A method for predicting the change trend of the liquid level of molten steel in a VD furnace

Abstract

This invention discloses a method for predicting the changing trend of molten steel level in a VD furnace, relating to the field of iron and steel metallurgy. The method includes: acquiring multi-source time-series data of the refining process in a VD furnace over historical periods, as well as the actual molten steel level at each historical moment; combining the multi-source time-series data, along with instantaneous change rates and historical sliding window statistics constructed based on the multi-source time-series data, to obtain a historical feature vector; inputting the historical feature vector into an extreme gradient boosting model, training the model with the objective of minimizing the root mean square error between the predicted and actual molten steel level, to obtain a dynamic prediction model for the molten steel level; and inputting the real-time feature vector into the dynamic prediction model to obtain the predicted molten steel level for future moments and perform decision control. This invention effectively overcomes the subjective errors of manual experience-based judgment in existing technologies, significantly improving the accuracy of predicting the changing trend of molten steel level in a VD furnace.

Description

Technical Field

[0001] This invention relates to the field of iron and steel metallurgy technology, and in particular to a method for predicting the changing trend of molten steel level in a VD furnace. Background Technology

[0002] VD furnace refining is a key process for improving steel quality. Its core lies in achieving deep degassing and composition adjustment of molten steel through precise control of the vacuum level inside the ladle and the bottom-blown argon gas. During this process, the surface of the molten steel fluctuates rapidly and non-linearly due to the violent escape of gas.

[0003] In current technical practice, the control process of the VD furnace liquid level monitoring method is as follows: When the liquid level in the VD furnace rises rapidly due to the vacuum degassing reaction, the operator must first visually judge the approximate height of the liquid level through the observation hole under the interference of high temperature, smoke and flame; then, based on personal experience, the operator judges whether the current rate of rise is dangerous and considers how much to reduce the argon flow rate or how much to close the vacuum valve; finally, the operator manually rotates the adjustment knob or issues adjustment commands through the control system interface, and the commands are then transmitted to the actuator (such as the valve positioner) via PLC (Programmable Logic Controller) to perform physical actions.

[0004] Existing methods for monitoring the liquid level in VD furnaces rely on the subjective decisions of operators. The control effect depends entirely on the individual's experience level, concentration, and on-site condition, resulting in significant individual differences and temporal fluctuations in process stability. It is difficult to guarantee the accuracy of predicting the trend of changes in the liquid level height in VD furnaces. Summary of the Invention

[0005] Therefore, it is necessary to provide a method for predicting the changing trend of the molten steel level in a VD furnace, addressing the aforementioned technical problems.

[0006] This invention provides a method for predicting the changing trend of molten steel level in a VD furnace, comprising: Acquire multi-source time-series data of the VD furnace refining process during historical periods, as well as the actual liquid level height at each historical moment; Based on multi-source time-series data, instantaneous rate of change is constructed to characterize the dynamic trend of liquid level and vacuum pressure at historical moments, and historical sliding window statistics are constructed to characterize the fluctuation characteristics of liquid level height and vacuum pressure at historical moments. The multi-source time-series data, instantaneous rate of change and historical sliding window statistics are combined to obtain a historical feature vector to characterize the dynamic change law of liquid level. The historical feature vector is input into the extreme gradient boosting model. The goal is to minimize the root mean square error between the predicted liquid level height and the actual liquid level height output by the extreme gradient boosting model. The extreme gradient boosting model is then trained to obtain a dynamic prediction model for the liquid level of molten steel for predicting the liquid level height at future moments. During the real-time operation of the VD furnace, the real-time feature vector obtained from real-time multi-source time-series data is input into the dynamic prediction model of molten steel level to obtain the predicted value of the liquid level height at future moments, and the VD furnace is controlled based on the predicted value of the liquid level height.

[0007] Optionally, based on multi-source time-series data, instantaneous rate of change for characterizing the dynamic trends of liquid level and vacuum pressure at historical moments, and historical sliding window statistics for characterizing the fluctuation characteristics of liquid level height and vacuum pressure at historical moments are constructed, specifically including: Multi-source time-series data, including: vacuum tank pressure, bottom-blown argon flow rate, vacuum valve opening, and liquid level; The first-order difference of the liquid level height is used as the first instantaneous rate of change to characterize the dynamic trend of the liquid level at historical moments, based on the following formula: ; The first-order difference of the pressure inside the vacuum tank is used as the second instantaneous rate of change to characterize the dynamic trend of the vacuum pressure at historical moments, based on the following formula: ; in, The rate of change at the first instant is... for t The liquid level at any given moment. for t The liquid level at time -1 The second instantaneous rate of change, for t The pressure inside the vacuum tank at any given time. for t Pressure inside the vacuum tank at time -1 T is the time interval between two adjacent samples; The first historical sliding window statistic, used to characterize the fluctuations in liquid level at historical moments, is determined based on the following formula: ; The second historical sliding window statistic, used to characterize the fluctuations in vacuum pressure at historical moments, is determined based on the following formula: ; in, This is the first historical sliding window statistic. This is the second historical sliding window statistic. The sampling interval is... iThis is the time index offset from the current moment when going back to the past. This represents the number of sampling points within the sliding window. This represents the average value of the vacuum pressure within the same window.

[0008] Optionally, based on the following formula, multi-source time-series data, instantaneous rate of change, and historical sliding window statistics are combined to obtain a historical feature vector characterizing the dynamic changes in the liquid surface: ; in, For historical feature vectors, for t The pressure inside the vacuum tank at any given time. for t The bottom-blown argon flow rate at any given time. for t The opening degree of the vacuum valve at any given moment. for t The liquid level at any given moment. for t The rate of change at the first instant of time, for t The second instantaneous rate of change at time t, for t The first historical sliding window statistics at any given moment for t The second historical sliding window statistics at any given time.

[0009] Optionally, historical feature vectors are input into the extreme gradient boosting model, with the objective of minimizing the root mean square error between the predicted liquid level height output by the extreme gradient boosting model and the actual liquid level height. Specifically, this includes: The predicted liquid level height output by the extreme gradient boosting model is determined based on the following formula: ; The root mean square error between the predicted liquid level and the actual liquid level output by the extreme gradient boosting model is determined based on the following formula: ; in, To predict liquid level height x ( t ) t The feature vector at time step, K The total number of regression trees in the ensemble model For the first k Regression trees, RMSE is the root mean square error. To determine the number of samples in the validation set, For the extreme gradient boosting model, the first iPredicted liquid level height for each sample For the first i The actual liquid level height of each sample.

[0010] Optionally, the extreme gradient boosting model is trained, specifically including: A strategy combining grid search and forward validation is used to optimize the model's hyperparameters, including the number of ensemble trees, maximum tree depth, and learning rate. Randomized training strategies are introduced during the end-to-end optimization training process. These randomized training strategies include: row subsampling strategy and feature sampling strategy. The row subsampling strategy includes: when training each decision tree, randomly selecting samples with a preset row subsampling rate from all training samples to construct the current tree; The feature sampling strategy includes: when training each decision tree, randomly sampling features from all feature dimensions at a preset feature sampling rate to find the optimal split point.

[0011] Optionally, when training an extreme gradient boosting model, an early stopping mechanism is introduced as a regularization strategy, specifically including: After each iteration, the root mean square error of the extreme gradient boosting model on the independent validation set is determined. When the root mean square error does not show significant improvement in several consecutive iterations, the training process is automatically terminated.

[0012] Optionally, decision control of the VD furnace is performed based on the predicted liquid level, specifically including: Preset the upper and lower safe operating thresholds for liquid level; When the predicted liquid level is greater than the upper limit threshold for safe operation or less than the lower limit threshold for safe operation, an alarm is immediately triggered and control commands are automatically generated and issued according to preset rules. The preset rules include at least one of the following: proportional adjustment rules, trend compensation rules, stage adaptive rules, and multivariate collaborative rules; Control commands include adjusting the target gas flow rate or the target vacuum valve opening.

[0013] Optionally, it also includes an online update step for the dynamic prediction model of molten steel level, specifically including: The actual liquid level data generated under control commands will be used as new training samples. The current initial dynamic prediction model of molten steel liquid level will be incrementally learned through the new training samples to obtain the optimized dynamic prediction model of molten steel liquid level. When the optimized dynamic prediction model of molten steel level meets the preset switching conditions, the initial dynamic prediction model of molten steel level will be replaced with the optimized dynamic prediction model of molten steel level; if the preset switching conditions are not met, the model will not be replaced. The preset switching conditions include: the root mean square error of the optimized molten steel level dynamic prediction model is reduced by more than a set threshold compared with the initial molten steel level dynamic prediction model, or the mean absolute percentage error of the optimized molten steel level dynamic prediction model is lower than the preset engineering acceptable threshold. The mean absolute percentage error of the optimized dynamic prediction model for molten steel level is determined based on the following formula: ; in, MAPE The mean absolute percentage error, To preset an acceptable threshold for the project, These are the predicted values ​​from the initial dynamic prediction model for molten steel levels. The predicted values ​​are from the optimized dynamic prediction model for molten steel levels.

[0014] The method for predicting the trend of molten steel level in a VD furnace provided in this embodiment of the invention has the following advantages compared with the prior art: This invention accurately characterizes the dynamic trends of liquid level and vacuum pressure through instantaneous rate of change, capturing the instantaneous response characteristics during the refining process; and describes the fluctuation characteristics and historical patterns of liquid level height and vacuum pressure over a period of time through sliding window statistics. By combining these two features, which deeply reflect the dynamic evolution of the liquid level, with original multi-source time-series data, a feature vector is constructed to train an extreme gradient boosting model. This allows the extreme gradient boosting model to fully learn the dynamic evolution logic of the VD furnace operating conditions, enabling it to predict future liquid level height based on real-time data. This effectively overcomes the subjective errors of manual experience-based judgment in existing technologies, thereby significantly improving the accuracy of predicting the trend of molten steel liquid level height changes in VD furnaces. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating a method for predicting the changing trend of molten steel level in a VD furnace, as provided in one embodiment. Figure 2 This is a trend comparison chart of a method for predicting the changing trend of molten steel level in a VD furnace, provided in one embodiment. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0017] In current technical practices, there are significant problems of perception and decision-making lag in the VD furnace liquid level monitoring system. The core issue is that the source information of the entire control closed-loop completely depends on the real-time measurement of the current liquid level height by sensors or cameras. However, this measurement is essentially a record of the occurred state. Any operation and adjustment based on this data, whether it is the calculation of an automated system or the manual intervention of an operator, can only be a "post hoc" reactive compensation for historical results. This mode is particularly prominent when relying on manual experience: operators have to make rough visual judgments with the naked eye through an observation hole with limited vision and harsh environment, under the strong interference of high temperature, smoke, and boiling flames, and then manually adjust the valves according to personal experience. This process not only has low accuracy and poor reliability in the perception link, but also leads to inevitable delays due to the long link from observation, thinking to execution, making the entire control process essentially in an open-loop or strongly lagged closed-loop state, and it is difficult to cope with the challenges of rapid non-linear changes in the liquid level.

[0018] This process has three fundamental limitations: First, the decision-making is highly subjective, and the control effect completely depends on the operator's experience, concentration, and on-site state, resulting in significant fluctuations in process stability with people and time periods, and the observation is easily interfered by the environment; second, the perception accuracy is poor, and the human eye is difficult to distinguish liquid level changes at the millimeter level; third, the response delay is long. From detecting changes, thinking and making decisions to manual operations, the entire link takes much longer than the actual rising speed of the liquid level. Especially when a large amount of gas escapes violently at the initial stage of vacuum pumping, the best control opportunity is often missed.

[0019] As Figure 1 shown, the embodiment of the present invention provides a method for predicting the change trend of the molten steel liquid level height in a VD furnace. The method includes: Obtain multi-source time-series data during the refining process of the VD furnace in a historical period and the corresponding actual liquid level height at each historical moment.

[0020] Based on the multi-source time-series data, construct an instantaneous change rate for characterizing the dynamic trend of the liquid level and vacuum pressure at historical moments and a historical sliding window statistic for characterizing the fluctuation characteristics of the liquid level height and vacuum pressure at historical moments. Combine the multi-source time-series data, the instantaneous change rate, and the historical sliding window statistic to obtain a historical feature vector for characterizing the dynamic change law of the liquid level.

[0021] Input the historical feature vector into the extreme gradient boosting model, and train the extreme gradient boosting model with the goal of minimizing the root mean square error between the predicted liquid level height output by the extreme gradient boosting model and the actual liquid level height, to obtain a molten steel liquid level dynamic prediction model for predicting the liquid level height at future moments.

[0022] During the real-time operation of the VD furnace, the real-time feature vector obtained from real-time multi-source time-series data is input into the dynamic prediction model of molten steel level to obtain the predicted value of the liquid level height at future moments, and the VD furnace is controlled based on the predicted value of the liquid level height.

[0023] A specific embodiment of the present invention is provided: S10: Acquire multi-source time-series data of the VD furnace within a preset time period, including data such as refining time, bottom-blown argon flow rate, and real-time liquid level.

[0024] S20: Perform preprocessing operations such as cleaning, alignment, and missing value removal on the time series data to transform the original dataset into a well-organized, trainable dataset.

[0025] S30: Based on the preprocessed multidimensional dataset, the target prediction model is trained using the xgboost regression algorithm.

[0026] S40: Load the pre-trained liquid level prediction model, take the real-time collected process feature vectors as input, and output the predicted value of the molten steel liquid level height in the future specified time domain.

[0027] S50: The predictive model can be iteratively updated online based on the historical database.

[0028] First, multi-source time-series data of the VD furnace refining process are acquired within a preset time period, including key process parameters such as refining time, bottom-blown argon flow rate, vacuum tank pressure, vacuum valve opening, molten steel temperature, and real-time liquid level.

[0029] Subsequently, the collected raw time series data is preprocessed by cleaning, alignment and missing value imputation to remove outliers and noise interference, and the data sequences with different sampling frequencies are aligned to the same time base to generate a regular, complete and structured dataset suitable for training machine learning models.

[0030] Based on this, using the preprocessed multidimensional dataset, the Extreme Gradient Boosting (XGBoost) regression algorithm is employed for model training. By optimizing the loss function and adjusting hyperparameters, a target prediction model that accurately reflects the dynamic changes in the molten steel surface is constructed. During the model deployment phase, the system loads this pre-trained model, using real-time collected process feature vectors as input. Through forward computation, the model outputs a predicted value of the molten steel surface height within a specified future time domain (e.g., 5–30 seconds), providing a decision-making basis for proactive control.

[0031] In addition, to enable continuous optimization of the model and adaptation to changes in operating conditions, it can support online incremental learning and iterative updates of the prediction model based on historical production data, thereby ensuring that it maintains high prediction accuracy and robustness in long-term operation.

[0032] A specific embodiment of the present invention is provided: Based on the fusion of simulation data and historical production data, the environmental and operating condition changes of the actual VD furnace refining process are simulated to verify the feasibility and effectiveness of this method in the task of predicting the height of molten steel.

[0033] S10: Collect raw multi-source time-series data during the VD furnace steelmaking process, clean and preprocess the raw data, and output the preprocessed dataset. The collected multi-source time-series data includes: 1. Furnace information: Furnace number, timestamp, and relative refining time (seconds).

[0034] If the production data only contains timestamps and does not include relative refining time, then a relative time data column that meets the model requirements can be generated based on the timestamps.

[0035] 2. Process parameters: bottom-blown argon flow rate (unit: L / min), vacuum pressure (unit: mbar), vacuum valve opening (unit: %).

[0036] 3. Liquid level monitoring data: Real-time liquid level height (unit: mm), sampling frequency is 1Hz.

[0037] S20: Based on the characteristics of industrial process data and the needs of machine learning modeling, systematic preprocessing and feature construction are performed on the acquired raw multi-source time series data, specifically including the following steps: 1. Based on the physical constraints and process knowledge of the VD refining process, perform data cleaning and quality assurance preprocessing on the available time-series data: 1.1 Boundary verification: Based on the equipment design parameters and process safety range, set reasonable upper and lower limits for each key variable (such as non-negative argon flow rate, liquid level not exceeding the effective volume height of the vacuum tank, etc.) and eliminate abnormal records that obviously violate physical laws.

[0038] 1.2 Missing Value Handling: For random missing values ​​that occur during data acquisition, linear interpolation between adjacent time points is used to fill them in to ensure temporal continuity. For segments with consecutive missing values ​​for more than 5 seconds, considering the potential changes in process conditions, the average historical operating conditions of the same steel grade and similar refining stages are used to fill them in to maintain the consistency of process logic.

[0039] 1.3 Outlier Detection and Handling: After missing value imputation, a sliding window-based 3D model is used. Statistical principles are used to detect outliers in the data: for each key process parameter, based on the most recent... Calculate the moving average for each valid sample. and standard deviation It will exceed Data points within the specified range were marked as anomalies. After secondary verification using process knowledge, linear interpolation was used to replace the anomalies. (Window length) The value can be adjusted according to the specific production line characteristics and steel grade process requirements. The typical range is 20 to 60. This embodiment uses... (For example).

[0040] 1.4 Multi-frequency data synchronization: To address the issue of heterogeneous sampling frequencies of different sensors (for example, if the vacuum pressure acquisition frequency is 0.5Hz and the liquid level monitoring frequency is 1Hz, a linear interpolation method is used to uniformly resample all variables to a 1Hz time base), ensuring strict alignment of timestamps for multi-source data.

[0041] 1.5 Spatiotemporal Alignment and Integration: All process parameter sequences and liquid level monitoring data are precisely aligned along a unified time axis to construct a multidimensional structured time-series dataset indexed by time and synchronized with multiple variables.

[0042] 2. Construction of Feature Engineering: 2.1 Extracting the current moment from a historical time period t Original parameters: (1) Pressure inside the vacuum tank , in mbar / Pa.

[0043] (2) Bottom-blown argon flow rate , in L / min.

[0044] (3) Vacuum valve opening ,unit%.

[0045] (4) Liquid level , unit mm.

[0046] 2.2 Calculate its first difference as the instantaneous rate of change: (5) The first instantaneous rate of change: represents the instantaneous rate of change of the liquid level (unit: mm / s).

[0047] ; in, for t The liquid level at any given moment. for t The liquid level at time -1.

[0048] (6) The second instantaneous rate of change: represents the instantaneous rate of change of vacuum pressure (unit: mbar / s).

[0049] ; in, for t The pressure inside the vacuum tank at any given time. for t Pressure inside the vacuum tank at time -1.

[0050] Among them (5) and (6) T is the sampling frequency (i.e., the time interval between two adjacent samples), which is set according to the system's sampling frequency in this embodiment. =1s.

[0051] 2.3 Calculate historical sliding window statistics: (7) : Represents the first historical sliding window statistic (sliding average of liquid level height, unit: mm, and...) H ( t )same).

[0052] ; in, This represents the number of sampling points within the sliding window. The sampling interval is 1 second in this embodiment. i This is the time index offset from the current moment when traversing back to history. i When =0, H ( t ) represents the current liquid level height. This corresponds to the oldest sampling point within the window. This feature characterizes the liquid surface at the most recent... The average position over a second reflects the short-term baseline level of the process.

[0053] (8) : Indicates the second historical sliding window statistic (sliding standard deviation of vacuum pressure, unit mbar).

[0054] ; in, The average value of the vacuum pressure within the same window quantifies the severity of recent fluctuations in vacuum pressure and can serve as an indicator of system stability or anomalous disturbances.

[0055] 2.4 Construction of statistical features of sliding window and determination of window parameters.

[0056] To further enhance the model's ability to perceive dynamic trends in the process, statistical features based on historical time windows are constructed. The number of sampling points within the sliding window is also considered. (corresponding time span) The determination of the following criteria (by calculating the average value of all sampling points within the window, high-frequency noise can be effectively smoothed, and the baseline trend of liquid level change in short-term history can be extracted) is as follows:

[0057] The principle of dynamic process matching is that the window time span should cover the typical physical response time of the molten steel surface in the VD furnace to changes in process parameters. Based on the kinetic analysis of processes such as gas rise and molten steel flow, this response time is approximately 20-50 seconds.

[0058] Data characteristics guiding principle: Time series analysis of historical liquid level data shows that its autocorrelation function decays significantly after a lag of about 30 seconds, indicating that historical information within this time scale has strong predictive value for the current state.

[0059] System design coordination principle: The window length should be coordinated with the prediction time domain (5 seconds in this example). To predict short-term changes in the future, the model needs to be aware of historical trends over a longer period, and the window length is usually set to 3-10 times the prediction time domain.

[0060] Based on the above principles, this embodiment selects a window length. (That is, the time span is 30 seconds).

[0061] 2.5 The original parameters, instantaneous rate of change, and historical sliding window statistics mentioned above are combined to form the final historical feature vector. : ; in, For historical feature vectors, for t The pressure inside the vacuum tank at any given time. for t The bottom-blown argon flow rate at any given time. for t The opening degree of the vacuum valve at any given moment. for t The liquid level at any given moment. for t The rate of change at the first instant of time, for t The second instantaneous rate of change at time t, for t The first historical sliding window statistics at any given moment for t The second historical sliding window statistics at any given time.

[0062] This vector fully integrates the static state variables and dynamic gradient information of the system, providing a high-information-density input feature space for subsequent time series prediction models.

[0063] S30: Model building and training.

[0064] To objectively evaluate the model's temporal generalization ability in real industrial scenarios, the dataset is divided into training, validation, and test sets in chronological order. In this embodiment, a dataset of 20 batches is obtained, with the first 10 batches used as the training set, the middle 5 batches as the validation set, and the last 5 batches as the test set.

[0065] Based on the preprocessed high-dimensional time-series feature dataset, a dynamic prediction model for molten steel level is constructed using the XGBoost ensemble learning algorithm. This model utilizes the aforementioned constructed feature vectors. x ( t ( ) as input, with future t Actual liquid level at any given time H ( t + t The goal of supervision is to perform end-to-end optimization training by minimizing a preset loss function (such as mean squared error).

[0066] 1. Based on the preprocessed original dataset described above, an extreme gradient boosting (XGBoost) algorithm is used to construct a prediction model. The model's prediction output is the sum of the predictions from multiple regression trees, mathematically represented as follows: ; Predicting the liquid level height. During model training, this will involve... The actual liquid level after 1 second is taken as the current moment. t The system predicts the liquid level height in seconds, but only uses it as a reference value for training predictions, not to directly copy the results.

[0067] x ( t ): t The feature vector at any given moment (such as the pressure inside the vacuum tank, the flow rate of bottom-blown argon gas, the opening degree of the vacuum valve, and the current liquid level).

[0068] : K The total number of regression trees in the ensemble model represents the total number of regression trees in the model. K The core mathematical expression of the XGBoost model is to sum the prediction results of each regression tree.

[0069] : Represents the first k A tree that has returned to its natural habitat. Each tree It is a simple piecewise constant function (mapping the input feature space to the predicted value). It divides the input feature space into multiple mutually exclusive regions (leaf nodes) and assigns a fixed predicted value (leaf node weight) to each region.

[0070] 2. In one specific implementation of this embodiment, the prediction time domain is... The time interval is set to 5 seconds, which means constructing a time-series extrapolation model to predict the liquid level height 5 seconds later. It should be understood that the prediction time domain can be flexibly configured according to specific process requirements and control response time, for example, it can be extended to different time scales such as 10 seconds, 20 seconds or 30 seconds, to adapt to the control requirements of different refining stages.

[0071] 3. Performance Monitoring and Early Stopping Mechanism: Optionally, to improve the model's generalization ability and suppress the risk of overfitting, this embodiment introduces a performance monitoring and early stopping mechanism based on an independent validation set as the core regularization strategy during training. Specifically, after each iteration (i.e., adding a new regression tree), the model updates its parameters on the training set and simultaneously performs forward inference on the independently reserved validation set to calculate the current model's prediction performance metrics on the validation set.

[0072] 3.1 In this embodiment, the specific performance indicator selected is the root mean square error (RMSE). RMSE The calculation formula is as follows: ; in, To determine the number of samples in the validation set, For the extreme gradient boosting model, the first i Predicted liquid level height for each sample For the first i The actual liquid level height of each sample.

[0073] RMSE The metrics are recorded in real time and used to quantify the model's generalization error. When the validation set performance metrics ( RMSE No significant improvement was observed in several consecutive iterations (e.g., 20 iterations). RMSE The decrease was less than the preset threshold. ,for example When the training process is completed, the training process will automatically terminate.

[0074] The core advantage of this mechanism lies in the fact that it shifts the model training process from solely pursuing goodness of fit on the training set to using an independent validation set as an objective benchmark for generalization performance. This ensures that the final model version is optimally performed on unseen data, rather than being the result of overfitting to training noise. This mechanism effectively prevents the model from overfitting to noise and random fluctuations on the training set, ensuring that the learned patterns possess good extrapolation stability. In addition... RMSE In addition, performance monitoring metrics may include commonly used evaluation metrics for regression tasks such as mean absolute error and coefficient of determination, or combinations thereof, to evaluate model performance from multiple dimensions.

[0075] 4. The XGBoost model includes several key hyperparameters that can be specifically tuned according to the characteristics of industrial data and the requirements of the prediction task. The following section, using the specific implementation of this embodiment, explains the basis for setting each core parameter:

[0076] 4.1 Number of Ensemble Trees: This parameter determines the learning capacity and complexity of the model. For the medium-sized industrial time-series dataset involved in this embodiment (typically containing tens of thousands to hundreds of thousands of sample points; this embodiment selects representative data from 20 heats for validation, corresponding to approximately 72,000 samples, covering different steel grades and different refining stages, meeting the training requirements of the XGBoost model for medium-sized data; in practical applications, it supports adding new heats to expand the training set), the number of ensemble trees is preferably in the range of 100 to 500. Too few trees can easily lead to underfitting of the model, making it difficult to fully capture process dynamics; too many trees may cause overfitting and significantly increase computational overhead. For example, this embodiment uses 200 regression trees to construct the ensemble model, achieving a good balance between prediction accuracy and computational efficiency.

[0077] 4.2 Maximum Tree Depth: This parameter controls the structural complexity and nonlinear representation capability of a single decision tree. For industrial processes with moderate nonlinearity, such as VD furnace liquid level prediction, a tree depth of 6 to 8 layers is preferred. Shallower depths (e.g., 3-5 layers) can enhance model robustness, but may be insufficient to characterize complex process coupling relationships; excessively deep trees (e.g., more than 10 layers) are prone to overfitting local noise in the training data. This embodiment, optimized through cross-validation, adopts a maximum depth of 7 layers, balancing the model's expressiveness and generalization performance.

[0078] 4.3 Learning Rate (also known as the shrinkage factor): This parameter controls the contribution weight of each newly added tree to the final prediction of the ensemble model, and is key to balancing convergence speed and optimization accuracy. A smaller learning rate (e.g., 0.01-0.1) makes the optimization process smoother and helps to obtain more accurate local optima, but requires a corresponding increase in the number of ensemble trees to ensure sufficient learning. In this embodiment, considering both prediction accuracy requirements and training efficiency, the learning rate is set to 0.03. This configuration ensures stable model convergence while achieving high-precision fitting of the dynamic features of the process by appropriately increasing the number of iterations (i.e., the number of ensemble trees).

[0079] 5. Randomization strategies to enhance model robustness.

[0080] To improve the model's robustness to data noise and abnormal fluctuations, and to prevent overfitting to specific samples or features, this embodiment further introduces the following randomization training strategy. This strategy introduces randomness into the construction of each tree, forcing the model to learn data from different perspectives, thereby building a more stable and more generalizable ensemble model.

[0081] 5.1 Row sampling strategy.

[0082] The subsampling rate is set to 0.8. When training each decision tree, this strategy randomly selects 80% of the samples from all training data to build the current tree, while the remaining 20% ​​are temporarily ignored during the training of that tree. The core function is to reduce the model's oversensitivity to specific samples in the training data, reduce model variance, and effectively alleviate overfitting.

[0083] 5.2 Feature sampling strategy.

[0084] The feature sampling rate is set to 0.8. When training each decision tree, this strategy randomly selects 80% of the features from all feature dimensions and uses only these selected features to find the optimal split point. Its core function is to increase the diversity of decision trees in the ensemble model, forcing the model to learn patterns from different feature combinations, thereby enhancing the model's overall stability and generalization ability on unknown data.

[0085] 6. Hyperparameter optimization for grid search and forward validation.

[0086] To further enhance the robustness and generalization ability of the model, this model can also employ a strategy combining grid search and forward validation to optimize the key hyperparameters of the XGBoost model. This strategy systematically traverses the key hyperparameters of the XGBoost model within a predefined reasonable search space. Considering the strict temporal dependence of VD furnace production data, the evaluation process adopts a forward validation method: data is divided according to furnace time sequence, historical furnace data is always used for training, and validation is performed on future furnace data that immediately follows in time. This simulates the inference scenario when the model is actually deployed, ensuring that the performance evaluation truly reflects its predictive ability for unknown operating conditions.

[0087] In this embodiment, the optimization process uses the root mean square error (RMSE) of the forward validation set as the core evaluation metric, automatically selecting the hyperparameter combination with the minimum validation error as the final model configuration. Optionally, the selection of core evaluation metrics includes, but is not limited to, root mean square error; commonly used evaluation metrics for regression tasks, such as mean absolute error and coefficient of determination, or combinations thereof, can also be used to evaluate parameter performance from multiple dimensions.

[0088] This method comprehensively evaluates parameter performance by dividing historical data into continuous-future segments, effectively improving the stability and reliability of parameter selection and avoiding the subjectivity and randomness of manual parameter adjustment. It is especially suitable for complex production environments with diverse working conditions and varying steel grades.

[0089] S40: A framework for industrial deployment and real-time operation of predictive models.

[0090] This embodiment provides a possible specific implementation method for integrating a fully trained XGBoost liquid level prediction model into an actual VD furnace control system, realizing a full-process industrial application from offline modeling to online decision-making.

[0091] 1. Model service encapsulation and system integration.

[0092] To meet the real-time and reliability requirements of industrial sites, the optimal prediction model obtained through training (i.e., the model version with the best performance monitoring index data on the validation set) needs to be encapsulated as a service and embedded as an independent functional module into the existing VD furnace control system architecture. In one specific implementation:

[0093] (1) Serialize the model parameters and structure into a standardized format file (such as JSON) and deploy it in the real-time computing unit or edge server of the control system.

[0094] (2) The model is encapsulated as a prediction microservice with standard input and output specifications. It receives real-time data streams and returns prediction results through a preset application programming interface, thereby achieving seamless integration with existing platforms such as host computer monitoring systems and distributed control systems.

[0095] 2. Online data stream processing and real-time feature construction.

[0096] During the online prediction phase, the system synchronously acquires raw process parameters from various sensors at a fixed frequency (e.g., 1Hz), including vacuum pressure, bottom-blown argon flow rate, vacuum valve opening, and real-time liquid level. The acquired raw data stream immediately enters a preprocessing pipeline consistent with the training phase, performing data cleaning and quality assurance preprocessing operations in step S20 in real time. This ensures that the construction logic of the online feature vectors is completely consistent with that of the offline training phase, guaranteeing the identical distribution of the model input space.

[0097] 3. Model forward computation and prediction output.

[0098] The constructed multidimensional feature vectors are fed into the pre-trained XGBoost model in real time for forward inference. The model performs computation in the aforementioned additive model format:

[0099] ; in, This represents the optimal number of trees determined by the early stopping mechanism. The system outputs the predicted liquid level height at future time steps. In one specific configuration of this embodiment, The interval is set to 5 seconds, meaning the system continuously outputs the estimated liquid level for the next 5 seconds, forming a continuous prediction trajectory.

[0100] 4. Empirical evidence and error analysis of predictive performance.

[0101] To verify the effectiveness of this method under actual operating conditions, continuous operation evaluation was conducted in a representative test furnace. The system made rolling predictions of the liquid level height for the next 5 seconds at a frequency of 1Hz, accumulating thousands of prediction-actual data pairs. Performance statistics show:

[0102] (1) Overall accuracy: The average absolute deviation between the predicted value and the actual monitored value is 1.8 mm, indicating that the model has extremely high prediction accuracy under steady-state and slowly changing working conditions.

[0103] (2) Dynamic tracking capability: During the rapid fluctuation of liquid level caused by step changes in bottom blowing argon flow rate and rapid adjustment of vacuum, the model can still effectively capture dynamic trends, and the instantaneous prediction error is strictly controlled within 4.5 mm, which proves its good fitting and generalization ability for nonlinear and fast time-varying processes.

[0104] 5. Visualization of prediction results and human-computer interaction applications.

[0105] In one feasible case, the prediction results can be fed back to the user interface in a multimodal manner, forming a closed loop of intelligent decision-making in human-machine collaboration: 5.1 Graphical trend display.

[0106] Real-time prediction curve: Two superimposed curves are dynamically drawn at a high refresh rate on the human-computer interface, such as... Figure 2 As shown: one line represents the historical trajectory of the liquid level as monitored in real time, and the other line represents the future trajectory output by the model. The predicted trajectory extends to the second. Contrasting colors are used to differentiate the two, visually demonstrating the degree of agreement between the prediction and the actual measurement.

[0107] Trend status label: The system is based on the slope of the predicted sequence (e.g., for...). and H ( t (Performs linear discrimination) and automatically generates and highlights three types of qualitative trend labels: "rising", "falling" or "stable", to assist operators in making quick situation judgments.

[0108] 5.2 Early warning and proactive intervention mechanism.

[0109] Threshold warning: Based on the vacuum tank design parameters and process safety regulations, preset upper and lower safety operating thresholds for liquid level in the system. and When the predicted value The system immediately triggers an alarm when the safety threshold is exceeded. For example, based on the effective volume of the vacuum tank (e.g., 1500 mm²), the threshold is set... (80% of the effective volume) (To avoid exposing the molten steel nozzle), the relevant areas of the operation interface flash warning colors, and the part of the predicted curve that exceeds the threshold is highlighted; at the same time, the audible and visual alarm is triggered to attract the attention of the operator.

[0110] This early warning system, based on predictions of future conditions, provides operators or automated control systems with a more proactive approach compared to traditional alarms based on current measured values. A two-second intervention window. For example, if it is predicted that the liquid level will overflow in 5 seconds, the system will immediately sound an alarm, giving operators or automatic control logic sufficient time to adjust the argon flow rate or the vacuum valve opening, thereby preventing the risk from occurring.

[0111] 6. Linked with commands from the control system.

[0112] In a more integrated implementation, the prediction module can directly interact with the underlying actuators: When spillover risk is predicted ( When the system is activated, it not only alarms, but also automatically generates and issues adjustment commands in advance based on preset rules or advanced control algorithms (such as model predictive control), such as reducing the set value of bottom blowing argon flow, to achieve a fully automatic closed loop from "prediction-early warning" to "prediction-control".

[0113] Preset rules include, but are not limited to: 1. Proportional adjustment rule: Based on the deviation between the predicted overflow amount and the safety threshold, the bottom blowing argon flow rate is adjusted according to a preset proportional coefficient.

[0114] 2. Trend compensation rule: Based on the rate of change of liquid level, a differential compensation term is added to the proportional adjustment.

[0115] 3. Stage Adaptive Rule: The adjustment coefficient is dynamically adjusted according to the refining stage.

[0116] 4. Multi-variable coordination rule: While adjusting the argon flow rate, coordinate the adjustment of the vacuum valve opening, pressure relief valve status, etc.

[0117] For example, when the predicted overflow is ≤5mm, the reduction in argon flow rate is: (L / min); when the predicted overflow is >5mm, multivariate collaborative control is triggered, and measures such as significantly reducing the argon flow rate and appropriately opening the vacuum valve are taken.

[0118] Through the above deployment and application, this method successfully transforms the XGBoost data-driven prediction model into a stable and reliable online industrial service, realizing advanced perception and proactive safety control of changes in the molten steel level in the VD furnace.

[0119] S50: Online iterative update mechanism for the model.

[0120] To further enhance the robustness and environmental adaptability of the prediction system during long-term operation, this embodiment provides an online iterative update and version management mechanism for the model. This mechanism aims to address the problem of input data distribution drift caused by factors such as adjustments to production processes, equipment performance degradation, and changes in raw material characteristics, ensuring that the prediction model can continuously track and adapt to dynamically changing industrial processes.

[0121] 1. In one possible implementation, an incremental learning strategy can be adopted to enable continuous optimization of the model without interrupting the online prediction service.

[0122] 1.1 During continuous operation, the system automatically archives newly added, quality-verified production process data to the historical database. Update training is not triggered in real time, but rather automatically starts according to preset strategies (such as during system idle periods or fixed low-load periods each day) to avoid impacting the computing resources of the real-time control system.

[0123] 1.2 When starting the update task, the system calls the incremental learning interface provided by the XGBoost framework. This process uses the currently deployed online model as the initial state and performs a limited number of iterative training rounds using only the newly added data as training samples. The newly added data must follow the preprocessing and feature construction process of S20 to ensure that the feature space is consistent with the historical training data. The core advantage of this method is:

[0124] 1.2.1 Strictly maintain the same feature engineering process and input vector dimensions as the base model to avoid model failure due to changes in feature definitions.

[0125] 1.2.2 The model is not retrained from scratch. Instead, it is fine-tuned on the basis of the existing knowledge structure (i.e., the constructed tree ensemble) by adding new trees or adjusting the weights of existing leaf nodes. This allows it to efficiently absorb new patterns contained in new data while retaining the knowledge of historical conditions.

[0126] 1.2.3 Compared to full retraining, incremental learning significantly reduces computation time and resource consumption, making it more suitable for routine operation and maintenance in industrial settings.

[0127] 2. After completing the incremental training, a rigorous performance evaluation of the optimized version of the molten steel surface dynamic prediction model is required to determine whether to deploy it online.

[0128] The following quantitative decision-making process is adopted: 2.1 Evaluation dataset: A separate model validation set is created from recent (e.g., the past week) new data that was not used in this training to fairly evaluate the generalization ability of the model before and after optimization.

[0129] 2.2 Core Performance Metrics: Calculate the root mean square error of the optimized prediction model on the validation set (RMSE). The root mean square error of the initial molten steel level dynamic prediction model on the same validation set ( ).

[0130] 2.3 Core Decision Criteria: Decision conditions are set to trigger version switching. If one of the following conditions is met, the optimized model is determined to have significantly better performance than the initial model, and a model update can be triggered: 2.3.1 Relative Lifting Criterion: That is, the optimized model. RMSE The accuracy was reduced by more than 5% compared to the unoptimized model, which is considered a significant improvement in prediction accuracy.

[0131] 2.3.2 Absolute accuracy criterion: The mean absolute percentage error of the optimized model on the validation set ( MAPE (Below the preset acceptable engineering threshold) (For example, setting) ).

[0132] ; MAPE The prediction accuracy is measured directly from the perspective of relative error, which is especially suitable for scenarios where the liquid level itself may change. These are the predicted values ​​from the initial dynamic prediction model for molten steel levels. The predicted values ​​are from the optimized dynamic prediction model for molten steel levels.

[0133] 3. Version switching and rollback protection.

[0134] 3.1 Seamless Switching: When the optimized model meets the switching conditions, the system automatically loads it into the prediction service, replacing the initial model and achieving a smooth upgrade of the online service version.

[0135] Version 3.2 Rollback: Before each model update, the system automatically performs a full snapshot backup of the current online model and its configuration files. If, after the optimized model is deployed, performance anomalies or systematic prediction deviations are detected during short-term trial operation monitoring (such as through real-time monitoring of the residuals between predictions and measured values), the system supports one-click quick rollback to any historical stable version, maximizing production safety and system availability.

[0136] 3.3 Data Management: All model versions are associated with and stored with corresponding training data time periods, hyperparameter configurations, performance evaluation reports and other metadata, forming a complete model lifecycle management archive.

[0137] By implementing the above-mentioned online iterative update mechanism, the concept drift problem in the industrial environment can be effectively addressed, enabling the prediction model to have continuous self-optimization and self-adaptation capabilities. This ensures that the model maintains high-precision predictive performance throughout the long-term operation of the VD furnace, providing sustained technical support for long-term production stability and intelligent upgrading.

[0138] This embodiment constructs and verifies a complete technical closed loop of "data acquisition → feature engineering → model building → online prediction → continuous optimization," systematically demonstrating that the intelligent prediction and control method for molten steel level in VD furnace based on XGBoost possesses both significant technological advancement and engineering practical value. Firstly, through multi-source heterogeneous data fusion processing, it achieves synchronous acquisition, cleaning, alignment, and deep feature derivation of multi-modal time-series data such as vacuum pressure, argon flow rate, valve opening, and liquid level, constructing a high-dimensional, high-information-density model input space that includes instantaneous values, first-order rates of change, and sliding window statistics.

[0139] Based on this, an extreme gradient boosting algorithm is used to construct a prediction model, which can accurately characterize the nonlinear dynamic evolution of the molten steel level in the VD furnace as process parameters change.

[0140] In this embodiment, the system operates stably at a frequency of 1Hz, achieving high-precision rolling prediction of the liquid level height for the next 5 seconds. The measured average absolute deviation is 1.8mm, and the maximum instantaneous error does not exceed 4.5mm under severe fluctuation conditions. Furthermore, through an online iterative update mechanism based on incremental learning and performance monitoring, the system possesses the ability to autonomously evolve and continuously adapt to process drift, ensuring sustained high-performance prediction.

[0141] Compared to existing single static feature prediction methods, this solution uses feature fusion of "dynamic change rate + sliding window statistics" to reduce the model's capture delay of rapidly changing liquid surface characteristics to less than 1 second. Compared to existing control methods that rely on hysteresis measurement and human experience, this solution provides accurate advance prediction information, shifting the control decision point from "post-event compensation" to "pre-event intervention," gaining valuable reaction time windows, thus significantly improving control accuracy and process safety, and effectively suppressing large fluctuations in liquid surface and the risk of steel spillage. Furthermore, this solution can be integrated into existing control systems without large-scale hardware modifications, achieving low-cost, highly flexible intelligent upgrades.

[0142] The model prediction method used in this embodiment not only provides real-time decision-making basis for the precise process control of VD furnace, but its output continuous prediction trajectory and dynamic characteristics can also serve equipment status monitoring and early fault warning, providing a technical paradigm with broad promotion value for the industry's digital transformation and intelligent upgrading.

[0143] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for predicting the changing trend of molten steel level in a VD furnace, characterized in that, include: Acquire multi-source time-series data of the VD furnace refining process during historical periods, as well as the actual liquid level height at each historical moment; Based on the multi-source time-series data, instantaneous rate of change is constructed to characterize the dynamic trend of liquid level and vacuum pressure at historical moments, and historical sliding window statistics are constructed to characterize the fluctuation characteristics of liquid level height and vacuum pressure at historical moments. The multi-source time-series data, the instantaneous rate of change, and the historical sliding window statistics are combined to obtain a historical feature vector to characterize the dynamic change law of liquid level. The historical feature vector is input into the extreme gradient boosting model. The extreme gradient boosting model is trained with the goal of minimizing the root mean square error between the predicted liquid level height output by the extreme gradient boosting model and the actual liquid level height, so as to obtain a dynamic prediction model of molten steel liquid level for predicting the liquid level height at future moments. During the real-time operation of the VD furnace, the real-time feature vector obtained from real-time multi-source time-series data is input into the dynamic prediction model of the molten steel level to obtain the predicted value of the liquid level height at future moments, and the VD furnace is controlled based on the predicted value of the liquid level height.

2. The method for predicting the changing trend of molten steel level in a VD furnace as described in claim 1, characterized in that, Based on the multi-source time-series data, the instantaneous rate of change for characterizing the dynamic trends of liquid level and vacuum pressure at historical moments, and historical sliding window statistics for characterizing the fluctuation characteristics of liquid level height and vacuum pressure at historical moments are constructed, specifically including: The multi-source time-series data includes: pressure inside the vacuum tank, bottom-blown argon flow rate, vacuum valve opening degree, and liquid level height; The first-order difference of the liquid level height is used as the first instantaneous rate of change to characterize the dynamic trend of the liquid level at historical moments, based on the following formula: ； The first-order difference of the pressure inside the vacuum tank is used as the second instantaneous rate of change to characterize the dynamic trend of the vacuum pressure at historical moments, based on the following formula: ； in, The rate of change at the first instant is... for t The liquid level at any given time. for t The liquid level at time -1 The second instantaneous rate of change, for t The pressure inside the vacuum tank at any given time. for t Pressure inside the vacuum tank at time -1 T is the time interval between two adjacent samples; The first historical sliding window statistic, used to characterize the fluctuations in liquid level at historical moments, is determined based on the following formula: ； The second historical sliding window statistic, used to characterize the fluctuations in vacuum pressure at historical moments, is determined based on the following formula: ； in, This is the first historical sliding window statistic. This is the second historical sliding window statistic. The time interval between two adjacent samples. i This is the time index offset from the current moment when going back to the past. This represents the number of sampling points within the sliding window. This represents the average value of the vacuum pressure within the same window.

3. The method for predicting the changing trend of molten steel level in a VD furnace as described in claim 2, characterized in that, The following formula is used to combine the multi-source time-series data, the instantaneous rate of change, and the historical sliding window statistics to obtain a historical feature vector characterizing the dynamic change pattern of the liquid surface: ； in, For historical feature vectors, for t The pressure inside the vacuum tank at any given time. for t The bottom-blown argon flow rate at any given time. for t The opening degree of the vacuum valve at any given time. for t The liquid level at any given time. for t The rate of change at the first instant of time, for t The second instantaneous rate of change at time , for t The first historical sliding window statistics at any given moment for t The second historical sliding window statistics at any given time.

4. The method for predicting the changing trend of molten steel level in a VD furnace as described in claim 1, characterized in that, The step of inputting the historical feature vector into the extreme gradient boosting model, with the objective of minimizing the root mean square error between the predicted liquid level height output by the extreme gradient boosting model and the actual liquid level height, specifically includes: The predicted liquid level height output by the extreme gradient boosting model is determined based on the following formula: ； The root mean square error between the predicted liquid level height output by the extreme gradient boosting model and the actual liquid level height is determined based on the following formula: ； in, To predict liquid level height x ( t ) t The feature vector at time step, K The total number of regression trees in the ensemble model For the first k A tree of return, RMSE Root mean square error To determine the number of samples in the validation set, For the extreme gradient boosting model, the first i Predicted liquid level height for each sample For the first i The actual liquid level height of each sample.

5. The method for predicting the changing trend of molten steel level in a VD furnace as described in claim 1, characterized in that, The training of the extreme gradient boosting model specifically includes: A strategy combining grid search and forward validation is used to optimize the model's hyperparameters, which include the number of ensemble trees, maximum tree depth, and learning rate. A randomized training strategy is introduced during the end-to-end optimization training process. The randomized training strategy includes: row subsampling strategy and feature sampling strategy. The row subsampling strategy includes: when training each decision tree, randomly selecting samples with a preset row subsampling rate from all training samples to construct the current tree; The feature sampling strategy includes: when training each decision tree, randomly selecting features with a preset feature sampling rate from all feature dimensions to find the optimal split point.

6. The method for predicting the changing trend of molten steel level in a VD furnace as described in claim 5, characterized in that, When training the extreme gradient boosting model, an early stopping mechanism is introduced as a regularization strategy, specifically including: After each iteration, the root mean square error of the extreme gradient boosting model on the independent validation set is determined. When the root mean square error does not show significant improvement in several consecutive iterations, the training process is automatically terminated.

7. The method for predicting the changing trend of molten steel level in a VD furnace as described in claim 1, characterized in that, The decision-making control of the VD furnace based on the predicted liquid level height specifically includes: Preset the upper and lower safe operating thresholds for liquid level; When the predicted liquid level is greater than the upper limit threshold for safe operation or less than the lower limit threshold for safe operation, an alarm is immediately triggered and a control command is automatically generated and issued according to preset rules. The preset rules include at least one of the following: proportional adjustment rules, trend compensation rules, stage adaptive rules, and multivariate collaborative rules; The control commands include adjusting the target gas flow rate or the target vacuum valve opening.

8. The method for predicting the changing trend of molten steel level in a VD furnace as described in claim 1, characterized in that, It also includes an online update step for the dynamic prediction model of molten steel level, specifically including: The actual liquid level data generated under the control command is used as new training samples. The current initial dynamic prediction model of molten steel liquid level is incrementally learned through the new training samples to obtain the optimized dynamic prediction model of molten steel liquid level. When the optimized dynamic prediction model of molten steel level meets the preset switching conditions, the initial dynamic prediction model of molten steel level will be replaced with the optimized dynamic prediction model of molten steel level; if the preset switching conditions are not met, the model will not be replaced. The preset switching conditions include: the root mean square error of the optimized molten steel surface dynamic prediction model is reduced by more than a set threshold compared with the initial molten steel surface dynamic prediction model, or the average absolute percentage error of the optimized molten steel surface dynamic prediction model is lower than a preset engineering acceptable threshold. The mean absolute percentage error of the optimized dynamic prediction model for molten steel level is determined based on the following formula: ； in, MAPE The mean absolute percentage error, To preset an acceptable threshold for the project, These are the predicted values ​​from the initial dynamic prediction model for molten steel levels. The predicted values ​​are from the optimized dynamic prediction model for molten steel levels.

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