Intelligent seamless steel tube production method based on digital twinning

Abstract

The invention discloses a seamless steel tube intelligent production method based on digital twinning, which comprises the following steps: collecting historical data and real-time monitoring data, and preprocessing to generate a standardized data set; establishing a high-dimensional digital twinning parent model, and reducing the order to obtain a digital twinning reduced-order model; performing parameter calibration on the model to obtain an initial parameter set and a state mapping matrix; inputting real-time monitoring data into the model to obtain updated key parameters, state variables and predictive control quantities; a Tikhonov regularization module is introduced, and a robust correction result is generated; the input model prediction control module generates a smooth control instruction; and collecting feedback data, and inputting the feedback data into the model for online correction and self-learning. By introducing the digital twin reduced-order model and the Tikhonov regularization module, real-time and robust control and high-precision process optimization in the seamless steel tube production process are realized.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing technology, and in particular to an intelligent production method for seamless steel pipes based on digital twins. Background Technology

[0002] With the rapid development of the steel manufacturing industry towards intelligence and digitalization, refined management and online quality control of the seamless steel pipe production process have become core requirements for industry upgrading. The processes of piercing, rolling, sizing, and cooling of seamless steel pipes are interconnected, involving multiple physical field effects such as temperature, stress, flow behavior, and microstructure changes. These processes are highly dynamic, with frequent parameter disturbances, and are extremely sensitive to product dimensional accuracy and internal microstructure. Traditional control methods typically rely on manual experience, static rules, or single physical models, making it difficult to fully describe the actual operating state across multiple processes, strong coupling, and numerous disturbances. Existing monitoring and control systems are mostly based on local data acquisition and decentralized adjustment, lacking the ability to uniformly model the entire process state. This results in limited prediction accuracy for key indicators such as wall thickness, outer diameter, rolling force, and temperature, making it difficult to meet the stringent requirements for real-time performance and stability in high-end steel pipe production.

[0003] To address the aforementioned issues, digital twin technology has begun to be introduced into the seamless steel pipe production process, improving process visualization and control accuracy through virtual-real synchronization, parameter mapping, and state prediction. However, existing digital twin models mostly employ high-dimensional multiphysics equations, resulting in enormous computational demands and making real-time prediction difficult. While some studies have attempted to introduce order reduction methods, the model structures remain relatively rigid, struggling to handle dynamic changes under complex operating conditions. Furthermore, they lack effective mechanisms to suppress cross-process correlations, noise interference, and parameter drift, leading to unstable virtual-real mapping accuracy. Moreover, most existing control strategies lack an optimization system coordinated with the digital twin model, resulting in insufficient management of abrupt changes in control variables and state change rates, failing to effectively suppress product quality fluctuations caused by non-smooth control.

[0004] Therefore, how to provide a smart production method for seamless steel pipes based on digital twins is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] One objective of this invention is to propose an intelligent production method for seamless steel pipes based on digital twins. This invention fully utilizes multiphysics mechanism modeling, digital twin order reduction technology, state assimilation technology, Tikhonov regularization, and model predictive control algorithms to achieve real-time modeling, robust prediction, and intelligent control of the entire process of piercing, rolling, sizing, and cooling. This invention constructs a high-dimensional digital twin parent model and reduces its dimensionality to form a digital twin order-reduced model; it utilizes a Tikhonov regularization module to suppress deviations in key parameters, changes in state variables, and the rate of change of control variables; and it generates smooth and stable control commands through model predictive control algorithms to achieve intelligent optimization and regulation of the entire process. This method possesses the advantages of high prediction accuracy, fast response speed, and strong robustness, and can significantly improve the stability, quality consistency, and intelligence level of the seamless steel pipe production process.

[0006] According to an embodiment of the present invention, a smart production method for seamless steel pipes based on digital twins includes:

[0007] Historical data and real-time monitoring data of the seamless steel pipe production process are collected, and the historical data and real-time monitoring data are preprocessed to generate a standardized dataset;

[0008] A high-dimensional digital twin model of the seamless steel pipe production process is established based on standardized datasets and multiphysics mechanism equations. The high-dimensional digital twin model is then reduced in order, the main modal features are extracted, and a low-dimensional state space-output mapping relationship is constructed to obtain a digital twin reduced-order model.

[0009] The parameters of the digital twin reduced-order model are calibrated based on a standardized dataset to obtain the initial parameter set and state mapping matrix.

[0010] Input real-time monitoring data into the digital twin reduced-order model, call the initial parameter set and state mapping matrix to perform state assimilation operation, and obtain updated key parameters, state variables and predictive control variables;

[0011] A Tikhonov regularization module is introduced, combined with a high-frequency noise suppression filter structure. It receives updated key parameters, state variables and predictive control variables, applies quadratic regular constraints to the deviation of key parameters, changes in state variables and the rate of change of predictive control variables, and generates robust correction results.

[0012] Based on the robustness correction results, the model predictive control algorithm is executed for rolling optimization to generate smooth control commands and send them to the production equipment.

[0013] The system collects feedback data after the device executes the smooth control command and inputs it into the digital twin reduced-order model for online correction and continuous self-learning. The system also updates the initial parameter set and state mapping matrix based on the feedback data.

[0014] Optionally, the historical data and real-time monitoring data specifically include historically collected and real-time monitored temperature data, rolling force data, rolling line speed and rotation speed data, wall thickness and outer diameter data, and cooling medium flow rate data during the seamless steel pipe production process.

[0015] Optionally, the preprocessing of historical data and real-time monitoring data specifically includes data cleaning, noise filtering, time synchronization, and feature extraction and normalization.

[0016] Optionally, obtaining the digital twin reduced-order model includes:

[0017] Based on a standardized dataset, time alignment and spatial location identification are unified to construct a multidimensional feature tensor.

[0018] Establish cross-process association structures based on the process sequence, define parameter transfer and continuity rules between processes, and form temporal topology relationships;

[0019] Based on the multidimensional characteristic tensor and temporal topological relationship, a multiphysics mechanism equation is introduced, which includes the heat conduction equation, the plastic mechanical equilibrium equation, and the tissue evolution dynamics equation. Furthermore, energy conservation constraints, momentum balance constraints, and correlation constraints on the influence of temperature on tissue evolution are introduced to obtain a high-dimensional state representation that satisfies physical consistency.

[0020] Based on the high-dimensional state representation, the composition of input quantities, state variables and output quantities is divided, and a set of parameters related to material and contact characteristics is set to form a high-dimensional digital twin matrix model with input-state-output mapping relationship and parameter framework that can be calculated.

[0021] Using the input quantities and parameter sets in the standardized data as driving and boundary conditions, offline simulation is performed on the high-dimensional digital twin parent model to generate the set of internal state variables and the corresponding set of output variables at different time points;

[0022] The state sequence is reconstructed based on historical data and real-time monitoring data, and the reconstructed state sequence is merged with the internal state variable set and the output variable set to form a sample library;

[0023] Based on the sample library, calculate the energy contribution and reconstruction error of the feature patterns, determine the dominant feature patterns, and construct the reduced-order basis set and the corresponding output mapping basis set.

[0024] A reduction-order mapping is implemented based on the reduced-order basis set, and a multi-dimensional feature fusion unit and a hierarchical output mapping structure are integrated to obtain the low-dimensional state representation and low-dimensional output mapping relationship, forming a digital twin reduced-order model. The digital twin reduced-order model consists of a multi-dimensional feature fusion unit, a multi-physical coupling and process topology interface, a reduced-order projection and low-dimensional state core unit, and a hierarchical output mapping structure, wherein:

[0025] The multi-dimensional feature fusion unit performs time alignment, spatial identification, and normalization on the input quantities to generate a unified feature tensor; the multi-physical coupling and process topology interface connects the multi-physical process topology interface and transmits parameters at the structural level; the reduced-order projection and low-dimensional state core unit maps high-dimensional states to low-dimensional representations based on the reduced-order basis and completes state updates and fast solutions in the low-dimensional space; the hierarchical output mapping structure converts low-dimensional states into observable results and outputs them.

[0026] Optionally, obtaining the initial parameter set and state mapping matrix includes:

[0027] The set of input variables and the reference output set are determined based on a standardized dataset;

[0028] Define the initial parameter set for the digital twin reduced-order model and establish an error evaluation function;

[0029] An iterative optimization method is used to minimize the error evaluation function. The initial parameter set is updated sequentially according to a given step size. When the error reduction between two adjacent iterations is less than a threshold, convergence is determined, and the converged parameter set is obtained.

[0030] The converged parameter set is input into the digital twin reduced-order model. The state update relationship of the next time step is determined by the state of the previous time step, the current input, and the parameter set. The correspondence between the state variables and the output is calculated and corrected to generate the state mapping matrix.

[0031] Optionally, obtaining the updated key parameters, state variables, and predictive control variables includes:

[0032] The multi-dimensional feature fusion unit receives real-time monitoring data, completes timestamp alignment, spatial location identification unification and dimensional normalization, and generates the standardized feature tensor and real-time observations at the current moment.

[0033] Based on the process sequence, the standardized feature tensor is mapped and parameter-bound according to the process sequence through multi-physical coupling and process topology interface, and process continuity rules and physical coupling constraints are loaded to form a structured input package;

[0034] After receiving the structured input packet, the reduced-order projection and low-dimensional state core unit first projects the high-dimensional information in the structured input packet into a low-dimensional representation based on the low-dimensional state of the previous moment, the current control information, and the key parameters of the previous moment. Then, it calculates the prior low-dimensional state and prior output of the current moment.

[0035] The real-time observations are compared with the prior outputs to obtain the observation residuals, and state correction instructions and weights are generated.

[0036] The prior low-dimensional state is corrected according to the state correction instruction to obtain the posterior low-dimensional state. The key parameters are then incrementally corrected based on the sensitivity information of the prior low-dimensional state to changes in key parameters to obtain the updated key parameters.

[0037] When the observation residual exceeds the threshold, the improvement mechanism is triggered to perform local re-evaluation and index update of the reduced basis, and to correct the posterior low-dimensional state and rate of change of adjacent process boundaries according to the process continuity rule. The corrected results are then written back to the core unit of the reduced projection and low-dimensional state, as well as the multi-physical coupling and process topology interface.

[0038] The posterior low-dimensional state and the updated key parameters are input into a hierarchical output mapping structure, which consists of a basic output layer and a correction output layer. First, the basic output layer generates a preliminary prediction result, and then the correction output layer corrects it according to the physical consistency relationship. At the same time, the predictive control quantity in the next time domain is calculated according to the predictive control law, so as to obtain the updated key parameters, state variables and predictive control quantity at this moment.

[0039] Optionally, generating the robustness correction result includes:

[0040] The Tikhonov regularization module receives the key parameters, state variables, and predictive control variables after state assimilation and update, and receives the observation residual formed by the difference between real-time observations and prior outputs. At the same time, it inputs the observation residual into a high-frequency noise suppression filter structure to perform frequency domain decomposition and high-frequency noise suppression on the residual components to obtain the noise-reduced residual.

[0041] In the Tikhonov regularization module, key parameter deviation regularization term, state smoothing regularization term, and control smoothing regularization term are constructed. The noise reduction residual is superimposed with the three types of regularization terms according to the weight coefficient to form a comprehensive objective function.

[0042] Iterative optimization is performed on the comprehensive objective function to calculate the correction amounts of key parameters, state variables, and predictive control variables, and the preliminary corrected key parameters, state variables, and predictive control variables are updated.

[0043] Based on the adjustment of the weight coefficients of the key parameter deviation regularization term, state smoothing regularization term, and control smoothing regularization term using the noise reduction residual, the comprehensive objective function optimization is re-executed after updating the weight coefficients to obtain the updated key parameters, updated state variables, and updated predictive control variables.

[0044] Quadratic regularization constraints are applied to the updated key parameters, state variables, and predictive control variables. Values ​​that do not meet the constraints are corrected to obtain the final key parameters, final state variables, and final predictive control variables, generating robustness correction results.

[0045] Optionally, generating smooth control commands and issuing them to production equipment includes:

[0046] Based on the robustness correction results, the observation residuals are combined with the parameter deviation regularization term, the state smoothing positive final key parameter, the final state variable, and the final predictive control quantity. The prediction time domain, the control time domain, and the process target trajectory corresponding to this process are set.

[0047] The predicted relationship between the state variables and the output of the digital twin reduced-order model in the time domain and the control variable sequence is calculated based on the final state variables and the final key parameters.

[0048] A rolling optimization problem is constructed, with the deviation between the predicted state variables and the output of the digital twin reduced-order model and the process target trajectory as the objective term, the increment of the control variable and the rate of change of the control variable as the penalty term, and the allowable range of values ​​of each key process physical quantity and the amplitude and rate of change of the control variable as the constraint conditions.

[0049] The rolling optimization problem is solved to obtain the optimal control quantity sequence in the prediction time domain, and the first step control quantity corresponding to the current sampling period is selected as the smooth control command.

[0050] The smooth control command is sent to the production equipment, and the prediction results and execution feedback for this cycle are recorded.

[0051] Optionally, updating the initial parameter set and state mapping matrix based on feedback data includes:

[0052] Collect feedback data from production equipment during the execution of smooth control commands, and mark the key process physical quantities and actual control quantities in the feedback data according to the sampling time and process segment;

[0053] The feedback data is preprocessed, and the preprocessed feedback data is incorporated into a standardized dataset and input into a digital twin order reduction model to obtain the error sequence of each key process physical quantity.

[0054] The initial parameter set and state mapping matrix are incrementally corrected based on the error sequence to obtain the updated initial parameter set and state mapping matrix, which are then stored in the parameter library.

[0055] Feedback data, corresponding smoothing control commands, and the predicted output of the digital twin reduced-order model are stored in a self-learning sample library. The digital twin reduced-order model is periodically updated based on the self-learning sample library to perform online correction and continuous self-learning.

[0056] The beneficial effects of this invention are:

[0057] This invention constructs a seamless steel pipe digital twin system that spans the entire process of piercing, rolling, sizing, and cooling by integrating a digital twin order reduction model with a Tikhonov regularization module. The invention first establishes a high-dimensional digital twin parent model using multiphysics mechanism equations and standardized datasets. Based on this, a digital twin order reduction model is formed through feature pattern filtering and order reduction mapping, enabling rapid computation of complex multi-field coupling processes in a low-dimensional space.

[0058] This invention further introduces a Tikhonov regularization module based on a digital twin reduced-order model. This module applies quadratic constraints to key parameter deviations, state variable changes, and the rate of change of predictive control variables, effectively suppressing the impact of field noise, parameter drift, and abrupt changes in control variables on system stability. Furthermore, it employs a model predictive control algorithm to construct a rolling optimization framework, generating smooth control commands that satisfy process and equipment constraints. Feedback data drives online model correction and self-learning. Compared to existing solutions that rely on empirical adjustment or offline calculations using high-dimensional models, this invention achieves real-time prediction, robust control, and continuous optimization of the seamless steel pipe production process. It significantly improves the accuracy and stability of temperature, rolling force, and geometric dimension control, enhancing product quality consistency and the level of intelligence in the production process. Attached Figure Description

[0059] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0060] Figure 1 This is a flowchart of a seamless steel pipe intelligent production method based on digital twin proposed in this invention;

[0061] Figure 2 This is a schematic diagram of the structure of a digital twin-based intelligent production method for seamless steel pipes proposed in this invention, representing a digital twin-based model with reduced order. Detailed Implementation

[0062] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0063] refer to Figure 1 and Figure 2 A smart production method for seamless steel pipes based on digital twins includes:

[0064] Historical data and real-time monitoring data of the seamless steel pipe production process are collected, and the historical data and real-time monitoring data are preprocessed to generate a standardized dataset;

[0065] A high-dimensional digital twin model of the seamless steel pipe production process is established based on standardized datasets and multiphysics mechanism equations. The high-dimensional digital twin model is then reduced in order, the main modal features are extracted, and a low-dimensional state space-output mapping relationship is constructed to obtain a digital twin reduced-order model.

[0066] The parameters of the digital twin reduced-order model are calibrated based on a standardized dataset to obtain the initial parameter set and state mapping matrix.

[0067] Input real-time monitoring data into the digital twin reduced-order model, call the initial parameter set and state mapping matrix to perform state assimilation operation, and obtain updated key parameters, state variables and predictive control variables;

[0068] A Tikhonov regularization module is introduced, combined with a high-frequency noise suppression filter structure. It receives updated key parameters, state variables and predictive control variables, applies quadratic regular constraints to the deviation of key parameters, changes in state variables and the rate of change of predictive control variables, and generates robust correction results.

[0069] Based on the robustness correction results, the model predictive control algorithm is executed for rolling optimization to generate smooth control commands and send them to the production equipment.

[0070] The system collects feedback data after the device executes the smooth control command and inputs it into the digital twin reduced-order model for online correction and continuous self-learning. The system also updates the initial parameter set and state mapping matrix based on the feedback data.

[0071] In this embodiment, the historical data and real-time monitoring data specifically include historically collected and real-time monitored temperature data, rolling force data, rolling line speed and rotation speed data, wall thickness and outer diameter data, and cooling medium flow rate data during the seamless steel pipe production process.

[0072] In this embodiment, the preprocessing of historical data and real-time monitoring data specifically includes data cleaning, noise filtering, time synchronization, and feature extraction and normalization.

[0073] In this embodiment, obtaining the digital twin reduced-order model includes:

[0074] Based on a standardized dataset, time alignment and spatial location identification are unified, and a multidimensional feature tensor is constructed. The construction of the multidimensional feature tensor specifically involves:

[0075] Temperature data, rolling force data, rolling line speed and rotation speed data, wall thickness and outer diameter data, and cooling medium flow rate of each standardized dataset channel are time-aligned and remapped to a unified sampling time axis to obtain an aligned time series. Spatial location identification is unified for each sensor, stand, and process position, and a unique spatial coordinate is assigned to each data point to obtain a unified spatial location. The aligned time series, the unified spatial locations, and the physical quantities after normalization of the standardized dataset are combined in a time-space-feature dimension manner to form a multidimensional feature tensor with a fixed dimension structure.

[0076] Establish a cross-process association structure based on the process sequence, define parameter transfer and continuity rules between processes, and form a temporal topology relationship. Specifically, forming the temporal topology relationship involves:

[0077] Based on the actual process sequence of seamless steel pipe production, the piercing, rolling, sizing, and cooling processes are arranged chronologically, and each process is assigned a unique step number and equipment tag number. For the input and output quantities of each process, a parameter transfer path is established from the upstream process to the downstream process, and the input-processing-output mapping of variables such as temperature, rolling force, wall thickness, outer diameter, and speed is linked together. According to the process requirements, continuity rules between each process are set, including temperature continuity, stress continuity, dimensional change rate continuity, and speed matching conditions. The step number, parameter transfer path, and continuity rules are combined to form a temporal topology with time sequence constraints and parameter flow laws.

[0078] Based on the multidimensional characteristic tensor and temporal topological relationship, a multiphysics mechanism equation is introduced, including the heat conduction equation, the plastic mechanical equilibrium equation, and the tissue evolution dynamics equation. Furthermore, energy conservation constraints, momentum balance constraints, and the correlation constraints of temperature's influence on tissue evolution are introduced to obtain a high-dimensional state representation that satisfies physical consistency, wherein:

[0079] The heat conduction equation describes the temperature variation with time and space of a steel billet during piercing, rolling, sizing, and cooling, and characterizes the way heat is transferred within the material.

[0080] The equilibrium equations of plasticity describe the plastic deformation behavior of steel pipes under external forces, and characterize the deformation process through force balance, stress distribution and material hardening laws.

[0081] The microstructure evolution kinetic equation describes the dynamic laws governing the changes in grain size, recrystallization behavior, and phase transformation process within steel as a function of temperature, strain, and time.

[0082] The energy conservation constraint constrains the relationship between the heat conduction equation and external heat exchange and the conversion of mechanical work into heat, so that the generation, transfer and loss of heat conform to the actual physical laws.

[0083] Momentum balance constraints ensure that stress, strain rate and external load satisfy momentum balance conditions during deformation, so that the solution space of the mechanical field has physical consistency;

[0084] The correlation constraint of the effect of temperature on tissue evolution establishes the coupling relationship between the temperature field and the tissue dynamics equation, and constrains the tissue evolution calculation to be synchronized with temperature changes, and does not allow the calculation to be out of sync;

[0085] The obtained high-dimensional state representation that satisfies physical consistency is specifically as follows:

[0086] Temperature, rolling force, speed, geometric dimensions, and microstructure-related features contained in the multidimensional feature tensor are used as initial field variables and input boundary conditions. These are substituted into the heat conduction equation, the plasticity equilibrium equation, and the microstructure evolution kinetic equation to solve for the evolution trajectories of the temperature field, stress field, strain field, and microstructure field. By applying energy conservation constraints, the input heat, internal heat generation, and convective heat dissipation during the heat conduction process are kept in balance. By applying momentum balance constraints, the external loads applied in each process are kept consistent with the internal stress distribution of the material. By applying correlation constraints on the influence of temperature on microstructure evolution, the microstructure kinetic equation is required to be synchronized with temperature changes.

[0087] During the synchronous iterative process of equation solving and constraint correction, calculation results that do not conform to physical laws are corrected in a timely manner. The time series of high-dimensional field variables gradually converges to a state that simultaneously satisfies the coupling relationship of the three fields of heat, force, and organization and the physical equilibrium condition, and finally obtains a high-dimensional state representation that satisfies physical consistency.

[0088] Based on high-dimensional state representation, the composition of input quantities, state variables, and output quantities is divided. A set of parameters related to material and contact characteristics is set, forming a computable high-dimensional digital twin matrix model with input-state-output mapping relationships and parameter framework, wherein:

[0089] The inputs include piercing speed, rolling speed, cooling medium flow rate and sizing temperature; the state variables include temperature field, stress-strain field and wall thickness and outer diameter characteristics; the outputs are the predicted temperature, wall thickness, outer diameter and rolling force; the parameter set includes material parameters, contact parameters, microstructure evolution parameters and thermo-mechanical coupling parameters.

[0090] The formation of the high-dimensional digital twin matrix model is specifically as follows:

[0091] By unifying the parameter set, input quantities, state variables, and output quantities into the same solution framework, simultaneous solutions are achieved in the heat conduction equation, plasticity equilibrium equation, and tissue evolution dynamics equation. By using the input quantities as boundary conditions, the parameter set as constant terms, and the state variables as iterative solution quantities, and solving them together with the energy conservation constraints, momentum balance constraints, and temperature-related constraints in the mechanism equation, a high-dimensional digital twin matrix model is formed with a complete input-state-output mapping relationship and parameter framework.

[0092] Using the input quantities and parameter sets in the standardized data as driving and boundary conditions, offline simulation is performed on the high-dimensional digital twin parent model to generate the set of internal state variables and the corresponding set of output variables at different time points;

[0093] State sequences are reconstructed based on historical data and real-time monitoring data, and then merged with internal state variable sets and output variable sets to form a sample library. Specifically, the reconstructed state sequences are as follows:

[0094] By performing time matching and missing data completion on historical data and real-time monitoring data, a reconstructed state sequence is obtained;

[0095] Based on the sample database, the energy contribution and reconstruction error of feature patterns are calculated to determine the dominant feature patterns. A reduced-order basis set and a corresponding output mapping basis set are then constructed. Specifically, the construction of the reduced-order basis set and the corresponding output mapping basis set involves:

[0096] The state variable set and output variable set in the sample library are arranged in chronological order. Covariance analysis is performed on each physical field variable to obtain the contribution ratio of different feature modes to the overall energy. Based on the sample library, a reconstruction experiment is carried out for each candidate feature mode. The high-dimensional state sample in the sample library is projected onto the reduced-order basis set composed of the current candidate feature mode to obtain the low-dimensional expression of the sample in the low-dimensional space. The low-dimensional expression is back-projected to the high-dimensional space through the output mapping basis set to reconstruct the corresponding high-dimensional state. By comparing the reconstructed state with the original high-dimensional state element by element, the difference is calculated, and the difference is accumulated in the entire time series to obtain the reconstruction error corresponding to the candidate feature mode.

[0097] Thresholds are set for both energy contribution and reconstruction error. Feature patterns with high energy contribution and small reconstruction error are selected as dominant feature patterns and combined to form a reduced-order basis set. Based on the projection relationship of the dominant feature patterns in the output variables, the corresponding output mapping basis set of the predicted output is generated.

[0098] A reduction-order mapping is implemented based on the reduced-order basis set, and a multi-dimensional feature fusion unit and a hierarchical output mapping structure are integrated to obtain the low-dimensional state representation and low-dimensional output mapping relationship, forming a digital twin reduced-order model. The digital twin reduced-order model consists of a multi-dimensional feature fusion unit, a multi-physical coupling and process topology interface, a reduced-order projection and low-dimensional state core unit, and a hierarchical output mapping structure, wherein:

[0099] The multidimensional feature fusion unit performs temporal alignment, spatial identification, and normalization on the input to generate a unified feature tensor.

[0100] Multi-physical coupling and process topology interface connect and transmit parameters of multi-physical process topology interfaces at the structural level;

[0101] The reduced-order projection and low-dimensional state core unit maps high-dimensional states to low-dimensional representations based on the reduced-order basis and completes state updates and fast solutions in the low-dimensional space.

[0102] The hierarchical output mapping structure transforms low-dimensional states into observable results and outputs them;

[0103] The formation of the digital twin reduced-order model specifically involves:

[0104] The multi-dimensional feature fusion unit, as a newly added input preprocessing layer, is directly linked to the input end of the digital twin reduced-order model. It performs time alignment, spatial identification and normalization on real-time monitoring data, unifies the input scale and enhances data adaptability.

[0105] A multi-physical coupling and process topology interface is added after the multi-dimensional feature fusion unit, and cross-process parameter transfer relationships are supplemented before and after dimensionality reduction calculation;

[0106] The reduced-order projection and low-dimensional state core unit are improved on the reduced-order mapping layer, making the mapping from high-dimensional state to low-dimensional state more stable and the solution efficiency higher.

[0107] The hierarchical output mapping structure, as a newly added output structure, is cascaded with the output layer of the digital twin reduced-order model. Through two-level mapping, the low-dimensional state is gradually transformed into observable results, improving the output accuracy and robustness after dimensionality reduction, and thus obtaining the digital twin reduced-order model.

[0108] In this embodiment, obtaining the initial parameter set and state mapping matrix includes:

[0109] The set of input variables and the reference output set are determined based on a standardized dataset, where:

[0110] The set of input variables includes piercing speed, rolling speed, sizing temperature, and cooling medium flow rate;

[0111] The reference output set includes temperature, wall thickness, outer diameter, and rolling force;

[0112] Define the initial parameter set for the digital twin order reduction model and establish the error evaluation function, where:

[0113] The initial parameter set consists of material parameters, contact parameters, and parameters related to microstructure evolution;

[0114] The establishment of the error evaluation function is specifically as follows:

[0115] The predicted outputs of the digital twin reduced-order model under the same input conditions are compared point by point with the reference output set. The deviations in time series and spatial distribution are calculated, and the output deviations are summed according to weights to form an error evaluation function.

[0116] An iterative optimization method is used to minimize the error evaluation function. The initial parameter set is updated sequentially according to a given step size. Convergence is determined when the error reduction between two adjacent iterations is less than a threshold, resulting in a converged parameter set. Specifically, obtaining the converged parameter set involves:

[0117] Starting with the initial parameter set, we input it into the digital twin order reduction model to obtain the corresponding predicted output. We then compare it with the reference output set using the error evaluation function to obtain the current error value. Based on the sensitivity of the current error value to each parameter, we determine the parameter update direction and update the material parameters, contact parameters, and tissue evolution parameters according to a given step size to obtain a new parameter set. We then use the new parameter set to drive the digital twin order reduction model to make predictions again. We recalculate the error between the predicted output and the reference output set and compare it with the error from the previous round to determine whether the error has been further reduced. By continuously repeating the process of prediction, error calculation, and parameter update, the error evaluation function is reduced round by round. When the error reduction of two consecutive iterations is less than the threshold, it is considered that the parameter update can no longer bring about improvement, and the iteration process has reached a stable range. The parameter set obtained from the last iteration is used as the converged parameter set.

[0118] The converged parameter set is input into the digital twin reduced-order model. The state update relationship for the next time step is determined based on the previous state, the current input, and the parameter set. The correspondence between state variables and output variables is calculated and corrected to generate a state mapping matrix. Specifically, generating the state mapping matrix involves:

[0119] Based on the converged parameter set, combined with the low-dimensional state representation of the previous time step and the input variables of the current time step, the preliminary low-dimensional state variables of the next time step are derived according to the state evolution relationship determined by the parameter set. The low-dimensional state variables are then sequentially input into the hierarchical output mapping structure, and each low-dimensional state variable generates a corresponding output quantity.

[0120] By organizing the combinations of low-dimensional state variables and corresponding output quantities at multiple consecutive time points, the correspondence between the changes in low-dimensional state variables and the changes in corresponding output quantities is represented as a set of fixed coefficients. Through least squares matching, the coefficient combination that minimizes the overall error is found at all time points, and the coefficient combination is organized into a matrix form to construct a state mapping matrix that maps low-dimensional state variables to output quantities.

[0121] In this embodiment, obtaining the updated key parameters, state variables, and predictive control variables includes:

[0122] The multi-dimensional feature fusion unit receives real-time monitoring data, completes timestamp alignment, spatial location identification unification, and dimensional normalization, and generates a standardized feature tensor for the current moment and real-time observations, including:

[0123] The process of generating the standardized feature tensor for the current time moment specifically involves:

[0124] The real-time monitoring data is timestamped and resampled to a unified time axis. Based on the equipment tag number, process number and spatial layout, each real-time monitoring data is mapped to a unified spatial location identification system. Dimensional normalization is performed, and temperature, force, velocity and geometric dimensions are converted into dimensionless form to obtain normalized values ​​with a unified scale. The data are then sorted and stacked according to the process sequence and physical quantity category to form a standardized feature tensor for the current moment.

[0125] The generation of real-time observations at the current moment specifically includes:

[0126] Extract the control quantity and observation quantity corresponding to the input quantity from the standardized feature tensor at the current moment, and use them as real-time observation quantities;

[0127] Based on the process sequence, the standardized feature tensor is mapped and parameter-bound according to the multi-physical coupling and process topology interface. Process continuity rules and physical coupling constraints are loaded to form a structured input package. Specifically, forming the structured input package involves:

[0128] The standardized feature tensor is mapped segment by segment according to the process sequence of seamless steel pipe production by multi-physics coupling and process topology interface. Features belonging to different processes are classified according to the corresponding process steps. The corresponding physical mechanism parameters are loaded for each process. The state connection and energy and force transmission relationship between adjacent processes are bound according to the process continuity rules. Then, the constraints related to thermal field, mechanical field and tissue evolution are embedded together with physical coupling constraints to form a structured input package.

[0129] After receiving the structured input packet, the reduced-order projection and low-dimensional state core unit, based on the previous low-dimensional state, current control information, and key parameters from the previous time step, first projects the high-dimensional information in the structured input packet into a low-dimensional representation. Then, it calculates the prior low-dimensional state and prior output for the current time step, where:

[0130] High-dimensional information refers to the complete set of information carried by structured input packages that still retains high-dimensional physical meaning and process-related characteristics;

[0131] The calculation of the prior low-dimensional state is specifically as follows:

[0132] The high-dimensional information in the structured input packet is reduced in order and mapped to obtain the preliminary state change result in the low-dimensional space. The low-dimensional state representation of the previous time step is combined with the preliminary change result to obtain the prior low-dimensional state at the current time step.

[0133] The calculation of the prior output is as follows:

[0134] The prior low-dimensional state is input into a hierarchical output mapping structure. Through feature extraction and mapping, observable physical quantities including temperature, rolling force, wall thickness and outer diameter are generated to obtain the prior output at this moment.

[0135] The real-time observations are compared with the prior outputs to obtain the observation residuals, and state correction instructions and weights are generated. Specifically, the generation of state correction instructions and weights involves:

[0136] The observation residuals are obtained by calculating the difference between the real-time observation and the prior output in each output dimension. The observation residuals of different dimensions are transformed to the same scale by normalization. Based on the sensitivity coefficient, each observation residual is multiplied by the corresponding sensitivity coefficient to obtain the preliminary correction amount for each dimension. Based on the fluctuation of the historical observation residuals and the relative size of the current observation residuals, the confidence value of each output quantity is calculated. The confidence value is combined with the preliminary correction amount to form the final state correction instruction.

[0137] Contribution values ​​are constructed based on the sensitivity of each output, the fluctuation of the observed residuals, and the confidence level, and then normalized to obtain the weights;

[0138] The prior low-dimensional state is corrected according to the state correction instruction to obtain the posterior low-dimensional state. Based on the sensitivity information of the prior low-dimensional state to changes in key parameters, the key parameters are incrementally corrected to obtain the updated key parameters. Specifically, obtaining the updated key parameters involves:

[0139] Based on the state correction instructions and weights, the allocated parameter increments are scaled and weighted to form the incremental adjustment amount of each key parameter. The incremental adjustment amount is then added to the key parameters of the previous time step to obtain the updated key parameters.

[0140] When the observed residual exceeds the threshold, an improvement mechanism is triggered to locally re-evaluate and update the index of the reduced-order basis. Based on the process continuity rule, the posterior low-dimensional states and rates of change at the boundaries of adjacent processes are corrected. The corrected results are then written back to the reduced-order projection and low-dimensional state core unit, as well as the multi-physics coupling and process topology interface.

[0141] The process continuity rule refers to the constraint rule that the physical quantities between different processes in the production of seamless steel pipes must remain continuous, traceable, and without abrupt changes.

[0142] The correction of the posterior low-dimensional state and rate of change of adjacent process boundaries based on the process continuity rule is specifically as follows:

[0143] The posterior low-dimensional state is corrected, including the temperature variable and the wall thickness and outer diameter. For the temperature variable, when the current process inlet temperature is too high or too low, the temperature is smoothly pulled back to the range close to the outlet temperature of the previous process by proportional approximation. For the wall thickness and outer diameter, the wall thickness and outer diameter values ​​are directly adjusted to be within the range that do not differ from the output of the previous process by more than the allowable threshold.

[0144] The rate of change in the posterior low-dimensional state is subject to trend continuity constraints. For key rates of change such as temperature change rate and wall thickness shrinkage rate, it is first determined whether the maximum allowable change range is exceeded. If the rate of change is found to be too fast, a linear interpolation method is used. The rate of change at the end of the previous process is used as the starting point, and the initial rate of change of the next process is used as the target point. Several transition points are evenly distributed according to the difference between the two to gradually and smoothly transition the rate of change from the end trend of the previous process to the starting trend of the next process, so as to avoid abrupt changes in the rate of change.

[0145] The posterior low-dimensional state and the updated key parameters are input into a hierarchical output mapping structure, which consists of a basic output layer and a correction output layer. First, the basic output layer generates preliminary prediction results, and then the correction output layer corrects these results based on physical consistency relationships. Simultaneously, the predictive control quantity for the next time domain is calculated based on the predictive control law, yielding the updated key parameters, state variables, and predictive control quantity for the current moment. Specifically, the calculation of the predictive control quantity for the next time domain based on the predictive control law involves:

[0146] The predictive control law infers the possible changes in temperature, geometric dimensions, and rolling force at the next moment based on the future evolution trend of the posterior low-dimensional state. Combined with the deviation of the control target, the feasibility of the control action is screened. Based on the degree of influence of the control action on the process stability, the control action is restricted, and the control variable that minimizes the target deviation is selected as the predictive control quantity in the next time domain.

[0147] In this embodiment, generating the robustness correction result includes:

[0148] The Tikhonov regularization module receives the key parameters, state variables, and predictive control variables after state assimilation and update, and also receives the observation residuals formed by the difference between real-time observations and prior outputs. Simultaneously, it inputs the observation residuals into a high-frequency noise suppression filter structure to perform frequency domain decomposition and high-frequency noise suppression on the residual components, obtaining a denoised residual.

[0149] The Tikhonov regularization module is directly connected to the hierarchical output mapping structure of the digital twin reduced-order model and receives the output of the digital twin reduced-order model.

[0150] The obtained noise reduction residual is specifically as follows:

[0151] The observed residuals are input into a high-frequency noise suppression filter structure. Based on the time sampling interval of the observed residuals, the observed residuals are divided into different frequency components. The low-frequency trend terms caused by normal changes in the process and the high-frequency noise components are distinguished by frequency characteristics. The amplitude of the high-frequency noise is reduced by a combination of smoothing filtering and band-stop separation. Smoothing suppression is performed on the continuously oscillating observed residuals to reduce the amplitude of the observed residuals. Single-point spike noise is replaced by the trend value of the observed residuals at the next nearby time, thus completing the high-frequency noise suppression. The low-frequency trend terms and the smoothed high-frequency noise terms are then recombined to form the noise-reduced residuals.

[0152] In the Tikhonov regularization module, key parameter deviation regularization terms, state smoothing regularization terms, and control smoothing regularization terms are constructed. The denoising residual is then superimposed with the three types of regularization terms according to their weight coefficients to form a comprehensive objective function, where:

[0153] The key parameter deviation regularization term is constructed by comparing the difference between the current key parameter and the key parameter at the previous time step. The larger the difference, the stronger the key parameter deviation regularization term. The state smoothing regularization term is constructed based on the change amplitude of low-dimensional state variables in consecutive time steps. The control smoothing regularization term is constructed by calculating the change amplitude between consecutive control quantities.

[0154] The formation of the comprehensive objective function is specifically as follows:

[0155] The key parameter deviation regularization term, state smoothing regularization term, and control smoothing regularization term are weighted and superimposed with the noise reduction residual to form the final comprehensive objective function;

[0156] Iterative optimization is performed on the comprehensive objective function to calculate the corrections for key parameters, state variables, and predictive control variables, and the preliminary corrected key parameters, state variables, and predictive control variables are then updated, where:

[0157] The calculation of the key parameter correction amount is as follows:

[0158] The deviation between the current key parameters and the reference parameters is compared. The key parameters with greater deviation are penalized more severely. Based on the changes in the deviation, the values ​​of the key parameters are adjusted in each iteration to reduce the deviation of the key parameters, forming a new key parameter. If the new key parameter can reduce the value of the comprehensive objective function, it is retained for use in the next iteration. After multiple iterations, the key parameters gradually converge. The change in the key parameters at the time of convergence constitutes the key parameter correction amount.

[0159] The calculation of the state correction amount is as follows:

[0160] If a significant discontinuity is found in the state variables, the state smoothing regularization term applies a forced suppression to this discontinuity, pushing the state variables to adjust in the smoothing direction. Based on the degree of influence of the observation residuals on each state variable, the observation residuals are assigned to the corresponding state dimensions for correction, gradually weakening the abnormal changes in the state variables and shifting the values ​​of the state variables in the direction of reducing the observation residuals. Through continuous adjustment, a set of state variables that have both smoothness and error reduction effects is finally obtained, and the change in the state variables is used as the state correction quantity.

[0161] The calculation of the predictive control correction amount is as follows:

[0162] Check if the current predictive control quantity has excessive fluctuations or changes too rapidly. If the rate of change of the predictive control quantity exceeds the allowable range, a penalty is applied. During iteration, the control quantity moves in the direction of decreasing rate of change of the predictive control quantity. Each iteration generates a new predictive control quantity. After multiple rounds of updates, a predictive control quantity change trajectory that balances stability and error reduction is finally obtained. The changed part is used as the predictive control quantity correction amount.

[0163] Based on the adjustment of the weight coefficients of the key parameter deviation regularization term, state smoothing regularization term, and control smoothing regularization term using the noise reduction residual, the comprehensive objective function optimization is re-executed after updating the weight coefficients to obtain the updated key parameters, updated state variables, and updated predictive control variables.

[0164] Quadratic regularization constraints are applied to the updated key parameters, state variables, and predictive control variables. Values ​​that do not meet the constraints are corrected to obtain the final key parameters, final state variables, and final predictive control variables, generating robustness correction results, where:

[0165] Quadratic regularization constraint refers to a penalty mechanism based on the square norm that is applied to key parameters, state variables and predictive control variables. It calculates the deviations between key parameters, state variables and predictive control variables and the target, and then squares and weights the deviations as a penalty term and adds them to the comprehensive objective function.

[0166] In this embodiment, generating smooth control commands and issuing them to the production equipment includes:

[0167] Based on the robustness correction results, the observation residuals are combined with the parameter deviation regularization term, the state smoothing positive final key parameter, the final state variable, and the final predictive control quantity. The prediction time domain, the control time domain, and the process target trajectory corresponding to this process are set.

[0168] The predicted relationship between the state variables and the output of the digital twin reduced-order model in the predicted time domain and the control input sequence is calculated based on the final state variables and the final key parameters, where:

[0169] The calculation of the state variables in the prediction time domain is specifically as follows:

[0170] Based on the final state variables and final key parameters, the digital twin reduced-order model is used to obtain the predicted state variables in the time domain.

[0171] The calculation of the predictive relationship between the output of the digital twin reduced-order model and the change in the control quantity sequence is as follows:

[0172] The state variables in the predicted time domain are converted into corresponding output variables. In this process, the sequence changes of the control variables are transmitted to the digital twin reduced-order model. By simulating different control input sequences, the influence of the control variables on the state variables in the future time domain is analyzed, and the predictive relationship between the output variable and the sequence changes of the control variables is obtained.

[0173] A rolling optimization problem is constructed, with the deviation between the predicted state variables and the output of the digital twin reduced-order model and the process target trajectory as the objective term, the increment of the control variable and the rate of change of the control variable as the penalty term, and the allowable range of values ​​of each key process physical quantity and the amplitude and rate of change of the control variable as the constraint conditions.

[0174] The rolling optimization problem is solved to obtain the optimal control quantity sequence in the prediction time domain. The first control quantity corresponding to the current sampling period is selected as the smoothing control command. Specifically, the selection of the smoothing control command is as follows:

[0175] The control quantity sequence is optimized throughout the entire prediction time domain. By minimizing the deviation between the predicted state quantity and the output of the digital twin reduced-order model and the process target trajectory, a set of optimal control quantity sequences is obtained, and the first step control quantity corresponding to the current sampling period is selected as the smooth control command.

[0176] The smooth control command is sent to the production equipment, and the prediction results and execution feedback for this cycle are recorded.

[0177] In this embodiment, updating the initial parameter set and state mapping matrix based on feedback data includes:

[0178] Collect feedback data from production equipment during the execution of smooth control commands, and mark the key process physical quantities and actual control quantities in the feedback data according to the sampling time and process segment;

[0179] The feedback data is preprocessed, then incorporated into a standardized dataset and input into a digital twin order reduction model to obtain the error sequence of each key process physical quantity. Specifically, the preprocessing of the feedback data includes:

[0180] The feedback data is cleaned, missing value imputed, time aligned, normalized, and smoothed.

[0181] The initial parameter set and state mapping matrix are incrementally corrected based on the error sequence to obtain the updated initial parameter set and state mapping matrix, which are then stored in the parameter library.

[0182] Feedback data, corresponding smoothing control commands, and the predicted output of the digital twin reduced-order model are stored in a self-learning sample library. The digital twin reduced-order model is periodically updated based on the self-learning sample library to perform online correction and continuous self-learning.

[0183] Example 1:

[0184] To verify the feasibility of this invention in practice, it was applied to the entire intelligent production process of a seamless steel pipe production line in a large steel pipe enterprise. This production line, from the heating furnace to the cooling line, is equipped with 30 infrared temperature acquisition points, 16 rolling force sensors, 3 sets of high-speed dimensional monitoring devices, and 12 cooling flow monitoring ports. From February 2025 to September 2025, it continuously collected various types of production data in real time, including piercing exit temperature, rolling force curve, rolling speed, wall thickness and outer diameter dimensions, and cooling medium flow rate. All data was aggregated to a digital twin server via a gigabit industrial gateway. After time alignment, spatial mapping, and normalization processing, the data was input into the digital twin reduced-order model proposed in this invention to achieve simultaneous virtual-real prediction and robust correction.

[0185] During the pilot phase, the production site was affected by multiple disturbances, including seasonal temperature differences, equipment maintenance, and fluctuations in raw material composition. Particularly during March–April and July–August, the maximum fluctuation in furnace outlet temperature reached ±55℃. Using the method of this invention, the system automatically performs state assimilation and regularization correction after data inflow, stabilizing the temperature prediction deviation within ±2.6℃, and generating updated states and predictive control quantities within 8–10ms. The model predictive control module continuously optimizes heating power, reduction, and cooling flow rate every 200ms, achieving continuous coordinated adjustment of multiple processes. In the high-strength steel continuous rolling task in June 2025, the system completed the identification and adjustment of abnormal piercing temperatures in approximately 2.8 seconds, ensuring that all subsequent 230 steel pipes met the wall thickness and outer diameter requirements.

[0186] Before the system of this invention was put into use, the wall thickness fluctuation of the production line was approximately ±0.46 mm, and the outer diameter control accuracy was approximately 0.81 mm. After batch switching, the process parameters typically took 4–6 minutes to stabilize. After 8 months of continuous operation, statistical results showed that the wall thickness fluctuation converged to approximately ±0.20 mm, the outer diameter control accuracy improved to approximately 0.36 mm, the average energy consumption per unit product decreased by 7.1%, and the stabilization time after batch switching was shortened to less than 1 minute. During this period, the system identified 14 potential temperature control issues, 9 abnormal rolling force trends, and 6 uneven cooling problems, and corrected the parameters before the deviations expanded. No batches of finished products were scrapped due to process fluctuations during the test. This verifies that the invention can maintain high-precision prediction and high-stability control under conditions of strong disturbance, high noise, and long-cycle operation, improving the quality consistency, energy efficiency, and intelligent operation level of the seamless steel pipe production process.

[0187] Table 1. Key performance comparison data of the method of the present invention during the trial operation of a seamless steel pipe production line.

[0188] Indicator Categories Specific indicators Average value before commissioning Average value after the invention is put into use Increase Remark Geometric dimensional control performance Wall thickness fluctuation (mm) ±0.46 ±0.20 ↓56.5% Sample size: 39,500 Geometric dimensional control performance Outer diameter deviation (mm) 0.81 0.36 ↓55.6% Statistics for 8 consecutive months Geometric dimensional control performance Wall thickness uniformity index 0.72 0.41 ↑43.1% The smaller the indicator, the more stable it is. Temperature field prediction performance Temperature fluctuation at the perforation outlet (°C) ±55 (actual fluctuation) ±2.6 (model error) Improved accuracy Responding to strong disturbances Temperature field prediction performance Predicted response latency (ms) 140–180 8–10 ↑ Approximately 17 times Advantages of low-dimensional reduction models Mechanical field stability Rolling force prediction error (%) ±12.1% ±4.3% ↓64.5% State assimilation + regularization Mechanical field stability Large fluctuation suppression capability No significant inhibition Volatility reduced by 40–60% — Winter and summer temperature difference operation condition verification Control performance indicators Process stabilization time (batch changeover) 4–6 minutes <1 minute ↓More than 80% Model predictive control implementation Control performance indicators Rate of change of control quantity High, often with sudden jumps Smooth changes improve Regularization smoothing effect Control performance indicators Control command calculation cycle (ms) 600–900 200 3-4 times increase Model Predictive Control Module Performance Anomaly identification and early warning Early warning of abnormal temperature (start) — 14 — 8 months of data Anomaly identification and early warning Abnormal trend in rolling force (start) — 9 — — Anomaly identification and early warning Uneven cooling is an abnormality (starting) — 6 — — Energy consumption and quality performance Unit energy consumption decreased by (%) — 7.1% — Measurements lasted for 8 months Energy consumption and quality performance First pass rate of finished products 95.8% 98.9% ↑3.1% Mass production Energy consumption and quality performance scrapped batches Occasionally 0 improve Throughout the pilot period

[0189] As can be seen from the data in Table 1, the method of this invention improves the geometric dimensional control capability in the seamless steel pipe production process. The wall thickness fluctuation decreased from ±0.46 mm before implementation to ±0.20 mm, and the outer diameter deviation decreased from 0.81 mm to 0.36 mm, with the fluctuation amplitude reduced by more than half. This indicates that the digital twin reduced-order model can continuously output stable and reliable dimensional prediction and control results under strong disturbance conditions, significantly enhancing the geometric accuracy and consistency of the finished pipe and greatly reducing the risk of dimensional deviations. The wall thickness uniformity index decreased from 0.72 to 0.41, also reflecting a more uniform distribution within the cross-section and along the length direction, resulting in better repeatability and controllability of the finished product quality.

[0190] Regarding process prediction and robustness, the data in the table shows that the actual fluctuation of the piercing outlet temperature can reach ±55℃, while the model prediction error is compressed to ±2.6℃. Simultaneously, the prediction response delay is reduced from the order of hundreds of milliseconds to 8–10 ms. This indicates that the combination of the multiphysics mechanism model and the reduced-order mapping significantly improves real-time performance while ensuring physical rationality, providing a reliable foundation for subsequent model predictive control. The rolling force prediction error is reduced from ±12.1% to ±4.3%, and it still exhibits 40%–60% fluctuation suppression capability under large fluctuation conditions. This demonstrates that the state assimilation and Tikhonov regularization modules have a significant suppression effect on parameter drift and noise interference, effectively avoiding model divergence and control strategy distortion.

[0191] From the perspective of control performance and operational effectiveness, the process stabilization time after batch switching was shortened from the original 4-6 minutes to less than 1 minute, and the calculation cycle of control commands stabilized at 200ms. This indicates that the model predictive control module, based on the digital twin reduced-order model and robustness results, can complete rolling optimization under constraints in a short time, achieving rapid coordinated adjustment of multiple processes. During the 8-month operation, the system identified 14 potential temperature control issues, 9 abnormal rolling force trends, and 6 uneven cooling problems. All were adjusted before the problems escalated, and no batches were scrapped due to process fluctuations during the trial phase. Unit energy consumption decreased by 7.1%, and the first-pass yield increased to 98.9%, comprehensively demonstrating the significant engineering application value of this invention in improving prediction accuracy, enhancing robustness, optimizing control quality, and reducing energy consumption.

[0192] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A seamless steel pipe intelligent production method based on digital twinning, characterized in that, The application relates to a seamless steel pipe production process digital twin model and a method for realizing model predictive control. The application comprises the following steps: Historical data and real-time monitoring data of a seamless steel pipe production process are collected, and the historical data and real-time monitoring data are preprocessed to generate a standardized data set; A high-dimensional digital twin parent model of the seamless steel pipe production process is established based on the standardized data set and multi-physical field mechanism equations, and the high-dimensional digital twin parent model is reduced in order to extract main modal characteristics, build a low-dimensional state space and output mapping relationship, and obtain a digital twin reduced model; The digital twin reduced model is parameterized based on the standardized data set to obtain an initial parameter set and a state mapping matrix; Real-time monitoring data are input into the digital twin reduced model, and the initial parameter set and the state mapping matrix are called to perform state assimilation operation to obtain updated key parameters, state variables and predictive control amounts; A Tikhonov regularization module is introduced, combined with a high-frequency noise suppression filter structure, to receive the updated key parameters, state variables and predictive control amounts, impose quadratic regularization constraints on key parameter deviations, state variable changes and predictive control amount change rates, and generate a robust correction result; Based on the robust correction result, a model predictive control algorithm is executed for rolling optimization to generate smooth control instructions and send the smooth control instructions to production equipment; 2. The seamless steel pipe intelligent production method based on digital twinning according to claim 1, characterized in that, Feedback data of the equipment after executing the smooth control instructions are collected and input into the digital twin reduced model for online correction and continuous self-learning, and the initial parameter set and the state mapping matrix are updated according to the feedback data.

3. The seamless steel pipe intelligent production method based on digital twinning according to claim 1, characterized in that, The historical data and real-time monitoring data specifically include historical and real-time monitoring temperature data, rolling force data, rolling line speed and rotating speed data, wall thickness and outer diameter data and cooling medium flow data in the seamless steel pipe production process.

4. The seamless steel pipe intelligent production method based on digital twinning according to claim 1, characterized in that, The pre-processing of the historical data and real-time monitoring data specifically includes data cleaning, noise filtering, time synchronization and feature extraction and normalization. The digital twin reduced model is obtained by the following steps: Based on the standardized data set, time alignment and spatial position identification are unified to build a multi-dimensional feature tensor; A cross-process association structure is established according to the process sequence, parameter transmission and continuity rules between processes are defined, and a time sequence topological relationship is formed; Multi-physical field mechanism equations are introduced based on the multi-dimensional feature tensor and the time sequence topological relationship, the mechanism equations include heat conduction equations, plastic mechanics balance equations and organization evolution dynamics equations; and energy conservation constraints, momentum balance constraints and constraints related to the influence of temperature on organization evolution are introduced to obtain a high-dimensional state representation meeting physical consistency; Based on the high-dimensional state representation, the composition of input, state variable and output is divided, a parameter set related to material and contact characteristics is set, a high-dimensional digital twin parent model with input-state-output mapping relationship and parameter framework and capable of calculation is formed; The input in the standardized data and the parameter set are taken as driving and boundary conditions, and the high-dimensional digital twin parent model is executed offline simulation to generate an internal state variable set and a corresponding output variable set at different time nodes; A state sequence is reconstructed based on the historical data and real-time monitoring data, and the reconstructed state sequence, the internal state variable set and the output variable set are combined to form a sample library. The energy contribution degree and reconstruction error of the feature mode are calculated based on the sample library to determine the dominant feature mode, and a reduced-order basis set and a corresponding output mapping basis set are constructed; On the basis of the reduced-order basis set, a reduced-order mapping is implemented, and a multi-dimensional feature fusion unit and a hierarchical output mapping structure are integrated to obtain a low-dimensional state representation and a low-dimensional output mapping relationship, thereby forming a digital twin reduced-order model; the digital twin reduced-order model comprises a multi-dimensional feature fusion unit, a multi-physical coupling and process topology interface, a reduced-order projection and low-dimensional state core unit, and a hierarchical output mapping structure, wherein: The multi-dimensional feature fusion unit performs time alignment, space identification and normalization on the input quantity to generate a unified feature tensor; the multi-physical coupling and process topology interface connects and transmits parameters of the multi-physical process topology interface at the structure level; the reduced-order projection and low-dimensional state core unit maps the high-dimensional state to a low-dimensional representation based on the reduced-order basis and completes state updating and rapid solving in the low-dimensional space; and the hierarchical output mapping structure converts the low-dimensional state into observable results and outputs them.

5. The seamless steel pipe intelligent production method based on digital twinning according to claim 1, characterized in that, The initial parameter set and the state mapping matrix are obtained by: determining an input variable set and a reference output set based on a standardized data set; setting an initial parameter set of the digital twin reduced-order model and establishing an error evaluation function; minimizing the error evaluation function by using an iterative optimization method, updating the initial parameter set in turn according to a given step size, determining convergence when the error reduction amplitude of adjacent two iterations is less than a threshold value, and obtaining a converged parameter set; inputting the converged parameter set into the digital twin reduced-order model, determining the state updating relationship of the next time state based on the state of the last time, the current input and the parameter set, calculating and correcting the corresponding relationship between the state variable and the output quantity, and generating a state mapping matrix.

6. The seamless steel pipe intelligent production method based on digital twinning according to claim 1, characterized in that, The updated key parameters, state variables and predictive control quantities are obtained by: receiving real-time monitoring data by the multi-dimensional feature fusion unit, completing time stamp alignment, space position identification and dimension normalization, generating a standardized feature tensor and real-time observation at the current time, and forming a structured input package by the multi-physical coupling and process topology interface according to the process sequence, process mapping and parameter binding of the standardized feature tensor, loading process continuity rules and physical coupling constraints, and projecting high-dimensional information in the structured input package into a low-dimensional representation based on the last time low-dimensional state, the current control information and the last time key parameters by the reduced-order projection and low-dimensional state core unit, and then calculating the prior low-dimensional state and prior output at the current time; comparing the real-time observation and the prior output to obtain an observation residual, and generating a state correction instruction and a weight; correcting the prior low-dimensional state according to the state correction instruction to obtain a posterior low-dimensional state, and incrementally correcting the key parameters according to the sensitivity information of the prior low-dimensional state to the key parameter changes to obtain updated key parameters; and ​ ​ When the observation residual exceeds the threshold value, a correction mechanism is triggered to locally re-estimate and update the index of the reduced basis, and to correct the posterior low-dimensional state and its rate of change at the adjacent process boundary according to the process continuity rule, and the corrected results are written back to the reduced projection and low-dimensional state core unit and the multi-physics coupling and process topology interface; The posterior low-dimensional state and the updated key parameters are input into a hierarchical output mapping structure composed of a basic output layer and a correction output layer. The basic output layer generates a preliminary prediction result, and the correction output layer corrects it according to the physical consistency relationship. At the same time, the prediction control amount in the next time domain is calculated according to the prediction control law, and the updated key parameters, state variables and prediction control amount at this time are obtained.

7. The seamless steel pipe intelligent production method based on digital twinning according to claim 1, characterized in that, The generation of the robust correction result comprises: The Tikhonov regularization module receives the key parameters, state variables and prediction control amount updated by state assimilation, and receives the observation residual formed by the difference between the real-time observation and the prior output, and simultaneously inputs the observation residual into a high-frequency noise suppression filter structure to perform frequency domain decomposition and high-frequency noise suppression on the residual components to obtain a noise-reduced residual; In the Tikhonov regularization module, a key parameter bias regularization term, a state smoothing regularization term and a control smoothing regularization term are constructed, and the noise-reduced residual and the three types of regularization terms are superimposed according to weight coefficients to form a comprehensive objective function; The comprehensive objective function is iteratively optimized to calculate the key parameter correction amount, the state correction amount and the prediction control amount correction amount, and the preliminary corrected key parameters, state variables and prediction control amount are updated; The weight coefficients of the key parameter bias regularization term, the state smoothing regularization term and the control smoothing regularization term are adjusted based on the noise-reduced residual, and after updating the weight coefficients, the comprehensive objective function optimization is performed again to obtain the updated key parameters, the updated state variables and the updated prediction control amount; The updated key parameters, state variables and prediction control amount are subjected to quadratic regularization constraints, and the values that do not meet the constraints are corrected to obtain the final key parameters, the final state variables and the final prediction control amount, and the robust correction result is generated.

8. The seamless steel pipe intelligent production method based on digital twinning according to claim 1, characterized in that, The generation of the smooth control instruction and the delivery to the production equipment comprises: Based on the robust correction result, the observation residual, the parameter bias regularization term, the state smoothing regularization term, the final key parameters, the final state variables and the final prediction control amount are set to set the prediction time domain, the control time domain and the process target trajectory corresponding to the current process; The prediction relationship between the state variables and the digital twin reduced model output variables and the control amount sequence in the prediction time domain is calculated according to the final state variables and the final key parameters; A rolling optimization problem is constructed, the deviations of the prediction state variables and the digital twin reduced model output variables from the process target trajectory are taken as the target items, the control amount increment and the control amount change rate are taken as the penalty items, and the allowed value range of each key process physical quantity and the control amount amplitude and change rate are set as the constraint conditions; The rolling optimization problem is solved to obtain the optimal control amount sequence in the prediction time domain, and the first step control amount corresponding to the current sampling period is selected as the smooth control instruction. The smooth control instruction is sent to the production equipment, and the prediction result and the execution feedback of the current period are recorded.

9. The seamless steel pipe intelligent production method based on digital twinning according to claim 1, characterized in that, The updating of the initial parameter set and the state mapping matrix according to the feedback data comprises: The feedback data of the production equipment in the process of executing the smooth control instruction is collected, and each key process physical quantity and the actual executed control quantity in the feedback data are marked according to the sampling time and the process section; The feedback data is preprocessed, the preprocessed feedback data is incorporated into the standardized data set and input into the digital twin reduced-order model, and the error sequence of each key process physical quantity is obtained; The initial parameter set and the state mapping matrix are incrementally corrected based on the error sequence, and the updated initial parameter set and the state mapping matrix are stored in the parameter library; The feedback data, the corresponding smooth control instruction and the prediction output of the digital twin reduced-order model are stored in the self-learning sample library, the digital twin reduced-order model is periodically updated based on the self-learning sample library, and online correction and continuous self-learning are performed.

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