Structure optimization method for protection structure of superconducting cable, protection structure of superconducting cable, and superconducting coil

Abstract

The invention provides a structure optimization method of a protection structure of a superconducting cable, the protection structure of the superconducting cable and a superconducting coil, and the structure optimization method comprises the steps: building a finite element simulation model of the protection structure, and determining a parameter range of design variables, sampling to obtain a plurality of first sample data sets including coil box thickness data and protective layer thickness data, and performing coupling analysis on the finite element simulation model to obtain a first stress result corresponding to each first sample data set, and constructing a response surface model based on the plurality of first sample data sets and the first stress result corresponding to each first sample data set, and defining an optimization equation and performing structure optimization on the protection structure by taking the sum of maximized stress margins as an optimization target in a constraint condition range so as to obtain a final protection structure optimization scheme. The optimization method provided by the invention has high optimization efficiency and can cover the global situation, so that the optimization result precision is improved.

Description

Technical Field

[0001] This invention relates to the field of superconducting coil technology, and in particular to a method for optimizing the structure of a protective structure for a superconducting cable, the protective structure of the superconducting cable, and a superconducting coil. Background Technology

[0002] A superconducting coil is a coil structure made by utilizing the zero resistance and perfect diamagnetism of a superconductor under specific conditions (low temperature, low pressure, etc.). A superconducting coil consists of a superconducting cable and a protective structure for the cable. This protective structure includes components such as the coil housing, insulation layer, and protective layer. The thickness of each part of the protective structure directly affects the stress level and stability of the overall structure. For example, if the coil housing is too thick, the design space for the insulation and protective layers will be compressed, potentially causing the stress in the insulation and protective layers to exceed the allowable stress. Conversely, if the coil housing is too thin, the stress in the coil housing will exceed its allowable stress. Therefore, how to rationally set the thickness of each part within a limited space is crucial for the overall structure.

[0003] Existing technologies employ exhaustive search and orthogonal methods to obtain the optimal stress distribution of the protection structure of superconducting cables. However, the exhaustive search method suffers from low optimization efficiency, massive computational load when multiple design variables are involved, and potential loss of optimal solutions due to data discretization. Similarly, the orthogonal method also suffers from massive computational load due to large sample sizes when multiple design variables are involved, and low accuracy of the optimal solution. Therefore, existing structural optimization methods for the protection structure of superconducting cables suffer from low optimization efficiency and difficulty in covering the entire spectrum in complex optimization scenarios with multiple design variables and constraints, resulting in low accuracy of the optimization results. Summary of the Invention

[0004] The purpose of this invention is to solve the problems of low optimization efficiency and difficulty in covering the whole in complex optimization scenarios with multiple design variables and multiple constraints in the existing structural optimization methods for obtaining the protection structure of superconducting cables, resulting in low accuracy of the optimization results.

[0005] To address the aforementioned technical problems, embodiments of the present invention provide a structural optimization method for the protective structure of a superconducting cable. The protective structure includes a protective layer, an insulating layer, and a coil box, which sequentially cover the outer periphery of the superconducting cable from the inside out. The structural optimization method includes the following steps: S1: Based on the geometric model of the protective structure, parametric modeling is performed to obtain a finite element simulation model of the protective structure. S2: The parameter range of the design variables is determined, including the coil box thickness and the protective layer thickness. S3: Based on the parameter range of the design variables, multiple first sample data sets are sampled, each first sample data set including sampled coil box thickness data and protective layer thickness data. Furthermore, a coupling analysis is performed on the finite element simulation model to obtain the first stress result corresponding to each first sample data set, including the maximum stress of the first coil box, the maximum stress of the first protective layer, and the maximum stress of the first insulating layer. S4: A response surface model is constructed based on the multiple first sample data sets and the first stress result corresponding to each first sample data set. The response surface model includes: a first response surface model, constructed based on the coil box thickness data, the protective layer thickness data, and the corresponding maximum stress of the first coil box; a second response surface model, constructed based on the coil box thickness data, the protective layer thickness data, and the corresponding maximum stress of the first protective layer; and a third response surface model, constructed based on the coil box thickness data, the protective layer thickness data, and the corresponding maximum stress of the first insulation layer. S5: Based on the response surface model, with the first stress result being less than or equal to the preset allowable stress as a constraint and maximizing the sum of stress margins as the optimization objective, an optimization equation is defined, and the protective structure is structurally optimized to obtain the final optimized protective structure scheme. The preset allowable stress includes the allowable stress of the coil box, the allowable stress of the protective layer, and the allowable stress of the insulation layer.

[0006] Using the above technical solution, step S1 involves parametric modeling of the protective structure's geometric model in the software, automatically generating a finite element simulation model of the protective structure. This facilitates the direct acquisition of design variable parameters based on the finite element simulation model, and allows for direct modification of these parameters within the model itself, eliminating the need for repeated model creation. Step S2 involves determining the parameter range of the design variables to limit the value range of the parameters to be optimized (coil box thickness and protective layer thickness), ensuring that the design variables are optimized within a range that guarantees the protective structure's normal protective function, avoiding invalid optimization results or results deviating from practical application scenarios. Step S3 involves sampling the first set of data, which uniformly covers the parameter range of the design variables, ensuring the reliability and engineering applicability of the sampling results. Compared to traditional exhaustive and orthogonal methods, this method requires less data, significantly reducing computational costs. Since the coil box thickness and protective layer thickness in the protective structure directly affect the coil box stress, protective layer stress, and insulation layer stress, coupling analysis of the finite element simulation model yields the first stress result corresponding to each first set of data. Step S4: A response surface model is constructed to reflect the relationship between the coil box thickness data, the protective layer thickness data, and the corresponding maximum stress of the first coil box, the first protective layer, and the first insulation layer, respectively. Step S5: The constraint condition that the first stress result is less than or equal to the preset allowable stress is used to avoid generating invalid optimization results. The optimization objective is to maximize the sum of stress margins, thereby reserving the maximum far-stress safety redundancy within the range of ensuring the safety and stability of the protective structure, and maximizing the safety, stability, and risk resistance of the protective structure.

[0007] In summary, the structural optimization method for the protection structure of superconducting cables provided by this invention has the beneficial effects of high optimization efficiency and the ability to cover the whole in complex optimization scenarios with multiple design variables and multiple constraints, thereby improving the accuracy of the optimization results.

[0008] According to another specific embodiment of the present invention, the optimization equation in step S5 of the method for optimizing the protective structure of a superconducting cable disclosed in this embodiment is:

[0009]

[0010] Among them, M sum The sum of stress margins, σ 线圈盒 σ is the maximum stress in the first coil box; 保护层 τ is the maximum stress of the first protective layer. 绝缘层 This represents the maximum stress in the first insulating layer.

[0011] According to another specific embodiment of the present invention, the structural optimization method for the protective structure of a superconducting cable disclosed in the embodiments of the present invention, after constructing a response surface model based on multiple first sample data sets and the first stress results corresponding to each first sample data set in step S4, further includes: extracting multiple second sample data sets from the finite element simulation model, each second sample data set including coil box thickness data and protective layer thickness data extracted from the finite element simulation model; performing coupling analysis on the finite element simulation model based on the second sample data sets to obtain the second stress results corresponding to each second sample data set, the second stress results including the maximum stress of the second coil box, the maximum stress of the second protective layer, and the maximum stress of the second insulation layer; and extracting the response surface stress results corresponding to each second sample data set from the multiple second sample data sets in the response surface model. The response surface stress results include the response surface coil box stress extracted from the first response surface model corresponding to each second sample data group, the response surface protective layer stress extracted from the second response surface model corresponding to each second sample data group, and the response surface insulation layer stress extracted from the third response surface model corresponding to each second sample data group. The stress error values ​​corresponding to multiple second sample data groups are calculated based on the response surface stress results and the second stress results for each second sample data group. If the stress error values ​​of multiple second sample data groups are greater than a preset error, the response surface accuracy verification fails, and the multiple second sample data groups are added to multiple first sample data groups, returning to step S3. If the stress error values ​​of multiple second sample data groups are less than or equal to the preset error, the response surface accuracy verification passes, and step S5 continues.

[0012] By adopting the above technical solution, the response surface accuracy is verified to determine whether the response surface model can reliably replace the geometric model of the original protective structure. If the response surface accuracy verification is passed, step S5 is continued to ensure the reliability and stability of the optimization results and improve the accuracy of the optimization results.

[0013] According to another specific embodiment of the present invention, the structural optimization method for the protective structure of a superconducting cable disclosed in the embodiments of the present invention includes root mean square error and / or mean absolute error in stress error values.

[0014] The formula for calculating the root mean square error is:

[0015]

[0016] Where RMSE is the root mean square error, m is the number of sample data in the second sample data group; y i The response surface stress result corresponding to the i-th second sample data group; The second stress result corresponds to the i-th second sample data group.

[0017] The formula for calculating the mean absolute error is:

[0018]

[0019] Where MAE is the mean absolute error, m is the number of sample data in the second sample data group; y i The response surface stress result corresponding to the i-th second sample data group; The second stress result is the i-th second sample data group; and the preset error includes a preset root mean square error and / or a preset mean absolute error. The root mean square error is compared with the preset root mean square error and / or the mean absolute error is compared with the preset mean absolute error to determine whether the response surface accuracy verification is passed.

[0020] By adopting the above technical solution, the stress error value is calculated by using one or a combination of root mean square error and mean absolute error. Through mathematical calculation, the deviation is quantified into a specific error value, so that the accuracy judgment is transformed from subjective feeling to objective standard, and the actual degree of deviation of the response surface model is clearly defined.

[0021] According to another specific embodiment of the present invention, the method for optimizing the structure of the protection structure of a superconducting cable disclosed in the embodiments of the present invention further includes step S5: using a multi-island genetic algorithm to obtain the optimal sample data set from the first sample data set and the second sample data set, and verifying the accuracy of the optimal sample data set. If the accuracy of the optimal sample data set meets the requirements, it indicates that the final structure optimization scheme of the superconducting coil has been obtained; if the accuracy of the optimal sample data set does not meet the requirements, the process returns to step S4 to increase the number of the second sample data set to optimize the response surface model.

[0022] According to another specific embodiment of the present invention, in the method for optimizing the structure of the protective structure of the superconducting cable disclosed in the embodiment of the present invention, in step S2: the parameter range of the coil box thickness is 28mm~40mm; the parameter range of the protective layer thickness is 2.4mm~4.6mm.

[0023] According to another specific embodiment of the present invention, the method for optimizing the structure of the protection structure of a superconducting cable disclosed in the embodiment of the present invention has a first sample data set of 30 to 70 items and a second sample data set of 3 to 15 items.

[0024] According to another specific embodiment of the present invention, the method for optimizing the structure of the protective structure of the superconducting cable disclosed in the embodiment of the present invention is that the coil box and the protective layer are made of metal materials, and the insulation layer is made of glass fiber and epoxy resin composite material.

[0025] The present invention also discloses a protective structure for a superconducting cable. The protective structure includes a protective layer, an insulating layer, and a coil box that are sequentially wrapped around the outer periphery of the superconducting cable from the inside out. The protective structure is optimized using a structural optimization method for the protective structure of the superconducting cable.

[0026] Embodiments of the present invention also disclose a superconducting coil, including a superconducting cable and a protective structure for the superconducting cable. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of an existing superconducting coil.

[0028] Figure 2 A flowchart illustrating a specific implementation of the structural optimization method for the protection structure of the superconducting cable provided in Embodiment 1 of the present invention;

[0029] Figure 3 This is a specific example of the first response surface model constructed in step S4 of the structural optimization method for the protective structure of the superconducting cable provided in Embodiment 1 of the present invention;

[0030] Figure 4 This is a specific example of the second response surface model constructed in step S4 of the structural optimization method for the protective structure of the superconducting cable provided in Embodiment 1 of the present invention;

[0031] Figure 5 This is a specific example of the third response surface model constructed in step S4 of the structural optimization method for the protective structure of the superconducting cable provided in Embodiment 1 of the present invention;

[0032] Figure 6 For not Figure 1 A schematic diagram of stress distribution in a specific protective structure during structural optimization.

[0033] Figure 7 This is a schematic diagram of the stress distribution of the protection structure after optimization using the final protection structure optimization scheme in a specific implementation of the protection structure optimization method for the superconducting cable provided in Embodiment 1 of the present invention.

[0034] Figure 8 For not Figure 1 A schematic diagram of stress distribution in a specific coil box during structural optimization of the protective structure;

[0035] Figure 9 This is a schematic diagram of the stress distribution of the coil box after the final optimized protection structure scheme is adopted in a specific implementation of the structure optimization method for the protection structure of the superconducting cable provided in Embodiment 1 of the present invention.

[0036] Figure 10 For not Figure 1 A schematic diagram of stress distribution in a specific protective layer during structural optimization of the protective structure in the diagram;

[0037] Figure 11 This is a schematic diagram of the stress distribution of the protective layer after the final optimized protective structure scheme is adopted in a specific implementation of the structural optimization method for the protective structure of the superconducting cable provided in Embodiment 1 of the present invention.

[0038] Figure 12 For not Figure 1 A schematic diagram of the stress distribution of a specific insulating layer during structural optimization of the protective structure in the diagram;

[0039] Figure 13 This is a schematic diagram of the stress distribution of the insulation layer after optimization using the final protection structure optimization scheme in a specific implementation of the structure optimization method for the protection structure of the superconducting cable provided in Embodiment 1 of the present invention.

[0040] Explanation of reference numerals in the attached figures:

[0041] 1. Superconducting coil;

[0042] 10. Superconducting cable; 11. Protective structure; 110. Protective layer; 111. Insulation layer; 112. Coil box. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0044] Example 1

[0045] This embodiment provides a structural optimization method for the protection structure of a superconducting cable, aiming to obtain the optimal protection structure solution within the allowable range of design variables. To more clearly illustrate the structural optimization method for the protection structure of a superconducting cable provided in this embodiment, the structure of an existing superconducting coil is first described, such as... Figure 1 As shown, the superconducting coil 1 includes a superconducting cable 10 and a protective structure 11. The protective structure 11 is a structure that covers the outer periphery of the superconducting cable 10 and provides protection and support for the superconducting cable 10. The protective structure 11 includes a protective layer 110, an insulating layer 111, and a coil box 112 that are sequentially covered around the outer periphery of the superconducting cable 10 from the inside out.

[0046] It should be noted that the protective layer 110 is wrapped around the outside of the superconducting cable 10, and its cross-section is usually circular or square. The protective layer 110 can be made of metal materials, such as 316LN stainless steel. The insulating layer 111 is used to insulate adjacent superconducting cables 10 from each other. The insulating layer 111 can be made of glass fiber and epoxy resin composite material (G10). The coil box 112 is the outermost structure wrapped around the superconducting cable 10 and provides support for the superconducting cable 10. The coil box 112 can be made of metal materials, such as 316LN stainless steel.

[0047] Specifically, such as Figure 2 As shown, the structural optimization method for the protection structure of a superconducting cable includes the following steps S1-S5.

[0048] S1: Based on the geometric model of the protective structure, perform parametric modeling to obtain the finite element simulation model of the protective structure.

[0049] Specifically, parametric modeling is performed in the modeling software based on the geometric model of the actual protected structure, which automatically generates a finite element simulation model of the protected structure. This makes it easy to directly obtain the parameters of the design variables based on the finite element simulation model, and the parameters of the design variables can be directly modified in the finite element simulation model without having to build the model again.

[0050] S2: Determine the parameter range of the design variables, which include the coil box thickness and the protective layer thickness.

[0051] To ensure the insulation performance of the insulation layer, its dimensions are not included in the optimization design. Under this premise, the protection structure can be optimized by optimizing the coil box thickness and the protective layer thickness; therefore, the coil box thickness and the protective layer thickness are used as design variables. It should be noted that when the cross-section of the protective layer is square, the thickness of the protective layer is equal to (the side length of the outer protective layer cross-section minus the diameter of the inner circular superconducting cable) / 2, which is the thickness at the thinnest point of the protective layer.

[0052] In step S2, determining the parameter range of the design variables is to limit the value range of the parameters to be optimized (coil box thickness and protective layer thickness), ensuring that the design variables are optimized on the premise that the protective structure can play its protective role normally, and avoiding invalid optimization results or deviating from the actual application scenario.

[0053] In one specific embodiment of the present invention, the coil box thickness ranges from 28mm to 40mm; the protective layer thickness ranges from 2.4mm to 4.6mm. Preferably, the coil box thickness ranges from 29mm to 39mm; the protective layer thickness ranges from 2.5mm to 4.5mm.

[0054] S3: Based on the parameter range of the design variables, multiple first sample data sets are obtained through sampling. Each first sample data set includes the sampled coil box thickness data and protective layer thickness data. It should be noted that the optimal Latin hypercube sampling (LHS) method can be used for stratified sampling to ensure uniform sample distribution and global coverage.

[0055] In another specific embodiment of the present invention, the number of the first sample data groups is 30 to 70. Preferably, in this embodiment, 40 first sample data groups can be selected for optimization design.

[0056] Furthermore, a coupled analysis was performed on the finite element simulation model to obtain the first stress result corresponding to each first sample data group. The first stress result includes the maximum stress of the first coil box, the maximum stress of the first protective layer, and the maximum stress of the first insulation layer.

[0057] In step S3, the first sample data set obtained by sampling can uniformly cover the parameter range of the design variables, ensuring the reliability and engineering practicality of the sampling results. Furthermore, compared to traditional exhaustive and orthogonal methods, it requires less data, significantly reducing computational costs. Since the thickness of the coil box and the protective layer in the protective structure directly affect the coil box stress, protective layer stress, and insulation layer stress, the first stress result corresponding to each first sample data set can be obtained through coupled analysis of the finite element simulation model.

[0058] It should be noted that a multiphysics analysis involving thermo-electromagnetic-structural coupling can be performed using a finite element simulation model. In the first stress result, the maximum stress of the first coil box refers to the local maximum yield stress of the coil box, the maximum stress of the first protective layer refers to the local maximum yield stress of the protective layer, and the maximum stress of the first insulation layer refers to the local maximum shear stress of the insulation layer.

[0059] S4: Construct a response surface model based on multiple first sample data sets and the corresponding first stress results for each first sample data set. It should be noted that Kriging interpolation can be used to construct the response surface model.

[0060] In step S4, a response surface model is constructed to reflect the relationship between the coil box thickness data, the protective layer thickness data, and the corresponding maximum stress of the first coil box, the maximum stress of the first protective layer, and the maximum stress of the first insulation layer.

[0061] According to another specific embodiment of the present invention, the structural optimization method for the protective structure of a superconducting cable disclosed in this embodiment further includes, after constructing a response surface model based on multiple first sample data sets and the first stress results corresponding to each first sample data set in step S4: extracting multiple second sample data sets from the finite element simulation model, each second sample data set including coil box thickness data and protective layer thickness data extracted from the finite element simulation model. In another specific embodiment of the present invention, the number of second sample data sets is 3 to 15. Preferably, this embodiment can extract 5 second sample data sets.

[0062] Furthermore, a coupled analysis is performed on the finite element simulation model based on the second sample data set to obtain the second stress result corresponding to each second sample data set. The second stress result includes the maximum stress of the second coil box, the maximum stress of the second protective layer, and the maximum stress of the second insulation layer. Additionally, response surface stress results corresponding to each of the multiple second sample data sets are extracted from the response surface model. These response surface stress results include the response surface coil box stress extracted from the first response surface model, the response surface protective layer stress extracted from the second response surface model, and the response surface insulation layer stress extracted from the third response surface model. The stress error value corresponding to the multiple second sample data sets is calculated based on the response surface stress result and the second stress result. If the stress error value of the multiple second sample data sets is greater than a preset error, the response surface accuracy verification fails, and the multiple second sample data sets are added to the multiple first sample data sets, returning to step S3. If the stress error value of the multiple second sample data sets is less than or equal to the preset error, the response surface accuracy verification passes, and step S5 continues.

[0063] Based on step S4 above, by performing response surface accuracy verification, it is determined whether the response surface model can reliably replace the geometric model of the original protective structure. If the response surface accuracy verification is passed, step S5 is continued to ensure the reliability and stability of the optimization results and improve the accuracy of the optimization results.

[0064] According to another specific embodiment of the present invention, the stress error value includes root mean square error and / or mean absolute error. Furthermore, the preset error includes a preset root mean square error and / or a preset mean absolute error. The root mean square error is compared with the preset root mean square error and / or the mean absolute error is compared with the preset mean absolute error to determine whether the response surface accuracy verification passes.

[0065] The stress error value is calculated by using one or a combination of root mean square error and mean absolute error. Through mathematical calculation, the deviation is quantified into a specific error value, so that the accuracy judgment is transformed from subjective feeling to objective standard, and the actual degree of deviation of the response surface model is clearly defined.

[0066] The formula for calculating the root mean square error is:

[0067]

[0068] Where RMSE is the root mean square error, m is the number of samples in the second sample data group; y i This represents the response surface stress result corresponding to the i-th second sample data group; This represents the second stress result corresponding to the i-th second sample data group.

[0069] It should be noted that, since the response surface stress results for each second sample data group include the response surface coil housing stress, the response surface protective layer stress, and the response surface insulating layer stress; and the second stress results for each second sample data group include the maximum stress of the second coil housing, the maximum stress of the second protective layer, and the maximum stress of the second insulating layer, it is necessary to calculate multiple root mean square error values ​​for the coil housing stress corresponding to each second sample data group based on the response surface coil housing stress and the maximum stress of the second coil housing, and to calculate multiple root mean square error values ​​for the coil housing stress corresponding to each second sample data group based on the response surface protective layer stress and the maximum stress of the second protective layer. The root mean square error (RMSE) of the protective layer stress corresponding to the second sample data group, and the root mean square error (RMSE) of the insulation layer stress corresponding to multiple second sample data groups are calculated based on the insulation layer stress and the maximum stress of the second insulation layer corresponding to each second sample data group. When using the RMSE for response surface accuracy verification, the RMSE values ​​of the coil box stress, protective layer stress, and insulation layer stress are compared, and the maximum value among the three is taken as the RMSE corresponding to multiple second sample data groups. This RMSE is then compared with a preset RMSE. When this RMSE is less than or equal to the preset RMSE, the response surface accuracy verification is considered passed.

[0070] The formula for calculating the mean absolute error is:

[0071]

[0072] Where MAE is the mean absolute error, m is the number of samples in the second sample data group; y i This represents the response surface stress result corresponding to the i-th second sample data group; This represents the second stress result corresponding to the i-th second sample data group.

[0073] It should be noted that, since the response surface stress results for each second sample data group include the response surface coil box stress, the response surface protective layer stress, and the response surface insulating layer stress; and the second stress results for each second sample data group include the maximum stress of the second coil box, the maximum stress of the second protective layer, and the maximum stress of the second insulating layer, it is necessary to calculate the mean absolute error (MAE) based on the response surface coil box stress and the maximum stress of the second coil box for multiple second sample data groups, and to calculate the MAE values ​​for the coil box stress of multiple second sample data groups based on the response surface protective layer stress and the maximum stress of the second protective layer for each second sample data group. The mean absolute error of the protective layer stress corresponding to the data group is calculated. Based on the response surface insulation layer stress and the maximum stress of the second insulation layer corresponding to each second sample data group, the mean absolute error of the insulation layer stress corresponding to multiple second sample data groups is calculated. When the mean absolute error is used to verify the accuracy of the response surface, the mean absolute error of the coil box stress, the mean absolute error of the protective layer stress, and the mean absolute error of the insulation layer stress are compared. The maximum value of the three is taken as the mean absolute error corresponding to multiple second sample data groups. The mean absolute error is compared with the preset mean absolute error. When the mean absolute error is less than or equal to the preset mean absolute error, the response surface accuracy verification is judged to be passed.

[0074] When using both root mean square error (RMSE) and mean absolute error (MAE) for response surface accuracy verification, it is necessary to compare the RMSE values ​​of coil box stress, protective layer stress, and insulation layer stress. The maximum value among these three is taken as the RMSE corresponding to multiple second sample data sets. This RMSE is then compared with a preset RMSE. Similarly, it is also necessary to compare the MAE values ​​of coil box stress, protective layer stress, and insulation layer stress. The maximum value among these three is taken as the MAE corresponding to multiple second sample data sets. This MAE is then compared with a preset MAE. The response surface accuracy verification is considered successful when both the RMSE and MAE are less than or equal to the preset RMSE. It should be noted that in this embodiment, the preset RMSE and preset MAE are preferably set to 5%.

[0075] A specific example of a response surface model obtained after constructing a response surface model during a particular optimization process. Figures 3-5 As shown, the first response surface model is a response surface model constructed based on the coil box thickness data and the protective layer thickness data, and the corresponding maximum stress of the first coil box. Figure 3It can be concluded that as the coil box thickness increases, the stress in the first coil box first rises and then falls; as the protective layer thickness increases, the stress in the first coil box gradually decreases. The second response surface model, based on the coil box thickness data and protective layer thickness data, and the corresponding maximum stress in the first protective layer, is a response surface model constructed according to... Figure 4 It can be concluded that as the coil housing thickness increases, the maximum stress of the first protective layer first increases and then decreases; as the protective layer thickness increases, the maximum stress of the first protective layer gradually decreases. The third response surface model, based on the coil housing thickness data and protective layer thickness data and the corresponding maximum stress of the first insulation layer, is a response surface model constructed according to... Figure 5 It can be concluded that as the thickness of the coil box increases, the maximum stress of the first insulation layer gradually decreases; as the thickness of the protective layer increases, the maximum stress of the first insulation layer gradually decreases.

[0076] S5: Based on the response surface model, with the first stress result being less than or equal to the preset allowable stress as a constraint and the goal of maximizing the sum of stress margins, an optimization equation is defined and the protective structure is structurally optimized to obtain the final optimized protective structure scheme; wherein, the preset allowable stress includes the allowable stress of the coil box, the allowable stress of the protective layer, and the allowable stress of the insulation layer.

[0077] In step S5, the first stress result is set to be less than or equal to the preset allowable stress as a constraint to avoid generating invalid optimization results. The optimization objective is to maximize the sum of stress margins, thereby reserving the far-stress safety redundancy to the maximum extent within the range of ensuring the safety and stability of the protected structure, and maximizing the safety, stability and risk resistance of the protected structure.

[0078] According to another specific embodiment of the present invention, the optimization equation in step S5 of the method for optimizing the protective structure of a superconducting cable disclosed in this embodiment is:

[0079]

[0080] Among them, M sum The sum of stress margins, σ 线圈盒 σ is the maximum stress in the first coil box; 保护层 τ is the maximum stress of the first protective layer. 绝缘层 This represents the maximum stress in the first insulating layer.

[0081] It should be noted that since the first stress result includes the maximum stress of the first coil box, the maximum stress of the first protective layer, and the maximum stress of the first insulation layer, the corresponding preset allowable stresses include the allowable stress of the coil box, the allowable stress of the protective layer, and the allowable stress of the insulation layer. The yield strength of the coil box at 4K (900 MPa) is taken as the allowable stress of the coil box; the yield strength of the protective layer at 4K (900 MPa) is taken as the allowable stress of the protective layer; and the shear strength of the insulation layer at 4K (68.6 MPa) is taken as the allowable stress of the insulation layer. Therefore, the constraint condition is: σ 线圈盒 ≤900MPa; σ 保护层 ≤900MPa; τ 绝缘层 ≤68.6MPa.

[0082] According to another specific embodiment of the present invention, the method for optimizing the structure of the protection structure of a superconducting cable disclosed in the embodiments of the present invention further includes step S5: using a multi-island genetic algorithm to obtain the optimal sample data set from the first sample data set and the second sample data set, and verifying the accuracy of the optimal sample data set. If the accuracy of the optimal sample data set meets the requirements, it indicates that the final structure optimization scheme of the superconducting coil has been obtained; if the accuracy of the optimal sample data set does not meet the requirements, the process returns to step S4 to increase the number of the second sample data set to optimize the response surface model.

[0083] In summary, the structural optimization method for the protection structure of superconducting cables provided in this embodiment has the advantages of high optimization efficiency, global coverage in complex optimization scenarios with multiple design variables and constraints, and improved accuracy of optimization results. Furthermore, finite element simulation significantly reduces reliance on physical experiments, cutting costs and time, and solving the problems of long cycles and time consumption in traditional optimization methods, thereby shortening the optimization design iteration cycle. The response surface model approximates the mapping relationship between coil box thickness, protective layer thickness, and stress by extracting limited sample data, which can significantly improve the optimization speed. The response surface model can approximately fit the global trend of the design space, and combined with global optimization algorithms (such as genetic algorithms), it can escape the "local trap" of trial and error and find a better design solution. Multiple design variables and constraints are simultaneously incorporated into the optimization equation optimization process. Through the optimization equation, constraints automatically satisfy all conditions, avoiding performance degradation caused by single-variable optimization. The optimized solution can be verified again through the finite element model (i.e., "substituting the optimal solution into the finite element simulation model to verify whether the performance meets the standards"), ensuring the reliability of the results.

[0084] To intuitively understand the effect of the optimization method for the protection structure of the superconducting cable provided in this embodiment, the following will be combined with... Figures 6-13 The stress distribution diagram obtained during a specific experiment will be used as an example for comparison and explanation. Figure 6 , Figure 8 , Figure 10 and Figure 12 They were not correct. Figure 1 Stress distribution diagrams of the protective structure and its components during structural optimization. Figure 7 , Figure 9 , Figure 11 and Figure 13 The stress distribution of the protection structure and its components after obtaining the final optimized protection structure scheme using the structural optimization method of the superconducting cable provided in this embodiment is described.

[0085] like Figure 6 As shown, no Figure 1 When the protective structure is optimized, the overall maximum stress of the protective structure is approximately 822 MPa. Figure 7 As shown, the overall maximum stress of the optimized protective structure is approximately 468 MPa, which means that the overall maximum stress of the optimized protective structure is reduced by about 43%.

[0086] like Figure 8 As shown, the maximum stress in the coil box before optimization was approximately 322 MPa. Figure 9 As shown, the maximum stress of the coil box after optimization is approximately 210 MPa, which means that the maximum stress of the coil box is reduced by about 35% after optimization.

[0087] like Figure 10 As shown, the maximum stress of the protective layer before optimization was approximately 822 MPa. Figure 11 As shown, the maximum stress of the optimized protective layer is approximately 468 MPa, which means that the maximum stress of the optimized protective layer is reduced by about 43%.

[0088] like Figure 12 As shown, the maximum stress of the insulation layer before optimization was approximately 45 MPa. Figure 13 As shown, the maximum stress of the optimized insulation layer is approximately 34 MPa, which means that the maximum stress of the optimized insulation layer is reduced by about 18%.

[0089] In other words, the optimization scheme obtained by the optimization method of the superconducting cable protection structure provided in this embodiment can reduce the stress in each part after redesigning the coil box and the thickness of the protective layer of the protection structure, thereby maximizing the stress margin and improving the structural safety and reliability.

[0090] Example 2

[0091] This embodiment provides a protective structure for a superconducting cable, such as... Figure 1As shown, the protective structure 11 includes a protective layer 110, an insulation layer 111, and a coil box 112, which are sequentially wrapped around the outer periphery of the superconducting cable 10 from the inside out. It should be noted that the protective layer 110 can specifically be an armored structure that integrates functions such as mechanical support, electromagnetic shielding, thermal protection, and insulation protection. The structural optimization method of the protective structure of the superconducting cable provided in Example 1 optimizes the structure of the protective structure 11.

[0092] Example 3

[0093] This embodiment provides a superconducting coil, such as Figure 1 As shown, the superconducting coil 1 includes a superconducting cable 10 and a protective structure for the superconducting cable provided in Embodiment 2. The superconducting coil 1 can be composed of multiple superconducting cables 10. The specific number of superconducting cables 10 can be set according to the application requirements of the superconducting coil 1, such as two, three, four, or more, as long as each superconducting cable 10 is covered by a protective layer 110, adjacent protective layers 110 are separated by an insulating layer 111, and the outermost part of the insulating layer 111 is covered by a coil box 112. It should be noted that, typically, to ensure sufficient magnetic field confinement capability when the superconducting cable 10 is used in a magnetic confinement device, or sufficient power transmission capability when used for power transmission, the size of the superconducting cable 10 is not included in the optimized design.

[0094] It should also be noted that the superconducting coil 1 can be used in stellarator devices. Due to the irregular shape of the stellarator superconducting coil, the gap between adjacent superconducting coils is small. Therefore, improving the space utilization rate of the superconducting coil's protective structure is very important. The optimization method for the superconducting cable's protective structure provided by this invention can reasonably optimize the coil box thickness and protective layer thickness, and rationally set the coil box thickness and protective layer thickness within a limited space, thereby ensuring the safe and stable operation of the superconducting coil. The protective layer of the superconducting coil used in stellarators generally adopts an armored structure.

[0095] It should be noted that, in addition to the specific embodiments described above, those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Although the description of the present invention will be presented in conjunction with preferred embodiments, this does not mean that the features of the invention are limited to those embodiments. On the contrary, the purpose of describing the invention in conjunction with embodiments is to cover other options or modifications that may be derived based on the claims of the present invention. To provide a thorough understanding of the invention, many specific details will be included in the following description. The invention may also be implemented without using these details. Furthermore, to avoid confusion or obscuring the focus of the invention, some specific details will be omitted in the description. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0096] It should be noted that in this specification, similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0097] In the description of this embodiment, it should be noted that the terms "upper", "lower", "inner", "bottom", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, or are the orientations or positional relationships in which the inventive product is usually placed when in use. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, they cannot be understood as limitations on the present invention.

[0098] The terms “first”, “second”, etc. are only used for distinguishing descriptions and should not be understood as indicating or implying relative importance.

[0099] In the description of this embodiment, it should be noted that, unless otherwise specified or limited, the terms "disposed," "connected," and "connected" should be understood broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; mechanical connections or electrical connections; direct connections or indirect connections through an intermediate medium; and internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in this embodiment based on specific circumstances.

[0100] Although the present invention has been illustrated and described with reference to certain preferred embodiments thereof, it should be understood by those skilled in the art that the above description is provided as a further detailed description of the present invention in conjunction with specific embodiments thereof, and that the specific implementation of the present invention is not limited to these descriptions. Those skilled in the art may make various changes in form and details, including simple deductions or substitutions, without departing from the spirit and scope of the present invention.

Claims

1. A method for optimizing the structure of a protection structure for a superconducting cable, characterized in that, The protective structure includes, from the inside out, a protective layer, an insulation layer, and a coil box that sequentially cover the outer periphery of the superconducting cable. The structural optimization method includes the following steps: S1: Based on the geometric model of the protective structure, perform parametric modeling to obtain the finite element simulation model of the protective structure; S2: Determine the parameter range of the design variables, including the coil box thickness and the protective layer thickness; S3: Based on the parameter range of the design variables, multiple first sample data groups are obtained by sampling. Each first sample data group includes the sampled coil box thickness data and protective layer thickness data. Furthermore, a coupling analysis is performed on the finite element simulation model to obtain the first stress result corresponding to each of the first sample data groups. The first stress result includes the maximum stress of the first coil box, the maximum stress of the first protective layer, and the maximum stress of the first insulation layer. S4: Construct a response surface model based on the plurality of first sample data groups and the first stress result corresponding to each first sample data group. The response surface model includes: The first response surface model is a response surface model constructed based on the coil box thickness data and the protective layer thickness data and the corresponding maximum stress of the first coil box; The second response surface model is a response surface model constructed based on the coil box thickness data and the protective layer thickness data and the corresponding maximum stress of the first protective layer. The third response surface model is a response surface model constructed based on the coil box thickness data and the protective layer thickness data and the corresponding maximum stress of the first insulation layer; S5: Based on the response surface model, with the first stress result being less than or equal to the preset allowable stress as a constraint and maximizing the sum of stress margins as the optimization objective, an optimization equation is defined and the protective structure is structurally optimized to obtain the final optimized protective structure scheme; wherein, the preset allowable stress includes the allowable stress of the coil box, the allowable stress of the protective layer, and the allowable stress of the insulation layer.

2. The structural optimization method for the protection structure of the superconducting cable as described in claim 1, characterized in that, The optimization equation in step S5 is: Among them, M sum The sum of stress margins, σ 线圈盒 σ is the maximum stress in the first coil box; 保护层 τ is the maximum stress of the first protective layer. 绝缘层 This represents the maximum stress in the first insulating layer.

3. The structural optimization method for the protection structure of the superconducting cable as described in claim 1, characterized in that, After constructing the response surface model based on the plurality of first sample data groups and the first stress result corresponding to each first sample data group in step S4, the following further includes: Multiple second sample data sets are extracted from the finite element simulation model, each second sample data set including coil box thickness data and protective layer thickness data extracted from the finite element simulation model; Based on the multiple second sample data sets, the finite element simulation model is coupled to obtain the second stress result corresponding to each second sample data set. The second stress result includes the maximum stress of the second coil box, the maximum stress of the second protective layer, and the maximum stress of the second insulation layer. Furthermore, the response surface stress results corresponding to each of the plurality of second sample data groups are extracted from the response surface model. The response surface stress results include the response surface coil box stress corresponding to each of the second sample data groups extracted from the first response surface model, the response surface protective layer stress corresponding to each of the second sample data groups extracted from the second response surface model, and the response surface insulation layer stress corresponding to each of the second sample data groups extracted from the third response surface model. The stress error value corresponding to the plurality of second sample data groups is calculated based on the response surface stress result and the second stress result corresponding to each second sample data group; wherein, if the stress error value of the plurality of second sample data groups is greater than a preset error, the response surface accuracy verification fails, the plurality of second sample data groups are added to the plurality of first sample data groups, and the process returns to step S3; if the stress error value of the plurality of second sample data groups is less than or equal to the preset error, the response surface accuracy verification passes, and the process continues to step S5.

4. The structural optimization method for the protection structure of the superconducting cable as described in claim 3, characterized in that, The stress error value includes root mean square error and / or mean absolute error; The formula for calculating the root mean square error is as follows: Where RMSE is the root mean square error, m is the number of sample data in the second sample data group; y i The response surface stress result corresponding to the i-th second sample data group; The second stress result corresponding to the i-th second sample data group; The formula for calculating the mean absolute error is: Where MAE is the mean absolute error, m is the number of sample data in the second sample data group; y i The response surface stress result corresponding to the i-th second sample data group; The second stress result corresponding to the i-th second sample data group; Furthermore, the preset error includes a preset root mean square error and / or a preset mean absolute error. The root mean square error is compared with the preset root mean square error and / or the mean absolute error is compared with the preset mean absolute error to determine whether the response surface accuracy verification passes.

5. The method for optimizing the structure of the protection structure of a superconducting cable as described in claim 3, characterized in that, Step S5 further includes: using a multi-island genetic algorithm to obtain the optimal sample data group from the first sample data group and the second sample data group, and verifying the accuracy of the optimal sample data group. If the accuracy of the optimal sample data group meets the requirements, it means that the final structural optimization scheme of the superconducting coil has been obtained. If the accuracy of the optimal sample data group does not meet the requirements, the process returns to step S4 to increase the number of the second sample data group to optimize the response surface model.

6. The method for optimizing the structure of the protection structure of a superconducting cable as described in claim 1, characterized in that, In step S2: the parameter range of the coil box thickness is 28mm~40mm; the parameter range of the protective layer thickness is 2.4mm~4.6mm.

7. The structural optimization method for the protection structure of the superconducting cable as described in claim 3, characterized in that, The number of samples in the first sample data group is 30 to 70, and the number of samples in the second sample data group is 3 to 15.

8. The method for optimizing the structure of the protective structure of a superconducting cable as described in any one of claims 1 to 7, characterized in that, The coil box and the protective layer are made of metal, and the insulating layer is made of a composite material of glass fiber and epoxy resin.

9. A protective structure for a superconducting cable, characterized in that, The protective structure includes a protective layer, an insulating layer, and a coil box that sequentially cover the outer periphery of the superconducting cable from the inside out. The protective structure is optimized using the structural optimization method described in any one of claims 1 to 8.

10. A superconducting coil, comprising a superconducting cable, characterized in that, It also includes the protective structure for the superconducting cable as described in claim 9.

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