Continuous casting roller thermal stress prediction method

Abstract

The invention discloses a continuous casting roller thermal stress prediction method which specifically comprises the following steps: step 1, performing continuous casting roller finite element simulation based on thermal balance analysis of a continuous casting roller in operation; 2, constructing a data set S according to the simulation result obtained in the step 1 and the working condition information; a continuous casting roller thermal stress prediction model based on K-fold cross validation and SVR is established, and temperature field and thermal stress real-time prediction in the continuous casting roller operation process is achieved. The problem that surface and internal thermal stress of the continuous casting roller is difficult to directly measure when the continuous casting roller operates under complex working conditions is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of continuous casting machine equipment fault diagnosis and relates to a continuous casting roller thermal stress prediction method. Background Art

[0002] The continuous casting machine is a key equipment in the production process of steel enterprises. Its efficient and stable operation is crucial to the quality of steel billets and production safety. The continuous casting machine is mainly assembled by fan-shaped sections such as bending sections, arc sections, straightening sections and horizontal sections. Each section works together to ensure that the molten steel is evenly distributed during the cooling and shaping process, thereby producing high-quality steel billets. The continuous casting roller is a key part of the continuous casting machine to achieve uniform cooling and shaping of the molten steel. Its performance directly determines the dimensional accuracy and uniformity of the internal structure of the steel billet.

[0003] During the service life of the continuous casting roller, its roller surface will repeatedly experience periodic temperature changes and bear various mechanical stresses imposed by the continuous casting billet, such as vertical sliding force, billet pulling force, bulging force, transmission resistance and straightening force, etc. These factors can easily cause the continuous casting roller to bend, fatigue crack, wear and other failures. The failure of the continuous casting roller will reduce the quality of billet production, cause the continuous casting machine to be frequently shut down for maintenance, reduce production efficiency and increase maintenance costs. Summary of the invention

[0004] The purpose of the present invention is to provide a method for predicting thermal stress of a continuous casting roller, which solves the problem that it is difficult to directly measure the thermal stress on the surface and inside of the continuous casting roller when the roller is running under complex working conditions.

[0005] The technical solution adopted by the present invention is a method for predicting thermal stress of a continuous casting roller, which specifically comprises the following steps:

[0006] Step 1, based on the thermal balance analysis of the continuous casting roller in operation, a finite element simulation of the continuous casting roller is performed;

[0007] Step 2, constructing a data set S according to the simulation results and working condition information obtained in step 1; establishing a continuous casting roller thermal stress prediction model based on K-fold cross validation and SVR to realize real-time prediction of temperature field and thermal stress during the operation of the continuous casting roller.

[0008] The present invention is also characterized in that:

[0009] The specific process of step 1 is as follows:

[0010] Step 1.1, respectively analyzing the heat conduction, heat convection and heat radiation of the heat balance model of the continuous casting roller;

[0011] Step 1.2, select the inner arc frame I in the continuous casting machine segment i j The continuous casting rolls of the roll group are taken as the simulation analysis object;

[0012] Step 1.3, performing finite element simulation modeling and parameter processing on the continuous casting roller selected in step 1.2;

[0013] Step 1.4, finite element simulation analysis of temperature / thermal stress of continuous casting roller.

[0014] The specific process of step 1.1 is:

[0015] The thermal conductivity calculus equation of continuous casting roller heat conduction is shown in formulas (1), (2) and (3):

[0016]

[0017] Where a is the thermal diffusivity of the continuous casting roll, W·m -2 ·min -1 , φ is the heat flux density of the continuous casting roller, W / m 3 , λ is the thermal conductivity, W·m -2 ·K -1 , A is the heat transfer area, m 2 , t is temperature, K, ρ is density of continuous casting roll, kg / m 3 , c is the specific heat capacity of the continuous casting roll, kJ·kg -1 ·K -1 , x, y, z are the coordinates on the heat conduction surface; the heat convection heat Q of the continuous casting roller is calculated as shown in formulas (4) and (5):

[0018] Q=hF(T W -T F ), T W >T F (4)

[0019] Q=hF(T F -T W ), T F >T W (5)

[0020] Where Q is the convective heat transfer of the continuous casting roller surface, W; h is the convective heat transfer coefficient of the continuous casting roller, W·m -2 ·K -1 , F is the convection heat transfer area of ​​the continuous casting roller, m 2 ; T W is the surface temperature of the continuous casting roller, K; T F is the cooling water / air temperature, K;

[0021] The radiation heat transfer rate Φ of the continuous casting roller, continuous casting billet and cooling water surface is calculated as shown in formula (6):

[0022] Φ=S·ε′·σ·T 4 (6)

[0023] Where Φ is the radiation heat transfer rate, W·m -2 ·min -1 ; S is the radiation surface area, m 2 ; σ is the radiation constant, W·m -2 ·K -4 , T is the thermodynamic temperature, K; ε′ is the emissivity of the material.

[0024] The specific process of step 1.3 is:

[0025] Step 1.3.1, establish the geometric model of the continuous casting roller, and add the material 42CrMo and its physical property parameters in the Engineering Data module;

[0026] Step 1.3.2, meshing the geometric model in step 1.3.1; there are M meshing nodes and m units in total;

[0027] Step 1.3.3, set boundary conditions for the meshed geometry model in step 1.3.2: thermal conductivity λ, W·m -2 ·K -1 ; Convective heat transfer coefficient h, W·m -2 ·K -1 ;Radiative heat transfer rateΦ, W·m -2 ·min -1 ;

[0028] Step 1.3.4, set the initial conditions of the continuous casting roller operation for the boundary conditions in step 1.3.3: set the displacement of the continuous casting roller unchanged, set the speed to v0, rad / s; keep the temperature of the continuous casting billet constant, and set the inlet temperature of the cooling water inside the continuous casting roller to be lower than T I , ℃; continuous casting billet drawing speed is v1, m / min; cooling water flow rate is v2, L / s.

[0029] The specific process of step 2 is:

[0030] Step 2.1, constructing a continuous casting roller thermal stress data set;

[0031] Step 2.2: Establish a continuous casting roller thermal stress prediction model based on K-fold cross validation and SVR.

[0032] The specific process of step 2.1 is:

[0033] Step 2.1.1, construct the sample index parameters of the continuous casting roller thermal stress data set;

[0034] Step 2.1.2, taking the simulation data and working condition information of the continuous casting roller as a data set, the data set is normalized.

[0035] In step 2.1.2, the normalized formula is as follows:

[0036]

[0037] Among them, σ is the mean difference of a certain indicator parameter of the sample; μ is the mean of a certain indicator parameter of the sample; x is the value of a certain indicator parameter in the sample.

[0038] The specific process of step 2.2 is:

[0039] Step 2.2.1, establish a continuous casting roller thermal stress prediction model based on SVR; the target formula of SVR optimization is:

[0040]

[0041] Among them, w is the weight vector, C is the regularization parameter, ε is the tolerance, ξ i is the relaxation factor, f(x) is the predicted value of thermal stress of continuous casting roller, y i is the true value of the thermal stress of the continuous casting roller, and n is the number of samples in the thermal stress data set of the continuous casting roller;

[0042] The Gaussian radial basis kernel function K(x i ,x j ), then f(x) in the SVR model is expressed as follows:

[0043]

[0044] in, a≥0 is the Lagrange multiplier, b is the threshold, x i ,x j The input data vectors of two samples i and j respectively represent the thermal stress of the continuous casting roller, and γ is the kernel function parameter;

[0045] Step 2.2.2, define the hyperparameter grid containing the SVR algorithm, including the penalty coefficient C, kernel function parameter γ, tolerance parameter ε, and kernel function type kernel. Combined with the continuous casting roller thermal stress dataset and the prediction model, set candidate values ​​for the hyperparameters: C∈{0.001,0.1,1,10,100}, γ∈{0.001,0.01,0.1,1}, ε∈{0.001,0.01,0.1}, kernel∈{RBF,poly,sigmoid};

[0046] Step 2.2.3, use the mean absolute error MAE, root mean square error RMSE and determination coefficient R 2 As the evaluation index of the thermal stress prediction model, MAE, RMSE and R 2 The calculation formulas are:

[0047]

[0048] Among them, t i is the actual value of thermal stress of continuous casting roller; i is the predicted value of the continuous casting roller thermal stress model; It is the average value of the actual value of thermal stress of continuous casting roller.

[0049] The beneficial effect of the present invention is that, in view of the problem that the surface and internal data of the continuous casting roller are difficult to directly measure when the continuous casting roller runs under complex working conditions, the present invention uses the three-dimensional CAD model of the continuous casting machine as a carrier, uses ANSYS to establish a continuous casting roller thermal stress simulation model, and simulates and obtains the surface and internal temperature and thermal stress of the continuous casting roller under different working conditions; a continuous casting roller thermal stress data set is constructed based on the continuous casting roller thermal stress simulation data and working condition information, and the K-fold cross validation is used to divide the data set to ensure full utilization of samples in model training and verification, and the advantages of SVR on small sample data sets are used to construct a continuous casting roller thermal stress prediction model based on K-fold cross validation and SVR, so as to achieve accurate prediction of its surface and internal temperature and thermal stress, and provide data support for continuous casting roller fatigue failure prediction. This method can overcome the problems of complex finite element simulation calculations and long running time. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 The continuous casting roller thermal stress prediction method of the present invention is used to analyze the continuous casting roller heating model;

[0051] Figure 2 It is a schematic structural diagram of a continuous casting roller used in the continuous casting roller thermal stress prediction method of the present invention;

[0052] Figures 3(a) to 3(j) It is the simulation result of the continuous casting roller temperature at 1050°C of the continuous casting billet in the continuous casting roller thermal stress prediction method of the present invention. DETAILED DESCRIPTION

[0053] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0054] Example 1

[0055] The method for predicting thermal stress of a continuous casting roll of the present invention specifically comprises the following steps:

[0056] Step 1, based on the thermal balance analysis of the continuous casting roller in operation, a finite element simulation of the continuous casting roller is performed;

[0057] Step 2, constructing a data set S by combining the simulation data of step 1.4 with the working condition information; establishing a continuous casting roller thermal stress prediction model based on K-fold cross validation and SVR to achieve real-time prediction of the temperature field and thermal stress during the operation of the continuous casting roller.

[0058] Example 2

[0059] The specific process of step 1 is:

[0060] Step 1.1, the continuous casting roller heat balance model is as follows Figure 1 As shown in the figure, due to the different heat transfer methods, the thermal stress analysis of the continuous casting roller during normal operation needs to be carried out separately from three aspects: heat conduction, heat convection and heat radiation.

[0061] The thermal conductivity calculus equation of continuous casting roller heat conduction is shown in formulas (1), (2) and (3):

[0062]

[0063] Where a is the thermal diffusivity of the continuous casting roll (W·m -2 ·min -1 ), φ is the heat flux density of the continuous casting roll (W / m 3 ), λ is the thermal conductivity (W·m -2 ·K -1 ), A is the heat transfer area (m 2 ), t is the temperature (K), ρ is the density of the continuous casting roll (kg / m 3 ), c is the specific heat capacity of the continuous casting roll (kJ·kg -1 ·K -1 ), x, y, z are the coordinates on the heat transfer surface, - indicates that the direction of heat transfer is opposite to the direction of temperature change rate.

[0064] The calculation of the heat convection heat Q of the continuous casting roller is shown in formulas (4) and (5):

[0065] Q=hF(T W -T F ), T W >T F (4)

[0066] Q=hF(T F -T W ), T F >T W (5)

[0067] Where Q is the convective heat transfer of the continuous casting roller surface (W), h is the convective heat transfer coefficient of the continuous casting roller (W·m -2 ·K -1 ), F is the convection heat transfer area of ​​the continuous casting roller (m 2 ), T W is the surface temperature of the continuous casting roll (K), T F is the cooling water / air temperature (K).

[0068] The radiation heat transfer rate Φ of the continuous casting roller, continuous casting billet and cooling water surface is calculated as shown in formula (6):

[0069] Φ=S·ε′·σ·T 4 (6)

[0070] Where Φ is the radiation heat transfer rate (W·m -2 ·min -1 ), S is the radiation surface area (m 2 ), σ is the radiation constant (W·m -2 ·K -4 )), T is the thermodynamic temperature (K), ε′ is the emissivity of the material.

[0071] Step 1.2, select Figure 2 The inner arc frame I in the continuous casting machine segment i shown j The continuous casting rolls of the roll group are taken as the simulation analysis objects.

[0072] Step 1.3, performing finite element simulation modeling and parameter processing on the continuous casting roller selected in step 1.2;

[0073] Reasonable simplification of the initial conditions of the continuous casting roller during operation:

[0074] (1) The temperature of the continuous casting billet is constant without temperature fluctuation.

[0075] (2) There are no defects in the internal materials of the continuous casting roller.

[0076] (3) The cooling water inlet temperature is constant.

[0077] (4) The contact stress between the continuous casting roller and the slab is not considered.

[0078] Step 1.4, finite element simulation analysis of temperature / thermal stress of continuous casting roller;

[0079] The temperature and thermal stress of the continuous casting roller during operation were simulated at different continuous casting billet temperatures T. The simulation results were analyzed to obtain the temperature and thermal stress data of the continuous casting roller under different working conditions, and the change law of its internal temperature and thermal stress was analyzed. The results showed that the temperature and thermal stress on the surface and inside of the continuous casting roller increased with the increase of the continuous casting billet temperature, and the overall temperature difference and thermal stress difference were significant.

[0080] Example 3

[0081] The specific process of step 1.3 is as follows:

[0082] Step 1.3.1, establish the geometric model of the continuous casting roller

[0083] The continuous casting roller is simplified to a certain extent, with an outer diameter of D (mm), a length of L (mm), and an inner diameter of d (mm). In the Engineering Data module, add the material 42CrMo and its physical properties.

[0084] Step 1.3.2, meshing the geometric model in step 1.3.1;

[0085] Before conducting finite element analysis of the temperature field and thermal stress of the continuous casting roller, the continuous casting roller model is meshed, with a total of M mesh nodes and m units.

[0086] Step 1.3.3, setting boundary conditions for the geometric model after meshing in step 1.3.2;

[0087] The boundary condition is to set the contact parameter information between the continuous casting roll and the continuous casting billet, mainly including the thermal conductivity λ (W·m -2 ·K -1 ), convective heat transfer coefficient h(W·m -2 ·K -1 ), radiation heat transfer rate Φ(W·m -2 ·min -1 ), in which the thermodynamic temperature (K) needs to be converted into Celsius temperature (℃) during the actual parameter setting process.

[0088] Step 1.3.4, setting the initial conditions for the continuous casting roller operation for the boundary conditions in step 1.3.3;

[0089] The displacement of the continuous casting roller is set to be constant, the speed is set to v0 (rad / s), the temperature of the continuous casting billet contact is kept constant, and the inlet temperature of the cooling water inside the continuous casting roller is set to be lower than T I (℃), continuous casting billet drawing speed is v1 (m / min), cooling water flow rate is v2 (L / s).

[0090] Example 4

[0091] The specific process of step 2 is:

[0092] Step 2.1, construction of continuous casting roller thermal stress data set;

[0093] Step 2.2, establish a continuous casting roller thermal stress prediction model based on K-fold cross validation and SVR.

[0094] Example 5

[0095] The specific process of step 2.1 is:

[0096] Step 2.1.1, constructing the sample index parameters of the data set. The thermal stress of the continuous casting roller is related to factors such as the continuous casting billet drawing speed, cooling water inlet temperature and cooling water flow rate. The sample index parameters of the continuous casting roller thermal stress data set are shown in Table 1.

[0097] Table 1 Parameters of the sample index of the continuous casting roller thermal stress data set

[0098]

[0099]

[0100] Step 2.1.2, normalize the data set consisting of the simulation data and working condition information of the continuous casting roller; in order to improve the model performance and reduce the influence of characteristic indicators of different magnitudes (a1-a4, t1-t8) on model training, the simulation data and working condition information of the continuous casting roller are used as the data set, and the Z-score normalization method is used to process it. The normalization processing formula is as follows:

[0101]

[0102] Among them, σ is the mean difference of a certain indicator parameter of the sample; μ is the mean of a certain indicator parameter of the sample; x is the value of a certain indicator parameter in the sample.

[0103] Example 6

[0104] The specific process of step 2.2 is:

[0105] Step 2.2.1, establishing a continuous casting roller thermal stress prediction model based on SVR;

[0106] SVR is to find a nonlinear mapping function in a given sample set. The input variables are mapped to a high-dimensional feature space, and then the SVR algorithm is used to calculate the optimal hyperplane function in the high-dimensional space to build a regression model, thereby solving the problem of samples that cannot be linearly regressed in the low-dimensional space. During the prediction process of the SVR algorithm, if the sample data is within the set interval band, the prediction is considered successful. To further improve the performance of the algorithm, a slack variable is added on this basis and i , the objective formula of SVR optimization is:

[0107]

[0108]

[0109] Among them, w is the weight vector, C is the regularization parameter, ε is the tolerance, ξ i is the relaxation factor, f(x) is the predicted value of thermal stress of continuous casting roller, yi is the true value of the thermal stress of the continuous casting roller, and n is the number of samples in the thermal stress data set of the continuous casting roller.

[0110] The Gaussian radial basis function (RBF) kernel function K(x i ,x j ), then f(x) in the SVR model can be expressed as follows:

[0111]

[0112] in, a≥0 is the Lagrange multiplier, b is the threshold, x i ,x j The two samples i and j represent the input data vectors of the thermal stress of the continuous casting roller respectively, and γ is the kernel function parameter.

[0113] Step 2.2.2, model parameter selection;

[0114] The thermal stress data set obtained through simulation is small in scale. SVR is combined with K-fold cross validation to make full use of limited sample data. The K-fold cross validation method is to divide the original data set N into K subsets. Each time the validation is performed, K-1 subsets are selected as training sets, and the remaining subset is used as the validation set. The hyperparameter grid containing the SVR algorithm is defined, including the penalty coefficient C, the kernel function parameter γ, the tolerance parameter ε, and the kernel function type kernel. Combined with the continuous casting roller thermal stress data set and the prediction model, a series of candidate values ​​are set for the hyperparameters: C∈{0.001,0.1,1,10,100}, γ∈{0.001,0.01,0.1,1}, ε∈{0.001,0.01,0.1}, kernel∈{RBF,poly,sigmoid}.

[0115] Step 2.2.3, prediction model performance evaluation;

[0116] The mean absolute error (MAE), root mean square error (RMSE) and determination coefficient (R-Square, R 2 ) is used as the evaluation index of the thermal stress prediction model, and the thermal stress prediction model is evaluated on the meta-test set. MAE represents the difference between the predicted value and the true value, and RMSE can keep the error result and the input data at the same level, which is convenient for observing the deviation between the predicted value and the true value. 2 Used to evaluate the fit between the predicted value and the true value, that is, the strength of the linear relationship between the predicted value and the true value, MAE, RMSE and R 2 The calculation formulas are:

[0117]

[0118] Among them, t i is the actual value of thermal stress of continuous casting roller; i is the predicted value of the continuous casting roller thermal stress model; It is the average value of the actual value of thermal stress of continuous casting roller.

[0119] Among the model evaluation indicators, the smaller the calculation results of MAE and RMSE, the higher the accuracy of the prediction model. 2 The evaluation range is [0, 1], R 2 The larger it is, the better the fitting effect of the prediction model is.

[0120] Example 7

[0121] The continuous casting roller of a company's 2150 continuous casting machine segment was taken as the research object. By analyzing the variation law of thermal stress of the continuous casting roller of the continuous casting machine segment, a sample of thermal stress data set of the continuous casting roller was constructed, and the thermal stress prediction model of the continuous casting roller based on SVR and K-fold cross validation was verified. The experimental steps are as follows:

[0122] Step 1, based on the thermal balance analysis of the continuous casting roller in operation, a finite element simulation of the continuous casting roller is performed;

[0123] Step 1.1, establishing a continuous casting roller geometric model;

[0124] The continuous casting roller is simplified to a certain extent, with an outer diameter D of 240 mm, a length L of 515 mm, and an inner diameter d of 30 mm. Add the material 42CrMo and its physical property parameters in the Engineering Data module.

[0125] Step 1.1.1, meshing the geometric model in step 1.1;

[0126] Before conducting finite element analysis of temperature field and thermal stress of continuous casting roller, the continuous casting roller model was meshed. The total number of mesh nodes was M, which was 273,387, and the total number of units was m, which was 193,160.

[0127] Step 1.1.2, setting boundary conditions for the geometric model after meshing in step 1.1.1;

[0128] The boundary condition is to set the contact between the continuous casting roll and the continuous casting billet, where the heat convection coefficient is λ, which is 11.63 (W·m -2 ℃ -1 ), the thermal conductivity is h is 5815 (W·m -2 ℃ -1 ), the operating environment temperature of the continuous casting roller is T R The temperature is 50℃, and the thermal radiation coefficient is Φ82.15(W·m -2·min -1 ).

[0129] Step 1.1.3, initializing the boundary settings in step 1.1.2;

[0130] The displacement of the continuous casting roller is set to be constant, the speed is set to v0 to be 0.024 rad / s, the contact temperature of the continuous casting billet is kept constant, and the inlet temperature of the cooling water inside the continuous casting roller is set to be lower than T I The temperature is 35°C, the continuous casting billet drawing speed v1 is 1.3m / min, and the cooling water flow rate v2 is 0.6L / s.

[0131] Step 1.2, finite element simulation analysis of temperature / thermal stress of continuous casting roller;

[0132] At different continuous casting billet temperatures T (T1=1050°C, T2=950°C, T3=850°C and T4=750°C), the temperature and thermal stress of the continuous casting roller during operation were simulated, and the simulation results were analyzed to obtain the temperature and thermal stress data of the continuous casting roller under different working conditions.

[0133] Step 1.2.1, take the continuous casting roller thermal stress simulation under the continuous casting billet at T1 = 1050℃ as an example for analysis, the specific parameters are adjusted: the continuous casting billet pulling speed is set to 1.3m / min, 1.4m / min, 1.5m / min, the cooling water inlet temperature is set to 33℃, 35℃, 37℃, the cooling water flow rate is set to 0.6L / s, 0.8L / s, 1.0L / s, the internal temperature and thermal stress simulation results are shown in Figures 3(a) to 3(j) shown.

[0134] (1) Analysis of temperature field and thermal stress field

[0135] ① From the temperature field cloud map in Figure 3(a), it can be seen that the temperature in the area in contact with the continuous casting billet is the highest, with a maximum temperature of 612.86°C; an obvious low-temperature area is formed near the cooling water channel, with a minimum temperature of 97.05°C; the temperature difference inside the casting roller is significant, as high as 515.81°C; the temperature change trend gradually decreases from the outer surface of the continuous casting roller to the center, showing a gradient change.

[0136] ② From the thermal stress field cloud map in Figure 3(b), it can be seen that the maximum thermal stress is 121.3MPa, the minimum is 37.32MPa, and the thermal stress difference is 83.98MPa; the thermal stress change trend is also gradually decreasing from the outer surface of the continuous casting roller to the center.

[0137] (2) Internal temperature and thermal stress analysis

[0138] In order to study the changing trend of the internal temperature and thermal stress of the continuous casting roller, the vertical radial l(0 ≤l≤240mm) was taken as the analysis object to study the variation of the internal temperature and thermal stress of the continuous casting roller along the radial direction (1 to 2 direction). The temperature of the cooling water channel was not extracted during the processing.

[0139] ① From the internal radial temperature cloud map in Figure 3(c), it can be seen that the maximum temperature reaches 580.2℃, while the minimum temperature is only 111.18℃, and the temperature difference is as high as 469.02℃.

[0140] ② From the internal radial temperature change curve in Figure 3 (d), it can be seen that the average temperature in the radial direction is 259.1759℃; in the radial front 9mm, that is, in the l∈[0,9)mm area, the temperature difference is as high as 193.78℃, and the temperature drop gradient is significant. The huge temperature difference is an important factor causing surface cracks on the continuous casting roller; in the radial l∈[9,81)mm area, the temperature drop gradient gradually decreases; in the radial l∈[81,105)mm area, due to the influence of cooling water on the internal temperature of the continuous casting roller, the temperature drop rate accelerates again; the temperature of the inner wall of the continuous casting roller (close to the cooling water channel) reaches the lowest value, and after passing through the cooling water channel, the temperature begins to rise steadily.

[0141] ③ From the radial thermal stress cloud map in Figure 3(e), we can see that the maximum thermal stress is 118.36MPa, the minimum is 39.022MPa, and the stress difference is as high as 79.338MPa.

[0142] ④ From the radial thermal stress change curve in Figure 3 (f), it can be seen that: the average value of the thermal stress value in the radial direction is 60.6002MPa;: in the radial l∈[0,9)mm area, the thermal stress difference is significant, reaching 24.859MPa; in the radial l∈[9,103)mm area, the thermal stress decrease gradient gradually tends to be stable; in the radial l∈[103,105]mm area, when approaching the continuous casting roller cooling water channel, the thermal stress increases slightly due to the rapid cooling effect of the cooling water; after passing through the cooling water channel, the thermal stress experiences a short decline phase and then gradually increases.

[0143] (3) Surface temperature and thermal stress analysis

[0144] In order to further explore the temperature and thermal stress variation characteristics of the continuous casting roller surface, the circumferential direction c (0≤c≤753.6mm) of the continuous casting roller surface was selected as the research object, and the variation law of the continuous casting roller surface temperature and thermal stress along the circumferential direction (1 to 2 counterclockwise) was studied.

[0145] ① From the circumferential temperature cloud diagram of the continuous casting roller surface in Figure 3(g), it can be seen that the maximum temperature is 612.69℃, the minimum temperature is 282.52℃, and the temperature difference is 330.17℃.

[0146] ② From the circumferential temperature change curve of the continuous casting roller in Figure 3 (h), it can be seen that the average value of the continuous casting roller surface in the circumferential direction is 326.8903℃; the circumferential temperature change of the continuous casting roller c shows a periodic change, and the starting point and the end point are both the contact point between the continuous casting roller and the continuous casting billet, that is, the highest point of the surface temperature; in the circumferential c∈[0,11)mm area, the temperature drops sharply, and the temperature difference is as high as 183.5℃; in the circumferential c∈[11,700)mm area, the temperature drop trend gradually slows down; in the circumferential c∈[700,753]mm area, when the continuous casting roller approaches the continuous casting billet again, it is affected by the thermal radiation of the continuous casting billet temperature, and the surface temperature of the continuous casting roller rises sharply, and the temperature difference is as high as 318.52℃; the temperature rises to the highest point again, completing a periodic change. Due to the significant difference in the surface temperature of the continuous casting roller, cracks and other faults are prone to occur on the surface.

[0147] ③ From the circumferential thermal stress cloud diagram of the continuous casting roller in Figure 3 (i), it can be seen that the maximum thermal stress is 121.3MPa, the minimum thermal stress is 58.976MPa, and the thermal stress difference is 62.324MPa.

[0148] ④ From the circumferential thermal stress variation curve of the continuous casting roller surface in Figure 3 (j), it can be seen that the average value of the circumferential c thermal stress is 67.5785MPa; the thermal stress on the outer surface of the continuous casting roller also shows periodic changes, which is similar to the trend of its surface temperature change; in the circumferential c∈[0,11)mm area, the thermal stress also drops sharply, and the difference reaches 24.227MPa; in the circumferential c∈[11,700)mm area, the thermal stress decrease trend gradually slows down and tends to be stable; in the circumferential c∈[700,753]mm area, due to the thermal radiation effect on the billet surface, the thermal stress increases accordingly, and the thermal stress difference reaches 24.227MPa.

[0149] Step 1.2.2, at three continuous casting billet temperatures of T2 = 950 °C, T3 = 850 °C and T4 = 750 °C, the simulation parameters are the same as those at 1050 °C, and the continuous casting rollers are simulated, and a total of 108 simulation data can be obtained.

[0150] Step 2, combining the continuous casting roller thermal stress simulation data of step 1.2.1 and step 1.2.2 with the working condition information, constructing a continuous casting roller thermal stress data set S, and establishing a continuous casting roller thermal stress prediction model based on K-fold cross validation and SVR;

[0151] Step 2.1, use the Z-score normalization method to preprocess the constructed continuous casting roller thermal stress data set S. After processing, the mean of the data set is 0 and the standard deviation is 1. Some data after sample normalization are shown in Table 2.

[0152] Table 2 Normalized data

[0153] No. <![CDATA[a1]]> <![CDATA[a2]]> … <![CDATA[t2]]> <![CDATA[t3]]> <![CDATA[t4]]> … <![CDATA[t7]]> <![CDATA[t8]]> 1 -1.3354 -1.2191 … -1.3502 -1.4818 -1.3176 … -0.7629 -1.3995 2 -1.3354 -1.2191 … -1.0246 -1.1934 -1.0438 … -0.9268 -1.0036 3 -1.3354 -1.2191 … -0.8497 -1.0340 -0.8945 … -1.0287 -0.7871 … … … … … 106 1.3354 1.2191 … 0.8981 0.8822 1.1252 … 1.7470 0.6578 107 1.3354 1.2191 … 1.3186 1.3029 1.4280 … 1.6134 1.2295 108 1.3354 1.2191 … 1.5418 1.5333 1.5914 … 1.5021 1.5283

[0154] Step 2.2, continuous casting roller thermal stress prediction model based on K-fold cross validation and SVR.

[0155] Step 2.2.1, establish a continuous casting roller thermal stress prediction model.

[0156] In the process of prediction by SVR algorithm, if the sample data is within the set interval band, it is considered to be a successful prediction. In order to further improve the performance of the algorithm, a relaxation variable is added on this basis and i , the target formula of SVR optimization is shown in the above formulas (10) and (11); the Gaussian radial basis function (RBF) kernel function K(x i ,x j ), then f(x) in the SVR model is as shown in the above formulas (12) and (13);

[0157] Step 2.2.2, model parameter setting. Use the hyperparameter optimization tool in the Scikit-learn library to traverse each parameter combination, use the 10-fold cross-validation method to divide and verify the data set, and select the optimal combination. After experiments and comparisons, the optimal hyperparameter combination is obtained: penalty coefficient C is 10, kernel function parameter γ is 10, tolerance parameter ε is 0.1, and kernel function type is RBF.

[0158] Step 2.2.3, thermal stress prediction model testing;

[0159] 45 sets of data are randomly selected from the simulation data set processed in step 2.1 and input into the continuous casting roller thermal stress prediction model with parameter setting completed in step 2.2.2 to obtain the predicted values, which are compared with the actual values ​​obtained by the continuous casting roller simulation.

[0160] Step 2.2.4, prediction model performance evaluation.

[0161] The evaluation index results of the continuous casting roller thermal stress prediction model are shown in Table 3. Although the RMSE value of the maximum thermal stress is relatively high, the MAE and RMSE values ​​of the minimum thermal stress, the internal radial average stress and the surface circumferential average thermal stress are low, indicating that the error between the predicted value of the model and the true value is the smallest, and the R2 values ​​are all greater than 0.9, indicating that the prediction results of the model have the best fitting effect.

[0162] Table 3 Evaluation index results

[0163]

[0164] In summary, the continuous casting roller thermal stress prediction model based on K-fold cross validation and SVR can show high prediction accuracy and fitting effect in the prediction of continuous casting roller thermal stress, indicating that this method can relatively accurately and real-time predict the temperature field and thermal stress distribution of the continuous casting roller during its working process.

[0165] The continuous casting roller thermal stress prediction method of the present invention uses finite element simulation, support vector regression (SVR) and K-fold cross validation method to perform continuous casting roller temperature / thermal stress analysis, finite element simulation modeling, and temperature field / thermal stress prediction, so as to achieve real-time and accurate prediction of the surface and internal temperature and thermal stress of the continuous casting roller; through the internal thermal stress distribution of the continuous casting roller, combined with the continuous casting roller working condition information, it can provide a basis and auxiliary data support for the continuous casting roller failure fault decision-making, and provide a basis for the preventive maintenance and overhaul of the continuous casting roller, so as to improve the continuous casting production efficiency and stability, reduce resource waste, and reduce production costs.

Claims

1. A method for predicting thermal stress of a continuous casting roller, characterized in that: The specific steps include: Step 1, based on the thermal balance analysis of the continuous casting roller in operation, a finite element simulation of the continuous casting roller is performed; Step 2, constructing a data set S according to the simulation results and working condition information obtained in step 1; A continuous casting roller thermal stress prediction model based on K-fold cross validation and SVR is established to realize real-time prediction of temperature field and thermal stress during the operation of continuous casting rollers.

2. The method for predicting thermal stress of a continuous casting roll according to claim 1, characterized in that: The specific process of step 1 is as follows: Step 1.1, respectively analyzing the heat conduction, heat convection and heat radiation of the heat balance model of the continuous casting roller; Step 1.2, select the inner arc frame I in the continuous casting machine segment i j The continuous casting rolls of the roll group are taken as the simulation analysis object; Step 1.3, performing finite element simulation modeling and parameter processing on the continuous casting roller selected in step 1.2; Step 1.4, finite element simulation analysis of temperature / thermal stress of continuous casting roller.

3. The method for predicting thermal stress of a continuous casting roll according to claim 2, characterized in that: The specific process of step 1 is as follows: The specific process of step 1.1 is as follows: The thermal conductivity calculus equation of continuous casting roller heat conduction is shown in formulas (1), (2) and (3): Where a is the thermal diffusivity of the continuous casting roll, W·m -2 ·min -1 , φ is the heat flux density of the continuous casting roller, W / m 3 , λ is the thermal conductivity, W·m -2 ·K -1 , A is the heat transfer area, m 2 , t is temperature, K, ρ is the density of the continuous casting roll, kg / m 3 , c is the specific heat capacity of the continuous casting roll, kJ·kg -1 ·K -1 , x, y, z are the coordinates on the heat conduction surface; the heat convection heat Q of the continuous casting roller is calculated as shown in formulas (4) and (5): Q=hF(T W -T F ), T W >T F (4) Q=hF(T F -T W ), T F >T W (5) Where Q is the convective heat transfer of the continuous casting roller surface, W; h is the convective heat transfer coefficient of the continuous casting roller, W·m -2 ·K -1 , F is the convection heat transfer area of ​​the continuous casting roller, m 2 ; T W is the surface temperature of the continuous casting roller, K; T F is the cooling water / air temperature, K; The radiation heat transfer rate Φ of the continuous casting roller, continuous casting billet and cooling water surface is calculated as shown in formula (6): Φ=S·ε′·σ·T 4 (6) Where Φ is the radiation heat transfer rate, W·m -2 ·min -1 ; S is the radiation surface area, m 2 ; σ is the radiation constant, W·m -2 ·K -4 , T is the thermodynamic temperature, K; ε′ is the emissivity of the material.

4. The method for predicting thermal stress of continuous casting rolls according to claim 3, characterized in that: The specific process of step 1 is as follows: The specific process of step 1.3 is as follows: Step 1.3.1, establish the geometric model of the continuous casting roller, and add the material 42CrMo and its physical property parameters in the Engineering Data module; Step 1.3.2, meshing the geometric model in step 1.3.1; there are M meshing nodes and m units in total; Step 1.3.3, set boundary conditions for the meshed geometry model in step 1.3.2: thermal conductivity λ, W·m -2 ·K -1 ; Convective heat transfer coefficient h, W·m -2 ·K -1 ;Radiative heat transfer rateΦ, W·m -2 ·min -1 ; Step 1.3.4, set the initial conditions of the continuous casting roller operation for the boundary conditions in step 1.3.3: set the displacement of the continuous casting roller unchanged, set the speed to v0, rad / s; keep the temperature of the continuous casting billet constant, and set the inlet temperature of the cooling water inside the continuous casting roller to be lower than T I , ℃; continuous casting billet drawing speed is v1, m / min; cooling water flow rate is v2, L / s.

5. The method for predicting thermal stress of continuous casting rolls according to claim 4, characterized in that: The specific process of step 1 is as follows: The specific process of step 2 is as follows: Step 2.1, constructing a continuous casting roller thermal stress data set; Step 2.2: Establish a continuous casting roller thermal stress prediction model based on K-fold cross validation and SVR.

6. The method for predicting thermal stress of continuous casting rolls according to claim 5, characterized in that: The specific process of step 1 is as follows: The specific process of step 2.1 is as follows: Step 2.1.1, construct the sample index parameters of the continuous casting roller thermal stress data set; Step 2.1.2, taking the simulation data and working condition information of the continuous casting roller as a data set, the data set is normalized.

7. The method for predicting thermal stress of continuous casting rolls according to claim 6, characterized in that: In step 2.1.2, the normalized formula is as follows: Among them, σ is the mean difference of a certain indicator parameter of the sample; μ is the mean of a certain indicator parameter of the sample; x is the value of a certain indicator parameter in the sample.

8. The method for predicting thermal stress of continuous casting rolls according to claim 6, characterized in that: The specific process of step 2.2 is as follows: Step 2.2.1, establish a continuous casting roller thermal stress prediction model based on SVR; the target formula of SVR optimization is: Among them, w is the weight vector, C is the regularization parameter, ε is the tolerance, ξ i is the relaxation factor, f(x) is the predicted value of thermal stress of continuous casting roller, y i is the true value of the thermal stress of the continuous casting roller, and n is the number of samples in the thermal stress data set of the continuous casting roller; The Gaussian radial basis kernel function K(x i ,x j ), then f(x) in the SVR model is expressed as follows: in, a≥0 is the Lagrange multiplier, b is the threshold, x i ,x j The input data vectors of two samples i and j respectively represent the thermal stress of the continuous casting roller, and γ is the kernel function parameter; Step 2.2.2, define the hyperparameter grid containing the SVR algorithm, including the penalty coefficient C, kernel function parameter γ, tolerance parameter ε, and kernel function type kernel. Combined with the continuous casting roller thermal stress dataset and the prediction model, set candidate values ​​for the hyperparameters: C∈{0.001,0.1,1,10,100}, γ∈{0.001,0.01,0.1,1}, ε∈{0.001,0.01,0.1}, kernel∈{RBF,poly,sigmoid}; Step 2.2.3, use the mean absolute error MAE, root mean square error RMSE and determination coefficient R 2 As the evaluation index of the thermal stress prediction model, MAE, RMSE and R 2 The calculation formulas are: Among them, t i is the actual value of thermal stress of continuous casting roller; i is the predicted value of the continuous casting roller thermal stress model; It is the average value of the actual value of thermal stress of continuous casting roller.

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