than the metrics of the produced rings, as performed in previous studies. Real data from the industry was used for modelling. The used model selection methodology is shown in detail to replicate such work for similar systems in the steel industry. The modelling results of ARX, ARMAX and orthonormal basis model structures are shown; additionally, they were validated considering SISO and MIMO systems. The modelling results were better when the subsystems considered were ARMAX and MISO than when ARX and SISO were taken into consideration. The best modelling results were obtained when physical knowledge was included in the model structure. Lastly, it was found that the model error of the horizontal subsystem could be used for predictive maintenance.

A digital twin of a mechanical system (a pair of axial rolls in a ring mill used in a steel plant) with poles close to the unit circle and the real axis in the discrete pole-zero map was built. The system was excited by a signal concentrated in the low-frequency band. For this particular case, it is shown that the ad-hoc combination of ARMAX and orthonormal basis filter model structures outperform model structures based on either ARMAX or orthonormal basis functions when estimating the poles of the basis by analyzing the data in the frequency domain. The followed modelling methodology of the system is described in detail to help replicate the work for similar systems in the steel industry. Real production data from a steel plant were used in contrast to previous studies, where the combination of ARX and ARMAX with orthonormal basis filter model structures was evaluated using simulated data instead of real data. We believe that the resultant model can be used when having systems with poles close to the unit circle and real axis and poor excited input signal concentrated in the low frequency band. The resultant model can be used for condition monitoring and failure detection.

This study presents models of an electro-hydraulic valve derived from physical principles and neural network techniques. Input-output models are constructed using experimental data from a hydraulic press machine in a steel manufacturing plant and as a plant of a closed loop system. The models are candidates for digital twins in the steel manufacturing plant. The physical model is derived based on fluid mechanics, fluid dynamics, and electronic principles. Two LSTM neural network models denoted NN1 and NN2 are employed for modeling the valve. The parameter estimation for each neural network model is conducted using distinct training datasets. This work compares the validation results of the models in the time and frequency domain. Both the physical model and NNs capture the main behavior of the valve. However, NNs have lower mean square error (MSE) compared to the physical model. NN2, trained the model using different operating conditions, is capable of modeling non-linearities (seen at high frequencies) and leakage effects of the system, that are not captured by NN1 and physical models. The fault caused by leakage is seen in the MSE vs cycles for the physical and NN1 models.

Digital Twins integrating degradation models can be harnessed to enable industrial digitalization and promote sustainable manufacturing processes. Research in control has transitioned from methods ensuring stability and performance in the presence of degradation or faults to strategies that balance the performance and degradation of complex systems. This work formulates the the lifetime distribution for systems with multiple subsystems and several possible failure modes, considering both deterministic and stochastic failure modes. The proposed formulation is applied to the design of a two-layer control strategy with an model predictive control-based upper-layer controller that updates the parameters of the lower-layer PID-controlled closed-loop subsystems. The proposed method was evaluated on a numerical example using two hydraulic valves operating in parallel, a system commonly found in a steel manufacturing processes. The upper layer controller achieved equal time to failures for both valves, by varying the load on respective valves. The results suggest that heterogeneous systems, in terms of lifetime distributions and failure modes, can be controlled by balancing degradation and performance.