Model-driven strip crown control digital twin system and method
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-01-16
- Publication Date
- 2026-08-11
AI Technical Summary
[0004]针对现有技术的缺陷和改进需求,本发明提供了一种基于模型驱动的板带凸度控制数字孪生系统和方法,能够针对凸度控制的复杂特性,建立高精度凸度预测模型,此外,以现场凸度控制系统的安全稳定运行,以及预测模型与现场凸度控制系统的兼容性为前提,构建了一套凸度在线控制优化框架,能够解决在小批量、多规格生产模式下板带凸度控制精度低的问题
[0038]在一些示例中,用于凸度控制的数字孪生系统功能应用层,通过特征提取、响应测试以及迭代优化三个服务的协同运作,为凸度关键参数调控提供了科学、稳定的优化方案,在保证系统稳定运行的前提下可有效提升了凸度控制精度。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of metal rolling, and in particular to a model-driven digital twin system and method for controlling strip convexity. Background Technology
[0002] Crown is a crucial evaluation indicator for the shape quality of hot-rolled strip. With continuous improvements in manufacturing capabilities, market demands for strip crown quality are becoming increasingly stringent. Currently, industrial practice typically employs traditional numerical models based on influence function methods to calculate strip crown, utilizing measured values for model self-learning. However, this traditional modeling method simplifies complex constraints and operating conditions, averaging the parameters matched to the model for each condition, leading to inherent systematic errors in the model. Furthermore, maintaining the accuracy of traditional models relies on expert knowledge and numerical simulations, making real-time accuracy difficult to guarantee.
[0003] In the context of multi-specification, small-batch production, abrupt changes in actual processing conditions and the complex, nonlinear, and strongly coupled relationships between various process variables pose significant obstacles to improving the accuracy of strip crown control. Traditional models cannot effectively elucidate the inherent complex mechanism of strip crown control or adapt to varying working conditions, resulting in low crown control accuracy in current industrial settings and severely impacting product quality. Summary of the Invention
[0004] To address the shortcomings and improvement needs of existing technologies, this invention provides a model-driven digital twin system and method for strip convexity control. It can establish a high-precision convexity prediction model for the complex characteristics of convexity control. Furthermore, based on the premise of safe and stable operation of the field convexity control system and the compatibility between the prediction model and the field convexity control system, a set of online convexity control optimization framework is constructed, which can solve the problem of low convexity control accuracy of strip in small-batch, multi-specification production mode.
[0005] To achieve the above objectives, the present invention is implemented through the following technical solutions:
[0006] This invention provides a model-driven digital twin system for controlling strip convexity, comprising:
[0007] The physical entity portion includes at least rolling equipment and a crown control system;
[0008] The digital twin data space portion includes at least: a data acquisition unit and a data processing unit. The data acquisition unit is used to acquire equipment parameters, real-time production data, historical quality data, and production plan data of the hot strip mill finishing unit. The data processing unit is used to perform spatiotemporal transformation on the equipment parameters, real-time production data, historical quality data, and production plan data of the finishing mill unit to generate training samples for the virtual model.
[0009] The virtual space component includes at least: a data-driven strip convexity prediction model to achieve accurate prediction of strip convexity under small-batch, multi-specification production conditions;
[0010] The functional application layer includes at least: a feature extraction service for extracting the importance of parameters affecting convexity, a response testing service for determining the consistency of convexity control characteristics between the virtual model and the physical entity, and an iterative optimization service for optimizing key control parameters. The physical entity part, the virtual space part, and the functional application layer part are interconnected through the digital twin data space and form an interactive framework through iterative optimization.
[0011] For example, the physical entity portion generates a real-time state through data to update the virtual model of the virtual space portion and evaluate its accuracy;
[0012] The virtual space component provides feedback commands to ensure that the physical entity component executes predefined process parameters. The normal operation and evolution of the virtual space component are supported by the services provided by the functional application layer component.
[0013] The functional application layer actively monitors the real-time status and data within the physical entity to formulate service requirements and provide corresponding services. The services are verified in the virtual space, and feedback on modification suggestions is provided to the functional application layer to improve the control accuracy of the board strip convexity.
[0014] For example, the production planning data includes: strip steel grade, strip exit thickness, strip exit width, and strip target convexity;
[0015] The equipment parameters include: working roll shape parameters, working roll diameter, and support roll diameter;
[0016] The real-time production data includes: intermediate billet crown, intermediate billet thickness, strip inlet temperature, finishing mill stand roll shifting position, finishing mill stand bending roll force, finishing mill stand rolling force, finishing mill stand work roll thermal expansion, and finishing mill stand work roll wear.
[0017] The historical quality data includes the full-length convexity hit rate and the measured convexity value of the strip.
[0018] For example, in the virtual space portion, the strip convexity prediction model is an XGBoost model.
[0019] For example, building an XGBoost model also includes:
[0020] Optimize the hyperparameters of the model and determine the objective function and constraints.
[0021] The global-local collaborative training strategy is optimized. Global training uses all historical data to train the model to ensure the basic prediction accuracy of the model. Local training uses the steel grade and target convexity of the strip as the selection criteria and selects several samples similar to the current training order for training to improve the model's training adaptability. The final result of the model can be expressed as: y=βy1+(1-β)y2, where y is the final prediction result of the model, y1 is the global training prediction result, y2 is the local training prediction result, and β is the model weight.
[0022] For example, in the functional application layer, the feature extraction service extracts the contribution of the input parameters to the convexity prediction model by considering the interaction between input parameters during model training, and sorts the input parameters from highest to lowest according to the importance of the contribution, so as to extract important convexity control parameters.
[0023] For example, in the functional application layer, the response testing service, based on the principle of controlled variables, generates equidistant model response test samples by changing the way the convexity control parameters are extracted, and inputs the test samples into the strip convexity prediction model in the virtual space to test the influence of the convexity control parameters on the convexity prediction results. The results are then compared with the strip convexity control characteristics in the physical entity to ensure the consistency between the predicted convexity control and the actual convexity control.
[0024] For example, in the functional application layer, the iterative optimization service uses the preset parameters issued by the convexity control model of the physical entity part as the input of the virtual convexity prediction model of the virtual space part, and compares the deviation with the target convexity as a benchmark. By continuously adjusting the key control parameters, the deviation between the calculation result of the virtual space convexity prediction model and the target convexity meets the requirements, so as to improve the convexity control accuracy.
[0025] In addition, the present invention also provides a model-driven method for controlling the convexity of a strip, comprising:
[0026] Collect real-time data of the physical entity, including at least equipment parameters, real-time production data, historical quality data, and production plan data;
[0027] The data is processed, spatiotemporal transformation is performed, and training samples for the strip convexity prediction model are generated.
[0028] Based on the training samples, a strip crown prediction model is trained. The input of the crown prediction model is rolling process data, and the output is the crown value of a single strip.
[0029] Extract the contribution of input parameters to the convexity prediction model, and sort the input parameters from highest to lowest according to the importance of their contribution, and extract the important convexity control parameters.
[0030] Generate model response test samples, input the test samples into the convexity prediction model, and test the influence of the convexity control parameters on the convexity prediction results;
[0031] The convexity prediction results generated by the convexity control parameters are compared with the convexity control characteristics of the physical entity plate and strip, and iterative optimization is performed.
[0032] The preset parameters issued by the convexity control model are used as input to the strip convexity prediction model. The output results are compared with the target convexity. Based on the deviation between the output results and the target convexity, the convexity control parameters are adjusted and optimized until they reach a reasonable deviation range. The convexity control parameters are then fed back to the control module of the physical system to improve the accuracy of convexity control.
[0033] For example, the training samples for generating the strip convexity prediction model include:
[0034] The initial sample is subjected to outlier detection according to Pauta's rule, and data that does not meet the requirements is removed.
[0035] Samples with complete rolling cycle information were selected for training the virtual spatial convexity prediction model.
[0036] In the above embodiments, based on model-driven digital twin technology, and using the equipment parameters, real-time production data, historical quality data, and production plan data of the finishing mill, the associated mapping of the physical entity, virtual space, digital twin space, and functional application layer of convexity control is realized, providing a complete system framework for optimizing the accuracy of convexity control.
[0037] In some examples, hyperparameter optimization ensures the predictive stability of the virtual prediction model. In addition, samples are selected based on complete rolling cycle information, and a global-local collaborative learning strategy is developed to ensure that the model can extract the influence of production sequence and cumulative working conditions on crown control during training, effectively improving the model's accuracy and adaptability.
[0038] In some examples, the functional application layer of the digital twin system used for convexity control provides a scientific and stable optimization scheme for the control of key convexity parameters through the coordinated operation of three services: feature extraction, response testing, and iterative optimization. This effectively improves the accuracy of convexity control while ensuring the stable operation of the system. Attached Figure Description
[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0040] Figure 1 This is a schematic diagram of the structural framework of a model-driven digital twin system for strip convexity control according to an embodiment of the present invention.
[0041] Figure 2 This is a schematic diagram illustrating the operation flow of the model-driven strip convexity control method according to an embodiment of the present invention. Detailed Implementation
[0042] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the scope of protection of the present invention.
[0043] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains. Terms such as "comprising" or "including" mean that the elements, objects, methods, schemes, systems, or devices preceding the term encompass the elements, objects, methods, schemes, systems, or devices listed following the term, and their equivalents, but do not exclude other elements, objects, methods, schemes, systems, or devices.
[0044] This invention provides a model-driven digital twin system for controlling strip convexity, such as... Figure 1 As shown, it includes: a physical entity component, a digital twin data space component, a virtual space component, and a functional application layer component. The physical entity component includes at least rolling equipment and a crown control system. The digital twin data space component includes at least: a data acquisition unit and a data processing unit. The data acquisition unit is used to acquire equipment parameters, real-time production data, historical quality data, and production plan data of the hot strip mill finishing unit. The data processing unit is used to perform spatiotemporal transformation on the equipment parameters, real-time production data, historical quality data, and production plan data of the finishing mill to generate training samples for the virtual model.
[0045] In addition, the virtual space component includes at least a data-driven strip convexity prediction model to achieve accurate strip convexity prediction under small-batch, multi-specification production conditions. The functional application layer includes at least a feature extraction service for extracting the importance of parameters affecting convexity, a response testing service for determining the consistency of convexity control characteristics between the virtual model and the physical entity, and an iterative optimization service for optimizing key control parameters. The physical entity component, the virtual space component, and the functional application layer component are interconnected through the digital twin data space, forming an interactive framework through iterative optimization.
[0046] In the above embodiments, based on model-driven digital twin technology, and using the equipment parameters, real-time production data, historical quality data, and production plan data of the finishing mill, a correlation mapping between the physical entity, virtual space, digital twin space, and functional application layer of convexity control is achieved, providing a complete system framework for optimizing convexity control accuracy. Hyperparameter optimization ensures the predictive stability of the virtual prediction model. Furthermore, by selecting samples based on complete rolling cycle information and developing a global-local collaborative learning strategy, the model can extract the impact of production sequence and cumulative operating conditions on convexity control during training, effectively improving model accuracy and adaptability. The functional application layer of the digital twin system for convexity control, through the collaborative operation of feature extraction, response testing, and iterative optimization services, provides a scientific and stable optimization scheme for the control of key convexity parameters, effectively improving convexity control accuracy while ensuring stable system operation.
[0047] In some examples, the physical entity portion generates real-time states through data to update the virtual model of the virtual space portion and evaluate its accuracy. The virtual space portion provides feedback commands to ensure that the physical entity portion executes predefined process parameters. The normal operation and evolution of the virtual space portion are supported by services provided by the functional application layer portion. The functional application layer portion actively monitors the real-time states and data within the physical entity portion to formulate service requirements and provide corresponding services. These services are verified in the virtual space, and feedback with modification suggestions is provided to the functional application layer to improve the control accuracy of the strip convexity.
[0048] In some examples, the production planning data includes: strip steel grade, strip exit thickness, strip exit width, and target strip crown. The equipment parameters include: work roll shape parameters, work roll diameter, and support roll diameter. The real-time production data includes: intermediate slab crown, intermediate slab thickness, strip inlet temperature, finishing mill stand roll shifting position, finishing mill stand bending roll force, finishing mill stand rolling force, finishing mill stand work roll thermal expansion, and finishing mill stand work roll wear; the historical quality data includes crown full-length hit rate and measured strip crown values.
[0049] In some examples, the strip convexity prediction model in the virtual space portion is an XGBoost model. The virtual space portion includes at least: a data-driven strip convexity prediction model to achieve accurate prediction of strip convexity under small-batch, multi-specification production conditions. The virtual space uses XGBoost to construct the convexity prediction model.
[0050] This embodiment achieves accurate prediction of strip crown under small-batch, multi-specification production conditions, including:
[0051] The hyperparameter optimization of the model, the objective function, and the constraints are determined as follows:
[0052] Obj=f(min_child_weight,max_depth,learning_rate,colsample_bytree,subsample,D)
[0053] stmin_child_weight∈(0,0.15)
[0054] max_depth∈(2,80)
[0055] colsample_bytree∈(0,1]
[0056] learning_rate∈(0,0.15)
[0057] subsample∈(0,1]
[0058] Where Obj is the minimum root mean square error of the model, f is the XGBoost model function, D is the model input data, and min_child_weight, max_depth, colsample_bytree, learning_rate, and subsample are all hyperparameters of the model.
[0059] The global-local collaborative training strategy is optimized. Global training uses all historical data to train the model, ensuring the basic prediction accuracy of the model. Local training uses the steel grade and target convexity as selection criteria, selecting several samples similar to the current training order for training to improve the model's training adaptability. The final result of the model can be expressed as:
[0060] y = βy1 + (1-β)y2
[0061] Where y is the final prediction result of the model, y1 is the global training prediction result, y2 is the local training prediction result, and β is the model weight.
[0062] In some examples, in the functional application layer portion, the feature extraction service extracts the contribution of the input parameters to the convexity prediction model by considering the interaction between input parameters during model training, and sorts the input parameters from highest to lowest importance according to the contribution to extract important convexity control parameters.
[0063] In some examples, in the functional application layer portion, the response testing service, based on the principle of controlled variables, generates equidistant model response test samples by changing the way the convexity control parameters are extracted. The test samples are then input into the strip convexity prediction model in the virtual space portion to test the impact of the convexity control parameters on the convexity prediction results. The results are then compared with the strip convexity control characteristics in the physical entity portion to ensure the consistency between the predicted convexity control and the actual convexity control.
[0064] In some examples, in the functional application layer, the iterative optimization service uses the preset parameters issued by the convexity control model of the physical entity part as the input of the virtual convexity prediction model of the virtual space part, and compares the deviation with the target convexity as a benchmark. By continuously adjusting the key control parameters, the deviation between the calculation result of the virtual space convexity prediction model and the target convexity meets the requirements, so as to improve the convexity control accuracy.
[0065] In various embodiments of the present invention, a system for optimizing the control of strip convexity is constructed using model-driven digital twin technology, which can effectively improve the accuracy and adaptability of convexity control.
[0066] In addition, this invention also provides a model-driven method for controlling the convexity of a strip, combined with... Figure 2 As shown, it includes:
[0067] S1: Collect real-time data of the physical entity, including at least equipment parameters, real-time production data, historical quality data, and production plan data;
[0068] S2: Process the data, perform spatiotemporal transformation, and generate training samples for the strip convexity prediction model;
[0069] S3: Based on the training samples, train the strip crown prediction model, where the input of the crown prediction model is rolling process data and the output is the crown value of a single strip.
[0070] S4: Extract the contribution of input parameters to the convexity prediction model, and sort the input parameters from highest to lowest according to the importance of their contribution, and extract the important convexity control parameters.
[0071] S5: Generate model response test samples, input the test samples into the convexity prediction model of the plate, and test the influence of the convexity control parameters on the convexity prediction results;
[0072] S6: Compare the convexity prediction result generated by the convexity control parameters with the convexity control characteristics of the physical entity part of the strip, and perform iterative optimization;
[0073] S7: The preset parameters issued by the convexity control model are used as the input of the strip convexity prediction model. The output results are compared with the target convexity. Based on the deviation between the output results and the target convexity, the convexity control parameters are adjusted and optimized until they reach a reasonable deviation range. The convexity control parameters are then fed back to the control module of the physical system to improve the accuracy of convexity control.
[0074] The above embodiments utilize real-time process parameter data, historical quality data, and production plan information data of strip production to construct a virtual model for predicting strip convexity in virtual space. Based on the production plan information, the convexity of the product strip is predicted. According to the trained virtual model, feature importance is extracted at the functional application layer to determine the key parameters affecting convexity control. Model response testing is performed at the functional application layer to determine the consistency of the convexity control characteristics of the virtual model and the physical entity. Finally, the key parameters are optimized through an iterative optimization module, and the parameters are fed back to the control module of the physical system.
[0075] In some examples, the training samples for generating the strip convexity prediction model include:
[0076] S21: Perform outlier detection on the initial sample according to Pauta's rule and remove data that does not meet the requirements;
[0077] S22: Select samples with complete rolling cycle information for training the virtual space convexity prediction model.
[0078] The model-driven strip crown control method of the present invention extracts the contribution of input parameters to the crown prediction model through feature extraction service, and sorts the input parameters from high to low according to the importance of the contribution to extract important crown control parameters. Taking the bending roll force and roll position of the frame as examples, the extracted parameters are extracted parameters.
[0079] The above embodiments generate model response test samples by changing the bending roll force and shifting roll position of the frame at equal intervals through a response test service. These test samples are then input into a virtual space strip crown prediction model to test the influence of the bending roll force and shifting roll position of the frame on the crown prediction results. The results are then compared with the strip crown control characteristics of the physical entity to ensure consistency between the two.
[0080] Furthermore, the above embodiments use iterative optimization services to take the preset parameters issued by the convexity control model of the physical entity part as the input of the virtual convexity prediction model of the virtual space part, and compare the deviation with the target convexity as a benchmark. By continuously adjusting the key control parameters, the deviation between the calculation result of the virtual space convexity prediction model and the target convexity meets the requirements, thereby achieving the purpose of improving the convexity control accuracy.
[0081] It should also be noted that the above description represents a preferred embodiment of the present invention. It should be pointed out that although preferred embodiments of the present invention have been described, those skilled in the art, once they understand the basic inventive concept of the present invention, can make several improvements and modifications without departing from the principles described herein. These improvements and modifications should also be considered within the scope of protection of the present invention. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present invention.
Claims
1. A model-driven digital twin system for controlling the convexity of a strip on a board, characterized in that, include: The physical entity portion includes at least rolling equipment and a crown control system; The digital twin data space portion includes at least: a data acquisition unit and a data processing unit. The data acquisition unit is used to acquire equipment parameters, real-time production data, historical quality data, and production plan data of the hot strip mill finishing unit. The data processing unit is used to perform spatiotemporal transformation on the equipment parameters, real-time production data, historical quality data, and production plan data of the finishing mill unit to generate training samples for the virtual model. The virtual space component includes at least: a data-driven strip convexity prediction model to achieve accurate prediction of strip convexity under small-batch, multi-specification production conditions; The functional application layer includes at least: a feature extraction service for extracting the importance of parameters affecting convexity, a response testing service for determining the consistency of convexity control characteristics between the virtual model and the physical entity, and an iterative optimization service for optimizing key control parameters. The physical entity part, the virtual space part, and the functional application layer part are interconnected through the digital twin data space and form an interactive framework through iterative optimization.
2. The model-driven digital twin system for strip convexity control based on claim 1, characterized in that, The physical entity portion generates a real-time state through data to update the virtual model of the virtual space portion and evaluate its accuracy; The virtual space component provides feedback commands to ensure that the physical entity component executes predefined process parameters. The normal operation and evolution of the virtual space component are supported by the services provided by the functional application layer component. The functional application layer actively monitors the real-time status and data within the physical entity to formulate service requirements and provide corresponding services. The services are verified in the virtual space, and feedback on modification suggestions is provided to the functional application layer to improve the control accuracy of the board strip convexity.
3. The model-driven digital twin system for strip convexity control based on claim 1, characterized in that, The production plan data includes: strip steel grade, strip exit thickness, strip exit width, and strip target convexity; The equipment parameters include: working roll shape parameters, working roll diameter, and support roll diameter; The real-time production data includes: intermediate billet crown, intermediate billet thickness, strip inlet temperature, finishing mill stand roll shifting position, finishing mill stand bending roll force, finishing mill stand rolling force, finishing mill stand work roll thermal expansion, and finishing mill stand work roll wear. The historical quality data includes the full-length convexity hit rate and the measured convexity value of the strip.
4. The model-driven digital twin system for strip convexity control based on claim 1, characterized in that, In the virtual space portion, the strip convexity prediction model is the XGBoost model.
5. The model-driven digital twin system for strip convexity control based on claim 4, characterized in that, Building an XGBoost model also includes: Optimize the hyperparameters of the model and determine the objective function and constraints. The global-local collaborative training strategy is optimized. Global training uses all historical data to train the model to ensure the basic prediction accuracy of the model. Local training uses the steel grade and target convexity of the strip as the selection criteria and selects several samples similar to the current training order for training to improve the model's training adaptability. The final result of the model can be expressed as: y=βy1+(1-β)y2, where y is the final prediction result of the model, y1 is the global training prediction result, y2 is the local training prediction result, and β is the model weight.
6. The model-driven digital twin system for strip convexity control based on claim 1, characterized in that, In the functional application layer, the feature extraction service extracts the contribution of the input parameters to the convexity prediction model by considering the interaction between the input parameters during model training, and sorts the input parameters from highest to lowest according to the importance of the contribution, so as to extract important convexity control parameters.
7. The model-driven digital twin system for strip convexity control based on claim 6, characterized in that, In the functional application layer, the response testing service, based on the principle of controlled variables, generates equidistant model response test samples by changing the way the convexity control parameters are extracted. The test samples are then input into the strip convexity prediction model in the virtual space section to test the impact of the convexity control parameters on the convexity prediction results. The results are compared with the strip convexity control characteristics in the physical entity section to ensure the consistency between the predicted convexity control and the actual convexity control.
8. The model-driven digital twin system for strip convexity control based on claim 1, characterized in that, In the functional application layer, the iterative optimization service uses the preset parameters issued by the convexity control model of the physical entity as input to the virtual convexity prediction model of the virtual space, and compares the deviation with the target convexity as a benchmark. By continuously adjusting the key control parameters, the deviation between the calculation result of the virtual space convexity prediction model and the target convexity meets the requirements, thereby improving the convexity control accuracy.
9. A model-driven method for controlling the convexity of a strip, characterized in that, include: Collect real-time data of the physical entity, including at least equipment parameters, real-time production data, historical quality data, and production plan data; The data is processed, spatiotemporal transformation is performed, and training samples for the strip convexity prediction model are generated. Based on the training samples, a strip crown prediction model is trained. The input of the crown prediction model is rolling process data, and the output is the crown value of a single strip. Extract the contribution of input parameters to the convexity prediction model, and sort the input parameters from highest to lowest according to the importance of their contribution, and extract the important convexity control parameters. Generate model response test samples, input the test samples into the convexity prediction model, and test the influence of the convexity control parameters on the convexity prediction results; The convexity prediction results generated by the convexity control parameters are compared with the convexity control characteristics of the physical entity plate and strip, and iterative optimization is performed. The preset parameters issued by the convexity control model are used as input to the strip convexity prediction model. The output results are compared with the target convexity. Based on the deviation between the output results and the target convexity, the convexity control parameters are adjusted and optimized until they reach a reasonable deviation range. The convexity control parameters are then fed back to the control module of the physical system to improve the accuracy of convexity control.
10. The model-driven strip convexity control method according to claim 9, characterized in that, The training samples for the generated plate convexity prediction model include: Outlier detection is performed on the initial sample according to Pauta's rule to remove data that does not meet the requirements; Samples with complete rolling cycle information were selected for training the virtual spatial convexity prediction model.
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