A data-driven continuous prediction method for longitudinal thickness of cold-rolled strip

Abstract

The present invention provides a data-driven continuous prediction method for the longitudinal thickness of cold-rolled strip, comprising: selecting measured data related to the cold rolling production line and the strip outlet thickness and process automation-level calculated data as preliminary input features; performing data cleaning and normalization processing on the measured data and the calculated data to obtain a preliminary modeling data set; dividing the cold rolling process into the head and tail acceleration and deceleration stages and the high-speed stable rolling stage, using a random forest algorithm to perform importance analysis on the preliminary input features, and selecting input features of different rolling stages in the cold rolling process; determining the topological structure of the DNN model of the two rolling stages based on the input feature selection results of the different rolling stages, selecting model parameters, and training the preliminarily established DNN model; using a genetic algorithm to optimize the DNN model during the training process to improve the prediction accuracy; and using the optimized DNN model to predict the strip outlet thickness.

Description

Technical Field

[0001] The invention belongs to the technical field of rolling process control and relates to a data-driven continuous prediction method for the longitudinal thickness of cold-rolled strip steel. Background Art

[0002] In the cold rolling production process, thickness accuracy is one of the most important indicators for measuring the quality of cold-rolled products and is also the quality issue that downstream industry users are most concerned about, as it determines the quality and cost of the processed products, and also determines the performance of subsequent processed products. With the rapid development of my country's economy and the gradual upgrading of its industrial structure, the quality requirements of cold-rolled sheet and strip products in industries such as automobiles, home appliances, construction, instrumentation, electronics, and food packaging are constantly increasing. Therefore, improving the thickness accuracy of cold-rolled sheet and strip products has always been a hot topic of research and development, and it is a very urgent practical need.

[0003] Because the actual cold rolling process is extremely complex and contains many unknown factors, it is difficult to establish a precise mathematical model. In recent years, a large amount of scientific research has been conducted both domestically and internationally to address these characteristics of the cold rolling process. Artificial intelligence methods such as machine learning and deep learning have excellent information processing and calculation capabilities, making them well-suited to handling the strong coupling, nonlinearity, and multivariate characteristics of the cold rolling process. In recent years, a large number of artificial intelligence methods have been applied to the cold rolling field.

[0004] Artificial intelligence methods driven by industrial data are increasingly being applied to the construction of digital twin models of the cold rolling production process, achieving significant breakthroughs. Several neural network prediction methods based on measured data from cold rolling lines have been proposed, achieving precise prediction of strip head thickness. The head thickness predictions from digital twin technology enable timely adjustments to the production process, particularly providing a reference for parameter corrections in process automation model settings. This allows for more precise on-site control, thereby improving product quality.

[0005] As artificial intelligence methods such as machine learning and deep learning are continuously applied to the field of cold rolling, thickness prediction has become a hot topic. A large number of methods for cold rolling thickness prediction continue to emerge. However, traditional thickness prediction mostly focuses on the thickness hits of the heads of different rolls of strip steel. The prediction area is concentrated on the head of each roll of strip steel, and the prediction object is different rolls of strip steel. It cannot reflect the thickness accuracy of a roll of strip steel along the entire length direction, and thus cannot reflect the quality of a roll of finished strip steel. Summary of the Invention

[0006] In order to solve the above technical problems, the present invention provides a data-driven continuous prediction method for the longitudinal thickness of cold-rolled strip. By establishing a DNN model and using a genetic algorithm to optimize the initial weights and thresholds of the DNN model, the outlet thickness is used as the output value of the DNN model to obtain a thickness fluctuation curve of a roll of strip in the full length direction, reflecting the thickness accuracy of a roll of strip in the full length direction. The prediction accuracy fully meets the accuracy requirements of cold rolling production.

[0007] The present invention provides a data-driven continuous prediction method for the longitudinal thickness of cold-rolled strip steel, comprising:

[0008] Step 1: Select the measured data related to the cold rolling production line and the strip outlet thickness and the process automation level calculated data as the primary input features;

[0009] Step 2: Clean and normalize the measured and calculated data to obtain the preliminary modeling data set;

[0010] Step 3: The cold rolling process is divided into the initial and final acceleration and deceleration stages and the high-speed stable rolling stage. The random forest algorithm is used to perform importance analysis on the pre-selected input features and select the input features of different rolling stages in the cold rolling process.

[0011] Step 4: Based on the input feature selection results of different rolling stages, the topological structure of the DNN model of the two rolling stages is determined, the model parameters are selected, and the initially established DNN model is trained;

[0012] Step 5: Use genetic algorithms to optimize the DNN model during training to improve prediction accuracy;

[0013] Step 6: Use the optimized DNN model to predict the strip exit thickness.

[0014] In the data-driven continuous prediction method for the longitudinal thickness of cold-rolled strip of the present invention, step 1 is specifically as follows:

[0015] Step 1.1: Select a five-stand cold rolling production line and determine the following important influencing factors: rolling force, bending roll force, tension, rolling speed, roll gap, rolling mileage, and entry thickness;

[0016] Step 1.2: Based on the important influencing factors, 34 preliminary input features are extracted from the field measured data and process automation level calculated data. The measured data include: inlet thickness, outlet thickness of F1 stand, outlet thickness of F4 stand, rolling speed of F1-F5 stands, front tension of F1-F5 stands, back tension of F1-F5 stands, rolling force of F1-F5 stands, roll gap of F1-F5 stands, and bending roll force of F1-F5 stands; the process automation level calculated data includes: rolling kilometers.

[0017] In the data-driven continuous prediction method for the longitudinal thickness of cold-rolled strip of the present invention, the normalization process in step 2 adopts the max-min normalization method, and the specific formula is as follows:

[0018]

[0019] Where: x' d is the normalized data, x d is the dth data, min(x d ) is the minimum value in the data sequence, max(x d ) is the maximum value in the data sequence.

[0020] In the data-driven continuous prediction method for the longitudinal thickness of cold-rolled strip of the present invention, the importance analysis of the primary input features using the random forest algorithm in step 3 is specifically as follows:

[0021] Step 3.1: Use repeated random sampling to obtain a set of data from the primary modeling data set for decision tree training. The data not used in the establishment of the decision tree constitutes the out-of-bag data set. For any decision tree, calculate the error of the out-of-bag data set, which is recorded as ERR 00B1 ;

[0022] Step 3.2: For a preselected input feature x of all data in the out-of-bag dataset, randomly add noise interference and calculate the error of the out-of-bag dataset again, which is recorded as ERR 00B2 ;

[0023] Step 3.3: Assume that there are N decision trees in the random forest, then the importance of the initial input feature x is imp x The calculation method is as follows:

[0024]

[0025] Among them, imp x The value is used to reflect the importance of the input feature. After the random noise is added, if the accuracy of the out-of-bag data is greatly reduced, resulting in ERR 00B2 becomes larger, then imp x The larger the value, the greater the impact of the input feature on the prediction result, that is, the higher the importance.

[0026] In the data-driven continuous prediction method for the longitudinal thickness of cold-rolled strip of the present invention, the step 4 is specifically as follows:

[0027] Step 4.1: The input features and output data form the modeling dataset of the corresponding DNN model and are divided into training set and test set in a ratio of 8:1;

[0028] Step 4.2: In the two rolling stages, the learning rate adjustment algorithm uses trainbr, the hidden layer activation function uses tansig, the output layer activation function uses purelin, and the learning rate is 0.01;

[0029] Step 4.3: Use the control variable method to determine the optimal number of hidden layers and the number of neurons in each layer, and determine the network structure;

[0030] Step 4.4: Deep Neural Network DNN forward propagation algorithm:

[0031] The training set data is input from the input layer, passed forward through multiple hidden layers in sequence to the output layer output, the output OUT of the i-th node in the hidden layer i for:

[0032]

[0033] Output OUT of the kth node in the output layer k for:

[0034]

[0035] Where f is the activation function between hidden layers, is the activation function of the output layer, H is the dimension of the input vector of the hidden layer, Q is the dimension of the input vector of the output layer, ω ij is the weight of the input layer and the hidden layer, ω kj is the weight of the hidden layer and the output layer; θ i and a k are the hidden layer and output layer thresholds respectively; x j is the actual input of the j-th node;

[0036] Step 4.5: Deep Neural Network DNN Backpropagation Algorithm:

[0037] Error back propagation uses the gradient descent method. The error goes from the output layer to the hidden layer and then to the input layer. The weights and thresholds are adjusted layer by layer to make the predicted output closer and closer to the expected output until the set accuracy is reached. The error function for each data q is:

[0038]

[0039] During training, the total error function for a total of M data training is:

[0040]

[0041] Among them, y i is the actual value of the outlet thickness, y' i is the predicted value of the outlet thickness. When the total error function reaches the set value and meets the accuracy requirement, the training ends.

[0042] In the data-driven continuous prediction method for the longitudinal thickness of cold-rolled strip of the present invention, the step 5 is specifically as follows:

[0043] Genetic algorithms are used to optimize the initial weights and thresholds of the DNN model to obtain better initial weights and thresholds. The optimal initial weights are assigned to the DNN model, and the test set data is input into the optimized DNN model for prediction.

[0044] In the data-driven continuous prediction method for the longitudinal thickness of cold-rolled strip of the present invention, the prediction results are evaluated by the performance indicators of mean square error (MSE), mean absolute error (MAE), mean absolute error percentage (MAPE), and correlation coefficient (R), and the prediction accuracy is analyzed. The error index expression is as follows:

[0045]

[0046]

[0047]

[0048]

[0049] Where y i is the actual value of the outlet thickness, y' i is the predicted value of the outlet thickness, and n is the number of data in the test set.

[0050] The data-driven continuous prediction method for the longitudinal thickness of cold-rolled strip of the present invention has at least the following beneficial effects:

[0051] (1) Based on the industrial big data of a multi-stand cold rolling production line, the present invention proposes a data-driven continuous prediction method for the longitudinal thickness of cold-rolled strip steel, which adopts a DNN model and uses a genetic algorithm for optimization to obtain a GA-DNN model. The fluctuation curve of the outlet thickness of a whole roll of strip steel as it changes with the rolling time can be predicted, which can intuitively and accurately reflect the thickness change and thickness accuracy of a roll of strip steel along its entire length. It can intuitively see whether a part of a roll of strip steel does not meet the thickness accuracy requirements, and thus the quality of each roll of strip steel can be better controlled. The high-precision prediction results can be used to adjust the production process in a timely manner, especially to provide a reference for the parameter correction of the process automation level setting model, so that the site can be more accurately controlled, thereby improving product quality.

[0052] (2) Based on a neural network model, this invention maps cold rolling industry data to export thickness, thereby reflecting the thickness quality of cold-rolled strip and achieving digital twinning. Analysis shows that after feature selection and optimization using a genetic algorithm, the relative error is reduced to within ±0.5% and ±0.1% during the acceleration and deceleration phases and the steady rolling phase, respectively. The prediction accuracy fully meets and exceeds the accuracy requirements of cold rolling production, achieving high-precision prediction of export thickness.

[0053] (3) Through the thickness fluctuation curve, the thickness of a roll of steel strip at each time point in the entire rolling process can be known in advance. According to the thickness at the specific time node, the parameter setting of the cold rolling process can be pre-adjusted at the accurate time node, so that the site can be more accurately controlled and the product quality can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is a flow chart of a data-driven continuous prediction method for the longitudinal thickness of cold-rolled strip according to the present invention;

[0055] Figure 2 Rolling speed variation curve of a coil of steel strip during rolling;

[0056] Figure 3 This is a comparison chart of the absolute error effects in the acceleration and deceleration stages before and after feature selection;

[0057] Figure 4 This is a comparison chart of the relative error effects in the acceleration and deceleration stages before and after feature selection;

[0058] Figure 5 This is a comparison chart of the absolute error effect in the stable rolling stage before and after feature selection;

[0059] Figure 6 The comparison diagram of relative error effect of stable rolling stage before and after feature selection;

[0060] Figure 7a This is a comparison chart of the absolute errors predicted by the DNN model and the GA-DNN model during the acceleration and deceleration stages;

[0061] Figure 7b A comparison chart of the absolute errors predicted by the DNN model and the GA-DNN model during the stable rolling stage;

[0062] Figure 8a This is a comparison chart of the relative errors predicted by the DNN model and the GA-DNN model during the acceleration and deceleration stages;

[0063] Figure 8b A comparison chart of the relative errors predicted by the DNN model and the GA-DNN model during the stable rolling stage;

[0064] Figure 9a This is the prediction effect diagram of the GA-DNN model in the acceleration and deceleration stages;

[0065] Figure 9b This is the prediction effect diagram of the GA-DNN model in the stable rolling stage. DETAILED DESCRIPTION

[0066] In order to make the purpose and advantages of this method clearer, the present invention will be further described in detail with reference to the accompanying drawings and examples. It should be understood that the examples described herein are only used to explain the present invention and are not limited to the present invention.

[0067] This example takes a domestic cold rolling production line as the basis, uses the relevant data of strip steel outlet thickness as the data for establishing the DNN model, and proposes a data-driven continuous prediction method for the longitudinal thickness of cold-rolled strip steel. The overall flow chart is as follows: Figure 1 The specific steps are as follows:

[0068] Step 1: Select the measured data related to the cold rolling production line and the strip outlet thickness and the process automation level calculated data as the primary input features. Step 1 is as follows:

[0069] Step 1.1: Select a five-stand cold rolling production line and determine the following important influencing factors: rolling force, bending roll force, tension, rolling speed, roll gap, rolling mileage, and entry thickness;

[0070] Step 1.2: Based on the important influencing factors, a total of 34 parameters, including field measured data and process automation-level calculated data, are extracted as preliminary input features. The measured data include: inlet thickness, outlet thickness of F1 stand, outlet thickness of F4 stand, rolling speed of F1-F5 stands, front tension of F1-F5 stands, back tension of F1-F5 stands, rolling force of F1-F5 stands, roll gap of F1-F5 stands, and bending roll force of F1-F5 stands; the process automation-level calculated data includes: rolling kilometers.

[0071] For example, taking the production process between two roll changes, a total of 9 rolls of strip steel are rolled during the roll change cycle.

[0072] Step 2: Extract relevant data from the PDA file and perform a series of data cleaning tasks such as outlier processing, missing point processing, and noise processing on the measured data and calculated data. The final specific data are shown in Table 1.

[0073] Table 1 Some specific data in a roll changing cycle

[0074]

[0075] The cleaned data is normalized using the max-min normalization method to obtain the preliminary modeling data set. The normalization formula is as follows:

[0076]

[0077] Where: x' d is the normalized data, x d is the dth data, min(x d ) is the minimum value in the data sequence, max(x d ) is the maximum value in the data sequence.

[0078] The data recorded in the factory PDA file is the real-time process data of the various physical quantities changing with time during the rolling process. At equal time intervals, each collector records the data in sequence, and the value of each physical quantity corresponding to the same horizontal coordinate represents the data of each physical quantity at the same time node. The present invention is based on a five-stand cold rolling production line, and preliminarily selects 34 characteristic data such as rolling force, bending roll force, front and rear tension, rolling speed, roll gap, rolling mileage and entrance thickness as model input. When modeling, each point on the strip wins a set of data, and each set of data consists of 34 preliminary input features and exit thickness, with a total of 35 dimensions. Each set of data records the physical state of the selected point on the strip at different stands at different times during the entire rolling process, and comprehensively records the entire rolling process of each point.

[0079] Step 3: The cold rolling process is divided into the first and last acceleration and deceleration stages and the high-speed stable rolling stage. The random forest algorithm is used to perform importance analysis on the primary input features and select the input features of different rolling stages in the cold rolling process.

[0080] The characteristic of cold rolling is that the threading speed is very low, and then it is accelerated to the rolling speed after threading. During the acceleration process, parameters such as speed, roll gap and tension are adjusted, and the acceleration time period is relatively long. Therefore, there are very obvious acceleration and deceleration stages and high-speed stable rolling stages on a roll of strip steel. In cold rolling production, different rolls of strip steel are connected together by welding. When a roll of strip steel begins to roll, the weld connected to the tail of the previous roll of strip steel enters the rolling mill, moves forward slowly, and passes through five frames in turn. After threading is completed, the five frames are accelerated to the rolling speed at the same time and enter a stable rolling state for a long time. After the stable rolling is completed, the rolling speed continues to decrease, waiting for the next roll of strip steel to enter. Extract the rolling speed curve of the F1 frame (the first frame) from the PDA file, and find the rolling speed change curve of each roll of strip steel according to the position of the weld, such as Figure 2 Through programming, the signal is automatically recognized and the data of each strip is divided into the acceleration and deceleration stages at the beginning and end and the high-speed stable rolling stage in the middle.

[0081] Before using random forests to select input features, 34 parameters were initially selected as input features for the DNN model. The production conditions of the same strip vary at different rolling stages, and the rolling mechanisms differ in the two rolling stages. Therefore, the importance of the same input feature varies, and the selection of input features differs significantly between the two rolling stages. Selecting too many input features can cause some less relevant input features to become noise, which in turn affects model accuracy and can cause overfitting. Selecting too few input features can result in incomplete feature extraction, which cannot fully reflect the actual situation and leads to poor model generalization. Selecting appropriate input features can optimize the model's prediction accuracy and generalization ability.

[0082] Random forests are a method that uses decision trees as a basic learning tool and integrates them into a model to solve a common problem. A large number of randomly generated decision trees are the fundamental building blocks of the random forest algorithm. Compared to decision trees, random forests have stronger generalization capabilities and better classification and prediction performance. The random forest algorithm analyzes input features. It outputs an array of the feature_importances parameter, which measures the importance of each input feature.

[0083] Based on the above analysis, the present invention uses the random forest algorithm to perform importance analysis on the primary input features, specifically:

[0084] Step 3.1: Use repeated random sampling to obtain a set of data from the primary modeling data set for decision tree training. The data not used in the establishment of the decision tree constitutes the out-of-bag data set. For any decision tree, calculate the error of the out-of-bag data set, which is recorded as ERR 00B1 ;

[0085] Step 3.2: For a preselected input feature x of all data in the out-of-bag dataset, randomly add noise interference and calculate the error of the out-of-bag dataset again, which is recorded as ERR 00B2 ;

[0086] Step 3.3: Assume that there are N decision trees in the random forest, then the importance of the initial input feature x is imp x The calculation method is as follows:

[0087]

[0088] Among them, imp x The value is used to reflect the importance of the input feature. After the random noise is added, if the accuracy of the out-of-bag data is greatly reduced, resulting in ERR 00B2 becomes larger, then imp x The larger the value, the greater the impact of the input feature on the prediction result, that is, the higher the importance.

[0089] At different rolling stages, the feature_importances parameters of each input feature are quite different. Some of the results are shown in Table 2.

[0090] Table 2 Input characteristic analysis results at different rolling stages

[0091]

[0092] The input feature analysis results in Table 2 show that the production conditions of the same strip vary at different rolling stages, resulting in different rolling mechanisms in the two different rolling stages. Consequently, the variable importance of the same input feature varies. To determine the input features for different rolling stages, we selected input features with a feature_importances parameter greater than 0.01 to optimize the number and composition of input features, thereby achieving the best prediction accuracy and generalization ability of the model. For the initial and final acceleration / deceleration stages, a total of 11 input features were selected: F5 stand rolling force, F5 stand front tension, F5 stand rolling speed, F4 stand back tension, rolling mileage, F4 stand exit thickness, F2 stand rolling speed, F3 stand front tension, F3 stand rolling force, F3 stand roll gap, and F4 stand rolling speed. In the high-speed stable rolling stage, 24 input features are selected, including F4 stand back tension, F1 stand rolling force, F1 stand bending roll force, F2 stand front tension, F5 stand front tension, F5 stand back tension, entrance thickness, F1 stand exit thickness, F4 stand exit thickness, F1 stand rolling speed, F1 stand front tension, etc. Figure 3-Figure 6 This is the effect comparison before and after feature selection. Figure 3 This is a comparison chart of the absolute error effects in the acceleration and deceleration stages before and after feature selection. Figure 4 This is a comparison chart of the relative error effects in the acceleration and deceleration stages before and after feature selection. Figure 5 The comparison diagram of the absolute error effect of the stable rolling stage before and after feature selection is shown in the figure. Figure 6 The figure shows the comparison of the relative error effect in the stable rolling stage before and after feature selection.

[0093] The comparison of prediction effects before and after feature selection is shown in Table 3 below. Analysis shows that after selecting input features, the error parameters are reduced, the correlation coefficient is increased, and the prediction accuracy is improved. Therefore, it is necessary and effective to use random forest for feature selection and optimize the number and composition of input features.

[0094] Table 3

[0095]

[0096] Step 4: Based on the input feature selection results of different rolling stages, the topological structure of the DNN model of the two rolling stages is determined, the model parameters are selected, and the initially established DNN model is trained. The specific steps of step 4 are as follows:

[0097] Step 4.1: The input features and output data form the modeling dataset of the corresponding DNN model and are divided into training set and test set in a ratio of 8:1;

[0098] For example, during a roll change cycle, nine rolls of steel strip are continuously produced, resulting in 7,235 sets of continuous data. The data from the first eight rolls serves as the training set, totaling 6,485 sets of data, while the data from the last roll serves as the test set, totaling 750 sets of data. In the subsequent steps, all data used is from the training set, and the model is trained using this data.

[0099] Step 4.2: Select an appropriate learning rate adjustment algorithm and its related parameters to prevent the learning rate from being too large, causing the network to fail to converge and hover near the optimal value, unable to find the optimal value. Also prevent the learning rate from being too small, causing the network to converge extremely slowly, resulting in a significant increase in training time, and easily entering a local extreme point and converging, failing to find the global optimal solution.

[0100] In the present invention, the learning rate adjustment algorithm in the two rolling stages adopts trainbr, the hidden layer activation function adopts tansig, the output layer activation function adopts purelin, and the learning rate is 0.01;

[0101] Trainbr, or the Bayesian regularization algorithm, is a type of training function and an improved optimization algorithm. It can limit the initial values of weights to a certain range, thereby achieving a certain optimization effect. Using Trainbr to train neural networks can improve the network's generalization ability and reduce the difficulty of determining the optimal network structure.

[0102] The Tansig function is a nonlinear activation function that can convert input signals into accurate output signals, thereby achieving the computational effect of the neural network. Purelin is a linear transfer function. The expressions of the two activation functions are as follows:

[0103]

[0104] purelin(b)=b

[0105] Among them, a is the total input of a node in the hidden layer, and b is the total input of the output layer node.

[0106] Step 4.3: Use the control variable method to determine the optimal number of hidden layers and the number of neurons in each layer, and determine the network structure;

[0107] Generally speaking, increasing the number of hidden layers and the number of neurons in each hidden layer can improve the learning and generalization capabilities of a neural network, thereby enhancing network performance. However, excessive neurons can lead to prolonged training time and overfitting, resulting in decreased performance. Currently, there is no unified method for setting the number of hidden layers and the number of neurons per layer. These are often determined through extensive experimentation, combining empirical formulas. Experimentation was used to determine the optimal number of hidden layers and the number of neurons per layer, and then to establish an outlet thickness prediction model. The control variable method was used to determine the network structure. The experimental results are shown in Table 4. The conclusion was that an 11-17-5-1 neural network was used for the acceleration and deceleration phases: 11 neurons in the input layer, 17 neurons in the first hidden layer, 5 neurons in the second hidden layer, and 1 neuron in the output layer. A 24-20-10-1 neural network was used for the steady-state rolling phase: 24 neurons in the input layer, 20 neurons in the first hidden layer, 10 neurons in the second hidden layer, and 1 neuron in the output layer.

[0108] Table 4 Comparison of network performance with different numbers of hidden layer neurons

[0109]

[0110] Step 4.4: Deep Neural Network DNN forward propagation algorithm:

[0111] The training set data is input from the input layer, passed forward through multiple hidden layers in sequence to the output layer output, the output OUT of the i-th node in the hidden layer i for:

[0112]

[0113] Output OUT of the kth node in the output layer k for:

[0114]

[0115] Where f is the activation function between hidden layers, is the activation function of the output layer, H is the dimension of the input vector of the hidden layer, Q is the dimension of the input vector of the output layer, ω ij is the weight of the input layer and the hidden layer, ω kj is the weight of the hidden layer and the output layer; θ i and a k are the hidden layer and output layer thresholds respectively; x j is the actual input of the j-th node;

[0116] Step 4.5: Deep Neural Network DNN Backpropagation Algorithm:

[0117] When training the network, if there is an error between the predicted output and the expected output, the error signal will be back-propagated in the direction opposite to the signal transmission, and the weights and thresholds between each neuron will be corrected in turn. The above process is repeated until the error reaches the set requirements and the training is completed.

[0118] Error back propagation uses the gradient descent method. The error goes from the output layer to the hidden layer and then to the input layer. The weights and thresholds are adjusted layer by layer to make the predicted output closer and closer to the expected output until the set accuracy is reached. The error function for each data q is:

[0119]

[0120] During training, the total error function for a total of M data training is:

[0121]

[0122] Among them, y i is the actual value of the outlet thickness, y' i is the predicted outlet thickness. M is the total number of data samples, which is 1347 during the acceleration and deceleration phase and 5138 during the steady rolling phase. Training ends when the total error function reaches the set value and meets the accuracy requirements.

[0123] Step 5: During the training process, the genetic algorithm (GA) is used to optimize the DNN model to improve the prediction accuracy.

[0124] In practice, each time a DNN model is trained, the initial weights and thresholds are randomly initialized, significantly increasing uncertainty. A genetic algorithm is used to optimize the initial weights and thresholds of the DNN model, obtaining more optimal initial weights and thresholds. These optimal initial weights are then assigned to the DNN model, resulting in a more optimized GA-DNN model and improved network performance. The GA-DNN model is then fed with test data for prediction.

[0125] The test data was fed into the GA-DNN model for prediction, resulting in a thickness fluctuation curve along the entire length of a steel strip. During the acceleration and deceleration phases and the high-speed, stable rolling phase, the GA-DNN model maintained relative errors within ±0.5% and ±0.1%, respectively, significantly lower than those of conventional DNN models. This demonstrates that using genetic algorithms for optimization can improve prediction accuracy, exceeding the precision requirements of cold rolling production.

[0126] To more comprehensively and accurately evaluate the overall performance of the GA-DNN model and the DNN model, the prediction results were evaluated using performance indicators such as mean square error (MSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and correlation coefficient (R), and the prediction accuracy was analyzed. The calculation results are shown in Table 5. The analysis shows that the GA-DNN model outperforms the DNN model without genetic algorithm optimization in all performance indicators. The optimized model has a smaller prediction error and a higher correlation coefficient, further demonstrating the optimization effect of the genetic algorithm.

[0127] The specific error index expression is as follows:

[0128]

[0129]

[0130]

[0131]

[0132] Where y i is the actual value of the outlet thickness, y′ i is the predicted value of the outlet thickness, and n is the number of data in the test set. In this embodiment, the data in the acceleration and deceleration stage is 155, and the data in the high-speed stable rolling stage is 595.

[0133] Table 5

[0134] Rolling stage Performance indicators GA-DNN model DNN models Acceleration and deceleration stages MSE <![CDATA[1.568×10 -7 ]]> <![CDATA[3.364×10 -7 <!-- 10 -->]]> MAE <![CDATA[2.9527×10 -4 ]]> <![CDATA[4.299×10 -4 ]]> MAPE 0.148 0.217 R 0.9993 0.9984 Stable rolling stage MSE <![CDATA[4.140x10 -9 ]]> <![CDATA[9.833×10 -9 ]]> MAE <![CDATA[5.233×10 -4 ]]> <![CDATA[7.203×10 -5 ]]> MAPE 0.0275 0.0379 R 0.9135 0.7909

[0135] Figure 7a This is a comparison chart of the absolute errors predicted by the DNN model and the GA-DNN model during the acceleration and deceleration stages. Figure 7b A comparison chart of the absolute errors predicted by the DNN model and the GA-DNN model in the stable rolling stage. Figure 8a This is a comparison chart of the relative errors predicted by the DNN model and the GA-DNN model during the acceleration and deceleration stages; Figure 8b The figure below compares the relative errors predicted by the DNN model and the GA-DNN model during the steady rolling phase. Analysis of the prediction results during the acceleration / deceleration phase and the steady rolling phase shows that the GA-DNN model achieved maximum relative errors of 0.4941% and 0.09447%, respectively, with relative errors within ±0.5% and ±0.1%, respectively. The GA-DNN model also achieved maximum absolute errors of 1.02μm and 0.17μm, respectively, with absolute errors within ±1.1μm and ±0.2μm, respectively, demonstrating lower errors than the DNN model.

[0136] Figure 9a This is the prediction effect diagram of the GA-DNN model in the acceleration and deceleration stages; Figure 9bThe following figure shows the prediction results of the GA-DNN model during the steady rolling phase. As can be seen, the GA-DNN model's predicted values match the true values better than the DNN model. After genetic algorithm optimization, the correlation coefficients (R) reached 0.9993 and 0.9135 during the acceleration and deceleration phases and the steady rolling phase, respectively, demonstrating strong correlation. The GA-DNN model demonstrated high prediction accuracy and a high degree of fit between the predicted and true values, successfully achieving highly accurate predictions of outlet thickness.

[0137] The GA-DNN model has high prediction accuracy and good fitting effect. The model has a simple structure, strong generalization ability, and is easy to promote and apply. It provides new ideas and methods for setting the thickness and controlling the precision of the cold rolling process.

[0138] Step 6: Use the optimized DNN model to predict the strip exit thickness.

[0139] The above description is only a preferred embodiment of the present invention and is not intended to limit the concept of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A data-driven continuous prediction method for the longitudinal thickness of cold-rolled strip, characterized in that: include: Step 1: Select the measured data related to the cold rolling production line and the strip outlet thickness and the process automation level calculated data as the primary input features; Step 2: Clean and normalize the measured and calculated data to obtain the preliminary modeling data set; Step 3: The cold rolling process is divided into the initial and final acceleration and deceleration stages and the high-speed stable rolling stage. The random forest algorithm is used to perform importance analysis on the pre-selected input features and select the input features of different rolling stages in the cold rolling process. Step 4: Based on the input feature selection results of different rolling stages, the topological structure of the DNN model of the two rolling stages is determined, the model parameters are selected, and the initially established DNN model is trained; Step 5: Use genetic algorithms to optimize the DNN model during training to improve prediction accuracy; Step 6: Use the optimized DNN model to predict the strip exit thickness.

2. The data-driven continuous prediction method for longitudinal thickness of cold-rolled strip according to claim 1, characterized in that: Step 1 is as follows: Step 1.1: Select a five-stand cold rolling production line and determine the following important influencing factors: rolling force, bending roll force, tension, rolling speed, roll gap, rolling mileage, and entry thickness; Step 1.2: Based on the important influencing factors, 34 preliminary input features are extracted from the field measured data and process automation level calculated data. The measured data include: inlet thickness, outlet thickness of F1 stand, outlet thickness of F4 stand, rolling speed of F1-F5 stands, front tension of F1-F5 stands, back tension of F1-F5 stands, rolling force of F1-F5 stands, roll gap of F1-F5 stands, and bending roll force of F1-F5 stands; the process automation level calculated data includes: rolling kilometers.

3. The data-driven continuous prediction method for longitudinal thickness of cold-rolled strip according to claim 1, characterized in that: The normalization process in step 2 uses the max-min normalization method. The specific formula is as follows: Where: x' d is the normalized data, x d is the dth data, min(x d ) is the minimum value in the data sequence, max(x d ) is the maximum value in the data sequence.

4. The data-driven continuous prediction method for longitudinal thickness of cold-rolled strip according to claim 1, characterized in that: In step 3, the importance analysis of the initial input features using the random forest algorithm is performed as follows: Step 3.1: Use repeated random sampling to obtain a set of data from the primary modeling data set for decision tree training. The data not used in the establishment of the decision tree constitutes the out-of-bag data set. For any decision tree, calculate the error of the out-of-bag data set, which is recorded as ERR 00B1 ; Step 3.2: For a preselected input feature x of all data in the out-of-bag dataset, randomly add noise interference and calculate the error of the out-of-bag dataset again, which is recorded as ERR 00B2 ; Step 3.3: Assume that there are N decision trees in the random forest, then the importance of the initial input feature x is imp x The calculation method is as follows: Among them, imp x The value is used to reflect the importance of the input feature. After the random noise is added, if the accuracy of the out-of-bag data is greatly reduced, resulting in ERR 00B2 becomes larger, then imp x The larger the value, the greater the impact of the input feature on the prediction result, that is, the higher the importance.

5. The data-driven continuous prediction method for longitudinal thickness of cold-rolled strip according to claim 1, characterized in that: The step 4 is specifically as follows: Step 4.1: The input features and output data form the modeling dataset of the corresponding DNN model and are divided into training set and test set in a ratio of 8:1; Step 4.2: In the two rolling stages, the learning rate adjustment algorithm uses trainbr, the hidden layer activation function uses tansig, the output layer activation function uses purelin, and the learning rate is 0.01; Step 4.3: Use the control variable method to determine the optimal number of hidden layers and the number of neurons in each layer, and determine the network structure; Step 4.4: Deep Neural Network DNN forward propagation algorithm: The training set data is input from the input layer, passed forward through multiple hidden layers in sequence to the output layer output, the output OUT of the i-th node in the hidden layer i for: Output OUT of the kth node in the output layer k for: Where f is the activation function between hidden layers, is the activation function of the output layer, H is the dimension of the input vector of the hidden layer, Q is the dimension of the input vector of the output layer, ω ij is the weight of the input layer and the hidden layer, ω kj is the weight of the hidden layer and the output layer; θ i and a k are the hidden layer and output layer thresholds respectively; x j is the actual input of the j-th node; Step 4.5: Deep Neural Network DNN Backpropagation Algorithm: Error back propagation uses the gradient descent method. The error goes from the output layer to the hidden layer and then to the input layer. The weights and thresholds are adjusted layer by layer to make the predicted output closer and closer to the expected output until the set accuracy is reached. The error function for each data q is: During training, the total error function for a total of M data training is: Among them, y i is the actual value of the outlet thickness, y' i is the predicted value of the outlet thickness. When the total error function reaches the set value and meets the accuracy requirement, the training ends.

6. The data-driven continuous prediction method for longitudinal thickness of cold-rolled strip according to claim 1, characterized in that: The step 5 is specifically as follows: Genetic algorithms are used to optimize the initial weights and thresholds of the DNN model to obtain better initial weights and thresholds. The optimal initial weights are assigned to the DNN model, and the test set data is input into the optimized DNN model for prediction.

7. The data-driven continuous prediction method for longitudinal thickness of cold-rolled strip according to claim 1, characterized in that: It also includes evaluating the prediction results through the performance indicators mean square error MSE, mean absolute error MAE, mean absolute error percentage MAPE, and correlation coefficient R, and analyzing the prediction accuracy. The error indicator expression is as follows: Where y i is the actual value of the outlet thickness, y' i is the predicted value of the outlet thickness, and n is the number of data in the test set.

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