Copper blowing process oxygen-enriched air control optimization method based on improved informer and kalman filter

Abstract

The present application relates to the technical field of oxygen-enriched air control optimization of copper blowing process, and discloses a copper blowing process oxygen-enriched air control optimization method based on improved Informer and Kalman filtering, historical data of the oxygen-enriched bottom blowing furnace is acquired and input into the improved Informer model for prediction to obtain future oxygen-enriched air input; real-time observation data of the oxygen-enriched bottom blowing furnace is acquired, and Kalman filtering dynamic correction is performed in combination with the future oxygen-enriched air input to obtain state estimation based on Kalman filtering and the future oxygen-enriched air input, model predictive control is performed, and the optimal control amount of the oxygen-enriched air valve opening degree is dynamically adjusted. The method combines the prediction result of the improved Informer and the state estimation of the Kalman filtering, designs a multi-step rolling optimization framework, solves through quadratic programming and applies physical constraints of valve opening degree range and change rate limit, and smooth adjustment of the valve opening degree is realized to ensure the stability of the blowing process.

Description

Technical Field

[0001] This invention relates to the field of oxygen-enriched air control optimization technology in copper blowing processes, specifically to an optimized method for oxygen-enriched air control in copper blowing processes based on improved Informer and Kalman filters. Background Technology

[0002] As an important pillar of my country's non-ferrous metals industry, the copper smelting industry's technological progress is of great significance for improving resource utilization efficiency, reducing environmental pollution, and enhancing international market competitiveness. Oxygen-enriched bottom-blown furnace copper smelting technology has become a trend in the industry due to its high efficiency and energy saving characteristics

[19] . However, its complex working mechanism and high dynamic characteristics pose a huge challenge to traditional control methods, resulting in problems such as high energy consumption and product quality fluctuations during the production process that are difficult to solve completely. This study introduces deep learning technology to predict and optimize the key parameters of the oxygen-enriched bottom-blown furnace copper smelting process, aiming to break through the limitations of traditional methods and improve the intelligent level of the process. Oxygen-enriched bottom-blown furnace copper smelting technology has become one of the mainstream technologies of modern copper smelting processes. The oxygen-enriched bottom-blown copper smelting process involves multivariate coupling, nonlinear dynamics, and uncertainties, making it a typical complex industrial system. Applying deep learning technology to parameter prediction and control optimization in this process can enrich the theoretical framework of industrial process modeling and control. However, this process involves complex physicochemical reactions, and the oxygen-enriched air input, as a key control parameter, exhibits high-frequency fluctuations, directly impacting smelting efficiency and furnace stability. Traditional control methods such as PID control, while simple to implement, are slow to respond to high-frequency disturbances and sudden process changes, failing to meet real-time and accuracy requirements. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides an optimized method for oxygen-enriched air control in copper smelting processes based on improved Informer and Kalman filtering. This method offers advantages such as ensuring the stability of the smelting process and solves the aforementioned technical problems.

[0004] To achieve the above objectives, the present invention provides the following technical solution: an optimization method for oxygen-enriched air control in copper blowing process based on improved Informer and Kalman filtering, including an Informer model, specifically comprising the following steps: S1: Obtain historical data of the oxygen-enriched bottom-blown furnace and input it into the improved Informer model to predict the future oxygen-enriched air input. S2: Obtain real-time observation data of the oxygen-enriched bottom-blown furnace, and combine it with the predicted future oxygen-enriched air input in S1 to perform dynamic correction using Kalman filtering, thereby obtaining a state estimate based on Kalman filtering. S3: Based on the state estimation from the Kalman filter and the future oxygen-enriched air input in S1, execute model predictive control to dynamically adjust the optimal control quantity for the opening of the oxygen-enriched air valve.

[0005] As a preferred technical solution of the present invention, the S1 improved Informer model specifically includes a feature embedding layer, a multi-head attention mechanism, and a feedforward neural network connected in sequence, and a layer normalization is set after the multi-head attention mechanism and the feedforward neural network respectively.

[0006] As a preferred embodiment of the present invention, the feature embedding layer performs high- and low-frequency feature decomposition and embedding on the input historical data of the oxygen-enriched bottom-blown furnace, and the specific steps are as follows: S1.1: Each variable sequence Applying the Fast Fourier Transform, we obtain the frequency domain representation; S1.2: Separate low-frequency components and high frequency components These constitute low-frequency and high-frequency sequences, respectively; in, , They represent respectively; S1.3: Input the low-frequency sequence and the high-frequency sequence into the multilayer perceptron for embedding, and generate the corresponding embedding vectors. The specific expressions are as follows: in, and These represent low-frequency time series subsequences and high-frequency time series subsequences, respectively. This represents the embedding vector of the low-frequency sequence. Represents the embedding vector of a high-frequency sequence. This indicates the low-frequency components separated during the copper blowing process. High-frequency time series subsequences Convert to embedding vector Operation; S1.4: Based on and The total embedding vector of variables is generated through weighted fusion. ; The multi-head attention mechanism specifically involves: during the Informer model training process, the query vector... Weighted adjustment of scores, and retention of only the scores before weighting in subsequent calculations. The key participates in the calculation: in, Indicates the query vector Weighted adjusted score, of which, Represents the key vector. Indicates the variable weight factor. It is a key vector The dimension; The feedforward neural network specifically replaces the ReLU activation function with the GLUE activation function, and the specific expression of the GLUE activation function is as follows: in, This represents the numerical value input to the activation function. Represents pi (π). Represents the hyperbolic tangent function; The layer normalization is expressed as follows: in, Represents a set of variable tokens. The feature vector representing a single variable token. express The mean, express The variance.

[0007] As a preferred embodiment of the present invention, the specific steps for dynamic Kalman filtering correction in step S2 are as follows: S2.1: Construct the state-space model, the specific expression of which is as follows: in, This represents the remaining state vector inside the blowing furnace. This represents the remaining state vector inside the furnace at the next time step (t+1). For the state dimension, This indicates the amount of oxygen-enriched air input. This represents the actual measured amount of oxygen-enriched air input, including sensor noise. The state transition matrix can be obtained by fitting historical data. The control input matrix represents the effect of the oxygen-enriched air input on the state. For the observation matrix, Let be the process noise, with a mean of zero and a covariance of . Gaussian white noise, For observation noise, let have a mean of zero and a covariance of . Gaussian white noise; S2.2: State estimation based on the previous time step and control input The prior state at the current moment is predicted using the state transition equation. The prior state estimate is calculated as follows: in; Estimate the state at the previous time step (t-1). Let A be the control input at the previous time step (t-1), and let B be the state transition matrix and B be the control input matrix.

[0008] The prior covariance matrix is ​​updated as follows: in: It is the covariance matrix of the state estimate at the previous time step, A is the state transition matrix, and Q is the process noise covariance.

[0009] S2.3: Based on the actual observed values ​​collected Combined with the predicted future oxygen-rich air input from S1 to form a comprehensive observation value. The specific expression is as follows: in, Indicates the weighting coefficient; S2.4: Based on comprehensive observations Update the state estimate: in, Let C be the Kalman gain and C be the observation matrix.

[0010] As a preferred embodiment of the present invention, step S3 involves transforming the optimization problem of the optimal control quantity for dynamically adjusting the opening of the oxygen-enriched air valve into a quadratic programming problem, specifically expressed as follows: in, The constraint matrix, where H is the quadratic term weight matrix. Let U be the coefficient vector of the first-order term, and U be the auxiliary vector of the control input. Describes the minimum value function, superscript Indicates transpose; S3 further includes solving the quadratic programming problem using a QP solver to obtain the final optimal valve control sequence. ; in, To optimize the optimal valve opening sequence obtained after solving the problem, This indicates the optimal control opening of the oxygen-enriched air valve at time t.

[0011] Compared with existing technologies, this invention provides an optimized method for oxygen-enriched air control in copper blowing processes based on improved Informer and Kalman filters, which has the following beneficial effects: This invention improves the Informer model, targeting the high-frequency and multi-scale characteristics of copper blowing process data. It designs optimization strategies such as high- and low-frequency feature decomposition, improved probabilistic sparse self-attention mechanism, GELU activation function, and variable independent layer normalization to enhance the model's ability to capture the temporal dynamics of oxygen-enriched air input while reducing computational complexity and improving industrial real-time adaptability. Secondly, by combining Kalman filtering and constructing a state-space model with a weighted fusion strategy, the improved Informer's prediction results are dynamically integrated with actual observation data, effectively correcting sensor noise and model bias, further improving the accuracy of oxygen-enriched air input estimation. Finally, model predictive control (MPC) is introduced. Based on the improved Informer's predictions and Kalman filter's state estimates, a multi-step rolling optimization framework is designed. Through quadratic programming and the application of physical constraints such as valve opening range and rate of change, smooth adjustment of valve opening is achieved, ensuring the stability of the blowing process. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the overall architecture of the present invention; Figure 2 This is a schematic diagram of the improved Informer architecture for predicting the amount of oxygen-enriched air input in the same blowing process according to the present invention. Figure 3 This is a schematic diagram comparing the controlled amount of oxygen-enriched air input with the actual value in the oxygen-enriched bottom-blown furnace copper smelting scenario of the various models of the present invention. Figure 4 This is a schematic diagram comparing the changes in oxygen concentration inside the furnace under the control of various optimization models of the present invention. Figure 5 This is a schematic diagram illustrating the cosine similarity variation of the oxygen-enriched air control method for the copper blowing process of the present invention under different control step sizes. Detailed Implementation

[0013] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0014] Please see Figures 1-5 An optimization method for oxygen-enriched air control in copper blowing process based on improved Informer and Kalman filtering, including the Informer model, specifically includes the following steps: S1: Obtain historical data of the oxygen-enriched bottom-blown furnace and input it into the improved Informer model to predict the future oxygen-enriched air input. Enter historical data Historical data includes oxygen-enriched air input, valve opening, etc. Where N is the length of the historical window, and N is the number of variables, including oxygen-enriched air input, valve opening, etc., the features are extracted by the encoder and directly mapped to the future. Predicted values ​​at each time step , ; The S1 improved Informer model specifically includes a feature embedding layer, a multi-head attention mechanism, and a feedforward neural network connected in sequence, with layer normalization set after the multi-head attention mechanism and the feedforward neural network respectively; In Informer, multiple variables at the same time are embedded into a single time token, and time dependencies are captured through an attention mechanism. However, in the copper blowing process, variables such as oxygen-enriched air input, valve opening, and oxygen concentration setpoint have different physical meanings and dynamic characteristics. This embedding method may smooth out the independence between variables and make it difficult to accurately reflect the temporal characteristics of each variable, especially in high-frequency sampling scenarios where trend and periodic features are mixed. To address this, this paper proposes an optimization method based on high- and low-frequency feature decomposition and embedding. After decomposing the trend and periodic features of the variable sequence using Fourier transform, the method is embedded. The feature embedding layer performs high- and low-frequency feature decomposition and embedding on the input historical data of the oxygen-enriched bottom blowing furnace. The specific steps are as follows: S1.1: Each variable sequence Applying the Fast Fourier Transform, we obtain the frequency domain representation; S1.2: Separate low-frequency components and high frequency components These constitute low-frequency and high-frequency sequences, respectively; in, , They represent respectively; S1.3: Input the low-frequency sequence and the high-frequency sequence into the multilayer perceptron for embedding, and generate the corresponding embedding vectors. The specific expressions are as follows: in, and These represent low-frequency time series subsequences and high-frequency time series subsequences, respectively. This represents the embedding vector of the low-frequency sequence. Represents the embedding vector of a high-frequency sequence. This indicates the low-frequency components separated during the copper blowing process. High-frequency time series subsequences Convert to embedding vector Operation; S1.4: Based on and The total embedding vector of variables is generated by splicing or weighted fusion. ; Traditional Informer models employ probabilistic sparse self-attention, which, compared to Transformer models, reduces time complexity from... reduce By filtering the dominant query and focusing only on a subset of keys, long-term series prediction tasks can be effectively handled. However, in high-frequency data scenarios related to copper smelting processes, historical windows... The length can reach thousands of steps, even The complexity still easily leads to memory overflow, and the original mechanism lacks specificity in the sparse selection among variables, failing to fully capture the dynamic correlation between oxygen-enriched air input and other process parameters. Therefore, this paper further improves the mechanism design based on Informer's probabilistic sparse attention, enhancing computational efficiency and task adaptability, such as... Figure 1 As shown.

[0015] The improvement in this paper lies in the introduction of trainable variable weight factors. For each variable, the query selection strategy in sparse attention is dynamically adjusted during model training. Specifically, the multi-head attention mechanism in attention computation involves adjusting the query vector during Informer model training. Weighted adjustment of scores, and retention of only the scores before weighting in subsequent calculations. The key participates in the calculation:

[0016] in, Indicates the query vector Weighted adjusted score, of which, Represents the key vector. Indicates the variable weight factor. It is a key vector The dimension; Informer uses a feedforward network (FFN) in both the encoder and decoder to process the representation of time tokens. However, its main function is limited to extracting local features between variables, failing to utilize global information on the time series of a single variable. Furthermore, it typically employs the ReLU activation function, which is prone to gradient vanishing in complex nonlinear modeling. To adapt to the long-term dependence and nonlinear characteristics of oxygen-enriched air input in copper blowing, this paper enhances the functionality of the feedforward network, enabling it to focus on sequence representation learning and apply it to the time dimension of the variable sequence. This paper's feedforward network not only extracts periodic and trend-based global sequence representations but also implicitly stores temporal sequence information to replace the explicit positional encoding in the Informer. Furthermore, to further enhance nonlinear modeling capabilities, this paper introduces the GELU (Gaussian Error Linear Unit) activation function into the FFN to replace the traditional ReLU. GELU combines the sparsity of ReLU with the smoothness of Sigmoid, and its specific expression is as follows: in, This represents the numerical value input to the activation function. Represents pi (π). The hyperbolic tangent function is used to better capture the non-stationary fluctuations in oxygen-enriched air input in high-frequency data of copper blowing, thus improving the model's ability to fit complex dynamics. Layer normalization was initially proposed to improve the convergence speed and training stability of deep networks. In traditional Transformer prediction models such as Informer, layer normalization is applied to the multivariate representations at the same time point, gradually fusing the features of each variable. However, in the copper blowing process, the time points of variables such as oxygen-enriched air input and valve opening may not represent the same physical event. This operation can introduce interactive noise between non-causal or delayed processes, leading to prediction bias. Therefore, this paper optimizes the application of layer normalization, applying it to the independent representation of each variable sequence.

[0017] Specifically, for variable token sets ,in For the embedding dimension, the layer normalization in this paper is defined as: in, Represents a set of variable tokens. The feature vector representing a single variable token. express The mean, express The variance of the variable is calculated. Unlike Informer's time-step normalization, this method independently normalizes the representation of each variable sequence to approximate a Gaussian distribution. This design has been shown to be more effective in handling non-stationary problems. In the copper blowing scenario, the measurement units and distributions of oxygen-enriched air input and other process parameters differ significantly. This improvement can significantly reduce the impact of these inconsistencies and avoid the problem of excessive smoothing between time steps in layer normalization. S2: Obtain real-time observation data of the oxygen-enriched bottom-blown furnace, and combine it with the predicted future oxygen-enriched air input in S1 to perform dynamic correction using Kalman filtering, thereby obtaining a state estimate based on Kalman filtering. The core of Kalman filtering lies in describing the dynamic evolution of a system through a state-space model. In the copper blowing process, the change in the amount of oxygen-enriched air input depends not only on historical data but also on the implicit state within the furnace. Therefore, this paper abstracts the blowing process as a linear time-invariant system and establishes the following state-space model: in, This represents the remaining state vector inside the blowing furnace. For the state dimension; This represents the amount of oxygen-enriched air input, which is a controllable variable of the system. This represents the actual measured amount of oxygen-enriched air input, but includes sensor noise. Furthermore, The state transition matrix describes the evolution of the hidden states over time and can be obtained by fitting historical data. The control input matrix represents the effect of the oxygen-enriched air input on the state. The observation matrix maps the state to the observation space; As process noise, this study assumes it to have a mean of zero and a covariance of... Gaussian white noise reflects random disturbances in the system; To observe the noise, this study assumes it has a mean of zero and a covariance of . Gaussian white noise reflects the sensor measurement error; Kalman filtering achieves optimal state estimation by fusing prior estimates and observed data through two steps: prediction and update. In this study, Kalman filtering not only utilizes actual observations but also incorporates prediction results from an improved Informer model to further enhance estimation accuracy. Its design and implementation process is as follows: The implementation of Kalman filtering begins with a prediction step, based on the state estimate from the previous time step. and control input The prior state at the current moment is predicted using the state transition equation. The prior state estimate is calculated as follows: Meanwhile, to quantify the uncertainty of the prediction, the prior covariance matrix is ​​updated as follows: During the update phase, the Kalman filter further refines the state estimate by fusing actual observation data and prediction information. The data originates from the collected actual observations. And improve the Informer model's prediction of future oxygen-enriched air input. To generate a more reliable estimate, a weighted fusion strategy is designed to combine current observations with predicted values ​​to form a comprehensive observation value: in, This is an adjustable weighting coefficient used to balance the contributions of actual observations and predicted values. If sensor noise is high, it can be reduced. This increases the reliance on predictions; conversely, if the Informer model is improved to have higher prediction accuracy, then the reliance on predictions will increase. Then the Kalman gain is calculated: This gain determines the weight of the observed data on the state correction, and its value reflects the confidence distribution between the prior estimate and the observations. Then, based on the combined observations... The state estimate is then updated to: By comparing the predicted output With comprehensive observation The bias is dynamically corrected using prior states, thereby reducing the impact of noise and prediction bias. Simultaneously, the posterior covariance is updated as follows: Based on the updated state thereafter The corrected oxygen-enriched air input was estimated by back-calculating the observation equation: This paper utilizes the improved predictive power of the Informer model to enable traditional Kalman filtering, which not only compensates for the errors that may be introduced by a single observation, but also captures the inherent dynamic characteristics of the copper blowing process through the state-space model. S3: Based on the state estimation of Kalman filter and the future oxygen-enriched air input in S1, execute model predictive control to dynamically adjust the optimal control quantity of the oxygen-enriched air valve opening; The control objective of this study is to optimize the opening degree of the oxygen-enriched air valve. (Unit: %), to indirectly control the input of oxygen-enriched air, ensuring the efficiency and stability of the copper blowing process. Efficiency is reflected in maintaining the oxygen concentration in the furnace through appropriate valve openings, promoting sulfide oxidation and impurity removal; stability requires smooth changes in valve openings to avoid excessive fluctuations in input leading to furnace instability. To achieve this goal, the physical constraints of the process parameters must be comprehensively considered, summarized as follows: (1) The valve opening range is limited to 0-100%. The data comes from the actual production records of the oxygen-enriched bottom blowing furnace of Jiangxi Copper Guixi Smelter, reflecting the physical limitations of the actual control equipment.

[0018] (2) The oxygen concentration of the oxygen-enriched air is set in the range of 60-80%, which is the reasonable range of oxygen supply during the copper blowing process.

[0019] (3) Considering the continuity of the blowing process, the rate of change of the opening degree of the oxygen-enriched air valve. It also needs to be limited to avoid excessive adjustments impacting the system; In this study, MPC utilized an improved Informer model to predict future oxygen-enriched air input. The state estimated by Kalman filtering Build a prediction model and design optimization objectives.

[0020] The prediction model is the core of MPC, built upon a state-space model based on Kalman filtering, for current state estimation. The state has already been obtained through Kalman filtering; future state prediction is then performed through iterative calculation. in, For the future valve opening control sequence, the initial values ​​can be indirectly calculated from the predicted input. The optimization objective aims to balance control deviation and energy consumption, defined as the future... Cost function for each time step: in To achieve the desired oxygen-enriched air valve opening, This indicates the rate of change of valve opening, used to penalize excessive adjustment actions. The regularization coefficient balances control accuracy and stability. This multi-step optimization method comprehensively considers future trends, avoids local optima, and suppresses input fluctuations by defining the control oxygen-enriched valve opening vector. , target input vector Then the objective function can be expressed as: in, It is a difference matrix used for calculation Its form is: After expansion, the objective function can be further simplified to a standard quadratic form: in, for The identity matrix, It is a symmetric positive definite matrix, called a Hessian matrix. The vector of linear coefficients, and the constant term. This can be ignored during optimization; The constraints stem from the physical limitations of the process parameters in the oxygen-enriched bottom-blown copper smelting process. Here, the valve opening range corresponds to the upper and lower boundaries, set as follows: and Meanwhile, the oxygen concentration setpoint range indirectly constrains the input quantity. It is generally assumed that the input quantity and oxygen concentration have a linear relationship, which can be converted into... Additional constraints. Furthermore, the input rate of change. To avoid excessive adjustments, set it to... These constraints can be summarized as linear inequalities: Integrate into matrix form: in, , It is a vector consisting entirely of 1s.

[0021] In summary, the optimization problem of MPC can be formalized as a quadratic programming problem: This problem is convex, so this paper chooses to use the QP solver to obtain the final optimal valve control sequence. According to the rolling optimization principle of MPC, only the current control input is executed. And in the next step Repeat this process, using the updated state. and predicted value And it was re-optimized.

[0022] The QP-based solution method proposed in this study has the following advantages: the quadratic objective function and linear constraints guarantee the existence and uniqueness of the global optimal solution, while the Hessian matrix... The positive definiteness of the property ensures the numerical stability of the optimization problem. Furthermore, by adjusting... It can flexibly balance control accuracy and input smoothness. Compared with directly using the prediction value of the neural network, by combining the state space model and constraints, it can comprehensively consider the process limitations of copper blowing in multi-step prediction and avoid control errors that may be caused by a single prediction point. The pseudocode for the improved Informer and Kalman filter-based optimization method for oxygen-enriched air control in the copper blowing process is shown in Table 1.

[0023] Table 1. Pseudocode of the algorithms in this chapter ; This algorithm describes a closed-loop control optimization method for the oxygen-enriched air input during copper blowing. Dynamic adjustment is achieved through the collaborative work of the Informer module, the KALMAN state estimation module, and the MPC optimization control module. The entire process operates in a cyclical manner, as follows: In the Informer module, the system predicts future oxygen-enriched air input demand based on historical data. This module uses Fast Fourier Transform to decompose the data into low-frequency and high-frequency components, extracts and fuses features using a multilayer perceptron, and then generates a predicted sequence of input quantities with the help of an encoder. This step can capture the dynamic trend of input quantity changes, providing forward-looking guidance for subsequent control.

[0024] The state estimation module (Kalman) corrects the discrepancy between predicted and actual observations using Kalman filtering. Specifically, the module combines the state prediction equation with a weighted fusion mechanism to dynamically integrate real-time sensor data and predicted values ​​proportionally, continuously updating the estimated state of the current input. This design significantly improves the system's robustness to fluctuations in the production environment and measurement noise, ensuring that the state estimation more closely reflects real-world operating conditions.

[0025] Subsequently, the Optimized Control Module (MPC) generates the optimal valve control command based on the corrected state estimate by solving a constrained quadratic programming problem. The optimization process comprehensively considers tracking the target input, minimizing control fluctuations, and satisfying valve opening thresholds and rate of change limits. The final output control quantity is applied in real time to regulate the oxygen-enriched air valve, thereby dynamically balancing the input demand and process constraints.

[0026] The entire system operates around a main loop process, with prediction, state correction, and optimization control executed sequentially at each time step. The prediction module provides trend references for future input demands, the state estimation module integrates real-time observations to correct the current state, and the optimization control module generates precise instructions. The closed-loop collaboration of these three modules ensures that the oxygen-enriched air input remains stable in the dynamically changing copper blowing process, ultimately achieving the goals of energy efficiency optimization and product quality improvement. The dataset used in this study consists of actual production records from the oxygen-enriched bottom-blown furnace at the Guixi Smelter of Jiangxi Copper Industry. To address potential noise and outliers in the actual industrial data, this study employs a robust normalization method to standardize each variable's data along the time-series dimension. The specific formula is as follows: in, The median. The interquartile range (IQR) is used to convert each variable into a distribution centered on the median and scaled by the IQR. This method is more resistant to outlier interference than traditional normalization methods.

[0027] The preprocessed data was used in three stages of the model: improved Informer prediction, Kalman filter state estimation correction, and MPC optimization control. In the prediction stage, the input consisted of six variables from a historical window: oxygen-enriched air input, oxygen concentration setpoint, oxygen-enriched air valve opening, auxiliary air volume, furnace start / stop, and raw material feeding start / stop. The length of the historical time series, the output is the future. The oxygen-enriched air input at each time step is calculated; the estimation and correction stage integrates the actual observed oxygen-enriched air input and the predicted value, and outputs the corrected input estimate; the control optimization stage outputs the optimal oxygen-enriched air valve opening control sequence based on the state estimation.

[0028] The dataset is divided into a training set (70%, the first 166,315 time steps), a validation set (15%, the middle 35,632 time steps), and a test set (15%, the last 35,646 time steps) in chronological order to avoid time series data leakage and ensure that the experimental results can truly reflect the model's performance in real industrial scenarios. In the improved Informer model, high- and low-frequency eigenvalue decomposition is achieved by applying a Fast Fourier Transform (FFT) to each variable sequence, with the cutoff frequency... The value is set to 0.1. The low-frequency and high-frequency components are embedded through two layers of MLP, with a hidden layer dimension of 64 and an output embedding dimension of [missing value]. The encoder structure retains 3 layers, each containing an improved probabilistic sparse self-attention module and a feedforward network module. The number of attention heads is set to 8, with each head having a dimension of 16. The total dimension and the embedding dimension are calculated as follows. Consistent; the improved probabilistic sparse self-attention mechanism incorporates variable weight factors. Initialize to uniform distribution Through dynamic adjustment during training, the first log(T_1) (approximately 10) keys are selected for computation to ensure a sparsity rate exceeding 90%. Each layer of the feedforward network (FFN) contains two linear transformations: the first layer expands the dimension from 128 to 512, and the second layer compresses it back to 128. The dropout rate is set to 0.1 to prevent overfitting. Layer normalization is applied independently to each variable sequence to smooth the parameters. Set to 1×10⁻ 5 Training was performed using the AdamW optimizer with an initial learning rate of 1×10⁻ 4 With the cosine annealing scheduling strategy, the minimum learning rate is 1×10⁻ 6 The batch size is 32, the total number of training rounds is 500, and the early stopping patience value is 20 rounds.

[0029] For the Kalman filter module, the state dimension of the state-space model Set to 6, state transition matrix and control input matrix Initialization was performed using least squares fitting with historical data, followed by fine-tuning during training. The process noise covariance was also analyzed. Initialize to Observation noise covariance The value was set to 0.05, and all values ​​were adjusted to the optimal value through experiments. The weighting coefficients of the comprehensive observation values ​​were then used. Set to 0.7, each prediction and update is based on the current state. And improve the Informer's predictions Real-time calculation of Kalman gain In the MPC optimization control module, the rolling optimization step size is 1, and the regularization coefficient of the objective function is... Set to 0.5 to balance control deviation and valve opening change rate, with a change rate constraint. Oxygen concentrations ranging from 25% to 40% are converted via linear mapping. Constraints: The solver uses OSQP to handle quadratic programming problems, with a maximum number of iterations set to 1000 and a tolerance set to 1 × 10⁻. 6 During training, the Informer is first pre-trained independently, then jointly optimized with Kalman filtering and MPC. The validation set is used for hyperparameter tuning, and the test set is used for final performance evaluation. To verify the effectiveness of the oxygen-enriched air control optimization method based on improved Informer and Kalman filtering proposed in this study, this section uses the mean square error (MSE) between the oxygen-enriched air input control result and the actual demand, as well as the cosine similarity between the two, as evaluation indicators to reflect the accuracy and trend consistency of the control strategy.

[0030] The selected comparison methods are as follows, including: (1) Classical proportional-integral-derivative (PID) control, the goal of which is to adjust the valve opening based on the deviation between the real-time measured oxygen-enriched air input and the set value, and its parameters The Ziegler-Nichols method was used to tune the control frequency to 1.2, 0.5 and 0.3 respectively, with the control frequency matching the data sampling frequency. (2) Extended Kalman Filter (EKF) control improves the traditional KF for the nonlinear characteristics of the copper blowing process. The nonlinear system equation is linearized by Taylor expansion, the state dimension is set to 6, and the initial covariance is the same as that of KF-Control, but the Jacobian matrix needs to be calculated for each iteration. (3) LSTM+Kalman Filter control (LSTM+KF) first uses the LSTM model to predict the system state and optimizes the valve opening based on the estimated value. The noise covariance Q and R are set to 0.01 and 0.05 respectively. (4) Deep Deterministic Policy Gradient (DDPG) is a continuous action space control method based on reinforcement learning. The optimal control policy is learned through the Actor-Critic architecture. Its reward function is defined as the negative of the sum of squares of the deviations between the oxygen-enriched air input and the target value. The experimental results of each model are shown in Table 4-2, which records the mean and standard deviation of the MSE and cosine similarity of each method, calculated based on 5 runs on the test set.

[0031] Table 2 Performance Comparison of Different Control Methods Table 2 shows that the PID control has an MSE of 0.1152 and a cosine similarity of 0.572, with the smallest standard deviation, but its accuracy is very limited. This is mainly because it relies on real-time feedback and cannot effectively predict future trends. It is prone to oscillations under high-frequency disturbances, leading to direct distortion in later control. The EKF method has an MSE of 0.0389 and a cosine similarity of 0.891, which is an improvement over PID. This is due to the noise filtering effect of state estimation, but its lack of prediction correction for observations limits its ability to model the nonlinear dynamics of future valve control quantities. The LSTM+KF method constructs higher-quality state updates by incorporating neural network prediction, reducing the MSE to 0.0327. However, the LSTM model itself has limited ability to extract high-frequency time-series features in oxygen-enriched bottom-blown furnaces, and the prediction using only the KF method is sensitive to initial parameters. DDPG's MSE is 0.0224, demonstrating strong adaptability and performance close to the model in this chapter. This indicates that reinforcement learning can learn some potential patterns through long-term optimization. However, its long training time and heavy reliance on reward function design limit its application in real-time scenarios such as oxygen-enriched bottom-blown copper smelting furnaces. The method in this chapter, on the other hand, has an MSE of 0.0215 and a cosine similarity of 0.937, both of which outperform all the aforementioned methods. Figure 3The comparison between the oxygen-enriched air input control curve and the actual demand is shown in the test focus time step from 5000 to 5256. PID control exhibits significant lag in trend following, leading to direct distortion in later control stages and a complete deviation from the actual demand. KF-Control and EKF-Control can smooth noise well, but the former has a slow response speed to sudden changes, while the latter, although improved, does not completely eliminate deviations, especially when the oxygen concentration setpoint changes abruptly, resulting in overshoot and oscillations during the adjustment process. DDPG's control curve is relatively close to the actual demand, but overfitting still exists in local fluctuations. The control curve of the method presented in this chapter is closest to the actual demand, maintaining high accuracy in the steady segment and responding quickly and stably in the abrupt change segment, demonstrating the advantages of combining prediction and state estimation. Oxygen-enriched air content, as a core environmental condition in the blowing process, directly reflects the control strategy's ability to regulate furnace conditions. To further evaluate the actual effectiveness of various optimized control strategies in the oxygen-enriched bottom-blown copper blowing process, this study compares the degree of matching between the oxygen-enriched air content (i.e., oxygen concentration) in the furnace and the actual requirements under different control methods. Figure 4 The test set shows the comparison curves of the oxygen-enriched air content in the furnace with the actual value under the optimized control strategies of each model, between time steps 0 and 140. like Figure 4 As shown, the oxygen-enriched air content curve controlled by PID exhibits significant deviations when following actual demand, especially when the oxygen concentration setpoint changes abruptly. The response lag is obvious, the curve deviates far from the true value, and even oscillates in the later stages, reflecting its insufficient adaptability to high-frequency disturbances and nonlinear dynamics. The EKF and LSTM+KF methods improve the oxygen concentration tracking performance through state estimation and prediction capabilities. However, EKF still exhibits overshoot near the abrupt change point, while LSTM+KF, although able to capture trends well, shows large deviations at local high-frequency fluctuations, indicating limited modeling capabilities for complex time-series characteristics. The DDPG method, leveraging the long-term optimization capabilities of reinforcement learning, makes the oxygen concentration curve relatively close to the true value, but slight fluctuations still occur at some time steps, indicating that its robustness to instantaneous disturbances needs improvement. In contrast, the control method proposed in this chapter, based on an improved Informer and Kalman filter, produces an oxygen-enriched air content curve that best matches actual demand. It maintains high accuracy not only in the steady segment but also responds quickly and stably in the abrupt change segment, demonstrating the synergistic advantages of prediction, state estimation, and multi-step optimization. This result further verifies the superiority of this method in maintaining stable oxygen concentration in the furnace, promoting sulfide oxidation, and removing impurities.

[0032] In addition, to explore the control accuracy of the model in this chapter on the amount of oxygen-enriched air input under different prediction step lengths, this study used cosine similarity as an index to analyze the performance of control step lengths of 10, 50, 100, 200, 500 and 1000. The experiment was repeated 5 times for each step length to evaluate accuracy and stability. The results are as follows Figure 5 As shown, the control accuracy is highest with short step size. As the step size increases, the mean cosine similarity gradually decreases and the standard deviation increases slightly. Especially after the step size exceeds 200, the decrease is slightly more obvious due to the limited modeling ability of the model to model long-term dependencies and the influence of high-frequency disturbances in the data. However, it still has a cosine similarity of 0.8531 with a long step size of 1000, which verifies its superiority under long step size control.

[0033] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. An optimization method for oxygen-enriched air control in copper blowing process based on improved Informer and Kalman filtering, including the Informer model, characterized in that: Specifically, the following steps are included: S1: Obtain historical data of the oxygen-enriched bottom-blown furnace and input it into the improved Informer model to predict the future oxygen-enriched air input. The improved Informer model in S1 specifically includes a feature embedding layer, a multi-head attention mechanism, and a feedforward neural network connected in sequence, with layer normalization set after the multi-head attention mechanism and the feedforward neural network respectively; The feature embedding layer performs high- and low-frequency feature decomposition and embedding on the input historical data of the oxygen-enriched bottom-blown furnace. The specific steps are as follows: S1.1: Each variable sequence Applying the Fast Fourier Transform, we obtain the frequency domain representation; S1.2: Separate low-frequency components and high frequency components These constitute low-frequency and high-frequency sequences, respectively; in, Represents the input frequency characteristic components. Indicates the threshold values ​​for high and low frequency feature components; S1.3: Input the low-frequency sequence and the high-frequency sequence into the multilayer perceptron for embedding, and generate the corresponding embedding vectors. The specific expressions are as follows: in, and These represent low-frequency time series subsequences and high-frequency time series subsequences, respectively. Represents the embedding vector of a low-frequency sequence. Represents the embedding vector of a high-frequency sequence. Indicates will Low-frequency particles separated during copper blowing process High-frequency time series subsequences Convert to embedding vector Operation; S1.4: Based on and The total embedding vector of variables is generated by splicing or weighted fusion. ; The multi-head attention mechanism specifically involves: during the Informer model training process, the query vector... Weighted adjustment of scores, and retention of only the scores before weighting in subsequent calculations. The key participates in the calculation: in, Indicates the query vector Weighted adjusted score, Represents the key vector. Indicates the variable weight factor. It is a key vector The dimension; The feedforward neural network specifically replaces the ReLU activation function with the GLUE activation function, and the specific expression of the GLUE activation function is as follows: in, This represents the numerical value input to the activation function. Represents pi (π). Represents the hyperbolic tangent function; The improved Informer model also includes layer normalization, the specific expression of which is as follows: in, Represents a set of variable tokens. The feature vector representing a single variable token. express The mean, express The variance; S2: Obtain real-time observation data of the oxygen-enriched bottom-blown furnace, and combine it with the predicted future oxygen-enriched air input in S1 to perform dynamic correction using Kalman filtering, thereby obtaining a state estimate based on Kalman filtering. S3: Based on the state estimation from the Kalman filter and the future oxygen-enriched air input in S1, execute model predictive control to dynamically adjust the optimal control quantity for the opening of the oxygen-enriched air valve.

2. The method for optimizing oxygen-enriched air control in copper blowing process based on improved Informer and Kalman filtering as described in claim 1, characterized in that: The specific steps for dynamic Kalman filtering correction in S2 are as follows: S2.1: Construct the state-space model, the specific expression of which is as follows: the numerical value input to the activation function. in, Let represent the remaining state vector inside the furnace at time t. This represents the remaining state vector inside the furnace at the next moment. For the state dimension, This indicates the amount of oxygen-enriched air input. This represents the actual measured amount of oxygen-enriched air input, including sensor noise. The state transition matrix can be obtained by fitting historical data. The control input matrix represents the effect of the oxygen-enriched air input on the state. For the observation matrix, Let be the process noise, with a mean of zero and a covariance of . Gaussian white noise, For observation noise, let have a mean of zero and a covariance of . Gaussian white noise; S2.2: State estimation based on the previous time step and control input The prior state at the current moment is predicted using the state transition equation. The prior state estimate is calculated as follows: in, Estimating the state at the previous moment. Let A be the control input from the previous time step, and B be the state transition matrix and the control input matrix. The prior covariance matrix is ​​updated as follows: in, It is the covariance matrix of the state estimate at the previous time step, A is the state transition matrix, and Q is the process noise covariance; S2.3: Based on the actual observed values ​​collected Combined with the predicted future oxygen-rich air input from S1 to form a comprehensive observation value. The specific expression is as follows: in, Indicates the weighting coefficient. This indicates the amount of oxygen-enriched air to be input at the next moment; S2.4: Based on comprehensive observations Update the state estimate: in, C is the Kalman gain, and C is the observation matrix. This represents the predicted output value based on the state estimate from the previous time step.

3. The method for optimizing oxygen-enriched air control in copper blowing process based on improved Informer and Kalman filtering as described in claim 1, characterized in that: S3 involves transforming the optimization problem of the optimal control quantity for dynamically adjusting the opening of the oxygen-enriched air valve into a quadratic programming problem, with the specific expression as follows: in, The constraint matrix, where H is the quadratic term weight matrix. Let U be the coefficient vector of the first-order term, and U be the auxiliary vector of the control input. Describes the minimum value function, superscript Indicates transpose; S3 further includes solving the quadratic programming problem using a QP solver to obtain the final optimal valve control sequence. ; in, To optimize the optimal valve opening sequence obtained after solving the problem, This represents the optimal control opening of the oxygen-enriched air valve at time t.

Images