Co-optimization method of molten steel solidification rate and secondary cooling water distribution at the end electromagnetic stirring point

Abstract

This application relates to the field of metallurgical engineering technology and discloses a method for synergistic optimization of the solidification rate of molten steel at the end electromagnetic stirring position and the secondary cooling water distribution. The method includes: establishing a three-dimensional multi-physics coupled solidification heat transfer model of flow, heat transfer, mass transfer and solidification process based on the target casting machine parameters and the thermal property parameters of the target steel grade; determining the target solidification rate range of the billet at the end electromagnetic stirring position based on the model and industrial test data; constructing a multi-objective optimization model with this range as the core constraint and in combination with metallurgical criteria, the model including a set of objective functions defined based on metallurgical criteria and a set of constraint conditions including water volume constraints of each cooling section; using an optimization algorithm to iteratively solve the model, and inversely finding the water volume scheme that satisfies the constraint conditions and optimizes the objective function set as the optimal water distribution scheme; this application improves the internal quality and process stability of the billet.

Description

Technical Field

[0001] This application relates to the field of metallurgical engineering technology, and in particular to a method for synergistic optimization of the solidification rate of molten steel at the end electromagnetic stirring point and the secondary cooling water distribution. Background Technology

[0002] Continuous casting is a core component of modern steel production, and its process stability and billet quality directly determine the performance of the final product. During continuous casting, the cooling intensity of the secondary cooling zone has a decisive impact on the solidification structure, internal defects, and production efficiency of the billet. Front-end electromagnetic stirring (F-EMS) is an effective means to improve center segregation and increase the equiaxed crystal ratio of the billet, but its effectiveness is highly dependent on the thickness of the liquid core or the solidification rate of the billet at the point of application. If the solidification rate is too high, the molten steel has poor fluidity, and the stirring effect is difficult to transfer to the solidification front; if the solidification rate is too low, it may exacerbate center segregation or cause porosity defects.

[0003] Currently, secondary cooling water distribution in industrial production is mostly based on empirical formulas or fixed water meters, making it difficult to dynamically and accurately adjust according to changes in casting speed, steel grade, and cross-sectional dimensions. This results in significant fluctuations in the solidification state at the F-EMS location, hindering the stable achievement of optimal stirring effects. Traditional optimization methods often focus on single objectives such as surface temperature, lacking comprehensive consideration of multi-dimensional metallurgical criteria such as solidification rate, temperature gradient, and brittle zone. Furthermore, while some studies employ mathematical models for analysis, these models are often simplified and fail to fully account for the complex coupling effects between flow, heat transfer, mass transfer, and solidification, leading to insufficient prediction accuracy and making it difficult to support refined online optimization.

[0004] Therefore, there is an urgent need to develop a secondary cooling water distribution collaborative optimization method that can integrate a high-precision multi-physics field model, clarify the optimal solidification rate target, and intelligently seek optimization by combining multiple metallurgical criteria, so as to achieve stable and efficient control of segregation defects in continuous casting billets. Summary of the Invention

[0005] To address the aforementioned technical issues, this application provides a method for the coordinated optimization of the solidification rate of molten steel at the end electromagnetic stirring stage and the secondary cooling water supply. This method enables coordinated control of the secondary cooling water supply and the end electromagnetic stirring process, thereby improving the internal quality and process stability of the cast billet.

[0006] In a first aspect, this application provides a method for synergistic optimization of the solidification rate of molten steel at the end electromagnetic stirring point and the secondary cooling water distribution, the method comprising: Step S1: Based on the parameters of the target casting machine and the thermophysical properties of the target steel, establish a multiphysics coupled solidification heat transfer model that adapts to the three-dimensional flow, heat transfer, mass transfer and solidification process. Step S2: Based on the multi-physics coupled solidification heat transfer model and combined with industrial test data, determine the target solidification rate range of the billet at the end electromagnetic stirring position; Step S3: Using the target solidification rate range as the core optimization guide and combining the preset metallurgical criteria, construct a multi-objective optimization model for solving the cooling water volume of each section of the secondary cooling zone. The multi-objective optimization model includes a set of objective functions defined based on the metallurgical criteria and a set of constraint conditions including the water volume constraints of each cooling section. Step S4: Use an optimization algorithm to iteratively solve the multi-objective optimization model, invert the solution to satisfy all constraints, and take the water allocation scheme that achieves the optimal value of the objective function set as the optimal water allocation scheme.

[0007] Compared with the prior art, the beneficial effects of the present invention are at least as follows: This application provides a method for the coordinated optimization of the solidification rate of molten steel at the end electromagnetic stirring position and the secondary cooling water distribution. Compared with the prior art, it has the following advantages: By constructing a high-precision multi-physics coupling model that integrates three-dimensional flow, heat transfer, mass transfer and solidification processes, it realizes a true reflection of the complex physical behavior of multiphase and multi-field continuous casting process, overcomes the defect of insufficient prediction accuracy of traditional simplified models, and provides a reliable simulation evaluation basis for subsequent optimization; It establishes a quantitative mapping relationship between the solidification rate at the end electromagnetic stirring position and the carbon segregation index at the center of the billet, and determines the optimal solidification rate range based on a preset quality threshold, thereby transforming the core objective of improving segregation into specific, quantifiable and traceable process control parameters, fundamentally solving the problem of unstable stirring effect caused by traditional experience-based water distribution; Secondly, in the construction of the optimization model, not only is the target solidification rate range used as the core constraint and guide, but also multi-dimensional metallurgical criteria such as surface temperature control, billet shell thickness safety, temperature gradient suppression, and brittle zone avoidance are systematically incorporated, and these criteria are integrated into a unified total value function through normalized weighting. This multi-objective collaborative optimization mechanism ensures that the optimized water distribution scheme can comprehensively consider the surface quality of the billet, production safety, and internal segregation control, realizing a leap from single-objective optimization to multi-criteria collaborative decision-making. By coupling the high-fidelity physical simulation model with an intelligent optimization algorithm with global optimization capabilities in a closed loop, an automatic iterative optimization framework of "simulation evaluation - algorithm optimization" is formed. This framework can efficiently and automatically inversely derive the optimal secondary cooling water distribution scheme that satisfies all process and quality constraints, significantly improving optimization efficiency and the engineering practicality of the results. This provides an effective means for the refined and intelligent control of the continuous casting process, ultimately achieving a simultaneous improvement in the internal quality of the billet and the stability of the production process. Attached Figure Description

[0008] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0009] Figure 1 This is a flowchart of a method for synergistic optimization of the solidification rate of molten steel at the end electromagnetic stirring point and the secondary cooling water distribution in an embodiment of this application; Figure 2 This is a schematic diagram of the geometric structure of the continuous casting model in the embodiments of this application; Figure 3 This is a scatter plot showing the correlation between solidification rate and segregation index in the embodiments of this application. Figure 4 This is a curve showing the overall evaluation value as a function of the number of iterations in the embodiments of this application; Figure 5 This is a schematic diagram illustrating the change in surface temperature before and after optimization with respect to the distance from the meniscus in an embodiment of this application. Detailed Implementation

[0010] This application provides a method for synergistic optimization of the solidification rate of molten steel at the end electromagnetic stirring stage and the secondary cooling water distribution. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0011] For ease of understanding, the specific process of the embodiments of this application is described below. Please refer to [link / reference]. Figure 1 One embodiment of the method for synergistic optimization of the solidification rate of molten steel at the end electromagnetic stirring point and the secondary cooling water distribution in this application includes: Step S1: Based on the parameters of the target casting machine and the thermophysical properties of the target steel, establish a multiphysics coupled solidification heat transfer model that adapts to the three-dimensional flow, heat transfer, mass transfer and solidification process.

[0012] Step S1 includes: using the actual structural parameters of the target casting machine and the geometric parameters of the billet as the geometric basis, and achieving adaptation by adjusting the geometric parameters of the billet. The geometric parameter adjustment includes the coordinate correction of cross-sectional dimensions, cooling section length, and electromagnetic stirring installation position. Based on the actual structural parameters and the adjusted geometric parameters of the billet, a multi-physics coupled solidification heat transfer model for the three-dimensional flow, heat transfer, mass transfer, and solidification process is established, including a three-dimensional flow model, heat transfer model, mass transfer model, and solidification model. The thermal properties of the target steel are embedded and associated in the model, including the viscosity of molten steel and thermal conductivity.

[0013] Specifically, the target casting machine refers to a specific continuous casting machine for which secondary cooling water distribution is optimized. It has clear structural parameters, such as the division of the billet guide section, the length and arrangement of each secondary cooling zone, the fixed installation position of the end electromagnetic stirring device, and the size of the crystallizer. The target steel grade refers to the specific steel grade to be cast, such as 82B high carbon steel or other steels such as low carbon steel, medium carbon steel, alloy steel, etc. This application can adapt the same method framework to different target casting machines and target steel grades by calling and adjusting the geometric parameters and physical property parameters in the model.

[0014] Taking a continuous casting machine for producing 160mm×160mm square billets (steel grade 82B) at a steel plant as an example, the specific implementation process of this application is explained. First, the parameters are set. The continuous casting sections and dimensions of the target casting machine are shown in Table 1: including a crystallizer section with a length of 0.85m, a foot roll section with a length of 0.35m, and subsequent first to fourth sections with lengths of 1.95m, 2.45m, 3.45m, and 6.65m, respectively. The foot roll section and the first to third sections together constitute a complete secondary cooling zone. The corresponding water volume constraints for the secondary cooling zone are: foot roll section 4.23–6.68m³ / h, secondary cooling first section 6.12–8.40m³ / h, secondary cooling second section 2.67–4.68m³ / h, and secondary cooling third section 1.38–2.15m³ / h. The total water distribution ratio of the secondary cooling zone is approximately maintained at around 3:4:2:1. The fourth section is the air-cooled zone.

[0015] Table 1 First, for the selected target casting machine and target steel grade, such as 82B, a multiphysics coupled solidification heat transfer model is constructed. This model is based on the actual structural parameters of the target casting machine and the geometric parameters of the billet of the target steel grade. The actual structural parameters are the lengths of each section of the continuous casting machine, including the length of the crystallizer, the physical lengths of each cooling section in the secondary cooling zone, and their relative positions. The geometric parameters include the cross-sectional shape and size of the billet, as well as the installation distance of the end electromagnetic stirrer relative to the meniscus of the crystallizer. By adjusting these cross-sectional dimensions, cooling section lengths, and the coordinates of the end electromagnetic stirrer installation position in the model, flexible adaptation to different casting machine configurations and billet specifications can be achieved. Figure 2 The figure shows a geometric schematic diagram of the continuous casting model, which clearly shows the overall coordinate system (x, y, z) of the model. The figure indicates that the radius of the arc of the arc continuous casting machine model is 9000 mm, and the total length of the model is 15700 mm. The model covers the typical process range of the billet from the meniscus of the crystallizer to complete solidification, and provides a complete geometric space domain that matches the actual casting machine for the subsequent three-dimensional flow, heat transfer, mass transfer and solidification process coupling calculation.

[0016] The multiphysics coupled solidification heat transfer model is a unified computational system integrating flow, heat transfer, mass transfer, and solidification phase transformation processes. The three-dimensional flow model, based on computational fluid dynamics principles, simulates the turbulent flow behavior of molten steel in the crystallizer and secondary cooling zone by solving the mass and momentum conservation equations describing the flow of molten steel. Its core output is the three-dimensional velocity and pressure fields of the molten steel, which form the basis for subsequent calculations of convective heat transfer and solute convective transport. The heat transfer model, based on the law of energy conservation, solves a comprehensive energy equation including conduction, convection, and radiation under the convective heat transfer conditions provided by the flow model, simulating the entire heat transfer process from molten steel to the solidified billet shell and then to the environment. Its output is the three-dimensional transient temperature field of the billet within the entire computational domain, which directly determines the solidification process. The mass transfer model, based on the convection-diffusion equations of the solute, relies on the convective velocity field provided by the flow model to simulate the migration and redistribution of alloying elements such as carbon in the molten steel. Its output is the spatial distribution of solute concentration. The solidification model utilizes the temperature field calculated by the heat transfer model. By tracking the solid-liquid phase transition process, it calculates the release of latent heat during solidification, the increase in solid fraction, and the real-time position and thickness of the solidification front (slab shell). Its key outputs include the solid fraction distribution and the solidification rate at any position of the slab. The above sub-models achieve close bidirectional coupling by sharing physical field variables. Specifically, the molten steel flow field calculated by the flow model is used as a convection term and is simultaneously coupled to the governing equations of the heat transfer and mass transfer models to accurately characterize the enhancing effect of flow on heat transfer and solute migration. At the same time, the temperature field output by the heat transfer model is the fundamental input driving the phase transition calculation of the solidification model, while the latent heat released during solidification is fed back to the energy equation of the heat transfer model in real time as a source term, forming a closed-loop interactive calculation process. When constructing this coupled model system, it is necessary to systematically embed the dynamic thermophysical property parameters of the target steel grade (82B) as a function of temperature. These parameters include, but are not limited to, the steel liquid density of 7020 kg / m³, thermal conductivity of 170 W / (m·K), specific heat capacity, viscosity, and latent heat of solidification. The accuracy of these parameters is a key prerequisite for the model to achieve high-precision prediction.

[0017] Step S1 further includes: simulating the turbulent flow and convection effect of molten steel based on a three-dimensional flow model, outputting the three-dimensional flow field information of molten steel; solving the energy conservation equation of the billet based on a heat transfer model, simulating the heat transfer process including conduction, convection and radiation, and outputting the three-dimensional temperature field of the billet; solving the diffusion-convective transport equation of solute elements based on a mass transfer model, simulating the migration and redistribution process of solute elements in molten steel, and outputting the solute concentration field; coupling the three-dimensional flow field information output by the three-dimensional flow model as convection terms to the corresponding control equations of the heat transfer model and the mass transfer model respectively, and using the three-dimensional temperature field output by the heat transfer model as the input of the solidification model, and outputting the solid fraction distribution, billet shell thickness and solidification rate distribution of the billet by the solidification model.

[0018] Specifically, after completing the construction and parameter setting of the above model, the process proceeds to the specific calculation implementation stage in step S1. The core of this stage is to perform simulation calculations of the multiphysics coupled solidification heat transfer model to obtain key physical field information that accurately describes the continuous casting process. First, the simulation of the three-dimensional flow model is performed. This model is based on computational fluid dynamics, and its governing equations are derived from the classical Navier-Stokes equations. These equations consist of the mass conservation equation (continuity equation) and the momentum conservation equation, which are the fundamental physical laws describing the motion of viscous Newtonian fluids. In the continuous casting scenario, combining the physical properties of molten steel such as density and viscosity, and the set boundary conditions such as casting speed and crystallizer wall conditions, the equation set is discretized and iteratively solved using numerical methods such as the finite volume method. Specifically, within each computational unit and time step, the continuity equation and momentum equation are solved simultaneously. The momentum equation considers the natural buoyancy source term caused by temperature difference and the electromagnetic force source term generated by the electromagnetic stirrer to accurately simulate the complex turbulent flow behavior of molten steel driven by electromagnetic stirring, thermal convection, and other factors in the crystallizer and secondary cooling zone. Through repeated iterations until the flow field converges, stable and reliable three-dimensional flow field information is finally obtained. This information fully quantifies the motion state and mechanical environment of the molten steel in the computational domain in the form of a velocity vector field and a pressure scalar field. This flow field is a prerequisite and key input for subsequent heat and mass transfer calculations.

[0019] Subsequently, the temperature field of the cast billet was calculated based on the heat transfer model. This model is based on the law of conservation of energy, and its core governing equation is a comprehensive energy equation containing transient, convection, diffusion, and source terms. In practice, the three-dimensional velocity field calculated and output by the flow model is used as the velocity input for the convection term in the energy equation, thus accurately characterizing the enhanced effect of molten steel flow on heat transport. Simultaneously, temperature-dependent thermal conductivity parameters of the steel and solidified billet shell are set in the equation to characterize the heat conduction process. Corresponding heat transfer coefficients and ambient temperatures are set at the billet boundary according to process parameters to simulate the combined convection and radiation heat transfer between the billet surface and the atomized cooling water, rollers, and the surrounding environment. The latent heat released during solidification is treated as an internal heat source in the energy equation using the equivalent enthalpy method or the source term method. Numerical methods compatible with the flow model, such as the finite volume method, are used to spatially discretize and temporally advance the solution of the energy conservation equation. Within each computational step, a complete energy equation considering convection, conduction, radiation, and latent heat release is solved simultaneously. Through iterative calculations until the temperature field converges, the entire dynamic heat transfer process of the billet from the injection of molten steel and the formation of the billet shell to complete solidification is simulated with high precision. The final output of this computational process is a three-dimensional transient temperature field of the billet that continuously evolves with the casting time and spatial position throughout the entire computational domain. This temperature field is the fundamental basis for subsequent solidification process and solute segregation analysis.

[0020] Meanwhile, the distribution of solute elements in molten steel is simulated based on a mass transfer model. This model is established based on the principle of solute mass conservation, and its core governing equation is the convection-diffusion transport equation. In specific implementation, the three-dimensional velocity field obtained from the flow model is used as the direct input to the convection term in this equation to accurately describe the transport effect of macroscopic flow of molten steel on the migration of solute elements. Combining Fick's law, which describes microscopic diffusion phenomena, a solute diffusion coefficient related to temperature and composition is introduced into the equation. Under the specific background of continuous casting solidification, this model needs to specially handle the redistribution behavior of solute in the solid-liquid two-phase region, which is usually corrected by introducing an equilibrium distribution coefficient or using a model suitable for interdendritic flow. The convection-diffusion equation is discretized and solved using a numerical method consistent with the aforementioned model. During the calculation process, the equation is coupled and iterated with the flow field and temperature field: the flow field drives the convection of solute, and the temperature field determines the position of the solidification front and affects the diffusion coefficient and distribution behavior. By solving the model, it is possible to dynamically simulate the entire process of alloying elements such as carbon migrating and diffusing with the flow from the injection of liquid steel until they are enriched or depleted at the solidification front due to segregation. The final output of this calculation process is the concentration field distribution of solute elements, represented by carbon, in the computational domain as a function of time and space. This concentration field is a direct data source for quantitatively assessing the final degree of segregation in the cast billet.

[0021] Furthermore, the three-dimensional temperature field calculated by the heat transfer model is used as the core input driving the phase change and transmitted to the solidification model. Based on thermodynamic phase change theory, the solidification model tracks the evolution of the solid-liquid interface at macroscopic or microscopic scales by describing the solid-liquid interface energy through local enthalpy changes in the calculation unit or using the phase field method. In practice, the model determines the thermal state in real time within each calculation unit based on the input temperature field data: when the unit temperature is lower than the liquidus temperature of the steel grade, the model calculates the equilibrium solid fraction at the current temperature according to a preset solidification path, such as the lever law or the Scheil model; in the solid-liquid two-phase region, the latent heat released during solidification is accurately fed back and coupled back into the heat transfer model's calculations using the source term method or equivalent heat capacity method. The model continuously updates the solid fraction distribution at each spatial location within the entire calculation domain through iterative calculations. Based on this spatiotemporal evolution data, the real-time growth thickness of the billet shell can be directly calculated. Specifically, for the terminal electromagnetic stirring installation location, its solidification rate is defined and extracted using the solid fraction value of the unit at that location. For example, the solidification rate is defined as the ratio of the current solid fraction at that location to the solid fraction at complete solidification. This series of calculation steps involving flow, heat transfer, mass transfer, and solidification is performed sequentially or iteratively in a unified numerical simulation platform until the entire set casting length from the meniscus to the billet cutting point is simulated.

[0022] Ultimately, the process outputs a complete, self-consistent, and mutually coupled set of multiphysics field data, including flow field, temperature field, solute concentration field, solid fraction field, billet shell thickness field, and solidification rate field. These data provide a direct, accurate, and physically-based input data foundation for scientifically determining the target solidification rate range in subsequent steps and for calculating various evaluation functions in the multi-objective optimization model, such as temperature deviation, billet shell thickness, and solidification rate matching degree.

[0023] Step S2: Based on the multi-physics coupled solidification heat transfer model, determine the target solidification rate range of the billet at the end electromagnetic stirring position.

[0024] Step S2 includes: designing and simulating multiple secondary cooling water distribution schemes with different water volume distributions based on a multi-physics coupled solidification heat transfer model; for each scheme, obtaining the solidification rate of the billet at the fixed installation position of the end electromagnetic stirrer, and calculating the carbon segregation index at the center of the billet for each scheme through the solute concentration field output by the mass transfer model, and establishing a quantitative mapping relationship between the solidification rate of the billet and the carbon segregation index at the center of the billet; using the preset billet quality requirements as screening conditions, determining the range of billet solidification rates that can make the carbon segregation index meet the screening conditions from the quantitative mapping relationship, and determining it as the target solidification rate range at the end electromagnetic stirrer position under the current working conditions.

[0025] Specifically, after constructing and running a multi-physics coupled solidification heat transfer model to obtain simulation data that accurately reflects the thermal, fluid, and mass states of the billet under different secondary cooling water distribution schemes, in order to transform the process rules contained therein into clear optimization targets, it is necessary to scientifically define the solidification state range corresponding to the best effect of the end electromagnetic stirring based on these data, that is, to determine the target solidification rate range.

[0026] First, using a calibrated multiphysics coupled solidification heat transfer model as a digital experimental platform, and while keeping the physical installation position of the end electromagnetic stirrer fixed, a series of numerical simulation experiments were systematically designed and executed. By designing multiple secondary cooling water distribution schemes covering different water flow gradients, the experiments were ensured to cover common actual production conditions, thus guaranteeing the representativeness of the data. Each experiment corresponds to an independent water flow distribution scheme for each section of the secondary cooling zone. For example, in the case of 160mm square billets of 82B steel, by changing the cooling water flow rates of the four cooling sections in the secondary cooling zone (foot roll section, first to third sections) in Table 1, within a given constraint range (foot roll section 4.23–6.68 m³ / h, first secondary cooling section 6.12–8.40 m³ / h, second secondary cooling section...), the water flow rates were adjusted to... The flow rates of the first cooling section are 2.67–4.68 m³ / h, and the third cooling section is 1.38–2.15 m³ / h. These are combined and adjusted to generate a series of water distribution schemes covering high, medium, and low cooling intensities. These schemes are designed to simulate various cooling conditions that may arise in actual production due to process adjustments or fluctuations. For each set of water volume schemes, it is used as a boundary condition input in the model, and then a complete coupled calculation is run. After the calculation is completed, the model outputs a complete set of data including the flow field, temperature field, solute concentration field, and solidification field.

[0027] From these results, two key parameters were precisely extracted for subsequent analysis: the first parameter is the billet solidification rate, which refers to the solid fraction calculated by the solidification model based on the temperature at the fixed spatial coordinates of the end electromagnetic stirrer. This quantitatively describes the degree of solidification of the molten steel at that point, with a value between 0% (completely liquid) and 100% (completely solid). The second parameter is the billet center carbon segregation index, which is obtained by post-processing the solute concentration field across the entire billet cross-section calculated by the mass transfer model. The calculation method is as follows: Extract a predetermined number of points, for example eleven, equidistant from the diagonal of the billet cross-section. The carbon mass fraction at each sampling point is used. The carbon mass fraction at the 6th point (the intersection of the diagonals) is taken as the central carbon content, and the carbon mass fractions at the remaining 10 points are taken as the carbon content of the surrounding area. The carbon mass fraction at the central point is divided by the average carbon mass fraction of the remaining ten points; the resulting ratio is the carbon segregation index. This index is a core quality criterion for directly evaluating the uniformity of the internal composition of the billet and quantifying the severity of central segregation defects. The closer its value is to 1, the more uniform the composition. By collecting multiple sets of experimental data, a complete quantitative relationship was established from "specific water distribution scheme" to "fixed-position solidification rate" and then to "final carbon segregation index." This part of the experiment reveals how adjusting the water distribution can change the solidification state at the agitator's point of action, thereby affecting quality.

[0028] To isolate the complex effects of variations in water distribution and to more purely demonstrate the decisive role of "solidification state" in the stirring effect and final quality, under the original factory-optimized water distribution scheme (fixing a typical water volume), the effective range of the electromagnetic stirrer was flexibly defined using a user-defined function (UDF) in the software. This virtually moved the position of the end-effector electromagnetic stirrer, allowing it to act on the billet at different solidification rates, as shown in Table 2. This part of the experiment directly demonstrates that under the same cooling regime (same water distribution), simply changing the solidification rate position of the stirrer significantly alters the central carbon segregation of the billet, thus strongly and independently verifying the core mechanism that "solidification rate is a key state parameter affecting the stirring metallurgy effect." Table 2 Finally, by combining the experimental data from the two dimensions mentioned above, and by compiling the "solidification rate-segregation index" data pairs corresponding to all simulation experiments, a scatter plot reflecting the correlation between the two was drawn, as shown below. Figure 3As shown, a clear and quantitative mapping relationship is established from the process state (solidification rate) to the product quality (segregation index). This relationship intuitively demonstrates how the solidification state at the final electromagnetic stirring position affects the final internal quality of the billet. Next, a clear product quality standard is introduced as a screening criterion. For example, based on the process requirements for high-quality billets, the carbon segregation index is set to not exceed 1.08. Applying this screening criterion to the aforementioned mapping relationship allows for the reverse screening of all solidification rate values ​​that can achieve the segregation index target (i.e., ≤1.08). The continuous range formed by these qualified solidification rate values ​​is formally defined as the "target solidification rate range" under the current production conditions. Taking the 82B steel billet in this embodiment as an example, extensive simulation data analysis shows that when the solidification rate of the billet at the final electromagnetic stirring position is controlled within the range of 76.11% to 76.88%, the corresponding carbon segregation index consistently meets the quality requirement of not exceeding 1.08. Therefore, [76.11%, 76.88%] was determined as the target solidification rate range for this specific working condition.

[0029] Through systematic digital experiments and data analysis, the optimal stirring effect was transformed into a specific and quantifiable target solidification rate range. This provided a precise scientific target for subsequent optimization, directly solving the problem of control instability caused by target ambiguity in traditional methods. It ensured that the optimization of secondary cooling water distribution could always aim at the core goal of improving the internal quality of the billet, and was the key cornerstone for achieving precise control and improving process stability.

[0030] Step S3: Taking the target solidification rate range as the core optimization guide and combining the preset metallurgical criteria, construct a multi-objective optimization model for solving the cooling water volume of each section of the secondary cooling zone. The multi-objective optimization model includes a set of objective functions defined based on metallurgical criteria and a set of constraint conditions including water volume constraints of each cooling section.

[0031] Step S3 involves constructing a multi-objective optimization model to solve for the cooling water volume in each section of the secondary cooling zone, including setting the surface temperature control objective function: Where m is the number of key temperature monitoring points. The surface temperature of the billet at the i-th monitoring point is extracted from the three-dimensional temperature field output by the heat transfer model. To determine the corresponding process-specified temperature value, the deviation between the actual surface temperature of the billet and the target temperature at each monitoring point is controlled based on a temperature control objective function; a target function for the billet shell thickness is also set. Where n is the number of monitoring sections for the thickness of the billet shell. The thickness of the j-th segment of the blank shell was calculated using a solidification model. To set a preset safe thickness for the billet shell, a penalty is applied to monitoring sections where the billet shell thickness is lower than the preset safe thickness, based on the billet shell thickness safety objective function; a temperature gradient objective function is also set. ,in, The number of temperature gradient monitoring locations. This represents the temperature gradient value at the k-th monitoring location, calculated based on the heat transfer model. Assuming an upper limit for the allowable temperature gradient in the process, a penalty is imposed on temperature gradients exceeding this limit based on the temperature gradient control objective function; a temperature constraint objective function for the brittle region is also set. , [ , [ ] represents the surface temperature brittleness range of the target steel grade; set the objective function for solidification rate matching of the end electromagnetic stirring: , This represents the solidification rate of the billet at the final electromagnetic stirring position. These represent the target solidification rate ranges.

[0032] Specifically, after determining the target solidification rate range, in order to synergistically transform this core process objective with multiple key metallurgical quality requirements into quantifiable and evaluable optimization instructions, a systematic mathematical model needs to be constructed. This model integrates multi-dimensional objectives and ultimately guides the solution of cooling water volume for each section of the secondary cooling zone. First, a multi-objective optimization model is constructed to solve for the cooling water volume in each section of the secondary cooling zone. The core of this model is a set of objective functions defined based on pre-defined metallurgical criteria. These criteria are a series of key process requirements set to ensure the final quality of the billet and the safety of the production process. The construction of the objective function set specifically includes: setting a surface temperature control objective function f1. This function aims to minimize the normalized sum of squares of the deviations between the actual temperature and the process-specified target temperature at key monitoring points on the billet surface. By calculating the sum of squares of the relative deviations between the actual and target temperatures, the function value comprehensively reflects the overall accuracy of temperature control; the smaller the value, the closer the temperature is to the ideal temperature. Pathfinding is crucial for avoiding surface overheating or undercooling and reducing the risk of thermal stress cracking. A safety objective function f2 for billet shell thickness is set. The core purpose of this function is to ensure sufficient structural strength of the billet during solidification to prevent steel leakage accidents. This is achieved by penalizing any monitoring section where the billet shell thickness is below a preset safety thickness, such as 20mm. The lower the function value, the more uniform the overall billet shell thickness meets safety requirements, and the higher the production safety. A temperature gradient control objective function f3 is set. This function aims to systematically control the internal thermal stress concentration problem caused by uneven cooling intensity distribution during billet solidification. By post-processing the three-dimensional temperature field output by the heat transfer model, multiple key monitoring locations are selected along the length and cross-section of the billet, and the temperature gradient values ​​at each location are extracted. The core mechanism of this function is: only monitoring points where the actual temperature gradient exceeds the process allowable upper limit, such as 30℃ / mm, are penalized. The penalty intensity is squared relative to the relative magnitude of the gradient value exceeding the upper limit at that point; while for all monitoring points that do not exceed the allowable upper limit, the function contribution value is zero. This design allows the optimization process to actively suppress overheating or overcooling in localized areas, promoting a more uniform and gradual temperature field distribution. This effectively reduces the process risk of internal cracks in the cast billet caused by excessive thermal stress. The output value of this function quantitatively characterizes the overall severity of the risk of excessive internal thermal stress in the cast billet under the current water distribution scheme.

[0033] A brittle zone temperature avoidance objective function f4 is set. This function is used to ensure that the surface temperature of the billet avoids the specific temperature range where the mechanical properties of the steel are vulnerable throughout the process, such as [720, 870]℃ for 82B steel. In the billet surface temperature sequence calculated by the model, it is determined whether the temperature of each monitoring point falls within the pre-set brittle temperature range of the steel. If the temperature of the monitoring point is outside the range, it means that the billet at that point is not in a brittle sensitive state, the process is safe and controllable, so it is determined to be a safe state, and the contribution of the monitoring point to the function value is zero, that is, no penalty is imposed. Conversely, if the temperature of the monitoring point falls within the brittle range, the corresponding penalty value is calculated according to the degree to which its temperature deviates from the boundary of the range. The deeper the temperature goes into the brittle zone, the larger the penalty value. Finally, the penalty values ​​of all monitoring points are accumulated and normalized to form the final output of the objective function. This function, by introducing a mechanism of "zero penalty outside the interval and incremental penalty inside the interval," mathematically achieves precise avoidance of brittle temperature conditions, thereby guiding the optimization process to actively stay away from the process window that may lead to brittle fracture of the billet and ensuring the safety of subsequent production stages. An objective function f5 for matching the solidification rate of the final electromagnetic stirring is set. This function serves as the core guide of this optimization model and is specifically used to drive the optimization process to find a water distribution scheme that ensures the actual solidification rate of the billet at the final electromagnetic stirring position strictly falls within the determined target interval, such as [0.7611, 0.7688]. It achieves this by calculating the sum of penalty values ​​for the actual solidification rate deviating from the upper and lower limits of the target interval. A value of zero for this function represents the ideal state for achieving the best stirring effect.

[0034] By systematically defining and integrating multiple key objective functions, the complex multi-dimensional metallurgical criteria, namely temperature control, safe thickness, stress suppression, brittleness avoidance, and core solidification rate matching, are transformed into a well-structured and quantifiable mathematical optimization problem. This ensures that the optimization process can simultaneously take into account the surface quality of the billet, production safety, and internal segregation control of the core, providing a comprehensive and balanced decision-making framework for goal-oriented and precise secondary cooling water distribution. This effectively overcomes the limitations of traditional methods, which have a single optimization objective and are difficult to coordinate multiple requirements.

[0035] Step S3, which involves constructing a multi-objective optimization model for calculating the cooling water volume in each section of the secondary cooling zone, further includes: normalizing multiple objective functions using the range method and constructing a total value function using a weighted summation method. , The value after normalizing the output of the objective function. The non-negative weight coefficients of the corresponding objective function satisfy... ,satisfy .

[0036] Specifically, since the aforementioned objective functions have different physical dimensions and numerical ranges, normalization and weighted synthesis are required to integrate them into a single objective that can be uniformly compared and optimized. In practice, the range method is first used to normalize the original output value of each objective function. The range method is a data standardization method that scales data proportionally to a specific interval, typically [0, 1]. For each objective function *fi*, the calculated values ​​under all candidate water allocation schemes are iterated to find its maximum and minimum values. Then, for any scheme, the calculated value of the objective function under that scheme is subtracted from the minimum value among all values ​​of the function. This difference is then divided by the difference between the maximum and minimum values ​​of the function. The final quotient is the normalized value of the objective function under the current scheme, and this value is normalized to the range of zero to one.

[0037] The objective function described above is a penalty function. This type of function does not impose mandatory equality or inequality requirements. Instead, it quantifies undesirable process states as positive penalty terms and incorporates them into the total value function to be minimized. This guides the optimization algorithm to actively search for a water distribution scheme that makes all process indicators approach the ideal state within the feasible region that satisfies all hard constraints. Specifically, the penalty function and the following set of constraints together constitute a complete description of the optimization problem: the set of constraints establishes the basic feasible region and safety boundary of the optimization, while the penalty function establishes a refined and guided comprehensive evaluation system within this feasible region. The set of constraints is described below.

[0038] The constraint set includes the number of cooling sections in the secondary cooling zone determined by the actual configuration of the target casting machine, the water volume of each cooling section meeting the preset upper and lower bound constraints, the range of physical parameters of the steel grade, the casting speed range, the avoidance of the brittle zone of surface temperature, the minimum value of the billet shell thickness, and the upper limit of the temperature gradient; the constraint set also includes the carbon segregation index at the center of the billet not exceeding the preset threshold, and the liquid core thickness of the billet at the end electromagnetic stirring position being controlled within the preset range.

[0039] Specifically, after completing the construction of the multi-objective optimization model, that is, clarifying the total value function to be minimized and its composition, in order to ensure that the water distribution scheme obtained by the optimization algorithm is not only mathematically optimal, but also can be implemented safely, stably and with high quality in actual continuous casting production, it is necessary to set clear boundaries and red lines for the optimization process. These boundaries and red lines constitute the constraint set. The constraint set is specifically implemented as follows, and its function is to strictly limit the feasible domain of the optimization variables and ensure the engineering practicality of the solution. This set first includes a series of hard constraints directly related to equipment capacity and basic processes: the number of secondary cooling sections determined by the actual configuration of the target casting machine, which determines the optimization variables ( The dimensions of water volume in each section; the preset upper and lower bound constraints that the water volume in each cooling section must meet, which are usually determined based on pump capacity, pipeline design, and process experience to avoid water flow blockage or insufficient spraying. For example, in the case of 82B billet, the water volume in the foot roll section and the first to third sections of the secondary cooling zone must fall within the ranges of 4.23–6.68, 6.12–8.40, 2.67–4.68, and 1.38–2.15 cubic meters per hour, respectively; the allowable range of physical parameters of the target steel grade, such as the reasonable fluctuation range of density and heat capacity; and the adjustable range of the production process drawing speed. Drawing speed is the core variable affecting the solidification process, and optimization must be carried out within the preset stable drawing speed range. Secondly, the constraint set also includes several key process restrictions directly related to billet quality and production safety: avoidance of the brittle temperature zone on the surface, requiring that the optimized water distribution scheme must ensure that the surface temperature of the billet avoids the specific brittle temperature range of the steel grade throughout the process, such as 720℃ to 870℃ for 82B steel, to prevent brittle fracture during processes such as straightening; minimum billet shell thickness, requiring that the billet shell thickness at specific locations, such as before the straightening machine, must not be lower than a critical value, such as 20mm, to ensure safety and prevent steel leakage; and upper limit of temperature gradient, limiting the maximum allowable temperature difference between adjacent points inside the billet to avoid internal cracks caused by excessive thermal stress.

[0040] More importantly, the constraint set also includes core quality constraints directly linked to the final product quality, reflecting the end-to-end optimization philosophy of this method: the carbon segregation index at the center of the billet does not exceed a preset threshold, such as 1.08. This constraint directly requires the optimized solution to meet the high standard of compositional uniformity of the final product; the liquid core thickness of the billet at the end electromagnetic stirring position is controlled within a preset range, such as 40mm to 50mm. This constraint ensures from another physical dimension that the end electromagnetic stirring can operate in an appropriate solid-liquid two-phase region, thereby synergistically guaranteeing its stirring effect. These quality constraints are not directly applied to the optimization variables, but rather serve as mandatory requirements for the resulting state calculated by the multiphysics model from the optimization variables. During the optimization iteration process, any candidate water quantity scheme that fails to meet these quality constraints after model simulation will be considered an infeasible solution and excluded.

[0041] By systematically setting and implementing the comprehensive set of constraints covering equipment, process, safety, and final quality, the optimized secondary cooling water distribution scheme is ensured to be not only mathematically optimal but also a reliable process scheme that is fully feasible in engineering and can stably produce high-quality billets. This directly solves the problems in the background technology where "traditional optimization methods are difficult to take into account the overall quality of billets" and "the optimized scheme deviates greatly from actual production." By integrating key quality indicators as hard constraints into the optimization cycle, the mechanism ensures that the optimization direction never deviates from the goal of high-quality production, significantly improving the practicality and reliability of the optimization results, and laying a solid application foundation for realizing intelligent and refined control of the continuous casting process.

[0042] Step S4: Use an optimization algorithm to iteratively solve the multi-objective optimization model, inversely find the water volume scheme that satisfies all constraints, and take the water volume scheme that achieves the optimal value of the objective function set as the optimal water allocation scheme.

[0043] Step S4 includes: based on the optimization algorithm, using the cooling water volume of each section of the secondary cooling zone as the optimization variable, and according to the upper and lower bounds of the water volume of each section in the constraint condition set, initializing a population composed of multiple candidate water volume schemes; in each iteration, inputting each candidate water volume scheme in the population into the multiphysics coupled solidification heat transfer model for calculation, and calculating the overall evaluation value of the total value function based on the billet state parameters output by the model; evaluating the candidate water volume schemes based on the overall evaluation value until the preset maximum number of iterations is met, and outputting the candidate water volume scheme that makes the overall evaluation value optimal as the optimal water distribution scheme.

[0044] Specifically, after constructing a multi-objective optimization model containing a total value function and a comprehensive set of constraints, to automatically and efficiently search for the optimal secondary cooling water distribution scheme that minimizes the total value function from a broad feasible domain, it is necessary to use an intelligent optimization algorithm to drive the solution process. This application uses a heuristic intelligent optimization algorithm to solve the model. In this embodiment, the Whale Optimization Algorithm (WOA) is specifically applied. This algorithm is a metaheuristic algorithm that simulates the bubble-net predation behavior of humpback whales. It balances global exploration and local exploitation capabilities by simulating three strategies: "surrounding prey," "bubble-net attack," and "random search." It has the characteristics of strong global search capability and fast convergence speed. The algorithm encodes a potential solution to the optimization problem as a "whale individual." In this application, a whale individual represents a complete cooling water volume scheme for each section of the secondary cooling zone. During implementation, the algorithm is first initialized. Using the cooling water volume of each section of the secondary cooling zone as the optimization variable, a certain number of initial water volume schemes are randomly generated according to the upper and lower bounds of the water volume given in the constraint set, forming the initial whale population. Each water volume scheme must ensure that the water volume values ​​of each segment are within the preset upper and lower limits. Subsequently, the algorithm enters an iterative optimization loop. In each iteration, for each individual whale in the population, i.e., each candidate water volume scheme, it must be used as a boundary condition input into the constructed multiphysics coupled solidification and heat transfer model for a complete forward simulation calculation. As mentioned before, this model is a comprehensive calculation system integrating flow, heat transfer, mass transfer, and solidification processes. It receives the water volume scheme as input, solves a series of control equations, and finally outputs the complete physical state of the billet under the scheme, including the flow field, temperature field, solute concentration field, and solidification rate field. Based on the state parameters output by these models, the calculation logic of the total value function F defined in step S3 is called to calculate the overall evaluation value corresponding to the candidate water volume scheme. This value is the fitness evaluation value of the "individual whale" in the current iteration. The smaller the value, the better the overall quality of the scheme. The whale optimization algorithm identifies the current optimal individual based on the calculated population fitness and updates the positions of all individuals in the entire population according to its unique position update rules, such as mimicking encirclement, bubble net attacks, and random search. This adjusts the water volume values ​​for each segment. After the position update, the newly generated water volume values ​​undergo boundary processing to ensure they still satisfy the upper and lower bound constraints of each segment's water volume. Then, the algorithm determines whether a preset termination condition is met, such as reaching the maximum number of iterations (e.g., 300 generations) or the optimal value of the total value function changing less than a minimum threshold over multiple generations. If not met, the algorithm returns to the model calculation and fitness evaluation steps to start a new round of iterations; if met, the iteration terminates, and the algorithm outputs the water volume scheme represented by the whale individual with the best fitness (i.e., the smallest overall evaluation value) in all iterations. This scheme is the optimal water allocation scheme obtained in step S4.

[0045] Taking the optimization process of the 82B steel billet embodiment of this application as an example, the WOA algorithm was applied for 300 iterations of optimization. The curve of the overall evaluation value changing with the number of iterations is shown below. Figure 4 As shown, the water distribution exhibits a convergence characteristic of rapid decline followed by stabilization. The final optimal water allocation scheme is shown in Table 3 under "Optimized Scheme," and its specific water allocation differs from the original scheme. Table 3 The final optimized water distribution scheme was re-input into the calibrated multiphysics coupled solidification heat transfer model for full-process simulation verification. The simulation results show that at the fixed installation position of the end electromagnetic stirrer, the actual solidification rate of the billet is 76.21%, successfully falling within the target range [76.11%, 76.88%]. More importantly, the calculated carbon segregation index at the center of the billet further decreased to 1.01, which is better than the best result observed in the previous optimization experiment through "virtual moving electromagnetic stirring position". This phenomenon is not contradictory, but a direct manifestation of the effectiveness of the multi-objective collaborative optimization method of this invention: the range determination experiment in step S2 is a local optimization performed by only changing the stirring position under the solidification path determined by the original water distribution scheme; while the subsequent global optimization process is to adjust the water volume of each secondary cooling section through the system, while satisfying the core constraint of solidification rate, and synergistically improving the temperature field uniformity, morphology of the mushy zone and thermal stress distribution of the entire billet, thereby reshaping a better global solidification environment. In this new environment, electromagnetic stirring plays a more thorough role in homogenizing the melt at the optimal solidification point, enabling the segregation control level to break through the local optimum under the original process framework and achieve a global improvement in the internal quality of the billet. At the same time, the optimized billet surface temperature profile is more evenly and reasonably distributed throughout the secondary cooling zone, confirming that this method can comprehensively improve multiple key process indicators while ensuring the core objectives.

[0046] By tightly coupling a high-fidelity multiphysics simulation model with a highly efficient intelligent optimization algorithm (WOA), an automatic closed loop of "simulation evaluation - algorithm optimization" is formed. This effectively solves the problems of "low optimization efficiency and susceptibility to local optima" in the background technology. The powerful global search capability of the WOA algorithm ensures that it can find the globally optimal or near-optimal solution in a complex multi-peak, multi-constraint solution space, while the multiphysics model provides accurate and reliable physical feedback for each evaluation. This combination enables the present invention to automatically and efficiently derive a secondary cooling water distribution scheme that satisfies all process safety constraints and achieves the best balance among multiple quality objectives. Ultimately, it achieves precise control of billet segregation and stable improvement of overall quality, proving that the method of the present invention combines theoretical advancement with engineering practicality.

[0047] In summary, this application provides a method for the coordinated optimization of the solidification rate of molten steel at the end electromagnetic stirring position and the secondary cooling water distribution. By establishing a high-precision multi-physics coupled solidification heat transfer model, it systematically reveals the intrinsic relationship between the solidification rate at the end electromagnetic stirring position and the carbon segregation at the center of the billet, and based on this, determines the target solidification rate range that optimizes segregation control. This method constructs a multi-objective optimization model centered on this target range and integrating multi-dimensional metallurgical criteria, including surface temperature control, billet shell thickness safety, temperature gradient suppression, and brittle zone avoidance, and employs an intelligent optimization algorithm for efficient solution. Practice has proven that this method can not only accurately and stably control the solidification rate at the end electromagnetic stirring position within the optimal range, but also reshape a more reasonable solidification path through global optimization. This further reduces the carbon segregation index at the center of the billet while satisfying all process safety constraints, and significantly improves the overall temperature field distribution. This application represents a leap from single-parameter empirical control to multi-physics coupled simulation and multi-objective intelligent optimization collaborative decision-making, providing a scientific, precise, and engineering-practical solution for improving the internal quality of continuously cast billets and the stability of the production process.

[0048] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0049] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0050] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for synergistic optimization of the solidification rate of molten steel at the end electromagnetic stirring point and the secondary cooling water distribution, characterized in that, The method includes: Step S1: Based on the parameters of the target casting machine and the thermophysical properties of the target steel, establish a multiphysics coupled solidification heat transfer model that adapts to the three-dimensional flow, heat transfer, mass transfer and solidification process. Step S2: Based on the multiphysics coupled solidification heat transfer model, determine the target solidification rate range of the billet at the end electromagnetic stirring position; wherein, Step S2 includes: based on the multiphysics coupled solidification heat transfer model, design and simulate multiple sets of secondary cooling water distribution schemes with different water volume distributions; for each scheme, obtain the billet solidification rate at the fixed installation position of the end electromagnetic stirring, and calculate the carbon segregation index at the center of the billet for each scheme through the solute concentration field output by the mass transfer model, and establish a quantitative mapping relationship between the billet solidification rate and the carbon segregation index at the center of the billet; using the preset billet quality requirements as screening conditions, determine the billet solidification rate range that can make the carbon segregation index meet the screening conditions from the quantitative mapping relationship, and determine it as the target solidification rate range at the end electromagnetic stirring position under the current working condition; Step S3: Using the target solidification rate range as the core optimization guide and combining it with preset metallurgical criteria, construct a multi-objective optimization model for solving the cooling water volume of each section of the secondary cooling zone. The multi-objective optimization model includes a set of objective functions defined based on the metallurgical criteria and a set of constraint conditions including water volume constraints for each cooling section. Specifically, constructing the multi-objective optimization model for solving the cooling water volume of each section of the secondary cooling zone in step S3 includes: setting the surface temperature control objective function. Where m is the number of key temperature monitoring points. The surface temperature of the billet at the i-th monitoring point is extracted from the three-dimensional temperature field output by the heat transfer model. To determine the corresponding process-specified temperature value, the deviation between the actual surface temperature of the billet and the target temperature at each monitoring point is controlled based on the temperature control objective function; the billet shell thickness objective function is set as follows: Where n is the number of monitoring sections for the thickness of the billet shell. The thickness of the j-th segment of the blank shell was calculated using a solidification model. For a preset safe thickness of the billet shell, based on the safe objective function for billet shell thickness, a penalty is applied to the monitoring segment where the billet shell thickness is lower than the preset safe thickness; a temperature gradient objective function is set: ,in, The number of temperature gradient monitoring locations. This represents the temperature gradient value at the k-th monitoring location, calculated based on the heat transfer model. Assuming an upper limit for the allowable temperature gradient in the process, a penalty is imposed on temperature gradients exceeding this limit based on the temperature gradient control objective function; a temperature constraint objective function for the brittle region is set as follows: , [ , [ ] represents the surface temperature brittleness range of the target steel grade; a target function for matching the solidification rate of the end electromagnetic stirring is set: , This represents the solidification rate of the billet at the final electromagnetic stirring position. These represent the target solidification rate ranges; Step S4: Use an optimization algorithm to iteratively solve the multi-objective optimization model, invert the solution to satisfy all constraints, and take the water allocation scheme that achieves the optimal value of the objective function set as the optimal water allocation scheme.

2. The method for synergistic optimization of steel solidification rate and secondary cooling water distribution at the end electromagnetic stirring point according to claim 1, characterized in that, Step S1 includes: Based on the actual structural parameters of the target casting machine and the geometric parameters of the billet, the billet is adapted by adjusting its geometric parameters. The adjustment of geometric parameters includes the coordinate correction of cross-sectional dimensions, cooling section length, and electromagnetic stirring installation position. Based on the actual structural parameters and the adjusted billet geometry parameters, a multiphysics coupled solidification heat transfer model is established to adapt to the three-dimensional flow, heat transfer, mass transfer and solidification process. This model includes a three-dimensional flow model, a heat transfer model, a mass transfer model and a solidification model. The thermal properties of the target steel grade are embedded and associated in the model. These thermal properties include the viscosity of the molten steel and its thermal conductivity.

3. The method for synergistic optimization of steel solidification rate and secondary cooling water distribution at the end electromagnetic stirring point according to claim 2, characterized in that, Step S1 also includes: Based on the three-dimensional flow model, the turbulent flow and convection effect of molten steel are simulated, and the three-dimensional flow field information of molten steel is output. Based on the heat transfer model, the energy conservation equation of the billet is solved to simulate the heat transfer process including conduction, convection and radiation, and the three-dimensional temperature field of the billet is output. Based on the mass transfer model, the diffusion-convective transport equation of solute elements is solved to simulate the migration and redistribution process of solute elements in molten steel, and the solute concentration field is output. The three-dimensional flow field information output by the three-dimensional flow model is coupled as a convection term to the corresponding control equations of the heat transfer model and the mass transfer model, respectively. The three-dimensional temperature field output by the heat transfer model is used as the input of the solidification model. The solidification model outputs the solid fraction distribution, the shell thickness, and the solidification rate distribution of the billet.

4. The method for synergistic optimization of steel solidification rate and secondary cooling water distribution at the end electromagnetic stirring point according to claim 1, characterized in that, Step S3, which involves constructing a multi-objective optimization model for solving the cooling water volume of each section of the secondary cooling zone, also includes: Multiple objective functions are normalized using the range method, and a total value function is constructed using a weighted summation method: , The value after normalizing the output of the objective function. The non-negative weight coefficients of the corresponding objective function satisfy... ,satisfy .

5. The method for synergistic optimization of steel solidification rate and secondary cooling water distribution at the end electromagnetic stirring point according to claim 1, characterized in that, The set of constraints includes the number of cooling sections in the secondary cooling zone determined by the actual configuration of the target casting machine, the upper and lower limits of the water volume in each cooling section, the range of physical parameters of the steel grade, the casting speed range, the avoidance of the brittle zone of surface temperature, the minimum value of the billet shell thickness, and the upper limit of the temperature gradient.

6. The method for synergistic optimization of steel solidification rate and secondary cooling water distribution at the end electromagnetic stirring point according to claim 5, characterized in that, The set of constraints also includes ensuring that the carbon segregation index at the center of the billet does not exceed a preset threshold and that the liquid core thickness of the billet at the end electromagnetic stirring position is controlled within a preset range.

7. The method for synergistic optimization of steel solidification rate and secondary cooling water distribution at the end electromagnetic stirring point according to claim 1, characterized in that, Step S4 includes: Based on the optimization algorithm, the cooling water volume of each section of the secondary cooling zone is used as the optimization variable. According to the upper and lower bounds of the water volume of each section in the constraint condition set, a population consisting of multiple candidate water volume schemes is initialized. In each iteration, each candidate water quantity scheme in the population is input into the multiphysics coupled solidification heat transfer model for calculation, and the overall evaluation value of the total value function is calculated based on the billet state parameters output by the model. The candidate water allocation schemes are evaluated based on the overall evaluation value until the preset maximum number of iterations is met. The candidate water allocation scheme that makes the overall evaluation value optimal is then output as the optimal water allocation scheme.

8. The method for synergistic optimization of steel solidification rate and secondary cooling water distribution at the end electromagnetic stirring point according to claim 7, characterized in that, The optimization algorithm employs a heuristic intelligent algorithm with global optimization capabilities.

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