Sintered ore alkalinity prediction method and device and prediction model construction method

Abstract

The invention discloses a sinter alkalinity prediction method and device and a prediction model construction method, and belongs to the technical field of sinter alkalinity prediction. The model construction method comprises the following steps: data acquisition and preprocessing: acquiring sinter alkalinity and process parameter time sequence sample data related to the sinter alkalinity, and dividing the sample data into a training set and a test set; constructing a sinter alkalinity prediction model based on the regularization self-organizing GRU; and training optimization is carried out on the model by adopting training set data. By adopting a structure self-organizing growth strategy based on neuron sensitivity analysis, self-adaptive matching of a network scale and task complexity can be realized; and through a self-adaptive regularization mechanism based on weight dispersion and a prediction error change rate, regularization intensity can be dynamically adjusted according to a network training state, so that the defect of structure solidification of a conventional deep learning model is overcome.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of sinter ore alkalinity prediction, and more particularly relates to a sinter ore alkalinity prediction method and device and a prediction model construction method. BACKGROUND

[0002] Sinter ore alkalinity is a key indicator affecting the metallurgical properties of sinter ore, and its level directly determines the mineral composition and structure of the sinter ore. Appropriate alkalinity can promote the generation of calcium ferrite and other binding phases, improve the strength and reducibility of the sinter ore, improve the softening performance, and reduce low-temperature reduction pulverization. If the alkalinity is too high, high-melting-point dicalcium silicate is easily generated, resulting in brittle and hard sinter ore and reduced reducibility, and if the alkalinity is too low, there is insufficient binding phase and poor strength. Therefore, precise control of the alkalinity of sinter ore is crucial to ensuring the smooth operation of blast furnaces, improving smelting efficiency, and reducing energy consumption. Research shows that when the sinter ore alkalinity fluctuation range is reduced from ±0.1 to ±0.05, the blast furnace production increases by 1.5%, the coke ratio decreases by 0.8%, and the economic benefits are significant.

[0003] However, the composition control of the sintering process is subject to double hysteresis, making it difficult to precisely regulate the sintering alkalinity. In terms of detection, offline sampling and testing takes several hours, and the non-continuous detection method cannot reflect the composition changes in real time. In the long process, there is a physical and chemical reaction delay of several hours from raw material ratio adjustment to finished product output. The coupling of "detection lag" and "process lag" makes it difficult for the control system to adjust in real time, and the alkalinity fluctuates frequently. Therefore, it is particularly important to build a sinter ore alkalinity prediction model, which integrates real-time process parameters and historical data to predict the alkalinity trend in advance and provide a forward-looking basis for control decisions. It is a core means to break through the hysteresis bottleneck and improve the precision of alkalinity control.

[0004] In the early exploration of sinter ore alkalinity prediction, shallow neural networks such as improved BP algorithms, and machine learning methods including random forests, XGBoost, gray least squares support vector machines, mechanism-ELM hybrid models, and Stacking ensemble algorithms were widely used to build prediction models. These early attempts have achieved certain results, such as a hit rate of more than 90% and a goodness of fit of more than 0.94 for some models, but they perform poorly in capturing long-term dependencies and dynamic characteristics when dealing with the inherent strong nonlinearity, multivariate coupling, and complex time series characteristics of the sintering process.

[0005] In view of the shortcomings of the shallow model, researchers gradually turn their attention to the field of deep learning, especially the recurrent neural network (RNN) and its variants LSTM and GRU. By constructing a hybrid model, such as GMM-KNN-LSTM, GRU-PLS, using intelligent optimization algorithms such as GA-RNN, and introducing a working condition recognition mechanism, such as a multi-model integration framework, the prediction accuracy has been significantly improved. In some studies, the RMSE is reduced by 35.29%, fully demonstrating the significant advantages of deep learning methods in dealing with time series complexity compared with shallow models.

[0006] However, the current deep prediction model still faces two major problems. On the one hand, the network hidden layer structure needs to be fixed and set in advance, lacking the ability to adapt to the complexity of the task, i.e., there is a structure solidification problem; on the other hand, due to the limited sintering data samples and the susceptibility to noise interference, the traditional method of using a fixed regularization coefficient is difficult to effectively adapt to the dynamic changes of the process, thus producing a dynamic overfitting risk, leading to a decline in the generalization performance of the model.

[0007] In view of the structure solidification problem, existing research has explored self-organizing network optimization methods, such as improved self-organizing module neural network, cascaded double self-organizing algorithm, and SOFM network based on competitive learning, and has improved the adaptability of the model in specific tasks such as time series prediction and pattern recognition. However, these studies mainly focus on traditional structures such as multi-layer perceptron (MLP) and radial basis network, and there is a relative lack of research on the self-organizing mechanism of the gate recurrent unit (GRU) network structure, which is crucial in sequence prediction. SUMMARY

[0008] The first object of the present application is to provide a sinter ore alkalinity prediction model construction method, by constructing a prediction model (RSO-GRU) based on regularization self-organizing gate recurrent unit GRU, thereby effectively solving the structure solidification and / or dynamic overfitting problems caused by the use of fixed regularization coefficients in existing prediction models.

[0009] The first object of the present application is to provide a sinter ore alkalinity prediction method, thereby effectively improving the prediction accuracy of sinter ore alkalinity and achieving self-adaptive balance between prediction accuracy and weight decay.

[0010] The present application also provides a sinter ore alkalinity prediction device.

[0011] To achieve the above object, the technical solution provided by the present application is as follows: The first aspect of the present application provides a sinter ore alkalinity prediction model construction method, comprising: Data acquisition and preprocessing, collecting sinter basicity and time series sample data related to process parameters, and dividing the sample data into training set and test set; A sinter basicity prediction model based on regularized self-organizing GRU is constructed; The model is trained and optimized using training set data, and the number of hidden neurons is automatically adjusted using a dynamic growth strategy based on sensitivity analysis during model training; The model is tested using test set data.

[0012] Sinter basicity directly affects its strength, reducibility and softening performance by regulating mineral composition and structure, and is a core control index to ensure smooth operation of blast furnace and improve smelting efficiency. Sinter basicity prediction is an important means to break through the process industry process lag and traditional detection lag.

[0013] In view of the structural solidification problem of the existing prediction model, the model can be adaptively adjusted according to the complexity of the sintering condition by using a dynamic growth strategy, which can maintain a compact structure to avoid overfitting under simple working conditions, and can expand the capacity to improve the expression ability under complex working conditions, so as to realize the dynamic matching of structural complexity and task difficulty.

[0014] According to any of the technical solutions of the first aspect of the present application, the data acquisition and preprocessing further comprises: using a multi-level feature selection strategy, and using a method combining correlation analysis and random forest importance evaluation to reduce the dimension of the collected process parameters related to sinter basicity, to obtain a feature subset that contributes most to the prediction of sinter basicity. Through this processing, the number of variables input to the model can be effectively reduced, which is conducive to reducing the computational complexity of the model and further improving the prediction accuracy and generalization ability of the model. Further, the process parameters related to sinter basicity include raw material ratio, moisture and machine speed.

[0015] According to any of the technical solutions of the first aspect of the present application, the number of hidden neurons is automatically adjusted using a dynamic growth strategy based on sensitivity analysis, specifically, the sensitivity of each neuron is calculated θ k , and a sensitivity threshold θ 0 is given, and the condition for hidden neuron growth is defined as: ; Wherein, the sensitivity of each neuron θ k is calculated as follows: ; is the activation strength of the kth hidden neuron, and K is the number of hidden neurons.

[0016] According to any technical solution of the first aspect of the present application, the newly added neurons are initialized by using a high-sensitivity neuron-based transfer learning strategy. Specifically, the hidden neurons are arranged in descending order of sensitivity, and the parameters of the first two neurons are combined: ; wherein, are the weights of the two neurons with the highest sensitivity, respectively, is the corresponding bias.

[0017] The parameters of the new neurons are initialized by transferring the weights (weights + bias) of the high-sensitivity neurons, avoiding the destruction of learned knowledge caused by random initialization.

[0018] According to any technical solution of the first aspect of the present application, in the model training process, an adaptive regularization mechanism based on L2 norm is introduced on the basis of standard GRU, i.e., the input weights of all input data of the model are regularized, and the regularization coefficient is dynamically adjusted through a double feedback mechanism based on the weight dispersion and the prediction error change rate Δermse p . λ p : ; wherein, the weight dispersion is defined as follows: ; ; M represents the number of weights; W p is the weight vector at the iteration number p ; represents the average value of the weights; is the prediction error change rate Δermse p at the iteration number p. ; and are the predicted basicity value and the actual basicity value, respectively, and T is the number of training samples.

[0019] In the traditional method, the regularization coefficient is usually fixed and cannot adapt to the dynamic changes of the sintering conditions. By constructing a sinter basicity prediction model based on adaptive regularization GRU, the regularization coefficient can be adaptively adjusted based on the weight dispersion and the prediction error change rate, thereby improving the prediction accuracy of the sinter basicity and avoiding overfitting or underfitting, thus effectively meeting the prediction needs under dynamic conditions.

[0020] When the prediction error increases, the enhanced regularization constraint prevents overfitting; when the weight dispersion is high, the enhanced parameter constraint improves the stability of the model; when the model tends to converge, the automatic weakening of the regularization strength avoids underfitting.

[0021] According to any of the technical solutions of the first aspect of the application, the sinter alkalinity prediction model based on the regularized self-organizing GRU further comprises: using a backpropagation through time (BPTT) algorithm to adaptively learn the weight and bias parameters of the model.

[0022] According to any of the technical solutions of the first aspect of the application, the model is tested using test set data, and the model evaluation indicators during the testing include mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R²), and mean absolute percentage error (MAPE).

[0023] The second aspect of the application provides a sinter alkalinity prediction method, comprising: The sinter alkalinity prediction model is constructed using any of the methods of the first aspect of the application. Process parameters related to sinter alkalinity are collected and input into the sinter alkalinity prediction model for prediction, thereby obtaining a sinter alkalinity prediction result.

[0024] The third aspect of the application provides a sinter alkalinity prediction device, comprising: A model construction module for constructing a sinter alkalinity prediction model based on adaptive regularization GRU. A data collection module for collecting process parameters related to sinter alkalinity; and A prediction module for inputting the process parameters related to sinter alkalinity into the sinter alkalinity prediction model based on adaptive regularization GRU, thereby obtaining a sinter alkalinity prediction result.

[0025] According to any of the technical solutions of the third aspect of the application, the model construction module constructs the sinter alkalinity prediction model based on adaptive regularization GRU using any of the methods of the first aspect of the application.

[0026] Compared with the prior art, the present application can achieve the following beneficial effects: (1) The present application constructs a sinter alkalinity prediction model based on regularized self-organizing GRU, and introduces a structure self-organizing growth strategy based on sensitivity analysis during model training, thereby realizing adaptive matching of network size and task complexity, avoiding overfitting under simple working conditions or underfitting under complex working conditions, and proving the convergence of the algorithm through Lyapunov stability theory.

[0027] (2) The application further introduces an adaptive regularization mechanism based on weight dispersion and prediction error change rate, dynamically adjusts the regularization strength according to the network training state, automatically enhances the regularization when the weight dispersion increases or the error fluctuation intensifies, and inhibits overfitting; otherwise, weakens the constraint to avoid underfitting, so as to solve the problem that the traditional fixed regularization coefficient cannot adapt to dynamic working conditions.

[0028] (3) The mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE) of the RSO-GRU model constructed by the application are all obviously reduced compared with the standard GRU model, and the determination coefficient (R²) is effectively improved, proving that the used regularization self-organizing strategy has obvious optimization effect. Compared with SVR, RF, BP and LSTM, RSO-GRU performs best in all evaluation indexes and can meet the precision requirements of industrial applications. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 is a network structure diagram of a gated recurrent unit (GRU); Figure 2 is a schematic diagram of the dynamic growth process of neurons based on sensitivity analysis in the embodiment of the application; Figure 3 is the correlation between the CaO variable sequence of the mixture and the output variable (sinter basicity) at different time steps in the embodiment of the application; Figure 4 is the Pearson correlation between the main variables in the embodiment of the application; Figure 5 is the descending order arrangement of different input features according to the importance score of the random forest in the embodiment of the application; Figure 6 is a comparison between the prediction results and the true values of the RSO-GRU model in the embodiment of the application on the test set; Figure 7 is a dynamic change diagram of the number of hidden layer neurons in the model training process in the embodiment of the application; Figure 8 is the triggering condition of the neuron growth mechanism when the sensitivity threshold θ0=0.08 in the embodiment of the application; Figure 9 is the adaptive adjustment trajectory of the regularization parameter λ p in the model training process in the embodiment of the application; Figure 10 is a collaborative evolution diagram between the weight dispersion and the prediction error rate in the embodiment of the application; Figure 11 is a three-dimensional scatter diagram between the predicted values and the true values of different prediction models; Figure 12 is a frequency distribution histogram of prediction errors of different prediction models; Figure 13 is a flow framework diagram of the sinter basicity prediction method of the present application. DETAILED DESCRIPTION

[0030] In view of the complex time sequence dependence and limited precision of traditional methods in sinter basicity prediction, the present application proposes a prediction model and method based on regularized self-organizing gated recurrent unit (RSO-GRU). The present application improves the existing GRU, specifically, at the method level, an adaptive regularization mechanism based on weight dispersion and prediction error change rate is established, which can dynamically adjust the regularization strength according to the training state; a network structure dynamic adjustment strategy based on neuron sensitivity analysis is designed, when the sensitivity of all neurons θ k exceeds the set threshold θ0, the number of neurons is automatically increased, so that the network size can adapt to the modeling requirements of different complexities; at the same time, the convergence of the RSO-GRU model in the two cases of fixed structure and dynamic growth is proved by Lyapunov function analysis, which provides a theoretical basis for the stable training of the model.

[0031] To further understand the content of the present application, the present application will be described in detail below in combination with specific embodiments. However, it should be understood that these descriptions are only exemplary and are not intended to limit the scope of the present disclosure. In the following detailed description, many specific details are set forth in order to provide a thorough understanding of the embodiments of the present disclosure. However, it is obvious that one or more embodiments can be implemented without these specific details.

[0032] It should be understood that the terms "include", "contain" and the like in the present application indicate the existence of the described features, steps, operations and / or components, but do not exclude the existence or addition of one or more other features, steps, operations or components.

[0033] In addition, for the sake of clarity, certain features of the present disclosure can be described herein in the context of separate embodiments, but can also be provided in combination with each other in a single embodiment. That is, unless explicitly incompatible or specifically excluded, each separate embodiment is considered to be combinable with any other embodiment, and this combination is considered to represent another different embodiment. Conversely, for the sake of brevity, various features of the present disclosure described in the context of a single embodiment can also be provided separately or in any subcombination. Finally, although a particular embodiment can be described as part of a series of steps or part of a more general structure, each step or substructure can itself be considered an independent embodiment.

[0034] I. Model construction The formation of sinter basicity is a complex dynamic process with significant time-dependent characteristics. The basicity at any time not only depends on the current process parameters, but also is deeply influenced by the production status in the past, such as fluctuations in raw material composition, slow evolution of equipment conditions, etc. Therefore, an effective basicity prediction model must be able to capture and learn the long-term time-dependent relationship in the data.

[0035] Based on the time characteristics of the sintering process, the present invention constructs a multi-input single-output basicity prediction model: ; Where, x ( t - k ), x ( t – k+ 1) and x ( t -1) represent the process parameter observations at historical time, x ( t ) represents the process parameter input at the current time, including key variables such as raw material ratio, moisture, machine speed, etc. y 0( t ) represents the predicted sinter basicity value, i.e. the output of the model; represents the nonlinear mapping function to be learned.

[0036] As an improved recurrent neural network, the Gated Recurrent Unit (GRU) controls the information flow through reset and update gates, effectively handling long-term dependencies in time series data and overcoming the gradient vanishing problem of traditional RNNs. As shown in Figure 1 , the network structure of GRU is more concise than LSTM, with higher computational efficiency, making it more suitable for real-time sequence prediction requirements of the sintering process.

[0037] The reset gate of GRU controls the degree of forgetting historical information: ; The update gate determines the fusion ratio of current information and historical information: ; The candidate hidden state combines the current input and the reset historical state: ; By combining the above formulas, the final hidden state balances historical information and current information through the update gate: ; Where, h t-1 and x ( t) are the previous state and the current input, respectively.

[0038] denote the corresponding weight vectors, denote the bias of the corresponding gate, and represent the corresponding activation function.

[0039] , where β represents the input of the corresponding activation function.

[0040] To apply GRU to sinter alkalinity prediction, the optimal network parameters and structure need to be determined to minimize the prediction error. The root mean square error (RMSE) is used as the evaluation index in the present application: , where, and are the predicted alkalinity value and the actual alkalinity value, respectively, and T is the number of training samples.

[0041] II. Adaptive learning algorithm based on L2-norm Sintering process data usually has problems such as limited samples and noise interference, and standard GRU is prone to overfitting, affecting the generalization performance of alkalinity prediction. Therefore, the present application proposes an adaptive regularization learning algorithm based on L2-norm, which dynamically adjusts the regularization strength to balance the prediction accuracy and model complexity.

[0042] ; The connection weights of the GRU neuron are represented as W xr , W hr , W xz , W hz , W xh , W hh and W y where, denotes the weight between the hidden layer and the output layer. Then these connection weights are combined into a matrix denoted as W. Given the input and the output data , the objective function L based on L2-norm after forward propagation is represented as: ; where T represents the number of training samples, W p is the weight vector at iteration p,λ Indicates the penalty factor; It is the output vector of K hidden neurons.

[0043] In traditional methods, the regularization coefficient is usually fixed, making it difficult to adapt to the dynamic changes in sintering conditions. Therefore, this invention proposes an adaptive adjustment strategy that dynamically determines the regularization strength based on the weight dispersion and the rate of change of prediction error.

[0044] Weight dispersion is used to reflect model complexity and is defined as: ; ; Where M represents the number of weights; The average value representing the weights; The standard deviation represents the dispersion of the weights.

[0045] To reflect the prediction accuracy of GRU, an error rate is defined at iteration p as follows: ; Considering the prediction accuracy and weight dispersion of the network, an adaptive regularization term is defined as follows: .

[0046] The above design achieves the following effects: when the prediction error increases, the regularization constraint is strengthened to prevent overfitting; when the weight dispersion is high, the parameter constraint is strengthened to improve the model stability; when the model tends to converge, the regularization strength is automatically weakened to avoid underfitting.

[0047] Next, the backpropagation time (BPTT) algorithm is used to adaptively learn the parameters. The gradient vector of the GRU neuron is calculated as follows ( (This refers to the gradients transmitted from the previous layer and the next time step): ; ; Weight gradient calculation includes a regularization term: ; in It is a general symbol that can represent r, z, or h.

[0048] The parameters are updated using the BPTT algorithm as follows: ; Where α represents the learning rate.

[0049] III. Hidden Neuron Growth Strategy Based on Sensitivity Analysis The complex and changeable sintering conditions require the prediction model to have good self-adaptive ability. The GRU with fixed structure is difficult to adapt to the change of conditions with different complexity, which may lead to overfitting in simple conditions or underfitting in complex conditions. Therefore, the embodiment of the present application further proposes a neuron dynamic growth strategy based on sensitivity analysis, as shown in Figure 2 The model automatically adjusts the network size according to the activation characteristics of the current sample.

[0050] The importance of neurons is measured by the activation intensity. For the kth hidden neuron, the activation intensity is defined as: ; Wherein, is the kth component of the hidden state vector h t .

[0051] The neuron sensitivity reflects the response intensity of the current input: ; This index normalizes the activation value of each neuron, which is convenient for comparing the importance of different neurons.

[0052] When the sintering condition is complex and the existing neurons cannot fully represent the input characteristics, the activation intensity of all neurons is high. Given a sensitivity threshold θ 0, the condition for the growth of hidden neurons is defined as: ; This condition shows that the current sample can strongly activate all existing neurons, indicating that the network capacity is insufficient, and a new neuron needs to be added to enhance the expression ability.

[0053] The initialization of the new neuron adopts a transfer learning strategy based on high-sensitivity neurons. The hidden neurons are arranged in descending order of sensitivity, and the parameters of the first two neurons are combined: ; Wherein, are the weights of the two neurons with the highest sensitivity, is the corresponding bias.

[0054] The above transfer learning strategy based on high-sensitivity neurons is used to initialize the new neuron, which inherits the feature expression ability of important neurons and can effectively avoid the training instability that may be caused by random initialization; at the same time, the parameter averaging reduces the impact of the new neuron on the existing structure; and the absolute value operation ensures the effectiveness of the parameters.

[0055] And through the dynamic growth strategy, the model can adaptively adjust the structure according to the complexity of the sintering working condition, keep compact structure to avoid overfitting in simple working condition, and expand capacity to improve expression ability in complex working condition, realizing the dynamic matching of structure complexity and task difficulty.

[0056] IV. Theoretical convergence analysis Considering that dynamic structure change may affect the stability of the algorithm, this study establishes a convergence proof framework for RSO-GRU based on Lyapunov stability theory. For the fixed structure training phase and the dynamic growth phase, respectively, the corresponding Lyapunov function is constructed, and it is proved that under the condition of satisfying the specific learning rate, the algorithm can converge to the local optimal solution. In addition, the influence of structure growth on convergence is analyzed, which provides theoretical guidance for algorithm parameter setting and industrial application.

[0057] (1) Fixed structure For the fixed structure of GRU, a Lyapunov function is defined as follows: ; Where , in the training process, the change of Lyapunov function is defined as follows: ; Theorem 1. Assuming that the number of hidden neurons of RSO-GRU is K, the weights and bias parameters of the model are updated during the training process, and α represents the learning rate of RSO-GRU training phase. If , the convergence of RSO-GRU can be guaranteed.

[0058] Proof: The change of Lyapunov function can be expressed as: ; Where, when the learning rate α satisfies the condition, , that is, .

[0059] Therefore, the convergence of Theorem 1 is proved.

[0060] (2) Growth structure stage Theorem 2. For RSO-GRU, if a new sample satisfies the neuron growth mechanism, the convergence of the proposed RSO-GRU can be guaranteed.

[0061] Proof. Assuming that after adding a new neuron, the number of neurons in the hidden layer is K+1. The error of RSO-GRU with K neurons at cycle p is defined as . The error after adding a neuron is .

[0062] ; Since the weights and activation functions are usually initialized or constrained such that the added terms can reduce the error or have little impact, it can be proved that the error will not increase: ; Therefore, after adding neurons, the error of RSO-GRU will not increase. According to Theorem 1, = 0, thus completing the convergence proof of Theorem 2.

[0063] Based on Theorem 1 and Theorem 2, the convergence of the RSO-GRU model can be guaranteed.

[0064] In summary, the RSO-GRU method of the present application can guarantee the convergence and stability of sinter basicity prediction in theory through adaptive regularization and dynamic structure adjustment, thereby providing a reliable theoretical basis for industrial application.

[0065] Example 1 This example verifies the prediction model of the present application based on time series samples of an actual steel plant, combined with Figure 13 as shown in the figure, the specific verification process is as follows: I. Data set collection and preprocessing The data set used in this example is collected from the iron ore sintering process of a steel plant. To solve the problem of time delay between process variables and quality indicators, data collection is based on sampling point distance and running state of the sintering process. As shown in Table 1, based on different sampling times, 15 variables are collected, of which the sinter basicity of finished sinter is the output variable, and the rest are input variables closely related to the output variable. First, record the sampling time of the output variable, then use the backtracking strategy to obtain the sampling time of other variables.

[0066] Since there is a sampling error in the speed variable (e.g., the speed of the batching belt) in Table 1, the calculation accuracy of the time delay can be further improved by searching for the maximum correlation between the input sequence and the output in the next step.

[0067]

[0068] where k is the current sampling time, represents the input data collected by the backtracking strategy in Table 1, is the input sequence, s j is the delay step for adjusting the sampling time, is used to calculate the correlation coefficient between x and y: ; Taking the mixture CaO (variable 12) in Table 1 as an example, the correlation between the sequence and the output variable (sinter basicity) is shown in FIG. 1. Figure 3 When j is 105, the correlation coefficient reaches the maximum value. Therefore, the delay step j provides further correction to the sampling time.

[0069] Through the above measures, 1100 time series samples are obtained at intervals of 2 hours from the sintering process. The first 880 samples are used for training, and the remaining 220 samples are used for testing.

[0070] Table 1 Data collection based on different sampling times

[0071] wherein, v 1, v 2, v 1, 2, and 3 represent the belt speeds of different sections, l , l 1, l 2, l 1, 2, and 3 represent the corresponding distances, t 1, t 2 represent the mixing time, and D represents the diameter of the tray.

[0072] II. Feature selection The sintering process involves numerous process parameters. Directly using all variables for modeling not only increases computational complexity, but also may introduce noise interference, reducing the prediction accuracy and generalization ability of the model. To select the feature subset that contributes most to the prediction of sinter basicity from the 15 original process variables, this embodiment adopts a multi-level feature selection strategy, combining correlation analysis and random forest importance evaluation to achieve effective dimensionality reduction of features.

[0073] (1) Correlation analysis First, Pearson correlation analysis is used to preliminarily identify the linear relationship strength between each process variable and sinter basicity, as well as between variables.

[0074] Figure 4 The Pearson correlation coefficient matrix heat map of the main variables is shown in FIG. 2. From the figure, it can be observed that the mixture CaO content (%) and sinter basicity show the strongest positive correlation (r = 0.89), followed by the lime ratio (r = 0.72) and the mixture SiO2 (r = -0.65, negative correlation). At the same time, there is strong multicollinearity between some variables, such as the correlation coefficient between the mixture CaO and the lime ratio reaching 0.81, indicating that the problem of multicollinearity needs to be considered in subsequent modeling.

[0075] (2) Feature importance evaluation based on random forest Correlation analysis can identify the linear relationship between variables, but it is difficult to effectively capture the complex nonlinear relationship existing in the sintering process. Therefore, the embodiment further uses the random forest algorithm to evaluate the comprehensive contribution of each feature to the prediction of sinter basicity.

[0076] Random forest evaluates feature importance by constructing multiple decision trees and aggregating their prediction results. For regression tasks, the importance of a feature is measured by the average reduction in impurity across all decision trees: j

[0077] wherein, FI j represents the importance score of feature j , N is the number of decision trees, T i represents the set of all nodes of the i th tree, p (t) is the sample weight proportion of node t , and is the reduction in impurity caused by feature j at node t .

[0078] Figure 5 The results show that the importance score of the mixture SiO2 is the highest (0.4048), which is consistent with its status as the denominator of the sinter basicity calculation formula; the mixture CaO ranks second (0.3070), reflecting its direct contribution to basicity; the proportion of quicklime ranks third (0.1657), reflecting the important role of flux proportioning in basicity adjustment.

[0079] Based on the random forest evaluation results and considering engineering practice and calculation efficiency, the embodiment selects the top 10 features in terms of importance score as the input variables of the RSO-GRU model. Table 2 details the final selected features and their importance scores. The cumulative importance contribution of the top 10 features reaches 98.9%, effectively representing the main factors affecting sinter basicity in the sintering process.

[0080] Table 2 Final feature selection results based on random forest evaluation

[0081] III. Model evaluation indicators ​To comprehensively and multi-angelly evaluate the prediction performance of the proposed model, the present application selects four widely used statistical indicators: mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R²) and mean absolute percentage error (MAPE). Table 3 lists the formulas, definitions and physical meanings of each evaluation index in detail.

[0082] Table 3 Different evaluation methods

[0083] Note: In the table, is the true value, is the model prediction value, is the true average value, is the model prediction average value, and n is the sample size.

[0084] Four, RSO-GRU model effectiveness analysis 1. RSO-GRU model prediction performance evaluation Figure 6 The left area shows the comparison between the predicted value and the true alkalinity value of the RSO-GRU model on the 220 test samples. From the figure, it can be observed that the predicted curve is highly consistent with the true curve, and the model can accurately capture the trend of sinter alkalinity. Especially in the interval with large fluctuation of alkalinity value (samples 150-180), the model still maintains good tracking ability, indicating that the model has strong nonlinear mapping ability and generalization performance.

[0085] Figure 6 The right area shows the probability density distribution of the prediction error, which approximately obeys the normal distribution with mean 0, and 68.2% of the prediction error falls within ±0.02, and 95.4% of the prediction error is controlled within ±0.04. It shows that the model has no obvious systematic deviation, and the prediction result has good unbiasedness and consistency.

[0086] Table 5 lists the quantitative performance indicators of the RSO-GRU model in detail. The RMSE on the test set is 0.0201, and the MAE is 0.0158. Relative to the typical value range of sinter alkalinity (1.8-2.2), the prediction error is controlled at a low level. The R² value reaches 0.8505, indicating that the model explains 85.05% of the data variability. The MAPE is only 0.81%, which means that the average prediction error is less than 1%, meeting the precision requirements of industrial applications.

[0087] Table 5 RSO-GRU model prediction performance indicators

[0088] The above results show that the RSO-GRU model achieves excellent performance on the sinter basicity prediction task. To understand the internal reasons for the excellent performance of the model, the working principle of the core mechanism will be analyzed in detail below.

[0089] 2. Analysis of hidden neuron self-organizing process The key to the excellent performance of the RSO-GRU model lies in its dynamic structure adjustment capability, and this paper analyzes the neuron self-organizing growth mechanism based on sensitivity. As shown in Figure 7 , the evolution trajectory of the number of hidden layer neurons (red curve) and RMSE (blue curve) of the RSO-GRU model during training is shown. From the figure, it can be observed that the number of neurons presents a stepwise growth pattern, from the initial 10 neurons rapidly growing to 23 within the first 50 epochs, then the growth rate gradually slows down, reaching 26 neurons during 150-200 epochs, and finally stabilizing at 28 neurons, with a total growth rate of 180%. At the same time, the RMSE presents a clear downward trend, rapidly decreasing from 1.0 at the beginning of training to 0.4, then slowly converging and finally stabilizing at around 0.20. The two curves show a significant negative correlation: the rapid growth period of neurons corresponds to the sharp decline of RMSE, while the growth stagnation period of neurons corresponds to the stable convergence of RMSE. Meanwhile, the two growth stagnation periods near the 150th and 350th epochs correspond to the periods when RMSE reaches local stability, which verifies that the neuron growth strategy based on sensitivity analysis can dynamically adjust the network structure according to the performance requirements of the model, effectively controlling the model complexity while ensuring the prediction accuracy.

[0090] To further reveal the triggering mechanism of neuron growth, Figure 8 the role of the sensitivity threshold is detailed. As shown in Figure 8 , the triggering of the neuron growth mechanism is shown when the sensitivity threshold θ0=0.08. The blue solid line in the figure represents the change trajectory of the maximum neuron sensitivity θ k during training, the red dashed line marks the preset sensitivity threshold 0.08, and the red vertical line marks the triggering time that meets the growth condition. From the figure, it can be observed that the neuron growth presents obvious stage characteristics. In the early training period (0-50 epochs), due to the insufficient network capacity to fully represent the data features, θ k frequently exceeds the set threshold, triggering intensive neuron growth events, with an average of one growth triggered every 2-3 epochs. As the network structure gradually improves, the triggering frequency significantly decreases, with only 4 triggering events occurring during 50-150 epochs, and triggering becomes even rarer after 150 epochs. At the same time, the maximum sensitivity θ kThe overall level of the whole network shows a downward trend, from the initial 0.3 to gradually reduce to 0.07 or less and tend to be stable. This change mode verifies the adaptive characteristics of the proposed growth strategy: when the existing neurons cannot fully represent the input complexity, the network capacity is automatically expanded, and when the network capacity is sufficient, the growth is naturally stopped, achieving a dynamic balance between structural complexity and task demand.

[0091] 3. Analysis of adaptive regularization process As Figure 9 The adaptive regularization parameter changes in the training process. From the figure, we can observe that, shows a clear three-stage feature: Early training (0-50 epochs) The value is high, in the range of 10 -3 to 10 -2 orders of magnitude, reflecting the characteristics of uneven network weight distribution and large error changes; Mid-training (50-150 epochs) Gradually decreased to 10 -4 to 10 -3 orders of magnitude, but the fluctuation amplitude increases, indicating that the network has begun to converge but still needs dynamic adjustment; Late training (after 150 epochs) Stable at 10 -4 orders of magnitude, with significantly reduced fluctuations, indicating that the network has reached a good weight balance state.

[0092] This adaptive change mode verifies that the proposed regularization strategy can dynamically adjust the constraint strength according to the network training state, providing strong constraints to prevent overfitting in the early training stage, and reducing the constraints to avoid underfitting in the late training stage.

[0093] To further analyze the calculation mechanism of the adaptive regularization parameter . Figure 10 At the same time, the evolution trajectory of the weight dispersion (blue curve, left Y-axis) and the prediction error rate Δermsep (purple curve, right Y-axis) in the training process is shown. From the figure, we can observe that the two curves show a significant positive correlation, verifying the rationality of the adaptive regularization term . In the early training stage (0-50 epochs), the weight dispersion rapidly decreased from the peak value of 0.18 to about 0.10, while the prediction error rate Δermsep showed a sharp fluctuation, changing in the range of -0.006 to +0.006, corresponding to a strong regularization constraint requirement. In the mid-training stage (50-150 epochs), Continuing to decline slowly and stabilize in the 0.06-0.10 interval, the fluctuation amplitude of Δermsep gradually decreases and is concentrated in the ±0.003 range. In the later training period (after 150 epochs), Stable at a low level of about 0.06, Δermsep basically converges to 0, and the fluctuation amplitude is further reduced to ±0.002, indicating that the network weight distribution tends to be uniform and the prediction error is stable and improved. This synergistic change mechanism ensures that the regularization parameter can be accurately adjusted according to the actual training state of the network.

[0094] As shown in Table 7 below, the influence of different regularization strategies on model performance. The experimental results show that the MAE of the method without regularization is 0.0219, the RMSE is 0.0283, the R² is 0.7038, and the MAPE is 1.1236%; the method using a fixed regularization parameter λ p =0.01 significantly improves all indicators, with MAE reduced to 0.0176, RMSE to 0.0213, R² to 0.8317, and MAPE to 0.9032%; while excessive regularization (λ p =0.1) leads to a significant decline in performance, with MAE increasing to 0.0278, RMSE to 0.0361, R² to 0.5173, and MAPE to 1.4304%; while the adaptive regularization method proposed in the present application achieves the best results in all evaluation indicators, with MAE only 0.0158, RMSE 0.0201, R² 0.8505, and MAPE 0.8126%, proving that adaptive adjustment of the regularization parameter can more effectively improve the prediction accuracy and generalization performance of the model.

[0095] Table 7 Influence of regularization on model performance

[0096] In summary, the RSO-GRU model can effectively realize the dual adaptive adjustment of network structure and regularization strength through the synergistic effect of the two core mechanisms of dynamic neuron growth and adaptive regularization, thereby achieving excellent performance in the sinter basicity prediction task.

[0097] Four, comparison of model prediction performance To comprehensively verify the superiority of the RSO-GRU model, it is compared with various mainstream time series prediction methods, including traditional machine learning methods and deep learning methods, for comprehensive evaluation. To ensure the fairness of the comparison experiment, all models are trained and tested under the same hardware and software environment. The same data preprocessing method and training-test division strategy (80%-20%) are adopted, and the stability of the results is ensured through 5-fold cross-validation. The parameter configurations of each comparison model are shown in Table 8. Among them, the network structure in this embodiment is [10→45], indicating that the number of neurons increases from the initial fixed 10 to 45.

[0098] Table 8 Parameter configurations of various comparison models

[0099] The detailed performance comparison results of each model are shown in Table 9. According to Table 9, the RSO-GRU model exhibits the best performance in all evaluation indicators. Compared with the second-best GRU model, the MAE of RSO-GRU is reduced by 16.4%, the RMSE is reduced by 15.2%, the MAPE is reduced by 16.6%, and the R² is increased by 5.81 percentage points. These data strongly prove the effectiveness of the proposed adaptive structure adjustment and regularization mechanism in improving prediction accuracy.

[0100] Table 9 Prediction results of different models

[0101] To further evaluate the prediction performance of each model, this paper visualizes the prediction results of six models (RSO-GRU, LSTM, GRU, BP, SVR, RF). Figure 11 The three-dimensional scatter plot shows the fitting relationship between the predicted values and the true values of each model. In this figure, the degree of data points fitting the diagonal dashed line (i.e., predicted value = true value) directly reflects the prediction accuracy of the model. The observation results show that the scatter points (blue) of the RSO-GRU model are highly concentrated on the diagonal dashed line, showing a strong linear correlation, indicating that there is a very small deviation between the predicted values and the true values. In contrast, the scatter points of other models show different degrees of dispersion, among which the dispersion of traditional machine learning models RF and SVR is particularly significant, indicating that their prediction results have a large uncertainty.

[0102] For a more in-depth quantitative analysis of the prediction error, Figure 12Frequency distribution histograms of the prediction errors (defined as the difference between the predicted value and the true value) of each model are plotted. The prediction stability of the model can be measured by the concentration trend and the dispersion degree of the error distribution. As can be seen from the figure, the error distribution of the RSO-GRU model presents a narrow peak shape with an approximate mean of zero (μ = 0.002), and its standard deviation is the smallest among all the compared models. This shows that the prediction error of the RSO-GRU model not only has small systematic bias, but also has the optimal stability. The error distribution of other models is relatively wider, and the standard deviation is greater than that of the RSO-GRU, verifying that the fluctuation of the prediction results is the largest.

[0103] In summary, the present application has the following technical advantages over the prior art: 1. Dynamic adaptability and generalization ability The synergistic evolution of weight dispersion and error rate ensures that the regularization parameter dynamically adapts to the training state, avoiding overfitting. The self-organizing strategy realizes adaptive adjustment of the network size through neuron sensitivity analysis. In simple working conditions, a compact structure is maintained to avoid overfitting; in complex working conditions, the capacity is automatically expanded to improve the expression ability. Compared with LSTM, the self-organizing strategy reduces redundant neurons and optimizes the computational complexity, improving the training efficiency while ensuring accuracy, and is more suitable for industrial real-time prediction scenarios.

[0104] 2. Significant improvement in prediction accuracy (1) Compared with the standard GRU MAE is reduced by 16.4%, RMSE is reduced by 15.2%, MAPE is reduced by 16.6%, and the prediction error distribution is more concentrated; R² is increased by 5.8%, indicating that the model's ability to explain the changes in sinter basicity has significantly improved, and it can more accurately capture the nonlinear relationships in the data.

[0105] (2) Compared with traditional algorithms Compared with traditional algorithms such as SVR and RF, the R² of RSO-GRU is increased by 9.3% and 17.3% respectively, and the error distribution is more concentrated.

[0106] 3. Proof of theoretical convergence and dynamic stability Based on the Lyapunov stability theory, a convergence proof framework is constructed for the fixed structure and the growth stage respectively. Under the fixed structure, when the learning rate satisfies , the error converges to 0; after adding new neurons in the growth stage, the error does not increase ( ), ensuring stable training of the model.

[0107] In addition, the prediction model and method of the present application can achieve the following practical application values: 1. Breakthrough detection and process lag, support for implementation of control To address the dual constraints of "detection lag (offline testing for several hours)" and "process lag (process delay for several hours)" in the sintering process, the method predicts the alkalinity trend in advance by forecasting the range, controls the alkalinity fluctuation range within a certain range, guides the adjustment of raw material ratio, and avoids control errors caused by lag.

[0108] 2. Improve production quality and economic efficiency Accurate prediction of alkalinity can optimize the mineral composition of sintered ore, which is beneficial to promoting the formation of calcium ferrite and improving strength and reducibility. The model has R²=0.8505 and MAPE=0.8126%, which meets the requirements of industrial accuracy and promotes the transformation of prediction models from theoretical research to production applications.

[0109] 3. Robustness to adapt to complex working conditions Dynamic structural adjustment and adaptive regularization enable the model to maintain high reliability even under scenarios such as fluctuations in raw material composition and changes in equipment operating conditions.

Claims

1. A sinter ore alkalinity prediction model construction method, characterized by, The method comprises the following steps: Data acquisition and preprocessing: collecting time series sample data of sinter basicity and process parameters related thereto, and dividing the sample data into a training set and a test set; Constructing a sinter basicity prediction model based on a regularized self-organizing GRU; Training and optimizing the model using the training set data, and automatically adjusting the number of hidden neurons during the model training process using a dynamic growth strategy based on sensitivity analysis; Testing the model using the test set data.

2. The sinter basicity prediction model construction method according to claim 1, characterized by, The data acquisition and preprocessing further comprises: using a multi-level feature selection strategy to perform dimensionality reduction processing on the collected process parameters related to sinter basicity by combining correlation analysis and random forest importance evaluation, so as to obtain a feature subset that contributes most to the prediction of sinter basicity; wherein the process parameters related to sinter basicity include raw material ratio, moisture and machine speed.

3. The sinter basicity prediction model construction method according to claim 1, characterized by, The number of hidden neurons is automatically adjusted by using a dynamic growth strategy based on sensitivity analysis, specifically, the sensitivity of each neuron is calculated θ k , given a sensitivity threshold θ 0, the condition for hidden neuron growth is defined as: ； wherein the sensitivity of each neuron θ k is calculated as follows: ； is the activation strength of the kth hidden neuron, and K is the number of hidden neurons.

4. The sinter basicity prediction model construction method according to claim 3, characterized by, The newly added neurons are initialized using a high-sensitivity neuron-based transfer learning strategy, specifically, the hidden neurons are arranged in descending order of sensitivity, and the parameters of the first two neurons are combined: ； wherein, are the weights of the two neurons with the highest sensitivity, respectively, are the respective biases.

5. The sinter basicity prediction model building method according to any one of claims 1 to 4, characterized by, In the model training process, an adaptive regularization mechanism based on L2 norm is introduced on the basis of standard GRU, that is, the input weights of all input data of the model are regularized, and the regularization coefficient is dynamically adjusted through a double feedback mechanism based on the weight dispersion and the change rate of prediction error Δermse p . λ p : ; wherein the weight dispersion is defined as follows: ； ； M denotes the number of weights; W p is the number of iterations p the weight vector at iteration denotes the average of the weights; The rate of change of the prediction error at iteration p, Δermse p is defined as follows: ； and are the predicted and actual basicity values, respectively, and T is the number of training samples.

6. The sinter basicity prediction model construction method according to claim 5, characterized by, The sinter basicity prediction model based on the regularized self-organizing GRU further comprises: using a backpropagation through time (BPTT) algorithm to adaptively learn the weight and bias parameters of the model.

7. The sinter alkalinity prediction model construction method according to any one of claims 1 to 4, characterized by, The model evaluation indicators during the testing of the model using the test set data include mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R²), and mean absolute percentage error (MAPE).

8. A sinter ore alkalinity prediction method characterized by, The method comprises the following steps: Constructing a sinter basicity prediction model using the method of any one of claims 1-7; Collecting process parameters related to sinter basicity and inputting them into the sinter basicity prediction model for prediction, thereby obtaining a sinter basicity prediction result.

9. A sinter ore alkalinity prediction device characterized by, The method comprises the following steps: A model construction module for constructing a sinter basicity prediction model based on a regularized self-organizing GRU; A data acquisition module for acquiring process parameters related to sinter basicity; and A prediction module for inputting the process parameters related to sinter basicity into the sinter basicity prediction model based on a regularized self-organizing GRU, thereby obtaining a sinter basicity prediction result.

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