Intelligent optimization method for flow field in continuous casting crystallizer

Abstract

The invention provides an intelligent optimization method for a flow field in a continuous casting crystallizer, and belongs to the technical field of ferrous metallurgy continuous casting processes. The method comprises the following steps: firstly, constructing a multiphase flow numerical calculation model for simulating the flow behavior of molten steel in a crystallizer, and calculating flow field distribution corresponding to multiple groups of process parameter combinations; secondly, according to a numerical calculation result, constructing a data sample library of process parameters and flow field parameters, establishing a BP neural network flow field prediction model, and further establishing a multi-objective optimization function of the flow field parameters; and finally, solving a Pareto optimal solution set for minimizing the maximum flow velocity of the surface, minimizing the height difference of the liquid level and minimizing the tendency of the unstable flow by using a multi-target particle swarm algorithm, so as to realize multi-target optimization of the flow field in the crystallizer. According to the method, the states of the flow field in the crystallizer under different process conditions can be predicted, intelligent optimization of the flow field in the crystallizer is achieved according to the change of the process conditions, the surface quality of the continuous casting billet is effectively improved, and a good optimization effect and high adaptability are shown.

Description

Technical Field

[0001] The invention belongs to the technical field of continuous casting processes in steel metallurgy, and relates to an intelligent optimization method for a flow field in a continuous casting crystallizer. Background Art

[0002] The flow of molten steel within the mold affects inclusion capture, liquid level fluctuations, and slag entrainment, playing a key role in promoting the uniform growth of the primary solidified shell. A reasonable molten steel flow field is the basis for stable ingot quality. When the flow pattern of the molten steel is unreasonable, inclusions are easily captured by the dendritic solidification front or the hooked shell in the meniscus area, leading to steel defects. Therefore, optimizing the mold flow field through reasonable means to promote the floating removal of inclusions and reduce inclusion capture is of great significance for reducing steel defects and improving ingot surface quality.

[0003] Chinese invention patent CN113828746B proposes a method for evaluating the flow field of the crystallizer using the distribution of oscillation marks of the ingot. The method evaluates the quality of the crystallizer flow field by analyzing the characteristic parameters of the oscillation mark distribution, but it fails to provide a specific continuous casting process adjustment plan. Chinese invention patent CN113500173B proposes a method for controlling the flow field morphology of the molten steel in the crystallizer of a medium-section slab. The method measures the surface flow velocity through a velocity measuring device, determines the flow field morphology in the crystallizer, and establishes a quantitative relationship between the flow field morphology and the amount of steel passed and the argon gas volume fraction, thereby achieving accurate control of the flow field morphology of the molten steel in the crystallizer. However, it fails to provide an adaptive optimization plan in combination with different process parameters. Chinese invention patent CN108346366B proposes a crystallizer model and a crystallizer flow field simulation method for studying the flow field in the crystallizer. The method uses water simulation and numerical calculation models to predict the molten steel flow field, and then optimizes the design process operating parameters. However, its process optimization design method has the problem of insufficient adaptability.

[0004] In summary, while existing research has practical significance for evaluating and predicting mold flow fields, subsequent flow field optimization methods have certain limitations. Most existing studies focus on optimizing a single objective, failing to fully consider the synergistic relationships between flow field parameters. This makes it difficult to achieve multi-objective collaborative optimization, limiting the efficiency and adaptability of mold flow field optimization. Summary of the Invention

[0005] In response to the problems existing in the prior art, the present invention proposes an intelligent optimization method for the flow field in a continuous casting crystallizer, which can achieve effective control of the flow field in the crystallizer.

[0006] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0007] A method for intelligent optimization of the flow field in a continuous casting crystallizer. The optimization method comprises the following steps: first, constructing a multiphase flow numerical calculation model to simulate the flow behavior of molten steel in the crystallizer and calculating the flow field distribution corresponding to multiple sets of process parameter combinations; second, constructing a data sample library of process parameters and flow field parameters based on the numerical calculation results, and establishing a BP neural network flow field prediction model based on Bayesian optimization to predict the maximum surface flow velocity, liquid level height difference and flow field morphology; then, based on the BP neural network flow field prediction model, defining nonlinear mapping functions between process parameters and flow field parameters, and establishing a multi-objective optimization function for flow field parameters; finally, using a multi-objective particle swarm algorithm to solve the Pareto optimal solution set that minimizes the maximum surface flow velocity, minimizes the liquid level height difference and minimizes the tendency of unstable flow, thereby realizing multi-objective optimization of the flow field in the crystallizer. Specifically, the method comprises the following steps:

[0008] The first step is to build a numerical calculation model of multiphase flow in the crystallizer;

[0009] The following assumptions were made when establishing the numerical calculation model for multiphase flow in the mold: molten steel, mold powder, and air were considered incompressible Newtonian fluids; mold vibration and taper were neglected; the effects of heat transfer and solidification of the molten steel and mold powder were ignored; argon bubbles were considered inert spherical particles, the bubble size was set to follow the Rosin-Rammler distribution, and the interactions between argon bubbles were ignored. The specific steps for constructing the numerical calculation model for multiphase flow in the mold are as follows:

[0010] Step (1.1) grid division;

[0011] According to the cross-sectional dimensions of the ingot, nozzle dimensions, and slag layer thickness distribution during the steel plant's casting process, a three-dimensional geometric model that conforms to the actual situation is established, and the geometric model is imported into the commercial software ICEM to divide the structural grid.

[0012] Step (1.2) solves model selection;

[0013] The structured mesh obtained by meshing in step (1.1) was imported into the commercial software Fluent. The standard K-ε turbulence model, multiphase flow model, and discrete phase model were set to establish a numerical calculation model of multiphase flow in the crystallizer. The continuity equation, momentum equation, turbulence equation, interface tracking equation, and discrete phase particle motion equation were solved.

[0014] Step (1.3) physical property parameters and boundary conditions setting;

[0015] With reference to the actual casting information of the steel plant, the physical parameters of molten steel, protective slag and air are input into the multiphase flow numerical calculation model of the crystallizer. According to the flow continuity principle, with the help of the cross-sectional area A of the billet s , nozzle cross-sectional area A n With pulling speed v c, calculate the steel liquid inlet velocity v at the nozzle i , v i =A s ×v c / A n . Then, according to the inlet velocity v i and nozzle diameter D, calculate turbulent kinetic energy and the turbulent kinetic energy dissipation rate ε = k 1.5 / D, input k and ε into the inlet boundary condition settings. In addition, set the outlet of the fluid domain to a pressure outlet.

[0016] Step (1.4) numerical calculation;

[0017] The parallel computing mode is used to speed up the calculation of the numerical calculation model of the multiphase flow in the crystallizer until the continuity, velocity component, turbulent kinetic energy and turbulent dissipation rate residuals of the numerical calculation model of the multiphase flow in the crystallizer are basically stable.

[0018] The second step is to build a data sample library of casting process-flow field parameters;

[0019] Through the orthogonal experimental design concept, r calculation cases were set under different combinations of process parameters such as billet width, casting speed, nozzle immersion depth and argon blowing amount. The numerical calculation model of multiphase flow in the crystallizer constructed in the first step was used to calculate the flow field distribution in the crystallizer under the conditions of r groups of process parameters.

[0020] The calculation results of the flow field in the crystallizer under r group process parameters are post-processed to extract the calculated surface maximum flow velocity, liquid level height difference and flow field morphology, and construct a data sample library D about the flow field parameters. r×c . Among them, r is the number of rows in the sample library, indicating the number of samples in the data sample library, ensuring that r is not less than 40; c = 7 is the number of columns in the sample library, the sample data in the 1st to 4th columns are the billet width, casting speed, nozzle immersion depth and argon blowing amount, and the sample data in the 5th to 7th columns are the maximum surface flow velocity, liquid level height difference and flow field morphology; among them, the flow field morphology includes stable flow (double annular flow) and unsteady flow (complex flow, single annular flow).

[0021] The third step is to build a BP neural network prediction model;

[0022] Data sample library D of casting process-flow field parameters constructed in the second step r×c , respectively, constructing BP neural network prediction models to accurately predict the maximum surface velocity, liquid level height difference, and flow field morphology. The constructed models include a BP neural network-based maximum surface velocity regression prediction model, a liquid level height difference regression prediction model, and a flow field morphology classification prediction model. The construction ideas of the above three prediction models are generally consistent, and the specific construction steps are as follows:

[0023] Step (3.1) standardization preprocessing;

[0024] For the data sample library D r×c , the four features of billet width, casting speed, nozzle immersion depth and argon blowing amount are standardized and preprocessed, while keeping the original values ​​of surface maximum flow velocity, liquid level height difference and flow field morphology unchanged, so as to form a standardized preprocessed data sample library X r×c , the standardized calculation formula is shown in formula (1).

[0025]

[0026] Where, X ij is the data after standardized preprocessing, where i = 1, 2, ..., r, represents the i-th sample, j = 1, 2, ..., c-3, represents the j-th process parameter characteristics of the sample; D ij is the original sample database D r×c data; σ j is the original sample database D r×c The standard deviation of the jth feature data; μ j is the original sample database D r×c The average value of the j-th feature data.

[0027] Step (3.2) model data set division;

[0028] According to the three output objects to be predicted, namely, the maximum surface velocity, the liquid level height difference and the flow field morphology, a dataset K1, K2 and K3 containing r samples are constructed respectively. Each sample is a data sample library X after the standardization process in step (3.1). r×c The specific distribution of each data set is as follows:

[0029] K1={(x1,u1),(x2,u2),(x3,u3),…,(x r ,u r )}(2)

[0030] K2={(x1,y1),(x2,y2),(x3,y3),…,(x r ,y r )}(3)

[0031] K3={(x1,z1),(x2,z2),(x3,z3),…,(x r ,z r )}(4)

[0032] Where x i The feature vector of the i-th sample contains c-3 features of the sample (bill width, casting speed, nozzle immersion depth, argon blowing amount), where i = 1, 2, ..., r; ui Indicates the actual output value of the maximum surface velocity of the i-th sample; y i Indicates the actual output value of the liquid level height difference of the i-th sample; z i Indicates the actual output value of the flow field morphology of the i-th sample, the non-stable flow label is 1, and the stable flow label is 0.

[0033] The dataset K i (i=1,2,3) is randomly divided into training set K train-i and the test set K test-i , set each training set P i With the test set Q i The sample size ratio is 4:1.

[0034] Step (3.3) Bayesian search for hyperparameters;

[0035] The goal of the BP neural network model is to learn the nonlinear mapping relationship between input features and output target values ​​through a multi-layer feedforward network structure and back propagation algorithm, so that the true output value y of most training data samples is (i) With model output value Minimize the loss function between the i-th sample x i The model output value calculation formula is shown in Equations (5) and (6). The BP neural network model training process is as follows: input the training set data sample, calculate the output of each hidden layer through forward propagation, use the loss function to evaluate the prediction error of the BP neural network model, and then update the network weights and thresholds according to the back-propagation error gradient, and finally construct a prediction model f(x) with nonlinear fitting ability.

[0036]

[0037] Where, is the output of the jth hidden layer neuron of the i-th sample, where i = 1, 2, ..., r, j = 1, 2, ..., s; x ik is the kth eigenvalue of the i-th sample (input features include billet width, casting speed, nozzle immersion depth, and argon blowing amount); w kj is the weight from the kth feature of the input layer to the jth neuron of the hidden layer; θ j is the threshold of the jth neuron in the hidden layer; is the predicted output value of the i-th sample; w j is the weight from the j neurons in the hidden layer to the neurons in the output layer; θ is the threshold of the output neuron; f1 is the activation function of the hidden layer; f2 is the activation function of the output layer.

[0038] The hidden layer parameters and hyperparameters of the BP neural network model jointly determine the nonlinear expression ability and convergence speed of the BP neural network model. To optimize the performance of the BP neural network model, the gradient descent method is used to iteratively update the hidden layer parameters, and the Bayesian algorithm is used to optimize the hyperparameters to determine the optimal BP neural network prediction model. The specific implementation steps are as follows:

[0039] Step (3.3.1) defines the parameter space;

[0040] Given that the performance of BP neural networks depends on the proper selection of network structure and training parameters, it is necessary to define an appropriate hyperparameter space. Key parameters include the number of hidden layers, the number of neurons per layer, the learning rate, the type of activation function, and the number of training rounds. The number of hidden layers q and the number of neurons l jointly determine the model's capacity, the learning rate η affects the model's convergence speed and stability, the type of activation function f is suitable for data with different nonlinear characteristics, and the number of training rounds T determines the model's learning depth on the training set.

[0041] Step (3.3.2) determines the performance evaluation indicators;

[0042] For the regression prediction model, the mean square error is selected as the performance metric of the regression prediction model, and a 5-fold cross validation is used to test the training set K containing the maximum surface velocity. train-1 and the training set K containing the liquid level height difference train-2 For evaluation, the average root mean square error of 5 validations of each training set is calculated to evaluate the prediction performance of each regression prediction model. For the classification prediction model, the accuracy is selected as the performance metric of the classification prediction model. The training set K containing the flow field morphology is calculated. train-3 The average accuracy of 5 cross-validations was used to evaluate the prediction performance of the classification prediction model.

[0043] Step (3.3.3) performs Bayesian optimization;

[0044] A Bayesian algorithm is used to perform an efficient probabilistic search of the hyperparameter space, guiding the optimization process to converge toward regions with more optimal hyperparameters. The performance evaluation metric established in step (3.3.2) is used as the objective function for Bayesian optimization. A Gaussian process surrogate model is constructed to approximate the objective function. The acquisition function is used to balance the exploration of new regions with the utilization of known optimal regions, thereby obtaining high-performing hyperparameter combinations with a reduced number of evaluation iterations. Finally, the parameter combinations that perform best in cross-validation are selected as the final parameter configurations for the regression and classification prediction models, respectively.

[0045] Step (3.4) evaluates the performance of the regression prediction model and the classification prediction model;

[0046] Through the Bayesian search of hyperparameters in step (3.3), the surface maximum flow velocity regression prediction model, liquid level height difference regression prediction model and flow field morphology classification model based on BP neural network under the optimal hyperparameter combination can be obtained respectively.

[0047] For the regression prediction model, the test set K test-1 Input the optimal surface maximum velocity regression prediction model and set the test set K test-2 Input the optimal liquid level height difference regression prediction model and use the root mean square error RMSE i and the coefficient of determination The prediction effect of the regression prediction model is evaluated as shown in formulas (7) to (8).

[0048]

[0049] Where Q i is the test set K test-i The number of samples in , where i = 1, 2; f r-i (x j ) is the predicted value of the jth test sample of the i-th model, where j = 1, 2, ..., Q i ;y j is the actual value corresponding to the j-th test sample; For the i-th test set K test-i The average value of each sample in .

[0050] For the classification prediction model, the test set K test-3 The optimal flow field morphology classification prediction model is input, and the accuracy A, precision P, recall R and F1 score indicators are used to measure the prediction performance of the flow field morphology classification prediction model. The calculation formulas of the indicators are shown in formulas (9) to (12).

[0051]

[0052]

[0053] Where TN is the number of stable flow samples correctly predicted as stable flow; TP is the number of unstable flow samples correctly predicted as unstable; FN is the number of unstable flow samples incorrectly predicted as stable flow; FP is the number of stable flow samples incorrectly predicted as unstable flow.

[0054] Step (3.5) defines the nonlinear mapping function;

[0055] The prediction performance of the surface maximum velocity regression prediction model, the liquid level height difference regression prediction model, and the flow field morphology classification model is evaluated through step (3.4) to verify the generalization ability of the three models and quantify their prediction performance. If the prediction model performance is good, the nonlinear mapping relationship between the process parameters and the surface maximum velocity, liquid level height difference, and flow field morphology can be obtained, providing an optimization basis and reference for subsequent process parameter optimization. The nonlinear mapping functions corresponding to the surface maximum velocity regression prediction model, the liquid level height difference regression prediction model, and the flow field morphology classification prediction model are defined as f r-1 (x), f r-2 (x) and f c (x), x is a vector composed of four characteristics: billet width, casting speed, nozzle immersion depth, and argon blowing amount.

[0056] Step 4: Use multi-objective particle swarm optimization to optimize process parameters;

[0057] Taking the nonlinear mapping function of the BP neural network prediction model defined in the third step as the optimization objective function, the multi-objective particle swarm optimization algorithm is used to optimize the process parameters related to the flow field in the crystallizer. The specific steps are as follows:

[0058] Step (4.1) initialize the particle population;

[0059] M particles are randomly generated in the search space to form the initial population P(0), where each particle corresponds to a set of process parameter combinations consisting of four variables: casting speed, billet width, nozzle immersion depth, and argon blowing amount, forming a 4-dimensional solution space. Each particle has position and velocity attributes. The position of the i-th particle in the population in the 4-dimensional solution space can be described as x i =(x i,1 ,x i,2 ,x i,3 ,x i,4 ), whose velocity can be expressed as v i =(v i,1 ,v i,2 ,v i,3 ,v i,4 ).

[0060] Step (4.2) determines the fitness function;

[0061] The nonlinear mapping function corresponding to the BP neural network prediction model constructed in the third step is extracted, and the fitness function of the multi-objective particle swarm algorithm is composed of it.

[0062] Taking the position vector corresponding to each particle as input, we substitute the nonlinear mapping function f corresponding to the three BP neural network prediction models constructed. r-1 (x), f r-2 (x) and f c(x), and obtain the three function output values ​​corresponding to the process parameter combination, namely the surface maximum flow velocity, liquid level height difference, and flow field morphology probability distribution. At this time, the fitness value of the multi-objective particle swarm algorithm is a vector composed of the output values ​​of the three nonlinear mapping functions, as shown in formula (13). The main purpose of process parameter optimization is to improve the production quality of the casting by improving the stability of the flow field. Therefore, the multi-objective particle swarm algorithm takes minimizing the surface maximum flow velocity, minimizing the liquid level height difference, and minimizing the probability of unstable flow as optimization goals.

[0063] F(x)=[f r-1 (x),f r-2 (x),f c (x)](13)

[0064] Where F(x) is the fitness function of the multi-objective particle swarm optimization algorithm; f r-1 (x) is the nonlinear mapping function corresponding to the surface maximum velocity prediction model; f r-2 (x) is the nonlinear mapping function corresponding to the liquid level height difference prediction model; f c (x) is the nonlinear mapping function corresponding to the flow field morphology prediction model.

[0065] Step (4.3) updates the individual optimal position and the external archive set;

[0066] For the initial population P(0), the fitness function determined in step (4.2) is used to calculate the fitness values ​​of the M particles in the initial particle population. All particles are stratified based on the non-dominated sorting strategy to identify and construct the initial Pareto optimal solution set. An external archive set Ea with an upper limit of N particles is established to store and manage the non-dominated solutions discovered during the iteration process. The current position of each particle is regarded as its initial individual optimal position. All initial non-dominated solutions are stored in the external archive set Ea as the initial state of the global optimal solution set. If the number of initial non-dominated solutions exceeds N, the crowding distance of each solution is calculated and sorted from large to small according to crowding degree. The first N evenly distributed solutions are selected to form the initial external archive set. The crowding distance calculation formula is shown in Equation (14).

[0067]

[0068] Where C(i) is the congestion distance function of solution i; f m (i+1), f m (i-1) is the value of the two solutions adjacent to solution i after solution i is sorted by the mth objective function; m = 1, 2, 3 correspond to three objective functions respectively: the nonlinear mapping function of the surface maximum flow velocity regression prediction model, the nonlinear mapping function of the liquid level height difference regression prediction model, and the nonlinear mapping function of the flow field morphology classification prediction model.

[0069] For the t-th generation particle population P(t), calculate each particle x according to the fitness function i The fitness value of (t) is used to update the individual optimal position p of each particle based on the non-dominated relationship. i (t), the specific update rules are as follows: If x i (t) dominates p i (t-1), then p i (t) = x i (t); if p i (t-1) dominates x i (t), then p i (t) = p i (t-1); if p i (t-1) and x i (t) do not dominate each other, a selection is made by comparing their crowding distances. Subsequently, a non-dominated sorting algorithm is used to stratify P(t) and extract its non-dominated solution set. This non-dominated solution set is combined with the external archive set Ea to form a candidate solution set. This candidate solution set is then non-dominated sorted again, and the first Pareto front is extracted to update the external archive set Ea. If the number of non-dominated solutions exceeds the archive set upper limit N, the crowding distance of each solution is calculated to select evenly distributed representative solutions to form the updated external archive set.

[0070] Step (4.4) updates particle velocity and position;

[0071] The speed and position update formula of the i-th particle in the t+1 generation particle population P(t+1) is as follows:

[0072] v i (t+1)=wv i (t)+c1r1[p i (t)-x i (t)]+c2r2[g(t)-x i (t)](15)

[0073] x i (t+1)=x i (t)+v i (t+1)(16)

[0074] Where, v i (t+1) is the velocity vector of the i-th particle in the t+1 generation; w is the inertia weight, which controls the inertia of the particle; v i (t) is the velocity vector of the i-th particle in the t-th generation; c1 and c2 are acceleration constants that control the degree of acceleration of the particle toward the personal optimal position and the global optimal position; r1 and r2 are random numbers between 0 and 1 that increase the randomness of the algorithm; p i(t) is the optimal position vector of the i-th particle in the t-th generation; x i (t) is the position vector of the i-th particle in the t-th generation; g(t) is the t-th generation global guiding particle selected from the external Pareto archive, and its selection is based on the non-dominated solution with the largest crowding distance; x i (t+1) is the position vector of the i-th particle in the t+1th generation.

[0075] Step (4.5) multi-objective iterative optimization;

[0076] Repeat the above steps (4.2) to (4.4) in each generation of the population, including fitness function calculation, non-dominated sorting and individual optimal update, external archive set update, particle position and velocity adjustment, until the maximum number of iterations T or convergence condition is met.

[0077] Step (4.6) extracting process parameter optimization results;

[0078] The non-dominated solution set obtained in the current iteration is extracted from the final external archive set Ea, forming an approximate Pareto-optimal frontier solution set. These solutions not only demonstrate good compromise performance in the target space but also correspond to specific process parameter combinations, which can be directly used to guide actual process optimization. By restricting the range of casting speed and billet width, the corresponding approximate Pareto frontier solution set is obtained. The process parameter combinations contained in the Pareto solution set are extracted to achieve control of the flow field in the mold at high casting speeds and specified casting widths.

[0079] Furthermore, the above-mentioned crystallizer flow field optimization method is applicable to the intelligent optimization and control of the crystallizer flow field in the continuous casting process of slabs, square billets, round billets, special-shaped billets, etc.

[0080] The beneficial effects of the present invention are:

[0081] This paper proposes an intelligent optimization method for the flow field within the mold based on numerical calculation models, neural network prediction models, and multi-objective particle swarm optimization models. This method can predict the flow field state within the mold under different process conditions and intelligently optimize the flow field based on these changes, effectively improving the surface quality of continuous casting billets and demonstrating excellent optimization results and strong adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 It is a flow chart of the intelligent optimization process of the flow field in the crystallizer;

[0083] Figure 2 Schematic diagram of mesh division of the geometric model of molten steel flow: (a) is a schematic diagram of the global mesh, (b) is a schematic diagram of the local mesh at the top of the crystallizer, (c) is a schematic diagram of the local mesh at the symmetry surface, and (d) is a schematic diagram of the local mesh at the submerged nozzle.

[0084] Figure 3 The distribution diagram of the calculated results of the molten steel flow field in the crystallizer: (a) is the molten steel streamline distribution diagram in the central section, and (b) is the molten steel surface velocity distribution diagram;

[0085] Figure 4 This is the test result diagram of the surface maximum flow velocity regression prediction model;

[0086] Figure 5 This is the test result diagram of the liquid level height difference regression prediction model;

[0087] Figure 6 This is the confusion matrix diagram for the flow field morphology classification prediction model test;

[0088] Figure 7 This is the approximate Pareto front distribution diagram under the conditions of casting speed 2.0m / min and billet width 2000mm;

[0089] Figure 8 This is the approximate Pareto front distribution diagram under the conditions of casting speed 2.0m / min and billet width 1500mm;

[0090] Figure 9 This is the approximate Pareto front distribution diagram under the conditions of casting speed 2.0m / min and billet width 1300mm. DETAILED DESCRIPTION

[0091] The present invention will be further described below through specific embodiments in conjunction with the accompanying drawings, but the present invention is not limited thereto.

[0092] A method for intelligently optimizing the flow field in a crystallizer comprises the following steps:

[0093] The first step is to build a numerical calculation model;

[0094] like Figure 1 The figure shows a flow chart for the intelligent optimization process of the mold flow field. The main process is as follows: a numerical calculation model for multiphase flow in the mold is constructed to simulate the flow behavior of molten steel; based on this model, the flow field distribution corresponding to multiple sets of process parameter combinations is calculated, and a data sample library related to the flow field parameters is established; a Bayesian optimization algorithm is used to optimize the hyperparameters of the BP neural network model and construct an optimal BP neural network flow field prediction model; based on the BP neural network flow field prediction model, a multi-objective optimization function for the flow field parameters is defined, and a multi-objective particle swarm algorithm is used to solve the Pareto optimal solution set that minimizes the maximum surface flow velocity, minimizes the liquid level height difference, and minimizes the tendency of unstable flow, thus achieving multi-objective optimization of the mold flow field.

[0095] Taking the slab continuous casting mold of a steel plant as an example, the multiphase flow numerical calculation model of the mold is used to simulate the flow behavior of molten steel in the mold. The specific implementation steps are as follows:

[0096] Step (1.1) divide the grid;

[0097] According to the slab casting process parameters, a three-dimensional 1 / 2 molten steel flow geometric model is established. The three-dimensional geometric model is imported into ANSYS ICEM software and divided into a structured mesh, which includes 940,000 elements, such as Figure 2 The parameters required for the modeling and calculation of the crystallizer multiphase flow numerical calculation model are shown in Table 1.

[0098] Table 1 Parameters required for model calculation

[0099]

[0100] Step (1.2) select the solution model;

[0101] Import the structured grid obtained in step (1.1) into the Fluent software, select the standard K-ε turbulence model, multiphase flow model and discrete phase model, set the argon bubble injection mode to Rosin-Rammler distribution, and the initial size to 0.1 mm to 7 mm. Perform transient solutions for the pressure-velocity field, turbulence field, multiphase flow field and particle motion field, respectively.

[0102] Step (1.3) sets the calculation conditions;

[0103] The process parameters and material properties of the model in Table 1 are input into the numerical calculation model of multiphase flow in the crystallizer. s , nozzle cross-sectional area A n With pulling speed v c , calculate the steel liquid inlet velocity v i =A s ×v c / A n . Then, according to the inlet velocity v i and the nozzle diameter D = 0.08m, calculate the turbulent kinetic energy and the turbulent kinetic energy dissipation rate ε=2k 1.5 / D, input it to the inlet boundary condition.

[0104] Taking the process conditions of slab width 2010mm, nozzle immersion depth 140mm, argon blowing volume 3.2L / min, and casting speed 1.8m / min as an example, the calculated value of molten steel inlet velocity v is i =2.4m / s, calculated value of turbulent kinetic energy k=0.0576m 2 / s 2 , calculated value of turbulent kinetic energy dissipation rate ε=0.3456m 2 / s 3The parameters corresponding to the above boundary conditions are input into the crystallizer multiphase flow numerical calculation model, and the calculation task is submitted in the parallel calculation mode in the Fluent software until the results of the crystallizer multiphase flow numerical calculation model reach the default convergence criterion. At this time, the calculated flow field distribution is as follows: Figure 3 shown.

[0105] The second step is to build a casting process-flow field parameter data sample library;

[0106] Based on the orthogonal experimental design concept, the L48 (6×4×3×4) mixed-level orthogonal table was adopted to set multi-factor process parameter combinations of casting speed (6 levels), billet width (4 levels), nozzle immersion depth (3 levels) and argon blowing amount (4 levels). A total of 48 groups of balanced and representative calculation cases were generated, as shown in Table 2.

[0107] Table 2 Orthogonal experimental design table

[0108]

[0109] Through the numerical calculation model of multiphase flow in the crystallizer, the distribution of the flow field in the crystallizer under 48 sets of process parameter combinations was obtained. The maximum surface flow velocity, liquid level height difference and flow field morphology calculated by the model under each process parameter combination were extracted, and a data sample library D on flow field parameters was constructed. 48×7 ,The details of the data sample library are shown in Table 3.

[0110] Table 3 Details of flow field parameter data sample library

[0111]

[0112]

[0113] The third step is to build a BP neural network prediction model;

[0114] Step (3.1) standardizes the data sample;

[0115] For the data sample library D of flow field parameters 48×7 , retain the original values ​​of the maximum surface velocity, liquid level height difference and flow field morphology of columns 5 to 7, perform standardization on the four features of billet width, casting speed, nozzle immersion depth and argon blowing amount, and obtain a new data sample library X 48×7 .

[0116] Step (3.2) divides the model data set;

[0117] For the three indicators to be predicted (maximum surface velocity, liquid level height difference, and flow field morphology), datasets K1, K2, and K3, each consisting of 48 samples, were constructed. All samples were derived from the sample database after the standardization process in step (3.1). Each dataset was randomly divided according to the ratio of 4:1 between the number of training set and the number of test set samples. The specific distribution is as follows:

[0118] K train1 ={(x1,u1),(x2,u2),(x3,u3),…,(x r ,u 38 )}(17)

[0119] K test1 ={(x1,u1),(x2,u2),(x3,u3),…,(x 10 ,u 10 )}(18)

[0120] K train2 ={(x1,y1),(x2,y2),(x3,y3),…,(x 38 ,y 38 )}(19)

[0121] K test2 ={(x1,y1),(x2,y2),(x3,y3),…,(x 10 ,y 10 )}(20)

[0122] K train3 ={(x1,z1),(x2,z2),(x3,z3),…,(x 38 ,z 38 )}(twenty one)

[0123] K test3 ={(x1,z1),(x2,z2),(x3,z3),...,(x 10 ,z 10 )}(twenty two)

[0124] Where x i is the characteristic vector of the i-th sample, which includes four features: billet width, casting speed, nozzle immersion depth, and argon blowing amount; u i is the actual output value of the maximum surface velocity of the i-th sample; y i is the actual output value of the liquid level height difference of the i-th sample; z i is the actual output value of the flow field morphology of the i-th sample.

[0125] Step (3.3) Bayesian search for hyperparameters;

[0126] The specific search steps for the optimal hyperparameter combination are as follows:

[0127] Step (3.3.1) defines the parameter space;

[0128] The range of hyperparameters is as follows: the number of hidden layers q is in the range of [1,3], the number of neurons in each layer l is in the range of [10,200], and the learning rate η is in the range of [10 -4 ,10 -1 ], the maximum number of iterations T ranges from [100, 1000], the activation function f type optional value is ['relu', 'tanh', 'logistic'], the regularization parameter range is [10 -6 ,10 -2 ].

[0129] Step (3.3.2) uses Bayesian optimization method to optimize parameters;

[0130] By using 5-fold cross validation on the training set K train1 and training set K train2 The root mean square error is evaluated and the training set K train3 The classification accuracy was evaluated and the optimal surface maximum velocity prediction model, liquid level height difference prediction model and flow field morphology prediction model were obtained respectively.

[0131] The hyperparameter combinations corresponding to the optimal surface maximum velocity regression prediction model are as follows: the number of hidden layers q is 3, the number of neurons in each layer l is 45, 158, and 123, respectively, the learning rate η ranges from 0.002, the maximum number of iterations T is 190, the activation function f type is the relu function, and the regularization parameter is 3×10 -6 At this time, the root mean square error of the 5-fold cross-validation of the training set is between 0.062 and 0.102, and the average value of the root mean square error of the 5-fold cross-validation is 0.091. The verification results show that the model has good generalization ability.

[0132] The optimal hyperparameter combination for the liquid level height difference regression prediction model is as follows: the number of hidden layers q is 3, the number of neurons in each layer l is 200, 200, and 193, respectively; the learning rate η ranges from 0.006, the maximum number of iterations T is 909, the activation function f type is the ReLU function, and the regularization parameter is 0.01. At this point, the root mean square error of the training set for 5-fold cross-validation is between 0.0033 and 0.010, and the average root mean square error of the five cross-validation folds is 0.006. The validation results show that the model has good generalization ability.

[0133] The parameter combinations corresponding to the optimal flow field morphology classification prediction model are as follows: the number of hidden layers q is 3, the number of neurons in each layer l is 187, 200 and 196 respectively, the learning rate η range is 0.1, the maximum number of iterations T is 545, the activation function f type is relu function, and the regularization parameter is 7×10 -6 At this time, the 5-fold cross-validation accuracy of the training set is between 0.83% and 100%, and the average accuracy of the 5-fold cross-validation is 96.7%. The validation results show that the model has good generalization ability.

[0134] Step (3.4) evaluates model performance;

[0135] The test set K test1 , K test2 and K test3 The three BP neural network prediction models under the optimal parameter combination were input respectively to test the performance of each model. The test results of the surface maximum flow velocity prediction model are as follows: Figure 4 As shown, the root mean square error RMSE is 0.025 and the determination coefficient R 2 The test results of the liquid level height difference prediction model are as follows: Figure 5 As shown, the root mean square error RMSE is 0.0047 and the determination coefficient R 2 The test results of the flow field morphology prediction model are as follows: Figure 6 As shown in the figure, the accuracy, precision, recall and F1 score are 90%, 85.7%, 100% and 0.923 respectively, showing good prediction performance.

[0136] Step (3.5) defines the nonlinear mapping function;

[0137] The evaluation results of step (3.4) show that the prediction model has good performance. The nonlinear mapping functions corresponding to the surface maximum velocity regression prediction model, the liquid level height difference regression prediction model and the flow field morphology classification prediction model are defined as f re1 (x), f re2 (x) and f ce (x), x is a vector composed of four characteristics: billet width, casting speed, nozzle immersion depth, and argon blowing amount.

[0138] Step 4: Use multi-objective particle swarm optimization to optimize process parameters;

[0139] Step (4.1) initialize the particle population;

[0140] 500 particles are randomly initialized in the search space as the initial particle population P(0), and the external archive set Ea is initialized, and the upper limit of the number of Ea particles is set to 200. The current data sample has four input features, namely casting speed, billet width, nozzle immersion depth and argon blowing amount. In the particle swarm update process, the position and velocity of the i-th particle in the swarm in the 4-dimensional solution space are defined as x i =(x i,1 ,x i,2 ,x i,3 ,x i,4 ) and v i =(v i,1 ,v i,2 ,v i,3 ,v i,4 ), and combined with the orthogonal experimental design scheme in Table 2, the value range of each position is limited. Position lower limit x min It consists of the minimum value of the four input features, with the upper limit x max It consists of the maximum value of the four input features.

[0141] Step (4.2) determines the fitness function;

[0142] According to the nonlinear mapping function corresponding to the BP neural network prediction model constructed in the third step, the fitness function F of the multi-objective particle swarm algorithm is composed e (x), as shown in Equation (23). In order to improve the stability of the flow field in the crystallizer, the multi-objective particle swarm optimization algorithm should take minimizing the maximum surface flow velocity, minimizing the liquid level height difference and minimizing the probability of unstable flow as the optimization objectives.

[0143] F e (x)=[f re1 (x),f re2 (x),f ce (x)](23)

[0144] Where, F e (x) is the fitness function of the multi-objective particle swarm optimization algorithm; f re1 (x) is the nonlinear mapping function corresponding to the optimal surface maximum velocity prediction model; f re2 (x) is the nonlinear mapping function corresponding to the optimal liquid level height difference prediction model; f ce (x) is the nonlinear mapping function corresponding to the optimal flow field morphology prediction model.

[0145] Step (4.3) updates the individual optimal position and the external archive set;

[0146] For the initial population P(0), calculate the fitness values ​​of the 500 particles in the initial particle population P(0) according to the fitness function determined in step (4.2), and regard the current position of each particle as its initial individual optimal position. Stratify all particles based on the non-dominated sorting strategy to obtain the initial Pareto optimal solution set, which is stored in the external archive set Ea.

[0147] For the remaining generations of populations, the fitness value of each particle is calculated according to the fitness function. The individual optimal position of each particle is updated based on the non-dominated relationship. The current population is stratified using the non-dominated sorting algorithm to extract its non-dominated solution set. This non-dominated solution set is merged with the external archive set Ea to form a candidate solution set. The candidate solution set is non-dominated sorted again, and the first Pareto front is extracted to update the external archive set Ea.

[0148] Step (4.4) iterative optimization;

[0149] According to the speed and position update formula of the particle swarm algorithm, each generation of particle swarm and external archive set are updated and optimized until the maximum number of iterations set by the particle swarm algorithm, 200, is reached.

[0150] Step (4.5) extracting process parameter optimization results;

[0151] When the particle swarm reaches the maximum number of iterations, non-dominated solutions are extracted from the final external archive set Ea to construct the final approximate Pareto front. By limiting the range of values ​​for the pulling speed and billet width, the flow field in the crystallizer can be controlled under high pulling speed and specified casting width. For typical pulling speed and billet width casting conditions, the specific optimization scheme is as follows:

[0152] Taking the pulling speed of 2.0m / min as an example, Figure 7 、 Figure 8 、 Figure 9 Approximate Pareto frontiers for slab widths of 2000 mm, 1500 mm, and 1300 mm are presented. By extracting the process parameter optimization information corresponding to each Pareto solution set, the control ranges for nozzle immersion depth and argon blowing amount are obtained, as shown in Table 4. Taking a slab width of 1300 mm as an example, by adjusting the nozzle immersion depth and argon blowing amount, the maximum surface flow velocity can be optimized to 0.209–0.232 m / s, and the liquid level difference can be optimized to 0.009–0.018 m. Compared with other process combinations, the maximum surface flow velocity decreases by 10%–30%, and the liquid level difference decreases by 30%–40%, which has positive implications for stabilizing slab quality.

[0153] Table 4 Process parameter optimization interval

[0154]

[0155] The above-described embodiments merely express the implementation methods of the present invention, but should not be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several variations and improvements can be made without departing from the concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A method for intelligent optimization of flow field in a continuous casting mold, characterized in that: The optimization method comprises the following steps: The first step is to build a numerical calculation model of multiphase flow in the crystallizer to simulate the flow behavior of molten steel in the crystallizer and calculate the flow field distribution corresponding to multiple sets of process parameter combinations; The second step is to build a data sample library D of casting process and flow field parameters based on the numerical calculation results. r×c ; The third step is to build a BP neural network prediction model; The data sample library D of casting process and flow field parameters constructed in the second step r×c , construct a BP neural network prediction model based on Bayesian optimization to accurately predict the surface maximum flow velocity, liquid level height difference and flow field morphology; the constructed BP neural network prediction model includes a surface maximum flow velocity regression prediction model based on BP neural network, a liquid level height difference regression prediction model and a flow field morphology classification prediction model; Step 4: Use multi-objective particle swarm optimization to optimize process parameters; Based on the BP neural network prediction model defined in the third step, the nonlinear mapping functions between the process parameters and the flow field parameters are defined respectively, and a multi-objective optimization function of the flow field parameters is established; the multi-objective particle swarm algorithm is used to solve the Pareto optimal solution set that minimizes the maximum surface flow velocity, minimizes the liquid level height difference, and minimizes the unstable flow tendency, thereby realizing the multi-objective optimization of the flow field in the crystallizer.

2. The method for intelligent optimization of flow field in a continuous casting mold according to claim 1, characterized in that: The first step is specifically: Step (1.1) grid division; Based on the cross-sectional dimensions of the ingot, nozzle dimensions, and slag layer thickness distribution during the steel mill casting process, a three-dimensional geometric model that conforms to the actual situation is established. The geometric model is then imported into the commercial software ICEM to divide the structural mesh. Step (1.2) solves model selection; Import the structured mesh obtained in step (1.1) into the commercial software Fluent, set the standard K-ε turbulence model, multiphase flow model and discrete phase model, establish the numerical calculation model of multiphase flow in the crystallizer, and solve the continuity equation, momentum equation, turbulence equation, interface tracking equation and discrete phase particle motion equation; Step (1.3) physical property parameters and boundary conditions setting; With reference to the actual casting information of the steel plant, the physical parameters of molten steel, protective slag and air are input into the multiphase flow numerical calculation model of the crystallizer respectively; according to the flow continuity principle, with the help of the cross-sectional area A of the casting billet s , nozzle cross-sectional area A n With pulling speed v c , calculate the steel liquid inlet velocity v at the nozzle i , v i =A s ×v c / A n ; Then, according to the inlet velocity v i and the nozzle diameter D, calculate the turbulent kinetic energy k = 0.01v i 2 and the turbulent kinetic energy dissipation rate ε=k 1.5 / D, input k and ε into the inlet boundary condition settings; in addition, set the outlet of the fluid domain to a pressure outlet; Step (1.4) numerical calculation; The parallel computing mode is used to speed up the calculation of the numerical calculation model of the multiphase flow in the crystallizer until the continuity, velocity component, turbulent kinetic energy and turbulent dissipation rate residuals of the numerical calculation model of the multiphase flow in the crystallizer are basically stable.

3. The method for intelligent optimization of flow field in a continuous casting mold according to claim 2, characterized in that: In the first step, the following assumptions are made when constructing the numerical calculation model of the multiphase flow in the crystallizer: the molten steel, protective slag and air are regarded as incompressible Newtonian fluids; the vibration and taper of the crystallizer are ignored; the effects of heat transfer and solidification of the molten steel and protective slag are ignored; the argon bubbles are regarded as inert spherical particles, the bubble size is set to obey the Rosin-Rammler distribution, and the interaction between the argon bubbles is ignored.

4. The method for intelligent optimization of flow field in a continuous casting mold according to claim 1, characterized in that: The second step is specifically as follows: Through orthogonal experimental design, r calculation cases were set under different combinations of process parameters such as billet width, casting speed, nozzle immersion depth, and argon blowing amount. The numerical calculation model of multiphase flow in the crystallizer constructed in the first step was used to calculate the flow field distribution in the crystallizer under the r groups of process parameters. The calculation results of the flow field in the crystallizer under r group process parameters are post-processed to extract the calculated surface maximum flow velocity, liquid level height difference and flow field morphology, and construct a data sample library D of casting process and flow field parameters. r×c ; Where r is the number of rows in the sample library, indicating the number of samples in the data sample library; c is the number of columns in the sample library; where the flow field morphology includes steady flow and unsteady flow.

5. The method for intelligent optimization of flow field in a continuous casting mold according to claim 4, characterized in that: In the second step: the number of rows r of the sample library is not less than 40; the number of columns c of the sample library is 7, wherein the sample data in the 1st to 4th columns are the width of the casting billet, the pulling speed, the nozzle immersion depth and the argon blowing amount, and the sample data in the 5th to 7th columns are the maximum surface flow velocity, the liquid level height difference and the flow field morphology.

6. The method for intelligent optimization of flow field in a continuous casting mold according to claim 5, characterized in that: In the third step, the construction process of the three prediction models is basically the same, specifically: Step (3.1) standardization preprocessing; For the data sample library D r×c , the four features of billet width, casting speed, nozzle immersion depth and argon blowing amount are standardized and preprocessed, while keeping the original values ​​of surface maximum flow velocity, liquid level height difference and flow field morphology unchanged, so as to form a standardized preprocessed data sample library X r×c ; Step (3.2) model data set division; According to the three output objects to be predicted, namely, the maximum surface velocity, the liquid level height difference and the flow field morphology, a dataset K1, K2 and K3 containing r samples are constructed respectively. Each sample is a data sample library X after the standardization process in step (3.1). r×c Provided; the specific distribution of each data set is as follows: K1={(x1,u1),(x2,u2),(x3,u3),…,(x r ,u r )}(2) <h2 style=";text-align:left;direction:ltr">K2 = {(x1,y1),(x2,y2),(x3,y3),…,(x<h2 style=";text-align:left;direction:ltr"> r <h2 style=";text-align:left;direction:ltr"> ,y<h2 style=";text-align:left;direction:ltr"> r <h2 style=";text-align:left;direction:ltr"> (3) K3={(x1,z1),(x2,z2),(x3,z3),…,(x r ,z r )}(4) Where x i The feature vector of the i-th sample contains c-3 features of the sample, specifically the width of the billet, the casting speed, the nozzle immersion depth, and the amount of argon blowing, where i = 1, 2, …, r; u i represents the actual output value of the maximum surface velocity of the i-th sample; y i Indicates the actual output value of the liquid level height difference of the i-th sample; z i Indicates the actual output value of the flow field morphology of the i-th sample, the non-stable flow label is 1, and the stable flow label is 0; The dataset K i Randomly split into training set K train-i and the test set K test-i , i=1,2,3; Step (3.3) Bayesian search for hyperparameters; The goal of the BP neural network model is to learn the nonlinear mapping relationship between input features and output target values ​​through a multi-layer feedforward network structure and back propagation algorithm, so that the true output value y of the training data sample is (i) With model output value Minimize the loss function between the i-th sample x i The model output value calculation formula is shown in Equations (5) to (6). The BP neural network model training process is as follows: input the training set data sample, calculate the output of each hidden layer through forward propagation, use the loss function to evaluate the prediction error of the BP neural network model, and then update the network weights and thresholds according to the back-propagation error gradient, and finally construct a prediction model f(x) with nonlinear fitting ability. Where b j (i) is the output of the jth hidden layer neuron of the i-th sample, where i = 1, 2, ..., r, j = 1, 2, ..., s; x ik is the kth eigenvalue of the i-th sample, and the input features include billet width, casting speed, nozzle immersion depth, and argon blowing amount; w kj is the weight from the kth feature of the input layer to the jth neuron of the hidden layer; θ j is the threshold of the jth neuron in the hidden layer; is the predicted output value of the i-th sample; w j is the weight from the j neurons in the hidden layer to the neurons in the output layer; θ is the threshold of the output neuron; f1 is the hidden layer activation function; f2 is the output layer activation function; Step (3.4) evaluates the performance of the regression prediction model and the classification prediction model; Through the Bayesian search of hyperparameters in step (3.3), the surface maximum flow velocity regression prediction model, liquid level height difference regression prediction model and flow field morphology classification model based on BP neural network under the optimal hyperparameter combination are obtained respectively; Step (3.5) defines the nonlinear mapping function; Evaluate the prediction performance of the surface maximum flow velocity regression prediction model, the liquid level height difference regression prediction model, and the flow field morphology classification model through step (3.4) to verify the generalization ability of the three models and quantify their prediction performance. If the prediction model performance is good, the nonlinear mapping relationship between the process parameters and the surface maximum flow velocity, liquid level height difference, and flow field morphology is obtained, providing an optimization basis and reference for subsequent process parameter optimization. The nonlinear mapping functions corresponding to the surface maximum velocity regression prediction model, the liquid level height difference regression prediction model and the flow field morphology classification prediction model are defined as f r-1 (x), f r-2 (x) and f c (x), x is a vector composed of four characteristics: billet width, casting speed, nozzle immersion depth, and argon blowing amount.

7. The method for intelligent optimization of flow field in a continuous casting mold according to claim 5, characterized in that: In the third step: in step (3.1), the normalization calculation formula is as shown in formula (1); Where, X ij is the data after standardized preprocessing, where i = 1, 2, ..., r, represents the i-th sample, j = 1, 2, ..., c-3, represents the j-th process parameter characteristics of the sample; D ij is the original sample database D r×c Data; σ j is the original sample database D r×c The standard deviation of the jth feature data; μ j is the original sample database D r×c The average value of the jth feature data; In the step (3.2), each training set P is set i With the test set Q i The ratio of the number of samples is 4:1; In step (3.3), the gradient descent method is used to iteratively update the hidden layer parameters, and the Bayesian algorithm is used to optimize the hyperparameters to determine the optimal BP neural network prediction model. The specific implementation steps are as follows: Step (3.3.1) defines the parameter space; Given that the performance of BP neural networks depends on the reasonable selection of network structure and training parameters, it is necessary to define an appropriate hyperparameter space. The main parameters include the number of hidden layers, the number of neurons in each layer, the learning rate, the type of activation function, and the number of training rounds. The number of hidden layers q and the number of neurons l jointly determine the capacity of the model. The learning rate η affects the convergence speed and stability of the model. The type of activation function f is suitable for data with different nonlinear characteristics. The number of training rounds T determines the learning depth of the model on the training set. Step (3.3.2) determines the performance evaluation indicators; For the regression prediction model, the mean square error is selected as the performance metric of the regression prediction model, and a 5-fold cross validation is used to test the training set K containing the maximum surface velocity. train-1 and the training set K containing the liquid level height difference train-2 Evaluation was performed by calculating the average root mean square error of 5 validations for each training set to evaluate the prediction performance of each regression prediction model; for the classification prediction model, the accuracy was selected as the performance metric of the classification prediction model, and the training set K containing the flow field morphology was calculated. train-3 The average accuracy of 5 cross-validations is used to evaluate the prediction performance of the classification prediction model; Step (3.3.3) performs Bayesian optimization; A Bayesian algorithm is used to perform an efficient probabilistic search of the hyperparameter space, guiding the optimization process to converge toward a region with better hyperparameters. The performance evaluation index established in step (3.3.2) is used as the objective function of Bayesian optimization. A Gaussian process surrogate model is constructed to approximate the objective function. The acquisition function is used to balance the exploration of new regions with the utilization of known optimal regions, thereby obtaining a high-performance hyperparameter combination with a small number of evaluation iterations. Finally, the parameter combination that performs best in cross-validation is selected as the final parameter configuration for the regression prediction model and the classification prediction model, respectively. In the step (3.4): For the surface maximum velocity regression prediction model and the liquid level height difference regression prediction model, the test set K test-1 Input the optimal surface maximum velocity regression prediction model and set the test set K test-2 Input the optimal liquid level height difference regression prediction model and use the root mean square error RMSE i and the coefficient of determination R i 2 Evaluate the prediction effect of the regression prediction model; For the classification prediction model, the test set K test-3 The optimal flow field morphology classification prediction model is input, and the accuracy A, precision P, recall R and F1 score indicators are used to measure the prediction performance of the flow field morphology classification prediction model.

8. The method for intelligent optimization of flow field in a continuous casting mold according to claim 7, characterized in that: The fourth step is specifically as follows: Step (4.1) initialize the particle population; M particles are randomly generated in the search space to form the initial population P(0), where each particle corresponds to a set of process parameter combinations consisting of four variables: casting speed, billet width, nozzle immersion depth, and argon blowing amount, forming a 4-dimensional solution space; each particle has position and velocity attributes, and the position of the i-th particle in the population in the 4-dimensional solution space can be described as x i =(x i,1 ,x i,2 ,x i,3 ,x i,4 ), whose velocity can be expressed as v i =(v i,1 ,v i,2 ,v i,3 ,v i,4 ); Step (4.2) determines the fitness function; Extract the nonlinear mapping function corresponding to the BP neural network prediction model constructed in the third step, and use it to form the fitness function of the multi-objective particle swarm algorithm; Taking the position vector corresponding to each particle as input, we substitute the nonlinear mapping function f corresponding to the three BP neural network prediction models constructed. r-1 (x), f r-2 (x) and f c (x), obtain the three function output values ​​corresponding to the process parameter combination, including the maximum surface flow velocity, liquid level height difference and flow field morphology probability distribution; At this time, the fitness value of the multi-objective particle swarm algorithm is a vector composed of the output values ​​of the three nonlinear mapping functions, as shown in formula (13); the main purpose of process parameter optimization is to improve the quality of billet production by improving the stability of the flow field; Therefore, the multi-objective particle swarm optimization algorithm takes minimizing the maximum surface flow velocity, minimizing the liquid level height difference and minimizing the probability of unsteady flow as the optimization objectives; F(x)=[f r-1 (x),f r-2 (x),f c (x)](13) Where F(x) is the fitness function of the multi-objective particle swarm optimization algorithm; f r-1 (x) is the nonlinear mapping function corresponding to the surface maximum velocity prediction model; f r-2 (x) is the nonlinear mapping function corresponding to the liquid level height difference prediction model; f c (x) is the nonlinear mapping function corresponding to the flow field morphology prediction model; Step (4.3) updates the individual optimal position and the external archive set; For the initial population P(0), according to the fitness function determined in step (4.2), calculate the fitness values ​​of the M particles in the initial particle population, stratify all particles based on the non-dominated sorting strategy, identify and construct the initial Pareto optimal solution set; establish an external archive set Ea with an upper limit of N particles; regard the current position of each particle as its initial individual optimal position, and store all initial non-dominated solutions in the external archive set Ea as the initial state of the global optimal solution set; if the number of initial non-dominated solutions exceeds N, calculate the crowding distance of each solution, and sort them from large to small according to the crowding degree, and select the first N evenly distributed solutions to form the initial external archive set. The crowding distance calculation formula is shown in formula (14); Where C(i) is the congestion distance function of solution i; f m (i+1), f m (i-1) is the value of the two solutions adjacent to solution i after solution i is sorted by the mth objective function; m = 1, 2, 3 correspond to three objective functions: the nonlinear mapping function of the surface maximum velocity regression prediction model, the nonlinear mapping function of the liquid level height difference regression prediction model, and the nonlinear mapping function of the flow field morphology classification prediction model; For the t-th generation particle population P(t), calculate each particle x according to the fitness function i The fitness value of (t) is used to update the individual optimal position p of each particle based on the non-dominated relationship. i (t); Subsequently, the non-dominated sorting algorithm is used to stratify P(t) and extract its non-dominated solution set; the non-dominated solution set is merged with the external archive set Ea to form a candidate solution set, and the candidate solution set is non-dominated sorted again to extract the first Pareto front to update the external archive set Ea; if the number of non-dominated solutions exceeds the archive set upper limit N, the crowding distance of each solution is calculated to select representative solutions with uniform distribution to form the updated external archive set; Step (4.4) updates particle velocity and position; The speed and position update formula of the i-th particle in the t+1 generation particle population P(t+1) is as follows: v i (t+1)=wv i (t)+c1r1[p i (t)-x i (t)]+c2r2[g(t)-x i (t)](15) x i (t+1)=x i (t)+v i (t+1)(16) Where, v i (t+1) is the velocity vector of the i-th particle in the t+1 generation; w is the inertia weight, which controls the inertia of the particle; v i (t) is the velocity vector of the i-th particle in the t-th generation; c1 and c2 are acceleration constants that control the degree of acceleration of the particle toward the personal optimal position and the global optimal position; r1 and r2 are random numbers between 0 and 1 that increase the randomness of the algorithm; p i (t) is the optimal position vector of the i-th particle in the t-th generation; x i (t) is the position vector of the i-th particle in the t-th generation; g(t) is the t-th generation global guiding particle selected from the external Pareto archive, and its selection is based on the non-dominated solution with the largest crowding distance; x i (t+1) is the position vector of the i-th particle in the t+1 generation; Step (4.5) multi-objective iterative optimization; Repeat the above steps (4.2) to (4.4) in each generation of the population, including fitness function calculation, non-dominated sorting and individual optimal update, external archive set update, particle position and speed adjustment, until the maximum number of iterations T or convergence condition is met; Step (4.6) extracting process parameter optimization results; The non-dominated solution set obtained in the current iteration is extracted from the final external archive set Ea to form an approximate Pareto optimal frontier solution set; by restricting the value range of the pulling speed and the billet width, the corresponding approximate Pareto frontier solution set is obtained, and the process parameter combinations contained in the Pareto solution set are extracted to realize the regulation of the flow field in the crystallizer under high pulling speed and specified casting width.

9. The method for intelligent optimization of flow field in a continuous casting mold according to claim 8, characterized in that: In the fourth step: In the step (4.3), the individual optimal position p i (t) The specific update rules are as follows: If x i (t) dominates p i (t-1), then p i (t) = x i (t); if p i (t-1) dominates x i (t), then p i (t) = p i (t-1); if p i (t-1) and x i (t) If they do not dominate each other, the selection is made by comparing the crowding distances between the two.

10. An intelligent optimization method for flow field in a continuous casting mold according to any one of claims 1 to 9, characterized in that: The crystallizer flow field optimization method is suitable for intelligent optimization and control of the crystallizer flow field in the continuous casting process of slabs, square billets, round billets or profiled billets.

Images