A machine learning-based multi-physical field coupling optimization method for chaotic jet injection pool smelting

Abstract

The application discloses a kind of chaotic injection bath smelting multi-physics field coupling optimization methods based on machine learning, comprising: based on the distribution of two-mode adaptive chaotic switching mechanism regulation injection gas flow, according to the bubble number density fluctuation rate of real-time monitoring electrical resistance tomography adaptive selection chaotic mode;ERT is used to monitor the bath, and the distribution of multi-physics field is reconstructed by Tikhonov regularization, and key parameters such as flow field uniformity coefficient, bubble number density, bubble average equivalent diameter and slag layer thickness are extracted;Physical information constrained deep generative adversarial network is constructed, and fluid mechanics conservation equation is embedded into generator loss function for adversarial training;According to the deviation of model prediction result and preset threshold, PID control law adjusted by particle swarm optimization is used to dynamically adjust injection parameters.The application realizes the intelligent matching of chaotic injection strategy and actual state of bath, breaks through the working condition adaptability limitation of single chaotic mapping, and significantly improves smelting efficiency and furnace condition stability.

Description

Technical Field

[0001] This invention belongs to the field of non-ferrous metal metallurgical process optimization technology, and particularly relates to a multi-physics field coupling optimization method for chaotic blow-through molten pool smelting based on machine learning. Background Technology

[0002] In the smelting processes of non-ferrous metals such as copper, zinc, lead, and nickel, the mixing uniformity, flow field distribution, and temperature field stability of the gas-liquid-slag three-phase mixture within the molten pool directly determine the smelting reaction efficiency, metal recovery rate, product quality, and energy consumption level. Chaotic jetting technology, by chaotically controlling the distribution, pressure, and frequency of the jetting gas flow, enhances fluid disturbance within the molten pool and promotes thorough mixing of the three phases. It is a core technical means to improve smelting reaction conditions and enhance process parameters. However, current parameter control and multiphysics field monitoring in chaotic jetting smelting processes still face numerous technical challenges, specifically in the following aspects: Parameter control relies on experience and lacks quantitative basis. In traditional smelting processes, the adjustment of core parameters such as chaotic blowing pressure, frequency, and angle depends entirely on the operator's on-site experience and subjective judgment. There is a lack of real-time perception and quantitative analysis of the dynamic changes of multiple physical fields such as flow field, temperature field, and bubble distribution in the molten pool. This can easily lead to problems such as uneven mixing in the molten pool, insufficient local reaction, and bubble coalescence or excessively rapid escape. This not only reduces smelting efficiency and metal recovery rate, but also causes a large amount of energy waste and metal loss.

[0003] Multiphysics monitoring technology is limited in terms of accuracy and real-time performance. Existing molten pool monitoring methods mostly employ invasive detection or single-modal sensing technologies, which suffer from drawbacks such as response delay, interference with the molten pool flow field, and low imaging accuracy. Conventional non-invasive monitoring technologies struggle to achieve synchronous, high-precision, and visualized monitoring of the gas-liquid-slag three-phase multiphysics field, and cannot accurately extract key characteristic parameters such as flow field uniformity, slag layer thickness, bubble number density, and equivalent bubble diameter, making it difficult to support dynamic control of injection parameters and process optimization.

[0004] The data processing methods are simplistic and feature extraction is inefficient. The multi-source data collected during the molten pool smelting process, such as ERT monitoring data and blowing process parameters, are characterized by high dimensionality, heterogeneity, and strong coupling. Existing data processing methods mostly use a single dimensionality reduction algorithm, which cannot effectively remove data redundancy or screen key features that are strongly correlated with smelting efficiency. This results in low training efficiency and poor prediction accuracy of subsequent machine learning models.

[0005] Machine learning models suffer from poor generalization ability and inefficient hyperparameter tuning. Some metallurgical process optimization attempts have attempted to introduce simple machine learning models for molten pool performance prediction. However, these models are mostly built based on a single data source, lacking effective fusion of multi-physics coupled data. Furthermore, model hyperparameter tuning relies on traditional methods such as manual trial and error and grid search, resulting in problems such as low optimization efficiency, model overfitting, and poor generalization ability. At the same time, the models have not established a dynamic correlation mechanism with chaotic blowing parameters, making it impossible to achieve adaptive adjustment of blowing parameters based on multi-physics states.

[0006] The parameter control algorithm is simple and lacks adaptive and constraint mechanisms. Existing injection parameter control methods mostly adopt fixed ratio adjustment, which do not consider the dynamic changes of the multi-physical field of the molten pool, and do not set constraint ranges and amplitude limits for parameter adjustment. This can easily lead to violent fluctuations in the molten pool flow field, causing furnace instability and even production safety hazards.

[0007] In summary, existing technologies have not yet provided a method for optimizing molten pool smelting processes that enables real-time and accurate monitoring of multi-physics fields in the molten pool, efficient processing of multi-source heterogeneous data, precise quantification of the coupling relationship between chaotic blowing and multi-physics fields, and adaptive constraint optimization of blowing parameters based on monitoring and analysis results. This hinders the efficient and intelligent development of non-ferrous metal molten pool smelting processes. Therefore, there is an urgent need to develop an intelligent control method for molten pool smelting processes that enables real-time and accurate monitoring of multi-physics fields, efficient processing of multi-source heterogeneous data, precise quantification of the coupling relationship between chaotic blowing and multi-physics fields, and adaptive constraint optimization of blowing parameters. Summary of the Invention

[0008] To address the aforementioned technical problems, this invention proposes a multi-physics field coupling optimization method for chaotic blown molten pool smelting based on machine learning, comprising: The distribution of the jetting gas applied to the industrial molten pool is controlled by a dual-mode adaptive chaotic switching mechanism to obtain adaptive chaotic jetting parameters. The dual-mode adaptive chaotic switching mechanism includes a first chaotic mode and a second chaotic mode, and the chaotic mode is dynamically selected based on the bubble number density fluctuation rate obtained by real-time monitoring by resistivity tomography in the molten pool. The industrial molten pool is monitored in real time using resistivity tomography. Based on the original multiphysics response data obtained from the monitoring, the distribution of multiphysics inside the industrial molten pool is reconstructed using the Tikhonov regularization algorithm, and key feature parameters of multiphysics are extracted. The key feature parameters of multiphysics are associated and integrated with the adaptive chaotic blowing parameters to construct the original dataset of multiphysics for molten pool smelting. The original dataset of the multiphysics field of the molten pool smelting is standardized and preprocessed, and key feature sets are extracted; a deep generative adversarial network model with physical information constraints is trained. The training includes: embedding the residual constraint terms of the fluid dynamics continuity equation and momentum equation into the generator loss function, and performing iterative adversarial training based on the key feature sets to obtain the trained deep generative adversarial network model. The trained deep generative adversarial network model outputs predictions of the mixing uniformity and smelting efficiency of the industrial molten pool under its current state. Based on the deviation between the prediction result and the preset performance parameter threshold, the adaptive chaotic blowing parameters are dynamically adjusted within the preset parameter constraint range to achieve coupled intelligent optimization of multi-physics fields in industrial molten pool smelting.

[0009] Optionally, in the dual-mode adaptive chaos switching mechanism: The first chaotic mode employs an improved Sine-Tent composite chaotic map, and its iterative formula is as follows: ; in, For the first n The chaotic variable values ​​of the next iteration. For composite weighting coefficients, For disturbance parameters, This is the nonlinear adjustment factor in the first chaotic mode; The second chaotic mode employs an improved Tent chaotic map, and its iterative formula is as follows: ; in, For the first The chaotic variable values ​​of the next iteration. These are the bifurcation parameters in the second chaotic mode.

[0010] Optionally, when using resistive tomography to monitor the industrial molten pool in real time, an array structure of 16 to 32 electrodes is used to cover the outside of the molten pool, with the electrode area accounting for 80% to 90% of the circumference of the molten pool it covers. Based on the original multiphysics response data obtained from the monitoring, the Tikhonov regularized reconstruction algorithm is used to reconstruct the multiphysics distribution inside the molten pool. The objective function of this algorithm is: in, For the sensitivity matrix of electrical resistivity tomography monitoring, M For electrode measurements, N This represents the number of pixels divided into the molten pool. This represents the resistivity distribution vector within the molten pool; λ is the measured voltage vector acquired by resistivity tomography; λ>0 is the regularization coefficient.

[0011] Optionally, the key characteristic parameters of the multiphysics field include the flow field uniformity coefficient E, slag layer thickness, bubble number density ρ, and average equivalent bubble diameter d; The flow field uniformity coefficient is: in, This represents the total number of pixels in the molten pool tomography image. For the first i The flow velocity value corresponding to each pixel. This represents the average velocity value of the flow field within the molten pool. ; The bubble number density r Equivalent diameter of the bubble d The calculation formulas are as follows: in, This refers to the number of bubbles per unit volume of the molten pool. For the volume of the statistical unit, For the first i The actual volume of each bubble.

[0012] Optionally, the standardization preprocessing includes: removing outliers using the 3σ criterion, completing missing values ​​using linear interpolation, and eliminating dimensional differences using min-max normalization; the formula for min-max normalization is: in, The original data, , These are the maximum and minimum values ​​for that feature dimension, respectively.

[0013] Optionally, a combined algorithm of principal component analysis and t-distributed random neighborhood embedding is used to extract key feature sets. The process includes: performing linear dimensionality reduction on the preprocessed data through principal component analysis, and selecting the top features with a cumulative contribution rate of not less than 85%. A projection matrix is ​​constructed from eigenvectors; nonlinear dimensionality reduction is performed using a t-distributed random neighborhood embedding algorithm to map the data to 2 to 5 dimensions.

[0014] Optionally, in the deep generative adversarial network model with physical information constraints, the generator is a physical information neural network and the discriminator is a multilayer perceptron; the loss function of the generator includes the original generation loss, the residual constraint term of the fluid dynamics continuity equation, and the residual constraint term of the momentum equation; the generator and discriminator adopt an alternating training strategy: first fix the generator and update the discriminator to minimize the discrimination loss, then fix the discriminator and update the generator to minimize the total loss including the residual constraint term, and repeat until the model converges.

[0015] Optionally, in the iterative adversarial training, a Bayesian optimization algorithm is used to optimize the model hyperparameters, with a Gaussian process as the surrogate model and the mean square error of the model prediction as the objective function. The hyperparameter sampling points are determined by the expected improvement criterion, and k-fold cross-validation is used to validate the model.

[0016] Optionally, when outputting prediction results based on the trained deep generative adversarial network model, a weighted fusion method is adopted, in which the direct prediction value of the generator and the prediction value corrected by the discriminator are fused according to a preset weight, and the weight of the generator's prediction value is greater than or equal to the weight of the discriminator's corrected prediction value.

[0017] Optionally, the adaptive chaotic jetting parameters are dynamically adjusted using a proportional-integral-derivative adaptive control algorithm tuned by a particle swarm optimization algorithm. The particle swarm optimization algorithm optimizes the parameters using the sum of squared deviations of the proportional-integral-derivative control as the objective function. In the control law of the proportional-integral-derivative adaptive control algorithm, the proportional coefficient, integral time constant, and derivative time constant are determined by the particle swarm optimization algorithm. The control law outputs a real-time control amount of the jetting parameters, which is calculated based on the deviation between the predicted result and the preset performance parameter threshold.

[0018] Compared with the prior art, the present invention has the following advantages and technical effects: (1) This invention proposes a dual-mode adaptive chaotic switching mechanism for the first time, which realizes intelligent matching between chaotic blowing strategy and actual state of molten pool, breaks through the limitation of working condition adaptability of single chaotic mapping, and significantly improves the blowing efficiency of different smelting stages (feeding period, reaction period, slag discharge period).

[0019] (2) This invention embeds physical information constraints into a deep generative adversarial network and incorporates the residual constraint terms of the fluid dynamics continuity equation and momentum equation into the generator loss function, so that the model prediction results simultaneously satisfy data fitting and physical consistency. Compared with the black box model that relies solely on data driving in the prior art, it has stronger extrapolation ability and reliability.

[0020] (3) The present invention sets strict constraint ranges for the injection parameters (injection pressure 0.1-0.5MPa, injection frequency 1-10Hz, injection angle 15°-45°) and single adjustment range (≤15%). Combined with the PID control law tuned by the particle swarm optimization algorithm, the present invention achieves precise dynamic adjustment of the injection parameters under the premise of ensuring stable furnace conditions, and solves the problems of "only injection without measurement, only measurement without control" and unconstrained parameter adjustment in the existing technology.

[0021] (4) The present invention forms a complete closed-loop intelligent optimization system of "real-time monitoring of multi-physics field - dual-mode chaotic adaptive blowing - physical information driven prediction - parameter constraint optimization and control", realizing intelligent control of the entire process of molten pool smelting process, which can be widely applied to the molten pool smelting process of various non-ferrous metals such as copper, zinc, lead, and nickel.

[0022] (5) This invention adopts the PI-DGAN model and uses the Physical Information Neural Network (PINN) as the generator, which overcomes the limitation of the weak generation ability of traditional DBN; it adopts the non-saturated adversarial loss function and adaptive physical constraint weight coefficient to improve the stability of model training and prediction accuracy. Attached Figure Description

[0023] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart illustrating the multi-physics field coupling optimization parameter control process for chaotic blown molten pool smelting according to an embodiment of the present invention. Detailed Implementation

[0024] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0025] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0026] Example 1 like Figure 1 As shown, this embodiment provides a multi-physics field coupling optimization method for chaotic blown molten pool smelting based on machine learning, including: S1. Construct a molten pool smelting experimental platform integrating chaotic blowing and ERT monitoring. Based on the actual size, flow field characteristics, and mass transfer characteristics of the industrial molten pool, construct a scaled-down hydraulic physics model, adapting the model scale to the industrial scenario and experimental conditions. Configure a chaotic blowing module based on a dual-mode adaptive chaotic switching mechanism for the molten pool. This module includes a first chaotic mode (improved Sine-Tent composite chaotic mapping) and a second chaotic mode (improved Tent chaotic mapping). The chaotic mode is adaptively selected based on the bubble number density fluctuation rate monitored in real time by ERT. Set the blowing pressure, blowing frequency, and blowing angle as initial blowing parameters. Adjust the flow distribution and state of the blowing gas through a chaotic mapping algorithm to achieve chaotic control of the blowing gas, thereby enhancing fluid disturbance and three-phase mixing within the molten pool.

[0027] S2. The ERT monitoring module is used to perform non-invasive real-time monitoring of the molten pool, collecting real-time resistivity data of the gas-liquid-slag three-phase medium in the molten pool. The Tikhonov regularized reconstruction algorithm is used to process the raw resistivity data to solve the imaging ill-conditioning problem and generate a high-precision tomographic image of the three-phase distribution in the molten pool. Based on the tomographic image, key multi-physics characteristic parameters such as flow field uniformity coefficient, slag layer thickness, bubble number density, and average equivalent diameter of bubbles are extracted. At the same time, the real-time process parameters of the chaotic blowing module are collected synchronously through the data acquisition module. The multi-physics characteristic parameters are correlated and integrated with the blowing process parameters to construct the original dataset of multi-physics smelting in the molten pool, providing a complete and reliable data foundation for subsequent model training.

[0028] S3. Perform full-process standardized preprocessing on the original multi-physics field dataset of molten pool smelting. The 3σ criterion is used to identify and remove outliers, linear interpolation is used to accurately fill in missing values, and min-max normalization is used to eliminate the differences in the dimensions and numerical ranges of different features. In view of the high-dimensionality, heterogeneity and strong coupling characteristics of the preprocessed data, the PCA-t-SNE combined algorithm is used for dimensionality reduction and feature extraction. First, PCA is used to achieve linear dimensionality reduction of high-dimensional data, remove redundant features and retain core information. Then, t-SNE is used to complete nonlinear dimensionality reduction, explore the intrinsic correlation and coupling law between features, and finally select the key feature set that is strongly related to smelting efficiency. The dataset is divided proportionally and used to construct the model training dataset and the test dataset.

[0029] S4. Construct and train a physically constrained deep generative adversarial network (PI-DGAN) model, with the following structure: The generator employs a Physical Information Neural Network (PINN), consisting of 4 to 6 stacked fully connected layers with either Swish or Tanh activation functions. The output layer has a set number of neurons based on the prediction target. PINN embeds physical constraints into the loss function, ensuring that the model's predictions simultaneously satisfy data fit and physical consistency.

[0030] Discriminator: Employs a multilayer perceptron (MLP), consisting of 2 to 3 fully connected layers. The output layer uses the sigmoid function to output the probability that the sample is the true value.

[0031] The generator's loss function incorporates residual constraint terms from the fluid dynamics continuity equation and momentum equation, forming a physical information constraint loss. in, The original generation loss is replaced by a non-saturating adversarial loss. ; The residual of the continuity equation is ; The residual of the momentum equation is ; , The physical constraint weight coefficients are normalized to ensure that the losses of each item are of similar magnitude. The specific values ​​are determined by Bayesian optimization.

[0032] The loss function of the discriminator is: Model training strategy: The generator and discriminator are trained alternately. First, the generator is fixed, then the discriminator is updated to minimize the discriminative loss. Then, fix the discriminator and update the generator to minimize the total loss due to physical information constraints. Repeat the above process until the model converges.

[0033] Hyperparameter optimization: Bayesian optimization algorithm is used to optimize model hyperparameters. A Gaussian process (GP) is used as a surrogate model, and the mean squared error (MSE) of the model prediction is used as the objective function. in, These are the true values ​​of the molten pool performance parameters. The predicted value of the model. The number of test set samples is used. The next hyperparameter sampling point is determined by the Expected Improvement (EI) criterion, achieving efficient hyperparameter optimization.

[0034] Model validation: using Cross-validation is used to validate the model. The value ranges from 5 to 10. The training dataset is divided into... Using mutually exclusive subsets, the average accuracy is taken as the final validation result of the model after multiple training and validations, which effectively avoids overfitting and improves the model's generalization ability.

[0035] The training dataset is input into the model for iterative adversarial training to obtain the trained PI-DGAN quantitative analysis model.

[0036] S5. During the industrial molten pool smelting process, the tomographic imaging feature parameters collected in real time by the ERT monitoring module and the real-time process parameters of the chaotic jetting module are standardized according to the model input requirements and then input into the trained PI-DGAN quantitative analysis model.

[0037] The model prediction uses a weighted fusion method to output the final prediction result. The fusion formula is as follows: in, The direct prediction of the generator (PINN); The predicted value is the result of correction by the discriminator; , To integrate weights, satisfy ,and The specific value range is as follows: , ; The weights are dynamically allocated based on the model's cross-validation accuracy. Modules with higher validation accuracy have larger weights to ensure the accuracy of the prediction results.

[0038] S6. Based on the final prediction results of the molten pool mixing uniformity and smelting efficiency output in step S5, and combined with the production requirements and process indicators of different non-ferrous metal smelting processes, set the smelting efficiency threshold and mixing uniformity coefficient threshold in a personalized manner.

[0039] Comprehensive index of smelting efficiency: smelting efficiency The formula for calculating the comprehensive quantitative index of metal recovery rate and energy consumption utilization rate is as follows: in, The metal recovery rate of molten pool smelting. The energy consumption utilization rate of molten pool smelting. This is a weighting coefficient that can be dynamically adjusted according to the requirements of different non-ferrous metal smelting processes.

[0040] PID Adaptive Control Algorithm: A proportional-integral-derivative (PID) adaptive control algorithm, tuned using particle swarm optimization (PSO), is employed. The PID control law is: in, This refers to the real-time adjustment of the injection parameters; The deviation between the predicted value and the set threshold; This is the proportionality coefficient. The integral time constant is... The differential time constant; PSO parameter optimization: Using the sum of squared deviations (ISE) of PID control as the objective function, the optimal solution of PID parameters is obtained through the speed and position update formulas.

[0041] Based on the optimized PID algorithm, the blowing pressure, blowing frequency, and blowing angle of the chaotic blowing module are dynamically adjusted according to the deviation between the predicted value and the threshold. The specific control strategy is as follows: When the molten pool mixing uniformity coefficient Below the set threshold When the flow field distribution within the molten pool is uneven and the mixing effect of the gas-liquid-slag three phases is poor, the blowing pressure and blowing frequency should be increased to enhance the molten pool disturbance intensity, promote bubble breakage and dispersion, and improve mixing uniformity. The formula for calculating the control amount is: When smelting efficiency Below the set threshold When the reaction is incomplete or energy consumption is high, the injection angle should be adjusted first to optimize the distribution path and residence time of bubbles in the molten pool, while the injection pressure and frequency should be adjusted as a supplementary measure. The formula for calculating the control amount is: When the uniformity of molten pool mixing and smelting efficiency both meet the threshold requirements, the injection parameters are kept at their current values, and the process enters the steady-state monitoring and fine-tuning stage to avoid flow field fluctuations caused by frequent parameter adjustments.

[0042] Safety constraints for parameter adjustment: To ensure the stability of the molten pool flow field and the safe operation of the equipment, the following constraints must be strictly observed when adjusting the injection parameters: Instantaneous value after jet pressure adjustment Must meet ,and Instantaneous value after adjusting the blowing frequency Must meet ,and Instantaneous value after spray angle adjustment Must meet ,and When the controlled amount exceeds the constraint boundary, it will automatically be cut off to the boundary value and issue an early warning signal to prompt the operator to pay attention to changes in the furnace condition.

[0043] S7. Closed-Loop Optimization Iteration and Model Update. During the continuous operation of industrial molten pool smelting, steps S1 to S6 form a complete closed-loop intelligent optimization system. As the operating time accumulates, the original multiphysics dataset of the molten pool smelting continuously expands. When the amount of new data reaches 10% of the initial dataset size, the incremental model update mechanism is automatically triggered. Dataset expansion: The newly added ERT monitoring data and injection parameter data were standardized and preprocessed before being merged with the original dataset.

[0044] Feature extraction and update: Re-execute the PCA-t-SNE combined dimensionality reduction algorithm to verify the stability of the key feature set; if the addition of data causes changes in feature importance, dynamically adjust the feature selection.

[0045] Incremental training of the model: Using the current PI-DGAN model parameters as initial values, incremental training is performed in a limited number of rounds (usually 20 to 50 rounds) using the expanded dataset. While maintaining the original physical constraint embedding, the model is adapted to the new working conditions.

[0046] Adaptive hyperparameter adjustment: After every 3 to 5 incremental updates, Bayesian optimization is re-executed to calibrate the model's hyperparameters, ensuring that the model's performance remains at its optimal state.

[0047] PID parameter retuning: When the model prediction accuracy or operating characteristics change significantly, the PSO algorithm is re-executed to optimize and tune the PID parameters, maintaining the adaptability of the control strategy.

[0048] Through the aforementioned closed-loop iterative mechanism, the method of this invention can continuously adapt to the long-term evolution and operating condition fluctuations of the molten pool smelting process, and achieve intelligent operation with self-learning and self-optimization.

[0049] In step S1, the first chaotic mode in the dual-mode adaptive chaos switching mechanism adopts an improved Sine-Tent composite chaotic mapping, and its iterative formula is: in, , , , The second chaotic mode employs an improved Tent chaotic map, with the following iterative formula: The bubble number density ρ(t) is obtained through real-time monitoring using ERT, the volatility δ(t) is calculated, and a smooth switching of chaotic modes is achieved through an adaptive switching function S(t). When m When taking values ​​within this range, the algorithm exhibits completely chaotic characteristics. This can be addressed by adjusting... mThe value of can precisely control the degree of chaos in the airflow distribution; the flow distribution coefficient of each branch of the jet airflow is determined by normalizing the chaotic variable value, which ensures both the chaos of the flow distribution to enhance the disturbance of the molten pool and the uniformity of the distribution to avoid excessively strong or weak local airflow; the scale of the hydraulic physical model is in the range of 1:8 to 1:15, and the model material and structure are consistent with the industrial molten pool to ensure that the flow field and mass transfer characteristics of the model are highly similar to those of the industrial molten pool, thus ensuring the industrial applicability of the experimental data.

[0050] In step S2, the ERT monitoring module adopts an array structure of 16 to 32 electrodes. The electrode array covers the circumferential and axial sides of the molten pool. The area of ​​the circumferential electrodes accounts for 80%-90% of the circumference of the molten pool they cover. The spacing between the axial electrodes is 5 to 10 cm. The imaging speed of the monitoring module is 70-140 frames / s and the sampling frequency is 100-200 Hz, realizing high real-time and high-precision acquisition of multi-physics field data of the molten pool.

[0051] The objective function of the Tikhonov regularized reconstruction algorithm is: in, For the sensitivity matrix of ERT monitoring, M For electrode measurements, N This represents the number of pixels divided into the molten pool. This represents the resistivity distribution vector within the molten pool; λ is the measured voltage vector acquired by ERT; λ>0 is the regularization coefficient, with a value range of 0.01~0.05. It can be dynamically adjusted according to the noise level of the measured data to balance the data fitting error and the smoothness of the solution, thereby improving the accuracy of tomographic imaging.

[0052] In step S2, among the extracted multiphysics characteristic parameters, the flow field uniformity coefficient is... E Bubble number density r Equivalent diameter of the bubble d The calculation formulas are as follows: in, n This represents the total number of pixels in the molten pool tomography image. For the first i The flow velocity value corresponding to each pixel. This represents the average velocity value of the flow field within the molten pool; N This refers to the number of bubbles per unit volume of the molten pool. V For the volume of the statistical unit; For the first iThe actual volume of each bubble; the feature dimensions of the original dataset cover the multi-physics features monitored by ERT and the parameters of chaotic blowing process, with a sample size of no less than 5000 sets, to ensure the effectiveness and reliability of subsequent model training.

[0053] In step S3, the 3σ criterion calculates the mean Xˉ and standard deviation σ of the feature dimension data and eliminates those that satisfy the criterion. Abnormal data points; linear interpolation fills in missing values ​​by linearly fitting the data based on the acquisition time and values ​​of adjacent valid data points before and after the missing value, ensuring the temporal evolution of the data; min-max normalization maps the data to the [0,1] interval, and the normalization formula is: in, The original data, , These are the maximum and minimum values ​​for that feature dimension, respectively.

[0054] In step S3, the PCA-t-SNE combined algorithm first centers the preprocessed data, solves the covariance matrix, and performs eigenvalue decomposition. It then selects the top k eigenvectors with a cumulative contribution rate of at least 85% to construct a projection matrix, achieving linear dimensionality reduction. Next, the PCA-reduced data is input into the t-SNE algorithm. Using the Student t-distribution as the kernel function, nonlinear dimensionality reduction is achieved by minimizing the KL divergence between the high-dimensional and low-dimensional spaces, ultimately mapping the data to 2-5 dimensions and completing the accurate selection of key features. The formula for calculating the covariance matrix is: The formula for calculating the similarity of sample points in the low-dimensional space in the t-SNE algorithm is as follows: In step S4, the PI-DGAN model employs a Physical Information Neural Network (PINN) as its generator, consisting of 4 to 6 fully connected layers. The number of hidden layer neurons is determined based on the input feature dimension and the output prediction target (e.g., 128-64-32-16), and the activation function is either Swish or Tanh. The discriminator MLP consists of 2 to 3 fully connected layers, with 64 and 32 hidden layer neurons respectively. The activation function is LeakyReLU, and the output layer uses the Sigmoid function to output the probability that the sample is the true value. The generator's loss function incorporates residual constraint terms from the fluid dynamics continuity equation and momentum equation, forming a physical information constraint loss. The loss function of the discriminator is The formula is: The generator and discriminator are trained alternately until the model reaches Nash equilibrium.

[0055] Furthermore, in step S4, the Bayesian optimization uses a Gaussian process (GP) as a surrogate model and the mean squared error of model prediction (MSE) as the objective function. The objective function formula is: in, These are the true values ​​of the molten pool performance parameters. The predicted value of the model. n The number of test set samples is used; the next hyperparameter sampling point is determined by the expected improvement criterion (EI) to achieve efficient hyperparameter optimization; the value of k in k-fold cross-validation is 5~10, the training dataset is divided into k mutually exclusive subsets, and the average accuracy is taken as the final validation result of the model after multiple training and validation, which effectively avoids overfitting and improves the generalization ability of the model.

[0056] In step S5, the final prediction results of the molten pool mixing uniformity and smelting efficiency are output using a weighted fusion method, and the fusion formula is: in, The direct prediction of the generator (PINN) The predicted value after correction by the discriminator. , To integrate weights, satisfy ,and , The weights are dynamically allocated based on the cross-validation accuracy of the model. Modules with higher validation accuracy have larger weights to ensure the accuracy of the prediction results.

[0057] In step S6, the smelting efficiency or The formula for calculating the comprehensive quantitative index of metal recovery rate and energy consumption utilization rate is as follows: in, The metal recovery rate in molten pool smelting is the ratio of the actual amount of metal produced to the total amount of metal in the raw materials. α represents the energy utilization rate of molten pool smelting, which is the ratio of energy consumed in the effective reaction to the total input energy; α∈[0.5,0.8] is the weighting coefficient, which can be dynamically adjusted according to the requirements of different non-ferrous metal smelting processes. For precious metal smelting, priority is given to ensuring the metal recovery rate and a larger value is taken, while for ordinary non-ferrous metal smelting, energy utilization rate is taken into account and a smaller value is taken.

[0058] In step S6, the control law of the PID adaptive control algorithm is: in, This refers to the real-time adjustment of the injection parameters; The deviation between the predicted value and the set threshold, A threshold is set for the uniformity of molten pool mixing or smelting efficiency. These are the model's real-time predicted values; This is the proportionality coefficient. The integral time constant is... The three parameters, which are differential time constants, are adaptively optimized using the particle swarm optimization (PSO) algorithm to ensure optimal control performance of the PID algorithm.

[0059] In step S6, the particle swarm optimization (PSO) algorithm is used to adaptively optimize the PID parameters. The sum of squared deviations (ISE) of the PID control is used as the objective function, and the optimal solution for the PID parameters is obtained through the velocity and position update formulas. The velocity and position update formulas are as follows: in, For inertial weights, , As a learning factor, , A random number in the range [0,1]. This represents the optimal position for an individual particle. This is the globally optimal position for the particle swarm.

[0060] In step S6, the blowing parameters are strictly constrained: blowing pressure Blowing frequency Each adjustment increment is ≤15% of the current value, and the spray angle is... i ∈[15°,45°], with a single adjustment range of ≤5°, to ensure a stable flow field in the molten pool and stable furnace operation.

[0061] This invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. The processor, when executing the computer program, implements the machine learning-based multiphysics coupling optimization method for chaotic blown molten pool smelting described above. The processor employs a multi-core parallel computing architecture, enabling simultaneous ERT data reconstruction, model training, parameter optimization, and blown parameter control. Its computational efficiency is more than 50% higher than traditional serial computing, meeting the real-time control requirements of industrial molten pool smelting. The memory has a storage capacity of at least 1TB, enabling long-term storage and traceability of molten pool multiphysics data, providing data support for subsequent process optimization and model iteration.

[0062] The present invention also provides a computer-readable storage medium storing a computer program, characterized in that, when the computer program is executed by a processor, it implements the multi-physics coupling optimization method for chaotic blown molten pool smelting based on machine learning as described above. The computer-readable storage medium may be a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, etc., and is suitable for equipment deployment and program updates in industrial settings.

[0063] This method is applicable to the molten pool smelting process of various non-ferrous metals such as copper, zinc, lead, and nickel. The scale of the hydraulic physical model, the threshold of the injection parameters, the model hyperparameters and weight coefficients can be adjusted according to the characteristics of different smelting processes to achieve adaptation.

[0064] The following example applies this method to the copper smelting pool smelting process, specifically including the following steps: S1. Construct a molten pool smelting experimental platform with chaotic jetting and ERT monitoring, and build a hydraulic physical model of the industrial copper smelting pool at a 1:10 scale, using the same material as the industrial pool; configure a dual-mode adaptive chaotic jetting module, which includes: The first chaotic mode employs an improved Sine-Tent composite chaotic map, and its iterative formula is as follows: ; in, For the first n The chaotic variable values ​​of the next iteration. For composite weighting coefficients, For disturbance parameters, This is the nonlinear adjustment factor in the first chaotic mode; The second chaotic mode employs an improved Tent chaotic map, and its iterative formula is as follows: ; in, For the first The chaotic variable values ​​of the next iteration. These are the bifurcation parameters in the second chaotic mode.

[0065] Set the initial blowing parameters: blowing pressure 0.3MPa, blowing frequency 5Hz, blowing angle 30°.

[0066] The S2 and ERT monitoring modules employ a 16-electrode array structure, covering the outer side of the molten pool. The circumferential electrode area occupies 85% of the molten pool circumference, with an axial electrode spacing of 8 cm. The imaging speed is 100 frames / s, and the sampling frequency is 150 Hz. Real-time resistivity data of the gas-liquid-slag three-phase medium within the molten pool are collected, and the molten pool tomographic image is obtained using the Tikhonov regularized reconstruction algorithm. The algorithm's objective function is: Extracting the flow field uniformity coefficient E Slag layer thickness, bubble number density r Average equivalent diameter of bubbles d Characteristic parameters; synchronously collect real-time process parameters of the chaotic jetting module.

[0067] S3. Preprocessing the original dataset: Outliers are removed using the 3σ criterion, missing values ​​are filled using linear interpolation, and min-max normalization maps the data to the [0,1] interval. The normalization formula is as follows: The PCA-t-SNE combined algorithm is used for dimensionality reduction. First, the covariance matrix is ​​solved using PCA. Then, the top 10 eigenvectors with a cumulative contribution rate of 88% are selected to achieve linear dimensionality reduction. The formula for the covariance matrix is ​​as follows: The data was then reduced to 5 dimensions using t-SNE, and five key features were selected: flow field uniformity coefficient, slag layer thickness, bubble distribution density, injection pressure, and injection frequency. The dataset was then divided into training and testing datasets in an 8:2 ratio.

[0068] S4. Construct a Physical Information Constrained Deep Generative Adversarial Network (PI-DGAN) model. The generator uses a Physical Information Neural Network (PINN), consisting of four fully connected layers stacked together. The number of hidden layer neurons is 128, 64, 32, and 16 respectively, with the activation function being Swish. The output layer has the corresponding number of neurons set according to the prediction target. The discriminator uses a Multilayer Perceptron (MLP), consisting of two fully connected layers. The number of hidden layer neurons is 64 and 32 respectively, with the activation function being LeakyReLU. The output layer uses the Sigmoid function.

[0069] The generator's loss function incorporates residual constraint terms from the fluid dynamics continuity equation and momentum equation: in: The overall adversarial loss function of the model is: The training dataset was input into the model for 200 training epochs with a batch size of 64. Bayesian optimization was used to optimize hyperparameters such as the learning rate and regularization coefficient, with the model's predicted MSE as the objective function. The formula is as follows: The model was validated using 5-fold cross-validation to obtain the trained quantitative analysis model.

[0070] S5. After standardizing the feature parameters collected in real time by the ERT monitoring module and the real-time process parameters of the chaotic blowing module during the industrial copper smelting process, input them into the trained model; output the final prediction results of the molten pool mixing uniformity and smelting efficiency through a weighted fusion method. The fusion formula is as follows: in, The direct prediction of the generator (PINN) This is the predicted value after correction by the discriminator.

[0071] S6. Set the smelting efficiency threshold to 92%, the mixing uniformity coefficient threshold to 0.85, and the comprehensive smelting efficiency index to α=0.7. The calculation formula is as follows: Based on the prediction results, a PSO-optimized PID adaptive control algorithm is used to adjust the jetting parameters. The PSO algorithm is set with a particle count of 30 and 150 iterations. The velocity and position update formulas are as follows: Optimization yields PID parameters =1.2、 =0.5、 =0.1, the PID control law is: The jetting parameter adjustment constraint is as follows P ∈[0.1MPa,0.5MPa]、 f ∈[1Hz,10Hz]、 i ∈[15°,45°], single adjustment range ≤15% (angle ≤5°); when the mixing uniformity coefficient is lower than the threshold, increase the blowing pressure and frequency; when the smelting efficiency is lower than the threshold, adjust the blowing angle to optimize the bubble distribution.

[0072] High monitoring accuracy and reliable data support. This invention constructs an integrated chaotic jetting-ERT monitoring platform, employing ERT non-invasive monitoring technology with a 16-32 electrode array. Combined with the Tikhonov regularized reconstruction algorithm, it addresses imaging ill-conditioning issues, achieving an imaging speed of 70-140 frames / s. It can accurately extract key multi-physics features such as flow field uniformity and bubble distribution. Simultaneously, based on a dual-mode adaptive chaotic switching mechanism, it achieves precise control of the jetting airflow. The hydraulic physics model of the experimental platform is highly similar to that of an industrial molten pool, ensuring the industrial applicability of the collected data and providing a complete and reliable multi-source data foundation for subsequent model training and parameter optimization.

[0073] The data processing is highly efficient, and feature mining is accurate. This invention designs a full-process data preprocessing scheme of "3σ criterion, linear interpolation, and min-max normalization," which effectively eliminates data noise, fills in missing values, and eliminates dimensional differences. It also proposes a PCA-t-SNE combined dimensionality reduction algorithm to achieve a combination of linear and nonlinear dimensionality reduction. This not only removes redundant features from high-dimensional heterogeneous data but also uncovers the inherent coupling patterns between features, accurately selecting key features strongly correlated with smelting efficiency. This reduces the data dimension to 2-5 dimensions, significantly improving the training efficiency and prediction accuracy of subsequent machine learning models.

[0074] The model exhibits excellent performance, combining high prediction accuracy with strong generalization ability. This invention constructs a Physically Constrained Deep Generative Adversarial Network (PI-DGAN) model, which is trained adversarially between a PI-DGAN generator and an MLP discriminator. The residual constraints of the fluid dynamics continuity and momentum equations are embedded into the generator's loss function, ensuring that the model's predictions simultaneously satisfy data fitting and physical consistency. This approach uncovers the deep coupling between multi-physics features and molten pool performance, improving the reliability and extrapolation ability of the model's predictions. Furthermore, Bayesian optimization is employed to efficiently optimize hyperparameters, replacing traditional manual trial-and-error methods and improving optimization efficiency by over 60%. Combined with k-fold cross-validation, overfitting is effectively avoided, giving the model strong generalization ability in practical industrial applications.

[0075] Intelligent parameter control ensures stable and controllable furnace conditions. This invention designs a PSO-PID adaptive constraint control strategy. The PSO algorithm optimizes the PID parameters to suit the smelting conditions, obtaining the optimal parameter combination and improving the control accuracy of the injection parameters. Simultaneously, strict constraint ranges and single adjustment amplitudes are set for the injection parameters to avoid drastic fluctuations in the molten pool flow field, achieving stable dynamic adjustment of injection pressure, frequency, and angle, ensuring stable furnace operation, and solving the problems of traditional control methods being based on experience and lacking constraints.

[0076] The closed-loop control is highly efficient, and the process indicators are significantly improved. This invention forms a complete closed-loop control system of "real-time monitoring of multi-physics fields - multi-source data processing - quantitative prediction of coupling relationships - adaptive optimization of injection parameters", and explores the inherent coupling mechanism between chaotic injection and the multi-physics field of the molten pool, realizing intelligent control of the entire process of non-ferrous metal molten pool smelting.

[0077] With strong adaptability and broad prospects for promotion, the method of this invention is applicable to the molten pool smelting process of various non-ferrous metals such as copper, zinc, lead, and nickel. Adaptation can be achieved simply by adjusting the scale of the hydraulic physics model, the threshold values ​​of the injection parameters, the model hyperparameters, and the weighting coefficients according to the characteristics of different smelting processes. Simultaneously, the accompanying electronic equipment and computer-readable storage media are suitable for equipment deployment and program updates in industrial settings, enabling rapid implementation and providing a new technical solution for the efficient, energy-saving, and intelligent development of the metallurgical industry. It possesses significant industrial application value and broad prospects for promotion.

[0078] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A multi-physics field coupling optimization method for chaotic blown molten pool smelting based on machine learning, characterized in that, Includes the following steps: The distribution of the jetting gas applied to the industrial molten pool is controlled by a dual-mode adaptive chaotic switching mechanism to obtain adaptive chaotic jetting parameters. The dual-mode adaptive chaotic switching mechanism includes a first chaotic mode and a second chaotic mode, and the chaotic mode is dynamically selected based on the bubble number density fluctuation rate obtained by real-time monitoring by resistivity tomography in the molten pool. The industrial molten pool is monitored in real time using resistivity tomography. Based on the original multiphysics response data obtained from the monitoring, the distribution of multiphysics inside the industrial molten pool is reconstructed using the Tikhonov regularization algorithm, and key feature parameters of multiphysics are extracted. The key feature parameters of multiphysics are associated and integrated with the adaptive chaotic blowing parameters to construct the original dataset of multiphysics for molten pool smelting. The original dataset of the multiphysics field of the molten pool smelting was standardized and preprocessed, and key feature sets were extracted. A deep generative adversarial network model constrained by physical information is trained by: embedding the residual constraint terms of the fluid dynamics continuity equation and momentum equation into the generator loss function, and performing iterative adversarial training based on the key feature set to obtain the trained deep generative adversarial network model. The trained deep generative adversarial network model outputs predictions of the mixing uniformity and smelting efficiency of the industrial molten pool under its current state. Based on the deviation between the prediction result and the preset performance parameter threshold, the adaptive chaotic blowing parameters are dynamically adjusted within the preset parameter constraint range to achieve coupled intelligent optimization of multi-physics fields in industrial molten pool smelting.

2. The multi-physics field coupling optimization method for chaotic blown molten pool smelting based on machine learning according to claim 1, characterized in that, In the aforementioned dual-mode adaptive chaos switching mechanism: The first chaotic mode employs an improved Sine-Tent composite chaotic map, and its iterative formula is as follows: ； in, For the first n The chaotic variable values ​​of the next iteration. For composite weighting coefficients, For disturbance parameters, This is the nonlinear adjustment factor in the first chaotic mode; The second chaotic mode employs an improved Tent chaotic map, and its iterative formula is as follows: ； in, For the first The chaotic variable values ​​of the next iteration. These are the bifurcation parameters in the second chaotic mode.

3. The multi-physics field coupling optimization method for chaotic blown molten pool smelting based on machine learning according to claim 1, characterized in that, When using resistive tomography to monitor the industrial molten pool in real time, an array structure of 16 to 32 electrodes is used to cover the outside of the molten pool, with the electrode area accounting for 80% to 90% of the circumference of the molten pool it covers. Based on the original multiphysics response data obtained from the monitoring, the Tikhonov regularized reconstruction algorithm is used to reconstruct the multiphysics distribution inside the molten pool. The objective function of this algorithm is: in, For the sensitivity matrix of electrical resistivity tomography monitoring, M For electrode measurements, N This represents the number of pixels divided into the molten pool. This represents the resistivity distribution vector within the molten pool; λ is the measured voltage vector acquired by resistivity tomography; λ>0 is the regularization coefficient.

4. The multi-physics field coupling optimization method for chaotic blown molten pool smelting based on machine learning according to claim 1, characterized in that, The key characteristic parameters of the multiphysics field include the flow field uniformity coefficient E, slag layer thickness, bubble number density ρ, and average equivalent bubble diameter d. The flow field uniformity coefficient is: in, This represents the total number of pixels in the molten pool tomography image. For the first i The flow velocity value corresponding to each pixel. This represents the average velocity value of the flow field within the molten pool. ; The bubble number density ρ Equivalent diameter of the bubble d The calculation formulas are as follows: in, This refers to the number of bubbles per unit volume of the molten pool. For the volume of the statistical unit, For the first i The actual volume of each bubble.

5. The multi-physics field coupling optimization method for chaotic blown molten pool smelting based on machine learning according to claim 1, characterized in that, The standardization preprocessing is as follows: outliers are removed using the 3σ criterion; missing values ​​are filled using linear interpolation; and dimensional differences are eliminated using min-max normalization. The formula for min-max normalization is: in, The original data, , These are the maximum and minimum values ​​for that feature dimension, respectively.

6. The multi-physics field coupling optimization method for chaotic blown molten pool smelting based on machine learning according to claim 1, characterized in that, A combined algorithm of principal component analysis and t-distributed random neighborhood embedding is used to extract key feature sets. The process includes: linear dimensionality reduction of the preprocessed data through principal component analysis, and selecting the top features with a cumulative contribution rate of not less than 85%. A projection matrix is ​​constructed from eigenvectors; nonlinear dimensionality reduction is performed using a t-distributed random neighborhood embedding algorithm to map the data to 2 to 5 dimensions.

7. The multi-physics field coupling optimization method for chaotic blown molten pool smelting based on machine learning according to claim 1, characterized in that, In the deep generative adversarial network model with physical information constraints, the generator is a physical information neural network and the discriminator is a multilayer perceptron; the loss function of the generator includes the original generation loss, the residual constraint term of the fluid dynamics continuity equation, and the residual constraint term of the momentum equation. The generator and discriminator are trained using an alternating strategy: first, the generator is fixed and the discriminator is updated to minimize the discriminative loss, then the discriminator is fixed and the generator is updated to minimize the total loss including the residual constraint term, and this process is repeated until the model converges.

8. The multi-physics field coupling optimization method for chaotic blown molten pool smelting based on machine learning according to claim 1, characterized in that, In the iterative adversarial training, the Bayesian optimization algorithm is used to optimize the model hyperparameters, with a Gaussian process as the surrogate model and the mean square error of the model prediction as the objective function. The hyperparameter sampling points are determined by the expected improvement criterion, and k-fold cross-validation is used to validate the model.

9. The multi-physics field coupling optimization method for chaotic blown molten pool smelting based on machine learning according to claim 1, characterized in that, When outputting prediction results based on the trained deep generative adversarial network model, a weighted fusion method is adopted, in which the direct prediction value of the generator and the prediction value corrected by the discriminator are fused according to a preset weight, and the weight of the generator's prediction value is greater than or equal to the weight of the discriminator's corrected prediction value.

10. The multi-physics field coupling optimization method for chaotic blown molten pool smelting based on machine learning according to claim 1, characterized in that, The adaptive chaotic jetting parameters are dynamically adjusted using a proportional-integral-derivative adaptive control algorithm optimized by a particle swarm optimization algorithm. The particle swarm optimization algorithm optimizes the parameters using the sum of squared deviations of the proportional-integral-derivative control as the objective function. In the control law of the proportional-integral-derivative adaptive control algorithm, the proportional coefficient, integral time constant, and derivative time constant are determined by the particle swarm optimization algorithm. The control law outputs the real-time adjustment amount of the jetting parameters, which is calculated based on the deviation between the predicted result and the preset performance parameter threshold.

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