A flatness calculation method for hot strip laminar cooling process

Abstract

This invention discloses a method for calculating the flatness of hot-rolled strip steel during laminar cooling, relating to the field of hot-rolled strip steel process control technology. The method first obtains the parameters of the strip steel laminar cooling equipment and incoming material, matches the material temperature characteristics, constructs a dynamic correlation model including specific heat capacity, thermal conductivity, and coefficient of thermal expansion, and establishes an initial state benchmark. Secondly, a quarter-section of the strip steel is extracted and discretized using a mesh reduction method, and a spatiotemporally coupled numerical calculation matrix is ​​constructed by combining a difference strategy and heat transfer constraints. Subsequently, this matrix is ​​run to deduce temperature evolution, and the convective heat transfer operator is dynamically corrected by comparing the measured temperature with the calculated value, iteratively reconstructing a high-precision full-section temperature field. Finally, the temperature field is imported into the correlation model for thermo-mechanical coupling mapping, calculating the non-uniform thermal expansion and longitudinal thermal deformation ratio deviation of each partitioned unit, outputting a flatness evaluation index, and realizing online quantitative prediction of strip shape quality.

Description

Technical Field

[0001] This invention relates to the field of hot-rolled strip steel process control technology, specifically a method for calculating the straightness of hot-rolled strip steel during laminar cooling. Background Technology

[0002] With the continuous expansion of modern industrial applications, downstream manufacturing industries have placed more stringent requirements on the shape and quality precision of hot-rolled strip steel products. In the production process of hot-rolled strip steel, the post-rolling laminar cooling stage plays a decisive role in the final microstructure and shape quality of the strip steel. During water cooling, due to uneven distribution of the surface cooling medium and objective physical differences in heat transfer conditions across different internal regions, non-uniform temperature gradients and residual stress distributions are easily generated. When this non-uniform thermal stress exceeds the material's yield strength, it induces plastic deformation in the strip steel, leading to apparent waviness or potential shape defects in the final product. Even during subsequent cutting or stamping, once the internal residual stress equilibrium is disrupted, severe geometric deformation can still occur.

[0003] Existing technologies for monitoring and controlling laminar cooling processes often employ surface radiation temperature measurement devices to capture the temperature of discretely distributed characteristic points on the strip surface. This detection method can only obtain the local static temperature distribution on the strip surface and cannot reconstruct the two-dimensional high-precision temperature field evolution process inside the strip and across the entire cross-section in real time. Furthermore, existing cooling control strategies often rely on fixed physical parameters and static empirical convective heat transfer coefficients for one-way model extrapolation, exhibiting extremely poor adaptability to the nonlinear thermophysical property changes of the strip during drastic cooling and the fluctuations of the actual water-cooling environment, easily leading to severe cumulative extrapolation errors. In addition, in environments with dense cooling water flow coverage, existing detection equipment struggles to perform online dynamic measurement of the strip's flatness. This prevents the industrial control system from establishing a direct correlation between local temperature fluctuations and macroscopic physical deformation, making it difficult to accurately predict the strip shape evolution trend. Consequently, the actual cooling process parameter control is severely lagging, and the consistency of strip shape defect control is poor. Summary of the Invention

[0004] In order to overcome the above-mentioned defects of the prior art, the embodiments of the present invention provide a method for calculating the flatness of hot-rolled strip during laminar cooling process to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for calculating the flatness of hot-rolled strip in laminar cooling process, comprising the following steps: S1, obtaining the equipment parameters of the hot-rolled laminar cooling line and the incoming strip parameters, matching the material temperature dependence characteristics, constructing a dynamic correlation model of specific heat capacity, thermal conductivity and thermal expansion coefficient that dynamically evolves with the instantaneous temperature of the strip, and determining the initial temperature field distribution and initial flatness benchmark when the strip enters the cooling path; S2, extracting a quarter cross section of the strip as the core computational domain for mesh node division, and adopting central difference and forward difference strategies for the interface nodes and time nodes of the core computational domain, respectively, discretizing the heat transfer control equation into a spatiotemporally coupled numerical calculation matrix, combined with the cooling path environment. The configuration includes heat transfer boundary constraints for partitioned convection heat transfer operators; S3, run the numerical calculation matrix to solve the time-step temperature evolution of the grid nodes, compare the deviation between the calculated temperature value and the actual measured temperature data on site, and perform reverse dynamic correction and iterative calculation on the convection heat transfer operator in the heat transfer boundary constraints based on the comparison results until the calculation deviation converges to the preset threshold, and reconstruct the target full-section temperature field; S4, input the target full-section temperature field into the dynamic correlation model, calculate the non-uniform thermal expansion of each partitioned unit in the width direction of the strip through thermo-mechanical coupling mapping, extract the longitudinal thermal deformation deviation of each partitioned unit relative to the original reference length, and output the evaluation index characterizing the flatness of the strip shape quality during the instantaneous laminar cooling.

[0006] In a preferred embodiment, the specific process of obtaining the hot-rolled laminar flow cooling line equipment parameters and strip incoming material parameters, and matching the material temperature dependence characteristics, is as follows: Extracting cooling water temperature, water flow density, nozzle structural feature dimensions, and multi-stage cooling zone length arrangement data to generate an equipment parameter set; extracting strip running speed, inlet section temperature, material type, strip thickness, and strip width to generate a strip incoming material parameter set; calling a pre-set material property association database, mapping the material type, extracting the corresponding physical property evolution characteristic curves, and completing the matching of material temperature dependence characteristics.

[0007] In a preferred embodiment, the specific process of constructing a dynamic correlation model of specific heat capacity, thermal conductivity, and coefficient of thermal expansion that dynamically evolves with the instantaneous temperature of the strip, and determining the initial temperature field distribution and initial flatness benchmark when the strip enters the cooling path, is as follows: A piecewise interpolation algorithm is introduced to fit the specific heat capacity evolution function within different temperature ranges; a polynomial regression algorithm is used to construct the thermal conductivity evolution function and the coefficient of thermal expansion evolution function; the specific heat capacity evolution function, thermal conductivity evolution function, and preset constant density parameter are combined to derive the dynamic function of thermal diffusivity; multi-dimensional physical parameters are integrated to generate a dynamic correlation model; the non-uniform heat dissipation characteristics of the central and peripheral regions of the strip cross-section are analyzed to establish an initial temperature field distribution where the central region exhibits a benchmark high temperature and the peripheral region exhibits a gradient cooling; the physical deformation parameter of the strip shape is configured to be zero when the strip enters the cooling path to establish an initial flatness benchmark.

[0008] In a preferred embodiment, a quarter-section of the strip is extracted as the core computational domain for mesh node division. The specific process of using central difference and forward difference strategies for the interface nodes and time nodes of the core computational domain is as follows: Based on the strip thickness and width dimensions, the spatial mesh discretization step size is set, and orthogonal segmentation is performed on the core computational domain along the thickness and width directions to generate a two-dimensional mesh model containing horizontal and vertical coordinate nodes; the temperature gradient potential of adjacent spatial nodes in the two-dimensional mesh model is extracted, and spatial central difference discretization processing is performed on the interface nodes to obtain the spatial heat transfer flux; the time step is configured, the temperature state characteristics of the current time node are extracted, and forward difference discretization processing is performed to deduce the temperature state evolution trend of the next time node.

[0009] In a preferred embodiment, the specific process of discretizing the heat transfer control equation into a spatiotemporally coupled numerical calculation matrix and configuring heat transfer boundary constraints including partitioned convection heat transfer operators in conjunction with the cooling path environment is as follows: Analyze the topology of the two-dimensional mesh model and divide it into internal mesh nodes, surface mesh nodes, and side boundary nodes; configure adiabatic zero heat flux boundary constraints for the symmetrical cutting surface nodes; combine the cooling water temperature and water flow density to introduce a water-cooled medium forced heat transfer mechanism for the surface mesh nodes and configure a surface forced convection heat transfer operator; introduce air convection and thermal radiation mechanisms for the side boundary nodes and configure side natural heat transfer and radiation operators; integrate the adiabatic zero heat flux boundary constraints, surface forced convection heat transfer operators, and side natural heat transfer and radiation operators to configure and generate heat transfer boundary constraints; integrate the internal space heat transfer flux and heat transfer boundary constraints into the discretized temperature evolution equation and aggregate to generate a multi-node linked spatiotemporally coupled numerical calculation matrix.

[0010] In a preferred embodiment, the specific process of running a numerical calculation matrix to solve the time-step temperature evolution of the grid nodes and comparing the deviation between the calculated temperature values ​​and the measured temperature data on site is as follows: import the initial temperature field distribution and initial flatness benchmark into the spatiotemporal coupled numerical calculation matrix; execute the time-stepping iteration operator to analyze the thermal conduction driving potential and heat transfer boundary constraints of each grid node, and update the temperature state characteristics of each grid node; after completing the time node extrapolation of the preset cooling cycle, extract the calculated temperature values ​​of the grid nodes at the preset spatial location, simultaneously collect the measured surface temperature sequence at the corresponding spatial location of the laminar cooling site, compare the calculated temperature values ​​of the grid nodes at the preset spatial location with the measured surface temperature sequence, and generate spatial domain temperature residual characteristics.

[0011] In a preferred embodiment, the specific process of reconstructing the target full-section temperature field by performing reverse dynamic correction and iterative calculation on the convective heat transfer operator in the heat transfer boundary constraint condition according to the comparison results until the calculation deviation converges to a preset threshold is as follows: Determine whether the spatial domain temperature residual characteristics meet the preset convergence threshold; if it exceeds the preset convergence threshold, analyze the gradient evolution direction of the spatial domain temperature residual characteristics and reverse adjust the numerical characteristics of the partitioned convective heat transfer operator in the heat transfer boundary constraint condition; fuse the updated partitioned convective heat transfer operator to the spatiotemporal coupled numerical calculation matrix to trigger a new round of grid node temperature evolution deduction until the spatial domain temperature residual characteristics converge within the preset convergence threshold; extract the temperature state characteristics of all grid nodes under the convergence state, perform spatial matrix mirror topology expansion along the physical symmetry plane of the strip, and reconstruct the target full-section temperature field containing the complete physical boundary of the strip.

[0012] In a preferred embodiment, the specific process of inputting the target full-section temperature field into the dynamic correlation model and calculating the non-uniform thermal expansion of each segment in the strip width direction through thermo-coupling mapping is as follows: An orthogonal discretized solid element is constructed by running a segmentation algorithm along the strip width direction and longitudinal direction; the solid element at the longitudinal center position is extracted as the core evaluation unit to shield against longitudinal heat conduction gradient interference; the spatial node temperature parameters of the target full-section temperature field are mapped to the core evaluation unit to generate representative temperature features for each segment in the strip width direction; the thermal expansion coefficient matching the representative temperature features is extracted from the dynamic correlation model; the representative temperature features, thermal expansion coefficient, and initial longitudinal geometric dimensions of the segment are fused to deduce the non-uniform thermal expansion of each segment in the strip width direction.

[0013] In a preferred embodiment, the specific process of extracting the numerical value of the longitudinal thermal deformation deviation of each division unit relative to the original reference length, and outputting the flatness evaluation index characterizing the instantaneous strip shape quality during laminar cooling, is as follows: Aggregate the non-uniform thermal expansion of each division unit along the longitudinal path to obtain the total longitudinal geometric evolution characteristics of each local space in the strip width direction; integrate the overall size distribution in the strip width direction to extract the average state reference of longitudinal geometric evolution; compare the total longitudinal geometric evolution characteristics of each local space with the average state reference of longitudinal geometric evolution to extract the longitudinal thermal deformation deviation; perform dimensionless normalization mapping processing on the longitudinal thermal deformation deviation relative to the original reference length of the strip to generate a flatness evaluation index that maps the edge wavy characteristics and the middle wavy characteristics of the strip.

[0014] The present invention has the following beneficial effects: (1) A method for calculating the flatness of hot-rolled strip in laminar cooling process: This method acquires equipment parameters and strip material parameters to construct a dynamic correlation model of specific heat capacity, thermal conductivity, and thermal expansion coefficient that dynamically evolves with the instantaneous temperature of the strip. A quarter-section of the strip is extracted as the core computational domain. The heat transfer control equations are discretized into a spatiotemporally coupled numerical computation matrix using central difference and forward difference strategies. This improves upon the prediction distortion problem caused by using static physical parameters in existing technologies. Through dynamic property matching and symmetrical geometric dimensionality reduction discretization, the computational scale of the grid nodes is significantly reduced while ensuring the fine configuration of heat transfer boundary constraints in complex cooling environments. This improves the physical state fit and spatial computation execution efficiency of the online temperature field simulation of the strip.

[0015] (2) A method for calculating the straightness of hot-rolled strip steel during laminar cooling process. This method uses a numerical calculation matrix to solve for the temperature evolution of grid nodes. It utilizes the deviation between the measured temperature data and the calculated temperature values ​​to perform reverse dynamic correction and iterative convergence of the convective heat transfer operator. The reconstructed full-section temperature field is input into a dynamic correlation model. Through thermo-mechanical coupling mapping, the non-uniform thermal expansion and longitudinal thermal deformation deviation of each partitioned unit are calculated, and a straightness evaluation index is output. This overcomes the physical bottleneck of existing technologies where strip steel straightness cannot be directly measured online in dense water-cooling environments. It establishes a closed-loop correction mapping mechanism from high-precision temperature evolution to longitudinal macroscopic thermo-mechanical deformation, improving the reliability of temperature field reconstruction and the accuracy of instantaneous strip shape quality evaluation under actual working conditions.

[0016] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0017] Figure 1 This is a flowchart of a method for calculating the straightness of hot-rolled strip steel during laminar flow cooling, according to the present invention.

[0018] Figure 2 This is a schematic diagram of the temperature distribution along a quarter cross section of the strip in an embodiment of the present invention.

[0019] Figure 3 This is a columnar schematic diagram of the straightness distribution of the strip width direction in an embodiment of the present invention. Detailed Implementation

[0020] This application provides a method for calculating the flatness of hot-rolled strip during laminar cooling. This method solves the problems of existing cooling control methods relying on static parameters and local surface temperature measurement, which leads to severe distortion in the prediction of the instantaneous temperature field of the entire strip cross section and the inability to conduct online mapping and evaluation of the macroscopic deformation evolution trend of the strip under intensive water cooling environment.

[0021] The overall approach of the scheme in this application is as follows: a dynamic correlation model of thermal properties bound to the real-time thermal state of the strip is constructed, and differential discrete dimensionality reduction modeling is performed on the symmetrical cross-section of the strip to configure the heat transfer boundary; the convective heat transfer characterization parameters in the model are corrected by reverse iteration using measured surface temperature data, and a high-precision full-section target temperature field is reconstructed in a closed loop; finally, the thermal state distribution characteristics of each spatial division unit are converted into longitudinal non-uniform physical deformation parameters using a thermo-mechanical coupling mechanism to complete the quantitative evaluation of the flatness evolution trend of the strip cooling process.

[0022] Example 1; please refer to Figure 1 This invention provides a technical solution: a method for calculating the straightness of hot-rolled strip in laminar cooling process, comprising the following steps: S1, obtaining the equipment parameters of the hot-rolled laminar cooling line and the incoming strip parameters, matching the material temperature dependence characteristics, constructing a dynamic correlation model of specific heat capacity, thermal conductivity and thermal expansion coefficient that dynamically evolves with the instantaneous temperature of the strip, and determining the initial temperature field distribution and initial straightness benchmark when the strip enters the cooling path; S2, extracting a quarter cross-section of the strip as the core computational domain for mesh node division, and adopting central difference and forward difference strategies for the interface nodes and time nodes of the core computational domain, respectively, discretizing the heat transfer control equation into a spatiotemporally coupled numerical calculation matrix, and combining the cooling path environment configuration. The process includes: S3, running a numerical calculation matrix to solve the time-step temperature evolution of the grid nodes, comparing the calculated temperature values ​​with the actual measured temperature data, and performing reverse dynamic correction and iterative calculation on the convection heat transfer operator in the heat transfer boundary constraints based on the comparison results, until the calculation deviation converges to a preset threshold, and reconstructing the target full-section temperature field; S4, inputting the target full-section temperature field into the dynamic correlation model, calculating the non-uniform thermal expansion of each partition unit in the strip width direction through thermo-mechanical coupling mapping, extracting the longitudinal thermal deformation deviation of each partition unit relative to the original reference length, and outputting the evaluation index characterizing the instantaneous plate shape quality and straightness of the strip during laminar cooling.

[0023] In this implementation scheme, step S1 first collects equipment parameters such as cooling water temperature, water flow density, and nozzle spacing, as well as parameters such as incoming material thickness, width, and strip speed. The temperature dependence of the material refers to the physical property of the strip changing non-linearly with temperature during the laminar cooling stage. Based on this characteristic, this step uses a piecewise fitting formula to construct a dynamic correlation model, calculating in real time the specific heat capacity, thermal conductivity, and coefficient of thermal expansion of the strip at different temperature ranges. Considering the actual working condition that the strip's edges dissipate heat faster than its center during rolling, a non-uniform initial temperature distribution is set when the strip enters the laminar cooling section, and the initial straightness of the strip's water inlet is set to zero as the benchmark for subsequent evolution calculations.

[0024] Step S2 transforms the complex continuous heat transfer process of the strip steel into a numerical matrix that can be efficiently solved by a computer system through geometric dimensionality reduction and mathematical discretization. Considering the completely symmetrical physical characteristic of the temperature field distribution across the strip steel cross-section, only one-quarter of the strip steel's cross-section is extracted as the core computational domain, thereby significantly reducing the computational scale of the mesh nodes. In the discretization stage, the spatial mesh employs a central difference strategy to obtain the temperature gradient between adjacent spatial nodes, and the time nodes employ a forward difference strategy to extrapolate the temperature state at the next time step. The heat transfer boundary constraints are a mathematical boundary representation of the actual cooling environment of the strip steel. For example, an adiabatic boundary is set for the symmetrical cutting surface, a water-cooled forced convection heat transfer operator is introduced for the upper surface in direct contact with the cooling water, and natural air convection and thermal radiation operators are introduced for the opposite side surfaces, thereby accurately defining the heat exchange rules between the model and the outside world.

[0025] Step S3 involves dynamically solving the temperature field and introducing a closed-loop feedback mechanism based on on-site measured data to eliminate environmental evolution errors in the theoretical calculation model. The discretized numerical matrix is ​​run to solve for the instantaneous temperatures of grid nodes in different spatial regions, such as the interior of a quarter-section of the strip, the boundary, and corners. Reverse dynamic correction is the core control logic of this step. Specifically, the node temperature values ​​derived from the numerical matrix are compared with the measured data collected by the on-site temperature measurement equipment. If the spatial domain temperature residual exceeds the preset convergence range, the surface convection heat transfer coefficient and the lateral convection heat transfer coefficient in the boundary conditions are adjusted in reverse. The corrected heat transfer parameters are then substituted back into the matrix for iterative calculation until the error between the calculated and measured values ​​converges, ultimately reconstructing the instantaneous temperature field distribution of the entire strip cross-section that highly matches the actual heat transfer law.

[0026] Step S4 transforms the high-precision thermal temperature field distribution characteristics into quantifiable macroscopic mechanical deformation indices. Thermo-mechanical coupling mapping refers to the physical transformation process that causes inconsistent local thermal expansion or contraction due to non-uniform temperature gradient distribution within the strip, leading to mechanical deformation. In practice, the strip is divided into multiple solid evaluation units along its width and length, with the central unit selected to eliminate temperature difference interference along the length. The thermal expansion coefficient in the dynamic model is used to calculate the non-uniform thermal expansion of each width unit caused by the temperature difference between the center and edges of the strip. The longitudinal thermal deformation deviation relative to the original reference length refers to the ratio of the length change of each unit to the original reference length of the strip; this ratio is the flatness evaluation index characterizing the tendency of the strip to exhibit edge or center waviness.

[0027] Specifically, the process of obtaining equipment parameters and strip material parameters for the hot-rolled laminar flow cooling line, and matching the material temperature dependence characteristics, is as follows: Data on cooling water temperature, water flow density, nozzle structural feature dimensions, and multi-stage cooling zone length arrangement are extracted to generate a set of equipment parameters; strip running speed, inlet section temperature, material type, strip thickness, and strip width are extracted to generate a set of strip material parameters; a pre-set material property association database is called to map the material type and extract the corresponding physical property evolution characteristic curves, thus completing the matching of material temperature dependence characteristics.

[0028] In this implementation plan, the system performs parameter acquisition and physical feature mapping based on actual on-site production conditions. For the equipment parameter set, the system extracts cooling water temperature (e.g., 30 degrees Celsius), water flow density (e.g., 0.48), and multi-level cooling zone arrangement data, including a 20-meter coarse-adjustment zone and a 10-meter fine-adjustment zone. For the strip steel incoming parameter set, the system extracts operating speed (e.g., 15 meters per second), steel type (e.g., Q345B hot-rolled strip), strip thickness (3 mm), and strip width (1200 mm). After acquiring the above basic data, the system calls a pre-set material property correlation database and maps and extracts the corresponding physical property evolution characteristic curves for the laminar cooling temperature range of Q345B material from 450 degrees Celsius to 950 degrees Celsius. This provides an accurate basis for matching the material's temperature-dependent characteristics in subsequent thermodynamic simulations.

[0029] Specifically, the process of constructing a dynamic correlation model of specific heat capacity, thermal conductivity, and coefficient of thermal expansion that dynamically evolves with the instantaneous temperature of the strip, and determining the initial temperature field distribution and initial flatness benchmark when the strip enters the cooling path, is as follows: A piecewise interpolation algorithm is introduced to fit the specific heat capacity evolution function within different temperature ranges; a polynomial regression algorithm is used to construct the thermal conductivity evolution function and the coefficient of thermal expansion evolution function; the specific heat capacity evolution function, thermal conductivity evolution function, and preset constant density parameter are combined to derive the dynamic function of thermal diffusivity; multi-dimensional physical parameters are integrated to generate a dynamic correlation model; the non-uniform heat dissipation characteristics of the central and peripheral regions of the strip cross-section are analyzed to establish an initial temperature field distribution where the central region exhibits a benchmark high temperature and the peripheral region exhibits a gradient cooling; the physical deformation parameter of the strip shape is configured to be zero when the strip enters the cooling path to establish an initial flatness benchmark.

[0030] In this implementation scheme, the system constructs a dynamic calculation mechanism for each physical parameter based on the characteristic curves obtained through matching. For a specific cooling range, the system introduces a piecewise interpolation algorithm to fit the evolution function of specific heat capacity with temperature, and uses a polynomial regression algorithm to construct the evolution functions of thermal conductivity and coefficient of thermal expansion. To obtain key parameters that comprehensively characterize the heat transfer rate inside the strip steel, the system derives the dynamic function of thermal diffusivity by combining the above correlation functions, and its evolution control equation is: ;in, The dynamic thermal diffusivity parameter represents the ability of heat to be transferred and diffused within the strip. This represents the thermal conductivity parameter that matches the current instantaneous temperature evolution state. This represents the preset constant density parameter of the strip steel material; This represents the specific heat capacity parameter matching the current instantaneous temperature evolution state. Taking an average calculated temperature of 880 degrees Celsius as an example, the system retrieves the corresponding specific heat capacity, thermal conductivity, and constant density parameters under this state and inputs them into the aforementioned control equations. This allows for the fusion of multi-dimensional physical parameters and the generation of a dynamic correlation model. When establishing the initial state, the system analyzes the non-uniform heat dissipation law of the strip's edge being faster than the central region during the rolling process. It establishes an initial cross-sectional temperature field distribution where the wide nodes in the central region exhibit a baseline high temperature of 900 degrees Celsius, while the edge regions exhibit a gradient cooling of approximately 857 degrees Celsius. Simultaneously, the system forcibly configures the initial physical deformation parameter of the strip entering the laminar cooling section to be zero, using this as the absolute benchmark for calculating the macroscopic thermodynamic deformation evolution and flatness evaluation indicators during the subsequent cooling process.

[0031] Specifically, a quarter-section of the strip is extracted as the core computational domain for mesh node division. The specific process of using central difference and forward difference strategies for the interface nodes and time nodes of the core computational domain is as follows: Based on the thickness and width of the strip, the spatial mesh discretization step size is set, and orthogonal segmentation is performed on the core computational domain along the thickness and width directions to generate a two-dimensional mesh model containing horizontal and vertical coordinate nodes; the temperature gradient potential of adjacent spatial nodes in the two-dimensional mesh model is extracted, and spatial central difference discretization processing is performed on the interface nodes to obtain the spatial heat transfer flux; the time step is configured, the temperature state characteristics of the current time node are extracted, and forward difference discretization processing is performed to deduce the temperature state evolution trend of the next time node.

[0032] In this implementation scheme, the system utilizes the complete symmetry of the temperature field distribution of hot-rolled strip steel in physical space to reduce the computational domain from the entire strip cross-section to a quarter of the cross-section, thereby significantly reducing the computational power requirements for subsequent numerical solutions. Taking a strip steel with a thickness of 3 mm and a width of 1200 mm as an example, the system extracts a region with a thickness of 1.5 mm and a width of 600 mm as the core computational domain. Within this core computational domain, the system sets specific spatial grid discretization step sizes, for example, setting the spatial step size in the thickness direction to 0.5 mm and the spatial step size in the width direction to 6 mm, and performs orthogonal partitioning operations to construct a two-dimensional grid model composed of numerous regular nodes. In terms of the discretization solution mechanism, for the interface nodes in the grid model, the system uses the central difference method to extract the temperature gradient potential between adjacent spatial nodes, which is used to accurately quantify the spatial conduction flux of heat in the two-dimensional plane. At the same time, the system configures an independent time step parameter for the evolution process and uses the forward difference method for time nodes to deduce the temperature state evolution trend of the next time node based on the known temperature state characteristics of the current time node, thereby completing the transformation of the continuous heat transfer physical process into a discrete numerical calculation framework.

[0033] Specifically, the process of discretizing the heat transfer control equation into a spatiotemporally coupled numerical calculation matrix and configuring heat transfer boundary constraints including partitioned convection heat transfer operators in conjunction with the cooling path environment is as follows: The topology of the two-dimensional mesh model is analyzed, and internal mesh nodes, surface mesh nodes, and side boundary nodes are divided; adiabatic zero heat flux boundary constraints are configured for the symmetrical cutting surface nodes; based on the cooling water temperature and flow density, a forced heat transfer mechanism of water-cooled medium is introduced for the surface mesh nodes to configure a surface forced convection heat transfer operator; an air convection mechanism and a thermal radiation mechanism are introduced for the side boundary nodes to configure side natural heat transfer and radiation operators; the adiabatic zero heat flux boundary constraints, surface forced convection heat transfer operators, and side natural heat transfer and radiation operators are integrated to configure and generate heat transfer boundary constraints; the internal space heat transfer flux and heat transfer boundary constraints are integrated into the discretized temperature evolution equation, and a spatiotemporally coupled numerical calculation matrix with multi-node linkage is generated.

[0034] In this implementation scheme, the system configures appropriate heat transfer boundary constraints based on the topological location of the two-dimensional mesh model within the strip cross-section to realistically recreate the industrial cooling environment. First, the system meticulously divides the mesh nodes into internal nodes, surface mesh nodes (including the upper surface and lower boundary, etc.), and side boundary nodes. For the symmetrical bisecting surface nodes of the core computational domain, an adiabatic zero-heat-flux boundary constraint is forcibly configured, as the heat fluxes on both sides of the symmetrical surface cancel each other out, resulting in a zero actual temperature gradient. Second, combining parameters such as a cooling water temperature of 30 degrees Celsius and a water flow density of 0.48, the system configures a surface forced convection heat transfer operator for the upper surface mesh nodes of the strip, constructing surface water-cooled heat transfer boundary constraints. The surface convection heat transfer evolution equation is configured as follows: ;in, This refers to the physical parameter representing the thermal conductivity inside the strip steel. Represents the instantaneous temperature state parameters of the surface nodes of the mesh model; This represents the spatial coordinate parameters established along the thickness direction of the strip in the two-dimensional mesh model; This indicates the forced convection heat transfer operator of the surface to be corrected, with its initial estimated value set, for example, to 2500; This represents the real-time nodal temperature characteristic parameter of the upper surface of the strip. This represents the ambient cooling water temperature parameter. For the right-side boundary node of the strip, the system is configured with a hybrid operator incorporating both natural side heat transfer and radiation mechanisms. Its hybrid side heat transfer boundary constraint equation is configured as follows: ;in, This represents the spatial coordinate parameters established along the width direction of the strip in the two-dimensional mesh model; This indicates the side natural convection heat transfer operator to be corrected, with its initial estimated value set to, for example, 350. The real-time nodal temperature characteristic parameter representing the side boundary of the strip; This indicates the ambient temperature parameter of the cooling air. This indicates a thermal emissivity parameter configured as 0.8; This represents a fixed Stefan-Boltzmann physical constant parameter. The system integrates the boundary constraints covering adiabatic, water-cooled, and air-cooled radiation into a unified discretized temperature field evolution equation, ultimately generating a spatiotemporally coupled numerical calculation matrix capable of jointly solving all nodes across the entire cross-section of the strip.

[0035] Specifically, the process of running the numerical calculation matrix to solve the time-step temperature evolution of the grid nodes and comparing the deviation between the calculated temperature values ​​and the measured temperature data on site is as follows: import the initial temperature field distribution and initial flatness benchmark into the spatiotemporal coupled numerical calculation matrix; execute the time-stepping iteration operator to analyze the thermal conduction driving potential and heat transfer boundary constraints of each grid node and update the temperature state characteristics of each grid node; after completing the simulation of the preset cooling cycle time nodes, extract the calculated temperature values ​​of the grid nodes at the preset spatial locations, and simultaneously collect the measured surface temperature sequence at the corresponding spatial location of the laminar cooling site. Compare the calculated temperature values ​​of the grid nodes at the preset spatial locations with the measured surface temperature sequence to generate spatial domain temperature residual characteristics.

[0036] In this implementation scheme, after the spatiotemporal coupled numerical calculation matrix is ​​started, the system first imports the initial temperature field distribution of the strip as the zero-time state point for calculation, and simultaneously imports the initial flatness benchmark as the absolute zero point for subsequent deformation determination. When executing the time-stepping iterative operator, the system needs to analyze the thermal conduction driving potential of the internal grid nodes and update the temperature state of the nodes in combination with the heat transfer boundary constraints. For the discretized internal grid nodes, the time evolution extrapolation control equation is configured as follows: ;in, This represents the thermodynamic temperature state parameter of the spatial grid node at the next time step in the simulation. $m$ represents the real-time temperature state characteristic parameter of the spatial grid node at the current time step; $m$ represents the discrete coordinate spatial index number of the grid model along the strip thickness direction. Indicates the discrete coordinate space index number of the mesh model along the strip width direction; The discrete sequence evolution label represents the time step extrapolation of the system's cooling cycle. The physical parameter representing the dynamic thermal diffusivity, which characterizes the thermal diffusivity within the strip steel. This represents the forward differential discrete extrapolation step size parameter configured in the time domain of the system; This parameter represents the spatial grid discretization step size parameter configured in the thickness direction of the system. This represents the spatial grid discretization step size parameter configured in the width direction of the system. After the matrix completes the time extrapolation of the entire preset cooling cycle, for example, after executing a 3-second simulated cooling time, the system extracts the calculated temperature values ​​of the grid nodes at pre-defined spatial locations on the strip surface. Simultaneously, the system synchronously retrieves the measured temperature data sequence obtained by infrared surface temperature measurement devices deployed at the laminar flow cooling site at the corresponding spatial physical locations. By comparing the differences between the two, a spatial domain temperature residual feature characterizing the degree of distortion in the extrapolation model is generated. The aggregation evolution equation of this feature is: ;in, The spatial domain temperature residual comprehensive scalar represents the degree of distortion in the overall simulation model of the entire cross section. This parameter represents the total number of effective surface temperature measurement nodes that have been successfully deployed and synchronously collected data at the industrial site. The cyclic traversal index indicates the preset physical spatial location of the surface temperature measurement in the system; This represents the output of the system matrix derivation at the end of the current cooling cycle. Calculation parameters for surface node temperature at each spatial location; This indicates the actual data captured by the laminar flow cooling field sensor network. Measured surface temperature parameters corresponding to each spatial location.

[0037] Specifically, based on the comparison results, the convective heat transfer operator in the heat transfer boundary constraint conditions is dynamically corrected and iteratively calculated in reverse until the calculation deviation converges to a preset threshold. The specific process of reconstructing the target full-section temperature field is as follows: Determine whether the spatial domain temperature residual characteristics meet the preset convergence threshold; if it exceeds the preset convergence threshold, analyze the gradient evolution direction of the spatial domain temperature residual characteristics and adjust the numerical characteristics of the partitioned convective heat transfer operator in the heat transfer boundary constraint conditions in reverse; fuse the updated partitioned convective heat transfer operator to the spatiotemporal coupled numerical calculation matrix to trigger a new round of grid node temperature evolution deduction until the spatial domain temperature residual characteristics converge within the preset convergence threshold; extract the temperature state characteristics of all grid nodes under the convergence state, perform spatial matrix mirror topology expansion along the physical symmetry plane of the strip, and reconstruct the target full-section temperature field containing the complete physical boundary of the strip.

[0038] In this implementation scheme, the system determines the characteristics of the generated spatial domain temperature residual. Whether the convergence falls within a preset threshold is determined. This preset convergence threshold parameter is obtained by combining the allowable error limit of the on-site infrared temperature measurement device calibration with the allowable temperature fluctuation tolerance range of the plate surface in the rolling process. If the residual exceeds the threshold, the system analyzes the gradient evolution distribution direction of the residual characteristic in space, and then adjusts the partitioned convection heat transfer operator in the heat transfer boundary constraint conditions in reverse. and The system calculates specific values ​​to reduce the cumulative bias caused by the static estimation model. It then re-integrates the updated partitioned convection heat transfer operator into the spatiotemporal coupled numerical calculation matrix, dynamically replacing the original static parameters and triggering a new round of iterative evolution of the grid node temperature field. The aforementioned residual comparison and boundary heat transfer correction process continuously loops in the computational background until the latest spatial domain temperature residual characteristics output by the calculation strictly converge and fall below the preset convergence threshold. After the model converges and stabilizes, the system extracts the precise temperature state characteristics of all grid nodes within a quarter section, the original symmetrical topological geometry of the strip, and performs a mirror topological extension mapping of the spatial matrix along the physical symmetry plane of the strip, thereby completing the full-area reconstruction of spatiotemporal information and reconstructing a high-precision target full-section temperature field covering the complete physical macroscopic boundary of the strip. Combined with... Figure 2 As shown, under the condition of a simulated cooling time of 3 seconds, the reconstructed target full-section temperature field exhibits a significant non-uniform symmetrical distribution pattern with a high center and low sides. In the figure, the horizontal axis represents the node distance from the strip center to the edge, and the vertical axis represents the derived unit average temperature. Figure 2The evolution trend of the data curves shows that the center point, as the baseline high-temperature zone, has the slowest cooling rate; while towards the edge, the temperature decreases non-linearly in a parabolic manner, with the free edge forming the lowest temperature zone due to its location at the point of strongest bilateral heat dissipation. The maximum temperature gradient between the center and the edge reaches 14℃. This line graph visually verifies the accuracy of the spatiotemporal coupled numerical calculation matrix in deducing the physical laws of non-uniform heat transfer in laminar cooling.

[0039] Specifically, the process of inputting the target full-section temperature field into the dynamic correlation model and calculating the non-uniform thermal expansion of each segment in the strip width direction through thermo-mechanical coupling mapping is as follows: An orthogonal discretized solid element is constructed by running a segmentation algorithm along the strip width direction and longitudinal direction; the solid element at the longitudinal center position is extracted as the core evaluation unit to shield against longitudinal heat conduction gradient interference; the spatial node temperature parameters of the target full-section temperature field are mapped to the core evaluation unit to generate representative temperature features for each segment in the strip width direction; the thermal expansion coefficient matching the representative temperature features is extracted from the dynamic correlation model; the representative temperature features, thermal expansion coefficient, and initial longitudinal geometric dimensions of the segment are fused to deduce the non-uniform thermal expansion of each segment in the strip width direction.

[0040] In this implementation scheme, the macroscopic geometric deformation of the strip during laminar cooling is a physical response directly caused by internal temperature non-uniformity. To transform the purely thermal temperature field into boundary conditions for mechanical deformation calculation, the system constructs orthogonal discretized solid elements using a segmentation algorithm along the width and longitudinal direction of the strip. For example, a 1200 mm wide strip is uniformly divided into multiple solid elements along its width, and a 5-meter long strip is uniformly divided into multiple 0.1-meter long reference elements along its longitudinal direction. Since longitudinal temperature gradient interference is easily generated along the rolling direction on the cooling line, the system specifically extracts the solid element at the center of the longitudinal direction as the core evaluation unit to shield against this interference. Subsequently, the temperature parameters of the spatial nodes of the target full-section temperature field are mapped to this core evaluation unit, and their average values ​​are used to generate representative temperature characteristics specific to each segmented unit along the width direction of the strip. The system uses these temperature characteristics as an index to query the dynamic correlation model, extracts the matching thermal expansion coefficient, and then, combined with the initial longitudinal geometric dimensions of the core evaluation unit, deduces the non-uniform thermal expansion. The thermo-mechanical coupling deformation evolution equation is: ;in, Indicates the width direction of the strip. The longitudinal non-uniform thermal expansion evolution of each partitioned unit; This indicates the initial longitudinal geometric dimension cutoff reference parameter of the extracted core evaluation unit; This represents the nonlinear thermal expansion mapping coefficient that matches the current representative temperature feature of the unit in the query dynamic association model. This represents the representative temperature characteristic parameter generated within the core evaluation unit. This refers to the reference temperature parameter representing the environment without residual stress during the initial stage of strip steel entering the laminar cooling section after rolling and forming. This indicates the spatial location traversal index number of the strip width direction dividing unit.

[0041] Specifically, the process of extracting the proportional relationship between the longitudinal thermal deformation deviation of each division unit and the original reference length, and outputting the flatness evaluation index characterizing the instantaneous strip shape quality during laminar cooling, is as follows: The non-uniform thermal expansion of each division unit is aggregated along the longitudinal path to obtain the total longitudinal geometric evolution characteristics of each local space in the strip width direction; the overall dimensional distribution in the strip width direction is fused to extract the average state reference of longitudinal geometric evolution; the total longitudinal geometric evolution characteristics of each local space are compared with the average state reference of longitudinal geometric evolution to extract the longitudinal thermal deformation deviation; the longitudinal thermal deformation deviation is then subjected to dimensionless normalization mapping processing against the original reference length of the strip to generate a flatness evaluation index that maps the edge and middle wavy features of the strip.

[0042] In this implementation scheme, after acquiring the thermal expansion data of the individual core evaluation unit, the system performs macroscopic aggregation and accumulation processing on the non-uniform thermal expansion of each segment along the actual longitudinal rolling path of the strip, thereby calculating the total longitudinal geometric evolution characteristics of the strip in a specific width local space. Due to the existence of transverse temperature gradients within the strip, the final longitudinal contraction or expansion at different width positions will inevitably have physical differences. Therefore, the system integrates the transverse arithmetic mean of the geometric evolution characteristics of all segmented units within the full width of the strip, establishing it as the longitudinal geometric evolution average state benchmark. By comparing the total longitudinal geometric evolution characteristics of each local space with this average state benchmark, the system can accurately extract the substantial causes of strip warping, namely, longitudinal thermal deformation deviation. To enable this deviation to have universal evaluation capabilities across strip products of different specifications, the system performs dimensionless normalization mapping processing on the original reference length and average elongation of the strip. The normalization calculation equation for the flatness evaluation index is: ;in, This is a comprehensive index for evaluating the straightness of strip steel, used to quantitatively characterize the appearance of edge or center wavy features. Indicates the width direction of the strip. The total longitudinal geometric evolution feature quantity obtained by aggregating local spaces along the longitudinal path; This represents the longitudinal geometric evolution average state reference quantity extracted from the overall dimensional distribution of the integrated strip width direction; This represents the total length parameter of the original physical longitudinal reference of the strip steel participating in the solid segmentation evaluation. The system utilizes the aforementioned dimensionless evaluation calculation mechanism to eliminate the interference of the absolute length dimension of the strip steel on the judgment. According to the above logic, the central region unit exhibits a positive relative deformation bulge, with a positive calculated value for the flatness evaluation index, mapping to the intermediate wavy characteristics driven by internal residual stress; while the near-edge and free boundary regions produce a negative relative deformation contraction, with a negative calculated value for the flatness evaluation index, mapping to the edge wavy characteristics, ultimately completing the quantitative evaluation of the instantaneous plate shape quality during laminar cooling. Combined with... Figure 3 As shown, the final output straightness evaluation index can clearly determine the strip shape characteristics through the zero-point baseline. The horizontal axis in the figure represents the position of each core evaluation unit divided along the width direction of the strip, and the vertical axis represents the dimensionless straightness evaluation index value of each unit (magnified for ease of observation). Due to the aforementioned uneven distribution of the temperature field leading to differences in thermo-coupling deformation, the central region units exhibit positive relative deformation bulges (i.e., positive values), physically mapping to the evolution trend of mid-waves driven by internal residual stress; while the near-edge and free boundary regions cross the zero line and produce negative relative deformation contraction (i.e., negative values), physically mapping to the evolution trend of edge waves. This bar chart fully reveals the evolutionary mapping relationship from the macroscopic full-section temperature field to the final strip shape warping defect.

[0043] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for calculating the straightness of hot-rolled strip during laminar flow cooling, characterized in that, Includes the following steps: S1. Obtain the equipment parameters of the hot-rolled laminar flow cooling line and the parameters of the incoming strip steel, match the temperature dependence characteristics of the material, construct a dynamic correlation model of specific heat capacity, thermal conductivity and thermal expansion coefficient that evolves with the instantaneous temperature of the strip steel, and determine the initial temperature field distribution and initial flatness benchmark when the strip steel enters the cooling path. S2. Extract a quarter-section of the strip as the core computational domain and divide it into mesh nodes. For the interface nodes and time nodes of the core computational domain, adopt the central difference and forward difference strategies respectively. Discretize the heat transfer control equation into a spatiotemporal coupled numerical calculation matrix. Combine the cooling path environment to configure heat transfer boundary constraints including partitioned convection heat transfer operators. S3. Run the numerical calculation matrix to solve the temperature evolution of the grid nodes step by step, compare the temperature calculation value with the actual temperature data on site, and perform reverse dynamic correction and iterative calculation on the convection heat transfer operator in the heat transfer boundary constraint condition according to the comparison result until the calculation deviation converges to the preset threshold and the target full cross section temperature field is reconstructed. S4. Input the target full-section temperature field into the dynamic correlation model, calculate the non-uniform thermal expansion of each segment in the width direction of the strip through thermo-mechanical coupling mapping, extract the longitudinal thermal deformation deviation of each segment relative to the original reference length, and output the evaluation index characterizing the flatness of the strip shape quality during laminar cooling.

2. The method for calculating the straightness of hot-rolled strip during laminar cooling process according to claim 1, characterized in that: The specific process for obtaining the equipment parameters of the hot-rolled laminar flow cooling line and the incoming strip parameters, and matching the temperature dependence characteristics of the material, is as follows: Extract and arrange data such as cooling water temperature, water flow density, nozzle structural feature dimensions, and multi-stage cooling zone length to generate a set of equipment parameters; Extract the strip running speed, inlet section temperature, material type, strip thickness and width to generate a set of strip incoming parameters; The system calls upon a pre-defined material property association database, maps the material steel type, extracts the corresponding physical property evolution characteristic curves, and completes the matching of material temperature dependence characteristics.

3. A method for calculating flatness in laminar cooling of hot rolled strip according to claim 1, characterized in that: The specific process of constructing a dynamic correlation model of specific heat capacity, thermal conductivity, and coefficient of thermal expansion that evolves with the instantaneous temperature of the strip, and determining the initial temperature field distribution and initial flatness benchmark when the strip enters the cooling path, is as follows: A piecewise interpolation algorithm is introduced to fit the specific heat capacity evolution function in different temperature ranges, and a polynomial regression algorithm is used to construct the thermal conductivity evolution function and the thermal expansion coefficient evolution function. The dynamic function of thermal diffusivity is derived by combining the evolution functions of specific heat capacity, thermal conductivity, and preset constant density parameters, and a dynamic correlation model is generated by integrating multi-dimensional physical parameters. The non-uniform heat dissipation characteristics of the central and peripheral regions of the strip cross-section were analyzed, and an initial temperature field distribution was established in which the central region exhibits a reference high temperature and the peripheral region exhibits a gradient cooling. The physical deformation parameter of the strip shape was set to zero when the strip entered the cooling path to establish an initial flatness reference.

4. The flatness calculation method for the laminar cooling process of hot rolled strip according to claim 1, characterized in that: The process of extracting a quarter-section of the strip steel as the core computational domain for mesh generation, and employing central difference and forward difference strategies for the interface nodes and time nodes of the core computational domain respectively, is as follows: Based on the thickness and width of the strip, the spatial grid discretization step size is set, and the core computational domain is orthogonally divided along the thickness and width directions to generate a two-dimensional grid model containing horizontal and vertical coordinate nodes. Extract the temperature gradient potential of adjacent spatial nodes in the two-dimensional mesh model, and perform spatial center difference discretization processing on the interface nodes to obtain the spatial heat transfer flux. Configure the time step, extract the temperature state features at the current time node, and perform forward differential discretization processing to deduce the temperature state evolution trend at the next time node.

5. A method of calculating flatness in laminar cooling of hot rolled strip according to claim 4, characterized in that: The specific process of discretizing the heat transfer control equations into a spatiotemporally coupled numerical calculation matrix, and configuring heat transfer boundary constraints including partitioned convection heat transfer operators in conjunction with the cooling path environment, is as follows: The topology of the two-dimensional mesh model is analyzed, and internal mesh nodes, surface mesh nodes, and side boundary nodes are divided. Adiabatic zero-heat-fluid boundary constraints are configured for the nodes of the symmetrical cutting surface. Based on the cooling water temperature and flow density, a forced convection heat transfer operator is configured for the surface mesh nodes by introducing a water-cooled medium forced heat transfer mechanism. For the side boundary nodes, air convection and thermal radiation mechanisms are introduced to configure side natural heat transfer and radiation operators; By integrating adiabatic zero heat flux boundary constraints, surface forced convection heat transfer operators, and lateral natural heat transfer and radiation operators, heat transfer boundary constraint conditions are configured and generated. The internal space heat transfer flux and heat transfer boundary constraints are integrated into the discretized temperature evolution equation, and aggregated to generate a spatiotemporally coupled numerical calculation matrix with multiple nodes.

6. A method of calculating flatness in laminar cooling of hot rolled strip according to claim 1, characterized in that: The specific process of running the numerical calculation matrix to solve for the time-step temperature evolution of the grid nodes and comparing the calculated temperature values ​​with the actual measured temperature data is as follows: Import the initial temperature field distribution and initial flatness reference into the spatiotemporal coupling numerical calculation matrix; The execution time-stepping iterative operator is used to analyze the heat conduction driving potential and heat transfer boundary constraints of each grid node, and update the temperature state characteristics of each grid node. After completing the simulation of the preset cooling cycle time nodes, the calculated temperature values ​​of the grid nodes at the preset spatial locations are extracted. Simultaneously, the measured surface temperature sequence at the corresponding spatial location of the laminar cooling site is collected. The calculated temperature values ​​of the grid nodes at the preset spatial locations are compared with the measured surface temperature sequence to generate spatial domain temperature residual characteristics.

7. A method of calculating flatness in a laminar cooling process of a hot rolled steel strip according to claim 6, characterized in that: Based on the comparison results, the convective heat transfer operator in the heat transfer boundary constraint condition is dynamically corrected and iteratively calculated in reverse until the calculation deviation converges to the preset threshold. The specific process of reconstructing the target full-section temperature field is as follows: Determine whether the spatial domain temperature residual characteristics meet the preset convergence threshold; if they exceed the preset convergence threshold, analyze the gradient evolution direction of the spatial domain temperature residual characteristics and adjust the numerical characteristics of the partitioned convection heat transfer operator in the heat transfer boundary constraint conditions in the reverse direction. The fusion and update of the partitioned convection heat transfer operator to the spatiotemporal coupling numerical calculation matrix triggers a new round of grid node temperature evolution deduction until the spatial domain temperature residual characteristics converge within the preset convergence threshold. Extract the temperature state features of all mesh nodes under convergence, perform spatial matrix mirroring topological expansion along the physical symmetry plane of the strip, and reconstruct the target full-section temperature field containing the complete physical boundary of the strip.

8. A method of calculating flatness in laminar cooling of hot rolled strip according to claim 1, characterized in that: The specific process of inputting the target full-section temperature field into the dynamic correlation model and calculating the non-uniform thermal expansion of each segment in the width direction of the strip through thermo-mechanical coupling mapping is as follows: An orthogonal discretized solid element is constructed by running a segmentation algorithm along the width and longitudinal direction of the strip. Extract the vertically centered solid element as the core evaluation element to shield against vertical thermal conduction gradient interference; Map the spatial node temperature parameters of the target full-section temperature field to the core evaluation unit to generate representative temperature characteristics of each subdivided unit in the strip width direction. The thermal expansion coefficient of the dynamic correlation model is extracted to match the representative temperature features. The representative temperature features, thermal expansion coefficient and the initial longitudinal geometric dimensions of the division unit are integrated to deduce the non-uniform thermal expansion of each division unit in the width direction of the strip.

9. The method for calculating the straightness of hot-rolled strip during laminar flow cooling process according to claim 8, characterized in that: The specific process for extracting the proportional relationship between the longitudinal thermal deformation deviation of each division unit and the original reference length, and outputting the evaluation index characterizing the flatness of the strip during instantaneous laminar cooling, is as follows: The non-uniform thermal expansion of each partition unit is aggregated along the longitudinal path to obtain the total longitudinal geometric evolution characteristics of each local space in the strip width direction; By integrating the overall dimensional distribution of the strip in the width direction, the average state benchmark of longitudinal geometric evolution is extracted. The longitudinal thermal deformation deviation is extracted by comparing the total longitudinal geometric evolution characteristics of each local space with the average state benchmark of longitudinal geometric evolution. The longitudinal thermal deformation deviation is subjected to dimensionless normalization mapping processing based on the original reference length of the strip to generate a straightness evaluation index that maps the edge wavy features and the middle wavy features of the strip.

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