A slab longitudinal crack prediction method for unbalanced samples

Abstract

The present application relates to the technical field of steelmaking continuous casting, and is a slab longitudinal crack prediction method for unbalanced samples, comprising: collecting process parameter time series data and thermocouple temperature data; extracting the temperature time series of each thermocouple; extracting the statistical features of process parameters from the process parameter time series data; extracting the temperature features of the thermocouples from the temperature time series, and selecting a key area, and extracting the spatial aggregation features from the temperature time series of the key area; constructing a feature data set, and dividing the feature data set into a training set and a test set; calculating the weight by using an adaptive weighted mixed oversampling technology, and determining the synthetic samples to be generated according to the weight; introducing a physical constraint to check whether the generated synthetic samples are reasonable; using a LightGBM classifier to construct a slab state prediction model, outputting the slab state by using the trained slab state prediction model, and realizing slab longitudinal crack prediction. The present application can predict the slab state through the causes of longitudinal cracks.

Description

Technical Field

[0001] This invention relates to the field of steelmaking continuous casting technology, and in particular to a method for predicting longitudinal cracks in slabs from unbalanced samples. Background Technology

[0002] Continuous casting is a core process in modern steel production, and the surface quality of the slab directly determines the performance and yield of the final product. Among these defects, longitudinal cracks are one of the most common and harmful. They can lead to the downgrading or scrapping of a large number of products, and in severe cases, even cause steel leakage accidents, resulting in huge economic losses and production safety hazards. Therefore, achieving early and accurate prediction of longitudinal cracks in slabs, thereby guiding process adjustments and preventing the occurrence of defects, has extremely important industrial application value.

[0003] Currently, data-driven machine learning methods have become the mainstream research direction for solving this problem. Most existing solutions collect multi-dimensional process parameters (casting speed, superheat, water volume in each zone of the secondary cooling section, crystallizer vibration parameters, protective slag performance, and crystallizer thermocouple temperature) as features during continuous casting production, and use the presence or absence of longitudinal cracks in the offline detection results of the slab as labels to construct a supervised learning classification model, such as Support Vector Machine (SVM), Random Forest, Gradient Boosting Tree (XGBoost), or deep learning models.

[0004] However, in actual industrial production, the number of normal slabs far exceeds that of defective slabs. Normal slabs typically account for over 95%, even exceeding 99%, while defective samples with longitudinal cracks account for an extremely low percentage. This extreme imbalance in sample class distribution can severely bias machine learning models. To address this imbalance, traditional techniques use random under-sampling to randomly remove some samples from the majority class (normal samples) to achieve class balance. This approach loses a large number of samples that may contain important information, potentially leading to underfitting and insufficient information utilization.

[0005] In summary, existing imbalance handling methods, especially the direct application of the standard SMOTE, are insufficient to effectively address the imbalance classification problem of continuous casting process data, which exhibits strong temporal characteristics and multi-parameter coupling. Therefore, there is an urgent need for an improved method tailored to the characteristics of industrial time-series data to construct a high-performance slab longitudinal crack prediction model. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method for predicting longitudinal cracks in slabs using unbalanced samples. This invention addresses the critical issue of the severe imbalance between the number of normal and crack samples in continuous casting production process data, which leads to the failure of prediction models. It constructs a feature dataset, utilizes adaptive weighted mixed oversampling technology to generate synthetic samples, and trains a slab state prediction model using these synthetic samples to achieve slab state prediction.

[0007] The technical means employed in this invention are as follows:

[0008] A method for predicting longitudinal cracks in slabs using unbalanced samples includes: collecting time-series data of process parameters and thermocouple temperature data, and recording the state of the slab; recording the residence time of each slab in the crystallizer, and extracting the temperature time series of each thermocouple; extracting statistical features of the process parameters from the time-series data of the process parameters; extracting the temperature features of the thermocouples from the temperature time series, selecting key regions, and extracting spatial aggregation features from the temperature time series of the key regions; constructing a feature dataset using the statistical features of the process parameters and the temperature features of the thermocouples, and dividing the feature dataset into a training set and a test set; calculating weights using an adaptive weighted mixed oversampling technique, and determining the synthetic samples to be generated based on the weights; introducing physical constraints to verify the rationality of the generated synthetic samples; constructing a slab state prediction model using a LightGBM classifier, training the slab state prediction model using 5-fold cross-validation, and outputting the slab state using the trained slab state prediction model to achieve longitudinal crack prediction in the slab.

[0009] Furthermore, the acquisition frequency of the thermocouple temperature data is higher than that of the process parameter time series data. During the data acquisition process, the time of all systems is synchronized to ensure that the process parameters and temperature data at the same moment correspond accurately. The data of each slab is divided from the time of casting start to the time of leaving the crystallizer. The state of the slab includes normal and longitudinal crack.

[0010] Furthermore, the recording of the residence time of each slab in the crystallizer and the extraction of the temperature time series of each thermocouple specifically includes: for each slab, based on the average drawing speed... and the effective length of the crystallizer Calculate the residence time in the crystallizer. :

[0011] The residence time of the slab in the crystallizer The window is defined as the portion of the screen that is captured after the slab pouring start signal is triggered. Temperature data from each sampling point:

[0012] in, The frequency of thermocouple temperature data acquisition is determined by using... The temperature data from each sampling point constitutes the temperature time series of each thermocouple in the slab.

[0013] Furthermore, the statistical characteristics of the process parameters include: casting speed, primary cooling water volume, secondary cooling water volume, tundish temperature, and superheat, wherein: the casting speed is used to calculate the mean, standard deviation, and maximum value of the casting speed sequence within the slab casting cycle; the primary and secondary cooling water volumes are used to calculate the mean and standard deviation of the water volume sequence; the tundish temperature is used to calculate the mean, minimum, and standard deviation of the temperature sequence; and the superheat is calculated using the liquidus temperature of the steel grade and the tundish temperature, and the mean of the sequence is taken.

[0014] Furthermore, the temperature characteristics of the thermocouple include: maximum temperature, average temperature, temperature standard deviation, maximum temperature rise rate, and abnormal peak count; the maximum temperature... The average temperature represents the maximum temperature. The temperature represents the average temperature, and the temperature standard deviation represents the average temperature. The maximum rate of temperature rise is used to characterize temperature fluctuations. Used to identify the presence of crack tips:

[0015] in, Represents a temperature time series. Indicates time; When counting abnormal spikes S, a dynamic threshold is used. Defined as:

[0016] The number of times the temperature time series exceeds the dynamic threshold is counted as the abnormal spike count S; The critical region is determined based on statistical analysis of thermocouple temperature data. The critical region is a heat-sensitive area where longitudinal cracks are prone to initiation and manifestation. The spatial aggregation characteristics include the highest temperature in the critical region, the maximum rate of temperature rise in the critical region, and the average temperature difference in the critical region.

[0017] Furthermore, the construction of the feature dataset specifically includes: constructing a multi-dimensional feature vector using the statistical characteristics of the process parameters, the temperature characteristics of the thermocouples, and the spatial aggregation characteristics, representing each slab as a multi-dimensional feature vector. Each multidimensional feature vector corresponds to a binary label. ,when When, it indicates that the slab is in normal condition. When, it indicates that the slab is in a state with longitudinal cracks; the multidimensional feature vector With binary tags The feature dataset is constructed by establishing a one-to-one correspondence.

[0018] Further, the weights include density weights, boundary weights, and comprehensive weights, wherein: the density weight is obtained by calculating the average distance between each crack sample and its k nearest neighbor samples with longitudinal cracks in the multidimensional feature space, and the reciprocal of the average distance is used as the density weight; the boundary weight is obtained by calculating the proportion of each crack sample to the majority class of its m nearest neighbor samples; the comprehensive weight is a weighted sum of the density weight and the boundary weight, which is then normalized to determine the sampling weight of each crack sample; the physical constraint verification includes the following constraint conditions: standard deviation of tension speed. Maximum rate of temperature rise The temperature of the tundish is greater than the liquidus temperature of the steel grade; the highest temperature in the critical area is less than the melting point of the molten steel; if the generated synthetic sample violates the constraints, the synthetic sample is regenerated until a synthetic sample that meets all physical constraint verifications is obtained.

[0019] Furthermore, the slab state prediction model outputs the corresponding slab state by calculating the multidimensional feature vector of the slab.

[0020] Compared with the prior art, the present invention has the following advantages: The method for predicting longitudinal cracks in slabs using unbalanced samples provided by this invention integrates low-frequency process parameters with high-frequency temperature signals across frequencies and scales. This method includes both the process causes that lead to cracks and the temperature symptoms at the time of crack occurrence, thus achieving a unified modeling of the causes and manifestations of longitudinal cracks.

[0021] The feature engineering of this invention is highly targeted and interpretable, precisely focusing on nine thermocouple-sensitive regions that have been verified in industrial practice. The extracted features, such as the maximum rise rate and the number of abnormal spikes, have clear physical meanings and directly correspond to billet shell tearing and molten steel overflow. This makes the model decision-making process no longer a black box and provides a direct direction for process optimization.

[0022] The core algorithm of this invention is highly innovative. The AWH-SMOTE algorithm effectively solves the problem of extreme imbalance in industrial data. Its introduced physical constraint verification mechanism ensures that the data augmentation process conforms to the principles of metallurgy, and the generated samples are reasonable and effective, which greatly improves the generalization ability and prediction accuracy of the model.

[0023] The present invention has good forecasting performance and the scheme design fits the production rhythm. The forecast is made immediately after the slab exits the crystallizer. The forecast results have sufficient timeliness and high application value for adjusting subsequent processes and guiding the judgment of casting slabs. It can effectively reduce missed detections and misjudgments, and improve product quality and yield. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a flowchart of the method for predicting longitudinal cracks in slabs with unbalanced samples in this invention.

[0026] Figure 2 This is a comparison chart of the processing performance of the present invention with and without balancing processing, with standard SMOTE processing, and with the processing method of the present invention. Detailed Implementation

[0027] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0028] 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 clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0030] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0031] like Figure 1 As shown, this invention provides a method for predicting longitudinal cracks in slabs with unbalanced samples, including: collecting time-series data of process parameters and thermocouple temperature data, and recording the state of the slab; in a preferred embodiment of this invention, the collection frequency of thermocouple temperature data is higher than that of time-series data of process parameters. During the data collection process, the time of all systems is synchronized to ensure that the process parameters and temperature data at the same moment correspond accurately. The data of each slab is divided from the start time of its casting to the end time of leaving the crystallizer. The state of the slab includes normal and longitudinal crack.

[0032] Process parameter timing data were collected and recorded at a frequency of 1 Hz. Temperature data from all 156 thermocouples were collected and recorded at a frequency of 10 Hz; the higher frequency was to ensure that the rapidly changing temperature spikes during the occurrence of longitudinal cracks could be captured.

[0033] The residence time of each slab in the crystallizer is recorded, and the temperature time series of each thermocouple is extracted. In a preferred embodiment of the invention, for each slab, the average drawing speed is used to determine the temperature time series. and the effective length of the crystallizer Calculate the residence time in the crystallizer. :

[0034] The residence time of the slab in the crystallizer The window is defined as the portion of the screen that is captured after the slab pouring start signal is triggered. Temperature data from each sampling point:

[0035] in, The frequency of thermocouple temperature data acquisition is determined by using... The temperature data from each sampling point constitutes the temperature time series of each thermocouple in the slab, thereby ensuring that the characteristic data of each slab completely covers the process inside its crystallizer.

[0036] The statistical characteristics of process parameters are extracted from the time-series data of process parameters. In a preferred embodiment of the present invention, the statistical characteristics of process parameters include: casting speed, primary cooling water volume, secondary cooling water volume, tundish temperature, and superheat. Among them, the casting speed is used to calculate the mean, standard deviation, and maximum value of the casting speed sequence within the slab casting cycle; the primary and secondary cooling water volumes are used to calculate the mean and standard deviation of the water volume sequence; the tundish temperature is used to calculate the mean, minimum, and standard deviation of the temperature sequence; and the superheat is calculated by the liquidus temperature of the steel grade and the tundish temperature, and the mean of the sequence is taken.

[0037] Temperature features of thermocouples are extracted from temperature time series, and key regions are selected to extract spatial aggregation features from the temperature time series of the key regions. Specifically, in a preferred embodiment of this invention, the temperature features of the thermocouples include: maximum temperature, average temperature, temperature standard deviation, maximum temperature rise rate, and abnormal peak count; maximum temperature... Indicates the maximum temperature and the average temperature. This represents the average temperature and the standard deviation of the temperature. Used to characterize temperature fluctuations, maximum rate of temperature rise. Used to identify the presence of crack tips:

[0038] in, Represents a temperature time series. Indicates time; When counting abnormal spikes S, a dynamic threshold is used. Defined as:

[0039] The number of times the temperature time series exceeds the dynamic threshold is counted as the abnormal spike count S; The critical area was determined based on statistical analysis of thermocouple temperature data. During implementation, nine thermocouples in rows 1-3 and columns 5-7 of the wide face were precisely selected as the core monitoring points. This area, located below the meniscus and in the center of the cast billet, is a thermally sensitive zone where longitudinal cracks are most likely to initiate and manifest. Spatial aggregation characteristics include the highest temperature in the critical area, the maximum rate of temperature rise in the critical area, and the average temperature difference in the critical area.

[0040] A feature dataset is constructed using the statistical characteristics of process parameters and the temperature characteristics of thermocouples, and this dataset is divided into a training set and a test set. In a preferred embodiment of this invention, a multidimensional feature vector is constructed using the statistical characteristics of process parameters, the temperature characteristics of thermocouples, and spatial aggregation characteristics, representing each slab as a multidimensional feature vector. Each multidimensional feature vector corresponds to a binary label. ,when When, it indicates that the slab is in normal condition. When, it indicates that the slab is in a state with longitudinal cracks; the multidimensional feature vector With binary tags A one-to-one correspondence was established to construct the feature dataset. The dimensions of X include: 11 process statistical features, 5 features of 9 thermocouples, and 3 spatial aggregation features.

[0041] An adaptive weighted hybrid oversampling technique is used to calculate weights and determine the synthetic samples to be generated based on these weights. Physical constraints are introduced to verify the rationality of the generated synthetic samples. In a preferred embodiment of this invention, the weights include density weights, boundary weights, and a comprehensive weight. The density weight is obtained by calculating the average distance between each crack sample and its k nearest neighbors with longitudinal cracks in the multidimensional feature space, and the reciprocal of the average distance is used as the density weight; isolated points have higher density weights. The boundary weight is obtained by calculating the proportion of each crack sample to the majority class of its m nearest neighbors; samples closer to the classification boundary have higher boundary weights. The comprehensive weight is a weighted sum and normalized sum of the density weights and boundary weights, used to determine the sampling weight for each crack sample.

[0042] For each sample to be generated, randomly select one from its k=5 nearest neighbors, perform linear interpolation in the feature space, and add a small Gaussian noise. .

[0043] Physical constraint verification includes the following constraints: standard deviation of tension speed. Maximum rate of temperature rise The tundish temperature is greater than the liquidus temperature of the steel grade; the highest temperature in the critical zone is less than the melting point of the molten steel; if the generated synthetic sample violates the constraints, a new synthetic sample is generated until a synthetic sample that meets all physical constraint verifications is obtained. The generated synthetic crack samples are merged with the original training set to form a class-balanced training set.

[0044] A slab state prediction model is constructed using the LightGBM classifier and trained using 5-fold cross-validation. The trained slab state prediction model outputs the slab state to predict longitudinal cracks in the slab. In a preferred embodiment of this invention, the slab state prediction model calculates the multidimensional feature vector of the slab and outputs the corresponding slab state.

[0045] The advantages of using the LightGBM classifier lie in its high efficiency and speed in processing tabular data of moderate dimensionality, its automatic handling of feature interactions, and its provision of feature importance ranking. Five-fold cross-validation is used for model training and stability verification. Bayesian optimization is used for hyperparameter tuning, with the optimization objective being to maximize the F1-Score. The output is a well-trained, high-performance longitudinal crack prediction model.

[0046] The preprocessing pipeline (including feature extraction logic) and the trained model are integrated and deployed on the continuous casting process control server. For the currently cast slab, after it has completely passed through the crystallizer, the system automatically acquires its complete process sequence and temperature sequence data of 9 key thermocouples. The same feature engineering code as in the training phase is called to calculate the multidimensional feature vector of the slab in real time. The multidimensional feature vector is input into the model, and the model outputs a slab state: 0 indicates normal, and 1 indicates the presence of longitudinal cracks.

[0047] Example This invention is a method for predicting longitudinal cracks in slabs using unbalanced samples. This embodiment uses the production data of a steel plant's slab continuous casting machine in a certain year as an example for illustration.

[0048] S1. Data Acquisition and Preprocessing A total of 38,500 qualified slab records were collected, of which 197 slabs were confirmed to have longitudinal cracks, representing a positive sample rate of 0.51%. In chronological order, the first 30,700 slabs were used as the training set (containing 157 cracked slabs), and the last 7,800 slabs were used as the test set (containing 40 cracked slabs). Statistical features of process parameters and thermocouple temperature characteristics were extracted, resulting in 11 statistical features used as input.

[0049] S2. Imbalanced Sample Processing Based on AWH-SMOTE AWH-SMOTE was applied to the training set to synthesize 157 crack samples to a number comparable to the normal sample size (30,700), thus generating a balanced training set.

[0050] S3, Model Training Using LightGBM, the optimal parameter combination was obtained through Bayesian optimization, achieving an average F1-Score of 0.93 with 5-fold cross-validation. On a test set of 7800 slabs that were not used in training, the model's prediction performance is as follows: Longitudinal crack recall rate = 100%, successfully predicting 40 out of 40 cracked billets; The longitudinal crack precision was 91%, with 45 cracks detected, of which 40 were true and 4 were false alarms. The F1-Score was 0.95 and the AUC-ROC was 0.98.

[0051] Compared to the mode without balancing on the same test set, and the scheme using standard SMOTE, as shown in Table 1 and Figure 2 As shown, the F1-Score of the method of the present invention is improved by 0.24 and 0.13 respectively, which is a significant effect.

[0052] Table 1. Performance comparison of processing without balancing, using standard SMOTE processing, and using the present invention.

[0053] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A slab longitudinal crack prediction method for unbalanced samples, characterized by, include: Collect process parameter timing data and thermocouple temperature data, and record the state of the slab; Record the residence time of each slab in the crystallizer and extract the temperature time series of each thermocouple, specifically including: For each slab, the residence time in the crystallizer is calculated from the average casting speed and the effective length of the crystallizer :​ The residence time of the slab in the crystallizer The window is defined as the portion of the screen that is captured after the slab pouring start signal is triggered. Temperature data from each sampling point: in, The frequency of thermocouple temperature data acquisition is determined by using... The temperature data from each sampling point constitutes the temperature time series of each thermocouple in the slab. Extract statistical features of the process parameters from the time-series data of the process parameters; The temperature features of the thermocouples are extracted from the temperature time series, and key regions are selected to extract spatial aggregation features from the temperature time series of the key regions. The temperature characteristics of the thermocouple include: maximum temperature, average temperature, temperature standard deviation, maximum rate of temperature rise, and abnormal peak count; the maximum temperature... The average temperature represents the maximum temperature. The temperature represents the average temperature, and the temperature standard deviation represents the average temperature. The maximum rate of temperature rise is used to characterize temperature fluctuations. Used to identify the presence of crack tips: in, Represents a temperature time series. Indicates time; When counting abnormal spikes S, a dynamic threshold is used. Defined as: The number of times the temperature time series exceeds the dynamic threshold is counted as the abnormal spike count S; The key area was determined based on statistical analysis of thermocouple temperature data. Nine thermocouples in rows 1-3 and columns 5-7 of the wide face were selected as core monitoring points. The core monitoring points are located below the meniscus and in the center of the billet, which is the heat-sensitive area where longitudinal cracks are most likely to initiate and appear. The spatial aggregation characteristics include the highest temperature in the key area, the maximum rate of temperature rise in the key area, and the average temperature difference in the key area. A feature dataset is constructed using the statistical characteristics of the process parameters and the temperature characteristics of the thermocouples, and the feature dataset is divided into a training set and a test set; An adaptive weighted hybrid oversampling technique is used to calculate weights and determine the synthetic samples to be generated based on the weights; physical constraints are introduced to verify whether the generated synthetic samples are reasonable. A slab state prediction model is constructed using the LightGBM classifier, and the slab state prediction model is trained using 5-fold cross-validation. The trained slab state prediction model is then used to output the slab state, thereby realizing the prediction of longitudinal cracks in the slab.

2. The method for predicting longitudinal cracks in slabs using unbalanced samples according to claim 1, characterized in that, The thermocouple temperature data acquisition frequency is higher than the process parameter time series data. During the data acquisition process, the time of all systems is synchronized to ensure that the process parameters and temperature data at the same moment correspond accurately. The data of each slab is divided from the casting start time to the time of leaving the crystallizer. The state of the slab includes normal and longitudinal crack.

3. The method for predicting longitudinal cracks in slabs using unbalanced samples according to claim 1, characterized in that, The statistical characteristics of the process parameters include: casting speed, primary cooling water volume, secondary cooling water volume, tundish temperature, and superheat, wherein: The casting speed is used to calculate the mean, standard deviation, and maximum value of the casting speed sequence within the slab casting cycle; the primary cooling water volume and secondary cooling water volume are used to calculate the mean and standard deviation of the water volume sequence; the tundish temperature is used to calculate the mean, minimum value, and standard deviation of the temperature sequence; the superheat is calculated using the liquidus temperature of the steel grade and the tundish temperature, and the mean of the sequence is taken.

4. The method for predicting longitudinal cracks in slabs using unbalanced samples according to claim 1, characterized in that, The construction of the feature dataset specifically includes: By utilizing the statistical characteristics of the process parameters, the temperature characteristics of the thermocouples, and the spatial aggregation characteristics, a multidimensional feature vector is constructed, representing each slab as a multidimensional feature vector. Each multidimensional feature vector corresponds to a binary label. ,when When, it indicates that the slab is in normal condition. When, it indicates that the slab is in a state with longitudinal cracks; the multidimensional feature vector With binary tags The feature dataset is constructed by establishing a one-to-one correspondence.

5. The method for predicting longitudinal cracks in slabs using unbalanced samples according to claim 1, characterized in that, The weights include density weights, boundary weights, and combined weights, where: The density weight is obtained by calculating the average distance between each crack sample and its k nearest neighbor samples with longitudinal cracks in the multidimensional feature space, and the reciprocal of the average distance is used as the density weight. The boundary weights are obtained by calculating the proportion of each crack sample to the majority class of the m nearest neighbor samples; The comprehensive weight is a weighted sum and normalized sum of the density weight and the boundary weight, used to determine the sampling weight of each crack sample; The physical constraint verification includes the following constraints: Standard deviation of pulling speed ; Maximum rate of temperature rise ; The temperature of the tundish is higher than the liquidus temperature of the steel grade; The highest temperature in the critical area is lower than the melting point of molten steel; If the generated synthetic sample violates the constraints, the synthetic sample is regenerated until a synthetic sample that meets all physical constraint checks is obtained.

6. The method for predicting longitudinal cracks in slabs from unbalanced samples according to claim 4, characterized in that, The slab state prediction model outputs the corresponding slab state by calculating the multidimensional feature vector of the slab.

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