An Optimization Method for the Temperature Rise Uniformity of Induction Heating of Frozen Coal in Trains Based on Response Surface Method and Multi-parameter Optimization

Abstract

The present invention relates to the technical field of optimizing the temperature rise uniformity of electromagnetic heating, and discloses an optimization method for the temperature rise uniformity of induction heating of frozen coal in trains based on the response surface method and multi-parameter optimization. By establishing a refined electromagnetic-thermal coupling model including a carriage, a bogie, an induction coil, and an air domain, a second-order polynomial response surface model is established using the central composite experimental design. An axisymmetric coil layout based on the first-term constant parametric linear dynamic tolerance sequence is designed, and the NSGA-II multi-objective optimization algorithm is used to minimize the temperature sample standard deviation and maximize the average temperature with the temperature uniformity represented by the sample standard deviation under the constraint of the thawing temperature, and Pareto optimization is carried out. Finally, the optimal parameter combination is determined through the TOPSIS decision-making method. The invention of this application is verified by simulation, and this method can effectively improve the temperature field uniformity of electromagnetic heating on the inner surface of the frozen coal carriage, providing a theoretical basis for engineering applications.

Description

Technical Field

[0001] The present invention belongs to the technical field of optimizing the temperature rise uniformity of electromagnetic heating, and particularly relates to an optimization method for the temperature rise uniformity of induction heating of frozen coal in trains based on the response surface method and multi-parameter optimization. Background Art

[0002] In winter, railway coal is prone to freezing. Especially when the moisture content is higher than 8%, the freezing adhesion strength is great. After coal washing in China, the residual moisture is 6.5% - 14%, which is easy to form frozen coal and difficult to clean. After the operation of the car dumper in winter, 7% - 14% of frozen coal remains, which requires a large amount of manual cleaning, with low efficiency, affecting the enterprise benefits and vehicle turnover. Moreover, the cleaning of frozen coal depends on manual labor, with great potential safety hazards. Some residual frozen coal may also cause partial load of the carriage, posing a risk of overturning.

[0003] To solve the problems of difficult cleaning and low efficiency of frozen coal in trains, the industry has proposed the technology of using electromagnetic induction heating to solve frozen coal. The electromagnetic induction heating method generates an alternating electromagnetic field to generate eddy currents, so as to generate heat in the carriage, thereby achieving the heating effect and thawing the frozen coal. This method of thawing frozen coal has high heating efficiency, controllable temperature rise, and high safety. However, due to the structure of the carriage, the temperature rise uniformity of induction heating is poor, and there are problems of local overheating and local frozen coal that cannot be thawed.

[0004] Therefore, this application proposes an optimization method for the temperature rise uniformity of induction heating of frozen coal in trains based on the response surface method and multi-parameter optimization. Summary of the Invention

[0005] Aiming at the deficiencies of the prior art, the present invention provides an optimization method for the temperature rise uniformity of induction heating of frozen coal in trains based on the response surface method and multi-parameter optimization, which solves the problems in the prior art that due to the structure of the carriage, the temperature rise uniformity of induction heating is poor, and there are problems of local overheating and local frozen coal that cannot be thawed.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] An optimization method for the temperature rise uniformity of induction heating of frozen coal in trains based on the response surface method and multi-parameter optimization, the optimization method includes the following steps:

[0008] S1. Determine the parameters required for modeling and the material parameters required according to the train carrying frozen coal and the induction heating coil;

[0009] S2. Establish a second-order polynomial response surface model by using the central composite experimental design to generate a series of experimental parameter combinations;

[0010] S3. Establish an equi-proportion geometric model according to the parameters and experimental parameter combinations determined in step S1 and step S2;

[0011] S4. Divide meshes for all geometric models with equal proportions;

[0012] S5. Add the corresponding materials of each part of the model to the material parameters obtained in Step 1, set the magnetic field boundary conditions and the temperature field boundary conditions, set temperature probes equidistantly on the inner surface of the carriage, perform magneto-thermal coupling calculations on the models under all combinations of test parameters, and obtain the sequence of temperature values after heating ;

[0013] S6. Calculate the average temperature and the sample standard deviation based on the sequence of temperature values, and fit a second-order polynomial response surface model on this basis;

[0014] S7. Test the quality of the obtained second-order polynomial response surface model through analysis of variance;

[0015] S8. Evaluate the fitting degree of the second-order polynomial response surface model after testing according to the adjusted coefficient of determination;

[0016] S9. Take the second-order polynomial response surface model obtained after testing in Step S7 as the objective function, and obtain the Pareto solution set through an optimization algorithm;

[0017] S10. Obtain the optimal decision-making solution based on the TOPSIS method;

[0018] S11. Take the obtained optimal decision-making solution as the input variable, verify the fitting accuracy of the second-order polynomial response surface model through simulation calculations, and obtain the optimized heating effect.

[0019] As a further solution of the present invention: Step S2 is specifically that the induction heating coils are divided into 2n - 1 groups, and a longitudinal magnetic flux layout is adopted. Taking the central coil as the central axis, the two sides are in an axisymmetric shape. The distance between each group of coils is wide in the middle and narrow on both sides; each group of coils is numbered. The central coil is numbered 1, and the numbers are sequentially numbered from 1 to n outward. The coils on the left and right sides that are symmetric have the same numbers. The distance between each group of induction heating coils is arranged according to the first-term constant parametric linear dynamic tolerance sequence: Set, di is the distance between each group of induction heating coils, with the unit of m, i is the coil number, is the distance between the No. 1 coil and the No. 2 coil, with the unit of m, Fixed, d is the distance decreased each time, that is, the tolerance, with the unit of m, d The value of is variable; select the response surface method with the coil width, tolerance d , the current in the coil and the current frequency as the input variables, determine their numerical ranges, and establish a second-order polynomial response surface model using the central composite experimental design to generate a series of test parameter combinations.

[0020] As a further solution of the present invention: the equi-proportion geometric model in step S4 includes a train car body geometric model, a bogie geometric model, an induction heating coil model, and an air domain model. Free tetrahedral meshes are divided for all the equi-proportion geometric models, and then boundary layer meshes are divided for the train car body geometric model and the bogie geometric model. The thickness of the boundary layer mesh is set according to the formula where, l is the thickness of the boundary layer mesh, α is the conductivity of the material to be heated, is the vacuum permeability, is the permeability of the induction heating coil material, f is the frequency of the current in the induction heating coil.

[0021] As a further solution of the present invention: step S6 is specifically based on the temperature value sequence , and the sample standard deviation of each probe temperature is calculated according to the formula ; where, is the average value of each temperature value in the temperature value sequence. The above sample standard deviation represents the temperature uniformity of the inner surface of the car body after heating. The smaller the sample standard deviation , the better the temperature uniformity. Taking the average temperature of the inner surface of the car body and the sample standard deviation as output variables, a second-order polynomial response surface model is fitted with all input variables and output variables.

[0022] As a further solution of the present invention: step S7 is specifically to test the quality of the obtained second-order polynomial response surface model through variance analysis. In the variance analysis, for the terms with a p-value less than 0.05, they can be considered as significant terms. The significant terms are retained, and the non-significant terms are removed to form the second-order polynomial response surface model after testing.

[0023] As a further solution of the present invention: step S8 is specifically to evaluate the fitting degree of the second-order polynomial response surface model after testing according to the corrected determination coefficient . The closer the value of the corrected determination coefficient is to 1, the higher the fitting degree of the second-order polynomial response surface model.

[0024] As a further solution of the present invention: step S9 is specifically to use the sample standard deviation of the temperature value sequence as the evaluation index of the temperature rise uniformity; with the condition that the average temperature of the inner surface of the car body reaches the lowest thawing temperature of the frozen coal, and the standard deviation of each probe temperature as the optimization target, it is required that the sample standard deviation is as small as possible while the average temperature of the inner surface of the car body is as high as possible. With the coil width, the distance between the No. 1 coil and the No. 2 coil , current, with the current frequency as the optimization variable, configure the parameters of the multi-objective optimization algorithm to build a mathematical model, adopt the NSGA-II optimization algorithm, use the second-order polynomial response surface model obtained after verification in step S7 as the objective function, and obtain the Pareto solution set through the optimization algorithm.

[0025] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0026] 1. The present invention arranges and designs the coil spacing according to the first-term constant parametric linear dynamic tolerance sequence, effectively improving the temperature rise uniformity of induction heating, and solving the problems of local overheating and inability to thaw local frozen coal existing in the prior art.

[0027] 2. The present invention adopts a structure optimization design based on the response surface method. This method combines mathematical methods and statistical methods to model and analyze the response affected by multiple variables, improving the design efficiency and effect.

[0028] 3. The present invention uses a multi-objective optimization algorithm to optimize the temperature rise uniformity. This method can optimize with the average temperature of the inner surface of the carriage and the sample standard deviation as the objectives to obtain the Pareto solution set, and then make a decision using the TOPSIS method. Under the condition of balancing the weights of the average temperature and the sample standard deviation, the optimal parameter combination is obtained. Description of the Drawings

[0029] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on the structures shown in these drawings. Among them:

[0030] Figure 1 is the flowchart of the present invention;

[0031] Figure 2 is the structural diagram of the train model in the embodiment of the present invention;

[0032] Figure 3 is the structural diagram of the coil arrangement in the embodiment of the present invention;

[0033] Figure 4 is the layout diagram of the temperature probes in the quarter model in the embodiment of the present invention;

[0034] Figure 5 is the Pareto solution set diagram obtained in the embodiment of the present invention;

[0035] Figure 6 is the comparison diagram of the temperature uniformity before and after optimization in the embodiment of the present invention. Detailed implementation manners

[0036] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0037] Embodiment

[0038] Please refer to Figure 1 As shown, the present invention provides an optimization method for the temperature rise uniformity of the induction heating of frozen coal on trains based on the response surface method and multi-parameter optimization. The optimization method includes the following steps:

[0039] Step 1: Determine the parameters required for modeling and the material parameters required according to the train carrying frozen coal and the induction heating coil.

[0040] Step 2: The induction heating coil is divided into 2n - 1 groups. In this embodiment, the induction heating coil has a total of 500 turns, with 20 turns in each group, divided into 25 groups, and n is 13; a longitudinal magnetic flux layout is adopted, with the central coil as the central axis, and the two sides are in an axisymmetric shape. The distance between each group of coils is wide in the middle and narrow on both sides; each group of coils is numbered. The central coil is numbered 1, and the numbers are sequentially numbered from 1 to 13 outward. The coils on the left and right sides that are symmetric have the same number. The distance between each group of induction heating coils follows the first-term constant parametric linear dynamic tolerance sequence: Set di is the distance between each group of induction heating coils, with the unit of m, i is the coil number, is the distance between the No. 1 coil and the No. 2 coil, with the unit of m, is fixed. In this embodiment is 0.4m; d is the distance decreased each time, that is, the tolerance, with the unit of m, d The value of is variable; in this embodiment, the coil arrangement structure is as Figure 2 shown; select the response surface method with the coil width, tolerance d , the current in the coil and the current frequency as input variables, determine their numerical ranges, and conduct a central composite experimental design to generate a series of experimental parameter combinations; the variable range of the response surface experimental design variables in this embodiment is shown in Table 1 below:

[0041]

[0042] The response surface experimental design is shown in Table 2 below:

[0043] ;

[0044] Step 3: Establish a geometric model in proportion according to the parameters and experimental parameter combinations determined in Step 1 and Step 2. The geometric model in proportion includes a geometric model of a train carbody, a geometric model of a bogie, an induction heating coil model, and an air domain model. In this embodiment, the geometric model of the train carbody and the geometric model of the bogie are as Figure 3 shown;

[0045] Step 4: Divide free tetrahedral meshes for all geometric models in proportion, and then divide boundary layer meshes for the geometric model of the train carbody and the geometric model of the bogie. The thickness of the boundary layer mesh is set according to the formula ; In the formula, l is the thickness of the boundary layer mesh, α is the conductivity of the material to be heated, is the vacuum permeability, is the permeability of the induction heating coil material, f is the frequency of the current in the induction heating coil. In this embodiment, α is , is 1, is 1;

[0046] Step 5: Add corresponding materials to each part of the model according to the material parameters obtained in Step 1, set the magnetic field boundary conditions and the temperature field boundary conditions, set temperature probes equidistantly on the inner surface of the carbody, perform magneto-thermal coupling calculation on the entire model, and obtain a sequence of temperature values after heating ; In this embodiment, the layout of the temperature probes is as Figure 4 shown, and the simulation results of the magneto-thermal coupling calculation are shown in Table 2 above;

[0047] Step 6: Based on the sequence of temperature values , calculate the sample standard deviation of the temperature of each probe according to the formula ; In the formula, is the average value of each temperature value in the sequence of temperature values. The above sample standard deviation represents the temperature uniformity of the inner surface of the carbody after heating. The smaller the sample standard deviation , the better the temperature uniformity; Take the average temperature of the inner surface of the carbody and the sample standard deviation as output variables, and fit a second-order polynomial response surface model with all input variables and output variables;

[0048] Step 7: Test the quality of the obtained second-order polynomial response surface model through analysis of variance. In the analysis of variance, for the terms with a p-value less than 0.05, they can be considered significant terms. Retain the significant terms and remove the non-significant terms to form the tested second-order polynomial response surface model; In this embodiment The terms with a p-value less than 0.05 in the analysis of variance results are shown in Table 3 below, and the terms with a p-value less than 0.05 in the σ analysis of variance results are shown in Table 4 below:

[0049]

[0050]

[0051] According to Tables 3 and 4, in the results of the analysis of variance of the average temperature and the sample standard deviation l and d and I and f and If and and are the terms with p-values less than 0.05. The obtained second-order polynomial response surface model is composed of these terms and the constant term. The specific second-order polynomial response surface model is shown in Table 5 below:

[0052] ;

[0053] Step 8: Evaluate the goodness of fit of the second-order polynomial response surface model after testing according to the corrected determination coefficient . The closer the value of the corrected determination coefficient is to 1, the higher the goodness of fit of the second-order polynomial response surface model. In this embodiment, the evaluation result of the corrected determination coefficient is shown in Table 6 below:

[0054]

[0055] According to Table 6, the corrected determination coefficients of the average temperature and the sample standard deviation are 0.9758 and 0.9666 respectively, which are close to 1, indicating that the obtained second-order polynomial response surface model has a high fitting accuracy;

[0056] Step 9: Use the sample standard deviation of the temperature value sequence as the evaluation index for the temperature rise uniformity. With the average temperature of the inner surface of the carriage reaching the lowest thawing temperature of the frozen coal as the constraint condition, and the standard deviation of the temperatures of each probe as the optimization objective, it is required that the sample standard deviation is as small as possible while the average temperature of the inner surface of the carriage is as high as possible. Using the coil width, the distance between Coil 1 and Coil 2 , the current, and the current frequency as the optimization variables, configure the parameters of the multi-objective optimization algorithm to construct a mathematical model, adopt the NSGA-II optimization algorithm, use the second-order polynomial response surface model obtained in step S7 as the objective function, and obtain the Pareto solution set through the optimization algorithm. In this embodiment, the Pareto solution set is as shown in Figure 5 . The parameter values of the multi-objective optimization algorithm are set as shown in Table 7 below:

[0057] ;

[0058] Step 10: Based on the TOPSIS method, obtain the optimal decision solution. In this embodiment, the weight ratio of the average temperature of the inner surface of the carriage to the sample standard deviation is set to 0.1∶0.9;

[0059] Step 11: Take the obtained optimal decision solution as the input variable, verify the fitting accuracy of the second-order polynomial response surface model through simulation calculation, and obtain the optimized heating effect. The design results of the optimal decision solution in this embodiment are shown in Table 8 below:

[0060]

[0061] According to Table 8, the difference between the response value and the simulation result is small. The error of the average temperature is 1.64%, and the error of the sample standard deviation is 2.59%. Compared with the original model without coil design under the same current value and current frequency conditions, the relative standard deviation σ after optimization is reduced to 39.43% of the original, and the temperature uniformity is significantly improved;

[0062] Specifically, the present invention establishes a refined electromagnetic-thermal coupling model including a carriage, a bogie, induction coils, and an air domain, constructs a second-order polynomial response surface model with the width of each group of coils, the decreasing tolerance of the coil spacing, the current frequency, and the current as the input, and the temperature uniformity and the average temperature of the inner surface of the carriage as the output by using the central composite experimental design; designs an axisymmetric coil layout based on the first-term constant parameterized linear dynamic tolerance sequence, combines the boundary layer grid adaptive division technology to improve the calculation accuracy, and uses the NSGA-II multi-objective optimization algorithm to minimize the temperature sample standard deviation and maximize the average temperature as the objectives for optimization under the constraint of meeting the thawing temperature, obtains the Pareto solution set, and finally determines the optimal parameter combination through the TOPSIS decision method. After simulation verification, the comparison of the electromagnetic heating simulation temperature uniformity before and after optimization is as Figure 6 shown. This method can effectively improve the uniformity of the electromagnetic heating temperature field on the inner surface of the frozen coal carriage, providing a theoretical basis for engineering applications.

[0063] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A method for optimizing the uniformity of temperature rise of frozen coal induction heating on trains based on response surface methodology and multi-parameter optimization, characterized in that: The optimization method includes the following steps: S1. Determine the parameters required for modeling and the required material parameters according to the train carrying frozen coal and the induction heating coil; S2, using central composite experimental design to establish a second-order polynomial response surface model and generate a series of experimental parameter combinations; S3, establishing a proportional geometric model according to the parameters determined in step S1 and step S2 and the test parameter combination; S4, meshing all proportional geometric models; S5. Add the corresponding materials of each part of the model to the material parameters obtained in step 1, set the magnetic field boundary conditions and temperature field boundary conditions, set temperature probes at equal distances on the inner surface of the carriage, perform magnetic-thermal coupling calculations on the models under all test parameter combinations, and obtain the temperature value sequence after heating. ; S6, calculating the average temperature and the sample standard deviation according to the temperature value sequence, and fitting a second-order polynomial response surface model on this basis; S7. The quality of the obtained second-order polynomial response surface model was tested by variance analysis; S8. Evaluate the goodness of fit of the second-order polynomial response surface model after testing based on the corrected determination coefficient; S9, using the second-order polynomial response surface model obtained in step S7 as the objective function, and obtaining a Pareto solution set through an optimization algorithm; S10. Based on the TOPSIS method, the optimal decision solution is obtained; S11, using the obtained optimal decision solution as an input variable, verifying the fitting accuracy of the second-order polynomial response surface model through simulation calculation, and obtaining the optimized heating effect; Step S9 specifically includes converting the temperature value sequence The sample standard deviation is used as the evaluation index of temperature rise uniformity; the average temperature of the inner surface of the carriage reaches the minimum thawing temperature of the frozen coal as a constraint condition, and the standard deviation of each probe temperature is used as the optimization target. The sample standard deviation is required to be as small as possible while the average temperature of the inner surface of the carriage is as high as possible. The coil width, the spacing between coil 1 and coil 2 , current, and current frequency are optimized variables, and the multi-objective optimization algorithm parameters are configured to build a mathematical model. The NSGA-II optimization algorithm is used, and the second-order polynomial response surface model after inspection obtained in step S7 is used as the objective function. The Pareto solution set is obtained through the optimization algorithm.

2. A method for optimizing the uniformity of temperature rise of frozen coal induction heating in trains based on response surface methodology and multi-parameter optimization according to claim 1, characterized in that: Step S2 specifically includes dividing the induction heating coils into 2n-1 groups, adopting a longitudinal magnetic flux layout, taking the central coil as the central axis, and the two sides are axially symmetrical, and the spacing between each group of coils is wide in the middle and narrow on both sides; each group of coils is numbered, the central coil is numbered 1, and the numbering is sequentially from 1 to n outward, the symmetrical coils on the left and right sides have the same number, and the spacing between each group of induction heating coils is in accordance with the first constant parameterized linear dynamic tolerance sequence: set up, d is the distance between each set of induction heating coils, in m, i Number the coils, is the distance between coil 1 and coil 2, in m. fixed, d is the decreasing distance each time, i.e. the tolerance, in m. d The value of is variable; Select response surface methodology to use coil width, tolerance d , the coil current and current frequency are taken as input variables, their numerical ranges are determined, and a second-order polynomial response surface model is established using central composite experimental design to generate a series of experimental parameter combinations.

3. A method for optimizing the uniformity of temperature rise of frozen coal induction heating in trains based on response surface methodology and multi-parameter optimization according to claim 1, characterized in that: The proportional geometric model in step S4 includes a train carriage geometric model, a bogie geometric model, an induction heating coil model and an air domain model. Free tetrahedral meshes are divided for all proportional geometric models, and boundary layer meshes are divided for the train carriage geometric model and the bogie geometric model. The boundary layer mesh thickness is calculated according to the formula Setting, where l is the boundary layer mesh thickness, is the conductivity of the heated material, is the vacuum permeability, is the magnetic permeability of the induction heating coil material, f is the frequency of the current in the induction heating coil.

4. A method for optimizing the uniformity of temperature rise of frozen coal induction heating in trains based on response surface methodology and multi-parameter optimization according to claim 1, characterized in that: Step S6 is specifically based on the temperature value sequence , according to the formula Calculate the sample standard deviation of each probe temperature; where, is the average value of each temperature value in the temperature value sequence, with the above sample standard deviation Indicates the uniformity of the surface temperature in the heated cabin, sample standard deviation The smaller it is, the better the temperature uniformity; the average surface temperature of the carriage and the sample standard deviation are taken as output variables, and a second-order polynomial response surface model is fitted with all input variables and output variables.

5. A method for optimizing the uniformity of temperature rise of frozen coal induction heating in trains based on response surface methodology and multi-parameter optimization according to claim 1, characterized in that: Step S7 specifically tests the quality of the obtained second-order polynomial response surface model through variance analysis. In the variance analysis, items with p-values ​​less than 0.05 can be considered as significant items. The significant items are retained, and the non-significant items are removed to form the second-order polynomial response surface model after the test.

6. A method for optimizing the uniformity of temperature rise of frozen coal induction heating in trains based on response surface methodology and multi-parameter optimization according to claim 1, characterized in that: Step S8 is specifically to correct the determination coefficient Evaluate the goodness of fit of the tested second-order polynomial response surface model and correct the coefficient of determination The closer the value is to 1, the better the fit of the second-order polynomial response surface model.

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