Blast furnace molten iron silicon content prediction method based on improved grey goose algorithm

Abstract

The invention provides a blast furnace molten iron silicon content prediction method based on an improved grey goose algorithm, and relates to the technical field of intelligent prediction, and the method comprises the following steps: collecting multi-dimensional process parameters in a blast furnace operation process, and synchronously recording corresponding silicon content data; performing abnormal value elimination and normalization processing on original parameter data, dividing a training set and a test set, constructing an initial prediction model of the BP neural network, optimizing training parameters of the BP neural network by using an improved grey goose algorithm, and dynamically adjusting step parameters in the algorithm along with the distance between an individual and a global optimal solution. Fusing a velocity field constructed based on a local curvature factor and a local density factor, updating an individual position in a global search stage, reconstructing a final prediction model according to an optimization result, and performing convergence training by using a training set; and finally inputting the test set into the prediction model, and outputting a blast furnace molten iron silicon content prediction result. The method is suitable for blast furnace molten iron component control and has the advantages of being stable in optimization, small in error and high in real-time performance.

Description

Technical Field

[0001] This invention relates to the field of data prediction, and specifically to a method for predicting the silicon content of molten iron in blast furnaces based on an improved Grey Goose algorithm. Background Technology

[0002] The silicon content of blast furnace hot metal is one of the quality indicators that reflects the furnace's thermal intensity, reducing atmosphere, hearth reaction balance, and overall smelting status. Its changes not only directly affect the quality of hot metal, but also have a chain reaction on the production stability of the entire blast furnace, fuel consumption, raw material utilization efficiency, and subsequent steelmaking processes.

[0003] Meng et al. proposed an integrated data-driven method combining gradient boosting tree and automatic hyperparameter search to address the problem of silicon content prediction in blast furnace molten iron. The core of this method is to use the Optuna framework to optimize the hyperparameters of the GBDT model to obtain high-precision and stable silicon content prediction results. However, when the blast furnace condition fluctuates drastically and the coupling relationship is extremely complex, the fitting ability of GBDT is not as good as that of deep neural networks. In addition, GBDT itself does not have memory capabilities and cannot characterize temporal relationships.

[0004] The Grey Goose Optimization (GGO) algorithm employs a quadratic decay mechanism in its stochastic update model, causing the control parameter z to decrease rapidly in early iterations. This can lead to premature convergence of the GGO algorithm. Since the GGO algorithm still needs to search a wide range of solutions for the global optimum during the initial exploration phase, if the control parameter z decreases too quickly, it will prematurely fall into local optima and lack sufficient global exploration capability. In the design of the Grey Goose Optimization algorithm, the decay of the control parameter z depends entirely on the iteration number t and the maximum iteration number T, lacking the ability to dynamically adjust based on the quality of the current solution or the search state. This fixed decay method ignores the dynamic requirements of the Grey Goose Optimization algorithm in different problems or at different stages. Summary of the Invention

[0005] To address the issue of low accuracy in predicting silicon content in blast furnace hot metal using existing methods, this invention proposes a data analysis-based method for predicting silicon content in blast furnace hot metal. This method utilizes an improved Grey Goose Optimization (ZGGO) algorithm to optimize the number of hidden layers in a backpropagation (BP) neural network. With learning rate factor By adjusting parameters, the prediction accuracy of the BP neural network prediction model can be improved, meeting the requirements of complex geological environments and diverse data dimensions. It is an efficient, universal, and highly adaptable prediction method.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solution: a method for predicting the silicon content of blast furnace hot metal based on an improved grey goose algorithm, specifically including the following steps: Acquire process parameters during blast furnace operation and record silicon content data in molten iron at corresponding times; The process parameters are preprocessed to remove outliers and noisy data, and the data is normalized to divide the dataset into training and testing sets. A first model for predicting the silicon content of blast furnace molten iron is constructed using a BP neural network. The first prediction model includes an input layer, a hidden layer, and an output layer. The training parameters of the first prediction model are optimized using an improved grey goose optimization algorithm. The improved grey goose optimization algorithm includes improving the step size parameter using a relation factor and dynamically adjusting the step size parameter according to the distance between the current search individual position and the global best solution. A local curvature factor is constructed based on the spatial positional relationship between the current search individual and its neighboring individuals, and local density information is constructed based on the individual distribution of the current search individual within a preset neighborhood range. The local curvature factor and the local density information are used to construct a velocity field data vector. The positions of individual search objects in the global search phase are updated using improved step size parameters and velocity field data vectors; The prediction model for silicon content in blast furnace hot metal was reconstructed using the optimized training parameters, and then finally trained on the training set to obtain the second prediction model. The test set is input into the second prediction model, and the training is iterated continuously. The prediction effect is calculated through the mean square error function until the target prediction error of silicon content in blast furnace iron is reached, and the prediction result of silicon content in blast furnace iron is output.

[0007] Preferably, in the selected method for predicting the silicon content of molten iron in blast furnaces, multiple process parameters during blast furnace operation are selected as prediction input data, including four characteristic data: hot blast temperature, hot blast flow rate, oxygen enrichment, and pulverized coal injection rate. N sets of input data are recorded, and each set of input data includes the four characteristic data of hot blast temperature, hot blast flow rate, oxygen enrichment, and pulverized coal injection rate for the same time period. The output data is the silicon content of molten iron at the corresponding time.

[0008] Preferably, the random shuffling of multiple process parameters is used to prevent overfitting of the blast furnace hot metal silicon content prediction model, prevent data from exhibiting order dependencies, and ensure that the training and test sets have good representativeness. Data preprocessing after random shuffling, and the division into training and test sets, helps the prediction model better learn the impact of environmental parameters on the blast furnace hot metal silicon content. Data preprocessing includes handling missing and outlier values, and normalization. The training set is used to train the blast furnace hot metal silicon content prediction model. Through repeated training, the prediction model gradually learns the relationship between input features and the blast furnace hot metal silicon content. The test set is used to predict the blast furnace hot metal silicon content. The test set represents a real-world application scenario. The performance on the test set can be used to evaluate the effectiveness of the blast furnace hot metal silicon content prediction model in a real-world environment, i.e., whether the model can correctly predict the blast furnace hot metal silicon content on new data.

[0009] Preferably, the first model for predicting the silicon content of blast furnace hot metal is a prediction model constructed based on a standard BP neural network. In this model, the hidden layers extract useful feature representations from the input data features through weighted connections and nonlinear transformations. The number of hidden layers determines the accuracy of the prediction model for the silicon content of blast furnace hot metal. The predictive ability of the model increases with the number of hidden layers, but too many layers can lead to overfitting. Therefore, the number of hidden layers is a parameter that needs to be optimized using advanced methods in this invention to improve the accuracy of the prediction of silicon content in blast furnace hot metal.

[0010] Preferably, the training parameters include the number of hidden layers n and the learning rate factor k; a mapping relationship is established between the search individual positions of the improved Grey Goose optimization algorithm and the number of hidden layers and the learning rate factor of the prediction first model. In each iteration of the improved Grey Goose optimization algorithm, a set of candidate positions is generated by updating the mathematical model through the Grey Goose individual positions, wherein each candidate position represents a set of parameter combinations of the number of hidden layers n and the learning rate factor k.

[0011] Preferably, the learning rate factor k affects the weight update of the prediction model built on the standard BP neural network. The learning rate factor controls the step size of each weight update. If the learning rate is too large, the weights will be too large, resulting in unstable training of the prediction model. If the learning rate is too small, the training speed of the prediction model will be slow and it will be difficult to converge to the global optimum. For the prediction model of silicon content in blast furnace iron, the learning rate needs to be optimized and a suitable learning rate factor needs to be selected.

[0012] Preferably, the step size parameter is constructed by constructing a target range based on preset upper and lower limits of step size, normalizing the gradient statistics results corresponding to the current position of the search individual and the difference in current fitness, and proportionally mapping the improved step size parameter to the target range based on the function ratio between relation factors. The improved mathematical model for the step size parameter is as follows: ; In the formula, Let be the improvement step size parameter for the current i-th search individual. and These are the maximum and minimum values ​​of the step size parameter. Relationship factor; The search term is the average value of the position gradient function of the i-th individual in the t-th iteration. The mathematical model is as follows: ; In the formula, The position of the i-th search individual in the t-th iteration The distance from the i-th search individual's position to the t-th iteration is the k-th closest position. distance, for The fitness function value, for The fitness function value; Relationship Factor The mathematical model is as follows: ; In the formula, t is the current iteration number, and T is the maximum iteration number.

[0013] Preferably, an individual position update model is constructed based on the current solution of the current search individual and the positions of its three corresponding neighbor individuals. The solution difference and weighted response between the search individual and its neighbors are controlled by the first and second control factors, respectively, and the position of the current search individual is adjusted in combination with the improved step size parameter.

[0014] Preferably, the local curvature factor includes obtaining the spatial positions of all search individuals in the current iteration, and constructing a dynamic manifold vector from the positions of the N search individuals as a point set. This maps discrete search points to sampling points in continuous space. The dynamic manifold vector Select two reference points adjacent to the current search individual's position, construct a spatial difference component based on the positional difference between the two reference points and the current search individual, and construct the local curvature factor of the current search individual based on the spatial difference component. .

[0015] Preferably, the degree of clustering of the surrounding area of ​​the current search individual is accumulated based on the spatial distance between the current search individual and all other search individuals to obtain the local density information of the local area distribution state of the current search individual; Based on the local curvature factor and local density information of the current search individual, a curvature gradient vector representing the spatial variation trend is constructed using the curvature difference between the search individual and reference individuals in its neighborhood. The local curvature factor and local density information are then jointly processed and combined with the curvature gradient vector to construct a velocity field data vector representing the movement trend of the search individual. ; The position of the search individual at the current iteration time is updated based on the current position of the search individual and the velocity field data vector of the search individual's movement trend.

[0016] Preferably, the optimization of the training parameters of the prediction first model using the improved grey goose optimization algorithm includes: setting the total number of population N, the problem dimension Dim, the upper bound ub and lower bound lb of the search individual position, the maximum number of iterations T, and the maximum and minimum values ​​of the step size parameter in the improved grey goose optimization algorithm. The search individual positions of the improved grey goose optimization algorithm are randomly initialized, and the fitness function of the improved grey goose optimization algorithm is defined based on the real-time predicted and actual values ​​of silicon content in molten blast furnace iron. The fitness value of each individual's current position is calculated using the fitness function and compared with the fitness value of the individual's position in the previous iteration. The current minimum fitness value is retained. And the position of the search individual corresponding to the minimum fitness value is taken as the optimal position; If the current iteration number t is less than the maximum iteration number T, then update the search individual's position; otherwise, exit the optimization loop and output the optimal search individual's position. ,Will The optimal number of hidden layers and learning rate factor are determined. The improved Grey Goose optimization algorithm is used to update the position of the search individual. The updated position of the search individual is bounded between the upper bound ub and the lower bound lb. The current iteration number t is executed t+1, and the fitness value of each search individual position is calculated.

[0017] Preferably, the reconstructed blast furnace hot metal silicon content prediction model includes the following inputs: process parameters during blast furnace operation; an optimal number of hidden layers; and an output layer of 1. In the forward propagation, the input layer passes the input environmental parameter data to the hidden layers. Each hidden layer receives the input signal from the previous layer, calculates a weighted sum, and performs a nonlinear mapping using the ReLU activation function f. The output of the hidden layers, after final weighting, is passed to the output layer. The output layer performs the final calculation to obtain the current predicted value of the blast furnace hot metal silicon content. The prediction error is calculated using the mean squared prediction error function, and the weights in the prediction model are updated using the optimal learning rate factor and the prediction error backpropagated. The first prediction model re-propagates forward based on the new weights, calculates the new prediction error, and continues until the target prediction error for the silicon content of blast furnace molten iron is reached, and then outputs the final predicted silicon content of blast furnace molten iron.

[0018] Compared with the prior art, the beneficial effects of the present invention are: by introducing a dynamic step size adjustment mechanism for the fusion relation degree factor, the present invention solves the problem that the traditional grey goose optimization algorithm converges too quickly in the initial search stage and is prone to getting trapped in local optima. In the location update strategy, local curvature factor and local density information are jointly considered to construct a velocity field data vector with directionality and clustering. The solution is updated by the velocity field data vector, and the search individual can flexibly adjust the migration direction according to environmental changes, thereby significantly improving the global optimization ability and robustness. The improved Grey Goose optimization algorithm was applied to the prediction of silicon content in blast furnace hot metal. By adaptively adjusting the number of hidden layers and the learning rate factor of the BP neural network, the prediction model of silicon content in blast furnace hot metal can still maintain high accuracy and good generalization performance in the actual smelting scenario with large fluctuations in blast furnace process parameters and complex time series correlations. Attached Figure Description

[0019] Figure 1 A flowchart illustrating the steps of a method for predicting the silicon content in blast furnace molten iron.

[0020] Figure 2 The flowchart shows the predicted silicon content of blast furnace hot metal output by the second model.

[0021] Figure 3 A fitness comparison chart showing the number of hidden layers and learning rate factor of the first prediction model optimized by the improved Grey Goose Optimization Algorithm and the standard Grey Goose Optimization Algorithm.

[0022] Figure 4 A comparison of the learning rate factor results between the improved Grey Goose Optimization Algorithm and the standard Grey Goose Optimization Algorithm.

[0023] Figure 5 A comparison of the hidden layer number results obtained by the improved Grey Goose Optimization Algorithm and the standard Grey Goose Optimization Algorithm.

[0024] Figure 6 This is a comparison chart of the silicon content results of blast furnace molten iron trained by the prediction model of this invention and existing prediction models.

[0025] Figure 7 This is a comparison chart of the prediction results of the prediction model of the present invention and the existing prediction model for the silicon content of blast furnace hot metal. Detailed Implementation

[0026] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. The following embodiments are only a part of the embodiments of the present invention and are used to provide a clearer explanation of the technical solutions of the present invention. It is understood that the specific embodiments described are only used to explain the present invention, but the implementation of the present invention is not limited thereto.

[0027] This invention provides a method for predicting the silicon content of blast furnace hot metal based on an improved grey goose algorithm, such as... Figure 1 As shown, simulations are performed in Matlab according to steps S1 to S6, including: S1. Obtain the process parameters during the operation of the blast furnace and record the silicon content data in the molten iron at the corresponding time. S2. Preprocess the process parameters to remove outliers and noise data, normalize the data, and divide the dataset into training and testing sets. S3. Construct a first model for predicting the silicon content of blast furnace molten iron using a BP neural network. The first prediction model includes an input layer, a hidden layer, and an output layer. S4. The training parameters of the first prediction model are optimized using an improved grey goose optimization algorithm. The improved grey goose optimization algorithm includes improving the step size parameter using a relation factor and dynamically adjusting the step size parameter according to the distance between the current search individual position and the global best solution. A local curvature factor is constructed based on the spatial positional relationship between the current search individual and its neighboring individuals, and local density information is constructed based on the individual distribution of the current search individual within a preset neighborhood range. The local curvature factor and the local density information are used to construct a velocity field data vector. S5. The positions of the search individuals in the global search stage are updated using the improved step size parameters and velocity field data vectors. The prediction model for silicon content in blast furnace hot metal is reconstructed using the optimized training parameters and finally trained on the training set to obtain the second prediction model. S6. Input the test set into the second prediction model, train iteratively, calculate the prediction effect through the mean square error function until the target prediction error of silicon content in blast furnace iron is reached, and output the prediction result of silicon content in blast furnace iron.

[0028] In the implementation of this application, four process parameters—hot blast temperature, hot blast flow rate, oxygen enrichment, and pulverized coal injection rate—are used as input data for predicting the silicon content of blast furnace hot metal. These process parameters are acquired through sensors, and 110 sets of input data are recorded. Each set of process parameter input data includes four characteristic data points: hot blast temperature, hot blast flow rate, oxygen enrichment, and pulverized coal injection rate, all within the same time period. The output data is the silicon content of the blast furnace hot metal. The process parameters and silicon content of the blast furnace hot metal during operation are summarized in an Excel spreadsheet and imported into a Matlab project using the xlsread function. The sample size N is calculated using the code: N=size(X, 1).

[0029] Furthermore, the process parameters are preprocessed; In the implementation of this application, the environment parameter data is randomly shuffled using the randperm function in the Matlab project. The code is: X=X(randperm(N), :). The shuffled environment parameter data is then preprocessed, including normalizing the shuffled environment parameter data to between 0 and 1. The mathematical model is as follows: ; In the formula, Let j be the j-th feature data after normalization of environmental parameters, where j=1,2,3,4; The j-th feature data before environmental parameter normalization. Let j be the minimum value of the j-th feature data before normalization of the environmental parameters. This represents the maximum value of the j-th feature data before the environmental parameters are normalized.

[0030] In this embodiment, the normalization process is implemented as follows: X_min=min(X); X_max=max(X); X_normalized=(X-X_min) . / (X_max-X_min); The shuffled and preprocessed dataset is divided into training and test sets in an 8:2 ratio, as shown in the following code: train_ratio=0.8; num_samples=size(X_normalized, 1); num_train=round(train_ratio*num_samples).

[0031] Furthermore, a first model for predicting the silicon content of blast furnace molten iron using a BP neural network was constructed. The first model for predicting the silicon content of blast furnace hot metal is a prediction model built on a standard BP neural network. In this model, the hidden layers extract useful feature representations from the input data features through weighted connections and nonlinear transformations. The number of hidden layers determines the accuracy of the prediction model for the silicon content of blast furnace hot metal. The predictive ability of the model increases with the number of hidden layers, but too many layers can lead to overfitting. Therefore, the number of hidden layers is a parameter that needs to be optimized using advanced methods in this invention to improve the accuracy of the prediction of silicon content in blast furnace hot metal.

[0032] In the implementation of this application, the input layer in Matlab was set to 4, which represents the number of process parameter features; the hidden layer was initially set to 3 and the output layer to 1; the learning rate factor k was initially set to 0.5, the number of training iterations was 800, and the target prediction error was 1e. -4 A standard backpropagation (BP) neural network is built using the feedforwardnet function, as shown in the code below: net = feedforwardnet(hidden_layer_size).

[0033] Furthermore, the improved Grey Goose optimization algorithm is used to optimize the number of hidden layers and the learning rate factor of the second prediction model, including: first, improving the mathematical model for updating individual positions in the Grey Goose optimization algorithm; second, the mapping relationship between the individual positions of Grey geese in the improved Grey Goose optimization algorithm and the number of hidden layers and the learning rate factor of the first prediction model; and third, updating the mathematical model for updating individual positions in the improved Grey Goose optimization algorithm and updating the search individual positions, wherein the search individual position value is the value of the number of hidden layers and the learning rate factor of the first prediction model.

[0034] In this embodiment, the Grey Goose optimization algorithm is improved, including a pre-improvement of the Grey Goose optimization algorithm. During the global search phase of the improved Grey Goose optimization algorithm, including the optimization of the hidden layer number and learning rate factor of the predicted second model, the distance between the current individual's position and the average position of the entire population in the current iteration is considered. Select the appropriate strategy to update the current individual position (current solution). Greater than a fixed threshold When this occurs, it indicates that the current solution is within the search space. If the solution is located in the edge region, the manifold distortion exploration strategy proposed in this invention is executed to enhance the global search trend; otherwise, it indicates that the current solution is close to the target solution, and a three-neighbor swarm exploration strategy based on the improved step size parameter is executed with a fixed threshold. Values .

[0035] Furthermore, the manifold distortion exploration strategy achieves automatic adjustment of the search direction and search range of individuals by constructing the spatial structure of the group.

[0036] Furthermore, the spatial positions of all search individuals in the current iteration are obtained, and the positions of the N search individuals are used as a point set to construct a dynamic manifold vector. This maps discrete search points to sampling points in a continuous space; wherein, the manifold vector based on the aforementioned dynamics... This serves as a basis for subsequent directional and intensity assessments; For any search individual in the current iteration, from the dynamic manifold vector Select two reference points adjacent to its location, where the two reference points are determined based on the search individual's position. The order of operations is determined by constructing spatial difference components based on the positional differences between two reference points and the current search individual. Based on these spatial difference components, a curvature index characterizing the geometric curvature of the region where the current search individual is located is used to construct the local curvature value of the current search individual. The specific mathematical model for implementation is as follows: ; in, The spatial location of the currently searched individual. and Let be the spatial positions of the (i+1)th and (i-1)th search individuals, and be the two adjacent reference points of the current search individual. It is 0.0001.

[0037] In this embodiment, the spatial difference component reflects the spatial relationship between the current search individual's location and the adjacent regions. The local curvature value of the current search individual constructed based on it reflects whether there are abrupt and irregular phenomena in the current space, which affects the search direction of the solution, thereby providing a quantitative basis for determining the exploration direction.

[0038] Furthermore, for any search individual in the current iteration, the density metric of its local distribution state is obtained by accumulating the clustering degree of its surrounding area based on the spatial distance between that search individual and all other search individuals. This density metric is generated by weighted accumulation of the distance information of each search individual, and the specific mathematical model is as follows: ; in, This is the density metric value for the i-th search individual in the current iteration. The position of the search individual is excluding the current search individual, n is the number of search individuals in the surrounding area of ​​the search individual, and λ is the distance sensitivity adjustment coefficient, which is set to 0.3 in this implementation. The distance sensitivity adjustment coefficient controls the degree of attenuation of the density metric by distance. The larger the distance sensitivity adjustment coefficient value, the smaller the density metric of the search individual that is farther away.

[0039] In this embodiment, the density metric of the local area distribution reflects the distribution of the area around the current search individual, and determines whether there is a large number of search individuals clustered in the area. The area around the search individual is determined by a preset neighborhood size n=5.

[0040] Furthermore, based on the local curvature and local density values ​​of the search individual, a curvature gradient vector representing the spatial variation trend is constructed using the curvature difference information between the search individual and reference individuals in its neighborhood. The local curvature and local density information are jointly processed and combined with the curvature gradient vector to construct the velocity field data of the search individual's movement trend. The specific mathematical model for implementation is as follows: ;in, To search for the local curvature value of a reference individual within a preset neighborhood; The position of the search individual at the current iteration time is updated based on the current position of the search individual and the velocity field data vector of the search individual's movement trend. ;in, Let i be the position of the i-th search individual in the t-th iteration. Let i be the position of the i-th search individual in the (t+1)-th iteration. The torsion intensity parameter varies based on the density of the searched individuals, specifically implemented as follows: ,in The initial torsion intensity parameter value is 2. The larger the density metric, the more sufficient the neighborhood information is, thus reducing the perturbation intensity.

[0041] Furthermore, a three-neighbor swarm exploration strategy is constructed based on improved step size parameters; In this embodiment, the step size parameter z in the global search phase of the Grey Goose optimization algorithm is improved by designing a relation degree factor. To reflect the convergence of the grey goose optimization algorithm, and at the same time, by designing the gradient function of the individual grey goose position. To reflect the fitness improvement of an individual greylag goose relative to its neighboring greylag geese, the relationship factor is used. This can improve the overall convergence trend of the Grey Goose optimization algorithm in controlling individuals, while the position gradient function... This can improve the judgment of an individual's local performance and increase the algorithm's exploratory nature when necessary. The improved mathematical model for the step size parameter is as follows: ; In the formula, Let be the improved step size parameter for the current i-th gray goose individual. and To improve the maximum and minimum values ​​of the step size parameter, To set the relation degree factor; Let be the average value of the gradient function of the i-th individual at the position of the t-th iteration; Among them, the gradient function of individual greylag goose positions The mathematical model is as follows: ; In the formula, The position of the i-th gray goose in the t-th iteration The distance from the i-th individual greylag goose's position to the t-th iteration is the nearest position to the i-th individual. distance, for The fitness function value, for The fitness function value; Among them, the relation factor The mathematical model is as follows: ; In the formula, t is the current iteration number, and T is the maximum iteration number.

[0042] Furthermore, a mathematical model for updating the individual positions of grey geese in the global search phase of the improved grey goose optimization algorithm is established using the improved step size parameter. ; In the formula, Let i be the position of the i-th search individual in the t-th iteration. Let i be the position of the i-th search individual in the (t+1)-th iteration. The optimal search position for the individual in the t-th iteration. Let this be the improvement step size parameter value for the current i-th search individual. , and These are the weighting coefficients. , , The locations of three randomly selected individuals are given.

[0043] During the implementation of this application, Not as part of the perturbation vector, but as a separate reference direction, the new search individual's position is... Starting from this point, in this embodiment, the design reduces... The contribution ratio enhances the perturbation moderating amplitude formed by the inter-individual difference vector, and will , and Set to 0.2, 0.4, 0.4.

[0044] Furthermore, the improved grey goose optimization algorithm includes a global search phase and a local exploitation phase. The global search phase includes a manifold distortion exploration strategy and a three-neighbor swarm exploration strategy based on an improved step size parameter; the local exploitation phase includes a cooperative approach to the optimal solution strategy. The collaborative approach to the optimal solution strategy guides other search individuals to approach the target region (target solution) by using the three currently globally best search individual positions. Specifically, the positions of the three approximation candidates, X1, X2, and X3, are calculated: ; in, For the first There are several approximation candidate positions, and A and C are control coefficients for adjusting the approximation direction and amplitude. According to the standard grey goose optimization calculation, A = 2a·ra, C = 2·r; where a is a linearly decreasing number with a slope of 1 from 2 to 0 with each iteration, and r is a random number in [0,1]. The search individual's position is updated by the mean of the three approximate candidate positions; .

[0045] Furthermore, the mapping relationship between the search individual positions and the number of hidden layers and the learning rate factor of the predicted first model in the improved Grey Goose optimization algorithm is as follows: In each iteration of the improved Grey Goose optimization algorithm, a set of candidate positions is generated by updating the mathematical model through the search individual positions. Each candidate position represents a set of parameters for the number of hidden layers n and the learning rate factor k. The mathematical model is as follows: ; In the formula, The dimension is 2. Let i be the position of the i-th gray goose. Let be the hidden layer number corresponding to the position of the i-th gray goose. Let be the learning rate factor corresponding to the position of the i-th gray goose; This represents the total number of species.

[0046] Furthermore, the specific steps for deriving the optimal number of hidden layers and learning rate factor for predicting the first model using the improved Grey Goose optimization algorithm are as follows: S51. Set the total population N, problem dimension Dim, upper bound ub and lower bound lb of the search individual position, maximum number of iterations T, and maximum and minimum values ​​of the step size parameter for the improved Grey Goose optimization algorithm. S52. Randomly initialize the search individual positions of the improved grey goose optimization algorithm, and define the fitness function of the improved grey goose optimization algorithm based on the real-time predicted and actual values ​​of silicon content in molten blast furnace iron; ; In the formula, N is the number of samples in the test set. Let j be the predicted value for the j-th sample. This represents the true value of the j-th sample. S53. Calculate the fitness value of each search individual's current position using the fitness function, compare it with the fitness value of the search individual's position in the previous iteration, and retain the current minimum fitness value. And the position of the search individual corresponding to the minimum fitness value is taken as the optimal position; S54. Is the current iteration number t less than the maximum iteration number T? If yes, then update the search individual's position; otherwise, exit the optimization loop and output the optimal search individual's position. ,Will The optimal number of hidden layers and learning rate factor are determined. S55. The position update mathematical model of the improved Grey Goose optimization algorithm is used to update the position of the search individual. The updated position of the search individual is bounded between the upper bound ub and the lower bound lb. The current iteration number t is executed t+1, and the fitness value of each search individual position is calculated.

[0047] In the implementation of this application, in Matlab, the lower bound of the search individual position is set as lb=[6 1e-4], and the upper bound as ub=[32 1e-3]; the problem dimension Dim=2, i.e., the number of parameters to be optimized; and the total population N of the improved Grey Goose optimization algorithm is set as follows: max =30; Maximum number of iterations T=70, the maximum value of the improved step size parameter is 1 and the minimum value is 0.1. The improved Grey Goose Optimization (ZGGO) algorithm is used to obtain the optimal number of hidden layers and learning rate factor for predicting the first model. The Matlab code is: [Best_score, Best_pos, curve] =ZGGO(SearchAgents_no, Max_iteration, lb, ub,dim, fun); The optimal search individual position value is decoded and assigned to the optimal number of hidden layers and the optimal learning rate factor. The Matlab code is: best_hd = round(Best_pos(1,1)); best_lr = Best_pos(1,2).

[0048] Furthermore, the optimal number of hidden layers and learning rate factor are used to reconstruct the blast furnace iron silicon content prediction model based on a BP neural network. Please refer to [link to relevant documentation]. Figure 2 As shown; The input layer contains the number of process parameters during blast furnace operation, the hidden layers represent the optimal number of hidden layers, and the output layer is 1. In the forward propagation, the input layer transmits the input environmental parameter data to the hidden layers. Each hidden layer receives the input signal from the previous layer, calculates a weighted sum, and performs a nonlinear mapping using the ReLU activation function f. The mathematical model is as follows: Where V is the output activation value. This is the weight matrix. For environmental parameter data, the output of the hidden layer is passed to the output layer after final weighting. The output layer performs the final calculation to obtain the current silicon content of the blast furnace molten iron, and then calculates it using the mean square error function E. The prediction error is calculated, and the weights in the prediction model are updated using the optimal learning rate factor and backpropagation of the prediction error. The mathematical model is: ;in, and For the updated weights and the weights before the update, The optimal learning rate factor is... The gradient of the loss function E with respect to the weights is given. The first prediction model re-propagates forward based on the new weights, calculates the new prediction error, and continues until the target prediction error of the silicon content of blast furnace hot metal is reached, and then outputs the final prediction result of the silicon content of blast furnace hot metal.

[0049] Furthermore, to verify the beneficial effects of the method of the present invention, the standard Grey Goose Optimization Algorithm (GGO) is introduced and compared with the improved Grey Goose Optimization Algorithm (ZGGO). By comparing the blast furnace molten iron silicon content prediction model established based on the standard Grey Goose Optimization Algorithm with the blast furnace molten iron silicon content prediction model established based on the improved Grey Goose Optimization Algorithm, the following results are obtained: Figure 3 , Figure 4 , Figure 5 .

[0050] Please see Figure 3 As shown in the figure, the improved Grey Goose Optimization Algorithm (ZGGO) decreases in fitness value faster and has a lower fitness value when optimizing the first prediction model based on BP than the standard Grey Goose Optimization Algorithm. The lower the fitness value, the higher the optimization accuracy of the algorithm. As can be seen from the figure, the comparison of fitness values ​​shows that the improved Grey Goose Optimization Algorithm (ZGGO) is significantly better than the standard Grey Goose Optimization Algorithm (GGO) when predicting the silicon content of blast furnace hot metal. ZGGO can quickly find a better solution in the early stage of iteration and maintain a stable low fitness value in the later stage of iteration, indicating that the improved GGO algorithm has better optimization performance and convergence speed. In contrast, GGO has a slower optimization speed and a higher final fitness value, indicating that its performance is relatively poor.

[0051] Furthermore, the optimal learning rate and optimal number of hidden layers obtained through optimization are as follows: Figure 4 and Figure 5 As shown, after 60 iterations, the optimal learning rate of the ZGGO-BP prediction model was 0.0001 and the optimal number of hidden layers was 6. The optimal learning rate of the ZGGO-BP prediction model was 0.001 and the optimal number of hidden layers was 32. Using the optimal number of hidden layers and learning rate factor, the blast furnace iron silicon content prediction model was reconstructed and finally trained on the entire training set, yielding the results. Figure 6 Comparison of training results between the ZGGO-BP prediction model and the GGO-BP prediction model; Please see Figure 6 As shown in the analysis of the training results, the ZGGO-BP model's curve trend fits the actual silicon content of blast furnace hot metal more closely, and it can also track the changes in actual values ​​better in some areas with large fluctuations. While the GGO-BP model can also roughly reflect the changing trend of silicon content in actual blast furnace hot metal, it deviates significantly at some data points, especially in areas with more drastic fluctuations, exhibiting a certain degree of lag and overfitting. Overall, the ZGGO-BP model has a smaller prediction error, especially at sample peak and trough points, where its predicted values ​​are closer to the actual values. The GGO-BP model performs relatively poorly in extreme value areas, with larger errors, indicating the limitations of the standard Grey Goose optimization algorithm in handling complex nonlinear problems.

[0052] Furthermore, the test set is input into the second prediction model, and the output is as follows: Figure 7 The comparison chart showing the prediction results of the ZGGO-BP prediction model and the GGO-BP prediction model indicates that the improved Grey Goose Optimization Algorithm (ZGGO) combined with the BP neural network model has higher prediction accuracy and better generalization ability than the standard Grey Goose Optimization Algorithm (GGO) when predicting the silicon content of blast furnace hot metal. The ZGGO-BP model can better fit the actual data, especially when dealing with large data fluctuations, it can still maintain a small error.

Claims

1. A method for predicting silicon content in blast furnace hot metal based on an improved grey goose algorithm, characterized in that, Acquire process parameters during blast furnace operation and record silicon content data in molten iron at corresponding times; The process parameters are preprocessed to remove outliers and noisy data, and the data is normalized to divide the dataset into training and testing sets. A first model for predicting the silicon content of blast furnace molten iron is constructed using a BP neural network. The first prediction model includes an input layer, a hidden layer, and an output layer. The training parameters of the first prediction model are optimized using an improved grey goose optimization algorithm. The improved grey goose optimization algorithm includes improving the step size parameter using a relation factor and dynamically adjusting the step size parameter according to the distance between the current search individual position and the global best solution. A local curvature factor is constructed based on the spatial positional relationship between the current search individual and its neighboring individuals, and local density information is constructed based on the individual distribution of the current search individual within a preset neighborhood range. The local curvature factor and the local density information are used to construct a velocity field data vector. The positions of individual search objects in the global search phase are updated using improved step size parameters and velocity field data vectors; The prediction model for silicon content in blast furnace hot metal was reconstructed using the optimized training parameters, and then finally trained on the training set to obtain the second prediction model. The test set is input into the second prediction model, and the training is iterated continuously. The prediction effect is calculated through the mean square error function until the target prediction error of silicon content in blast furnace iron is reached, and the prediction result of silicon content in blast furnace iron is output.

2. The method for predicting silicon content in blast furnace hot metal based on the improved grey goose algorithm according to claim 1, characterized in that, Multiple process parameters during blast furnace operation are selected as prediction input data, including four characteristic data: hot blast temperature, hot blast flow rate, oxygen enrichment, and pulverized coal injection rate. N sets of input data are recorded. Each set of input data contains the four characteristic data of hot blast temperature, hot blast flow rate, oxygen enrichment, and pulverized coal injection rate for the same time period. The output data is the silicon content of molten iron at the corresponding time.

3. The method for predicting silicon content in blast furnace hot metal based on the improved grey goose algorithm according to claim 2, characterized in that, The training parameters include the number of hidden layers n and the learning rate factor k; A mapping relationship is established between the search individual position of the improved Grey Goose optimization algorithm and the number of hidden layers and learning rate factor of the first prediction model. In each iteration of the improved Grey Goose optimization algorithm, a set of candidate positions is generated by updating the mathematical model through the Grey Goose individual position. Each candidate position represents a set of parameters including the number of hidden layers n and the learning rate factor k.

4. The method for predicting silicon content in blast furnace hot metal based on the improved grey goose algorithm according to claim 3, characterized in that, The step size parameter is constructed by building a target range based on preset upper and lower limits of step size, normalizing the difference between the gradient statistics corresponding to the current position of the search individual and the current fitness, and mapping the improved step size parameter proportionally to the target range based on the function ratio between relation factors. The improved mathematical model for the step size parameter is as follows: ； In the formula, Let be the improvement step size parameter for the current i-th search individual. and These are the maximum and minimum values ​​of the step size parameter. Relationship factor; The search term is the average value of the position gradient function of the i-th individual in the t-th iteration. The mathematical model is as follows: ； In the formula, The position of the i-th search individual in the t-th iteration The distance from the i-th search individual's position to the t-th iteration is the k-th closest position. distance, for The fitness function value, for The fitness function value; Relationship Factor The mathematical model is as follows: ； In the formula, t is the current iteration number, and T is the maximum iteration number.

5. The method for predicting silicon content in blast furnace hot metal based on the improved grey goose algorithm according to claim 4, characterized in that, An individual position update model is constructed based on the current solution of the current search individual and the positions of its three neighboring individuals. The solution difference and weighted response between the search individual and its neighbors are controlled by the first and second control factors, respectively. The position of the current search individual is adjusted by combining the improved step size parameter.

6. The method for predicting silicon content in blast furnace hot metal based on the improved grey goose algorithm according to claim 1, characterized in that, The local curvature factor includes obtaining the spatial positions of all search individuals in the current iteration, and constructing a dynamic manifold vector from the positions of the N search individuals as a point set. This maps discrete search points to sampling points in continuous space. The dynamic manifold vector Select two reference points adjacent to the current search individual's position, construct a spatial difference component based on the positional difference between the two reference points and the current search individual, and construct the local curvature factor of the current search individual based on the spatial difference component. .

7. The method for predicting silicon content in blast furnace hot metal based on the improved grey goose algorithm according to claim 5, characterized in that, The aggregation degree of the surrounding area of ​​the current search individual is accumulated based on the spatial distance between the current search individual and all other search individuals to obtain the local density information of the local area distribution state of the current search individual; Based on the local curvature factor and local density information of the current search individual, a curvature gradient vector representing the spatial variation trend is constructed using the curvature difference between the search individual and reference individuals in its neighborhood. The local curvature factor and local density information are then jointly processed and combined with the curvature gradient vector to construct a velocity field data vector representing the movement trend of the search individual. ; The position of the search individual at the current iteration time is updated based on the current position of the search individual and the velocity field data vector of the search individual's movement trend.

8. The method for predicting silicon content in blast furnace hot metal based on the improved grey goose algorithm according to claim 1, characterized in that, The optimization of the training parameters of the prediction first model using the improved Grey Goose optimization algorithm includes: setting the total number of population N, the problem dimension Dim, the upper bound ub and lower bound lb of the search individual position, the maximum number of iterations T, and the maximum and minimum values ​​of the step size parameter in the improved Grey Goose optimization algorithm. The positions of individual geese in the improved gray goose optimization algorithm are randomly initialized, and the fitness function of the improved gray goose optimization algorithm is defined based on the real-time predicted and actual values ​​of silicon content in molten blast furnace iron. The fitness value of each individual's current position is calculated using the fitness function and compared with the fitness value of the individual's position in the previous iteration. The current minimum fitness value is retained. And the position of the search individual corresponding to the minimum fitness value is taken as the optimal position; Check if the current iteration number t is less than the maximum iteration number T. If so, execute S55; otherwise, exit the optimization loop and output the optimal search individual position. ,Will The optimal number of hidden layers and learning rate factor are determined. The improved Grey Goose optimization algorithm is used to update the position of the search individual. The updated position of the search individual is bounded between the upper bound ub and the lower bound lb. The current iteration number t is executed t+1, and the fitness value of each search individual position is calculated.

9. The method for predicting silicon content in blast furnace hot metal based on the improved grey goose algorithm according to claim 1, characterized in that, The reconstructed blast furnace molten iron silicon content prediction model includes the following inputs: process parameters during blast furnace operation; an optimal number of hidden layers; and an output layer of 1. In the forward propagation, the input layer passes the input environmental parameter data to the hidden layers. Each hidden layer receives the input signal from the previous layer, calculates a weighted sum, and performs a nonlinear mapping using the ReLU activation function f. The outputs of the hidden layers are then weighted and passed to the output layer. The output layer performs the final calculation to obtain the predicted value of the current blast furnace molten iron silicon content. The prediction error is calculated using the mean squared prediction error function, and the weights in the prediction model are updated using the optimal learning rate factor and the prediction error backpropagation. The first prediction model re-propagates forward based on the new weights, calculates the new prediction error, and continues until the target prediction error for the silicon content of blast furnace molten iron is reached, and then outputs the final predicted silicon content of blast furnace molten iron.

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