Method for optimizing the structure of a superconducting cable protection structure, superconducting cable protection structure and superconducting coil

Abstract

The application provides a structure optimization method of a protection structure of a superconducting cable, a protection structure of a superconducting cable and a superconducting coil, and the structure optimization method comprises the following steps: establishing a finite element simulation model of the protection structure, determining a parameter range of a design variable, sampling to obtain a plurality of first sample data groups comprising coil box thickness data and protection 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 group, constructing 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, defining an optimization equation and performing structure optimization on the protection structure to obtain a final protection structure optimization scheme, and the optimization method has high optimization efficiency and can cover the whole global range, thereby improving the accuracy of the optimization result.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of superconducting coil, and particularly relates to a structure optimization method of a protection structure of a superconducting cable, the protection structure of the superconducting cable and a superconducting coil. BACKGROUND

[0002] The superconducting coil is a coil structure made of superconductor under specific conditions (low temperature, low pressure, etc.) showing zero resistance and complete diamagnetic properties. The superconducting coil includes a superconducting cable and a protection structure of the superconducting cable, and the protection structure includes a coil box, an insulation layer, a protection layer and other components. The thickness of each part of the protection structure directly affects the stress level and stability of the overall structure. For example, if the thickness of the coil box is too high, the design space of the insulation layer and the protection layer will be compressed, which may cause the stress of the insulation layer and the protection layer to exceed the allowable stress; if the thickness of the coil box is too low, the stress of the coil box will exceed the allowable stress. Therefore, how to reasonably set the thickness of each part in the limited space is very important for the overall structure.

[0003] In the prior art, the exhaustive method and the orthogonal method are used to obtain the optimal stress distribution of the protection structure of the superconducting cable. However, the exhaustive method has the problems of low optimization efficiency, large amount of calculation when there are multiple design variables, and possible loss of optimal solution due to data discretization. The orthogonal method also has the problems of large amount of calculation and low accuracy of optimal solution when there are multiple design variables. Therefore, the existing structure optimization method of the protection structure of the superconducting cable has the problems of low optimization efficiency and difficulty in covering the global optimization in the complex optimization scene with multiple design variables and multiple constraint conditions, resulting in low accuracy of the optimization result. SUMMARY

[0004] The present application relates to the technical field of superconducting coil, and particularly relates to a structure optimization method of a protection structure of a superconducting cable, the protection structure of the superconducting cable and a superconducting coil.

[0005] To solve the above technical problems, an embodiment of the present application provides a structure optimization method of a protection structure of a superconducting cable, the protection structure comprising a protection layer, an insulation layer and a coil box which are sequentially wrapped on the outer periphery of the superconducting cable from inside to outside. The structure optimization method comprises the following steps: S1: parameterized modeling is performed according to a geometric model of the protection structure to obtain a finite element simulation model of the protection structure; S2: a parameter range of design variables is determined, the design variables comprising a coil box thickness and a protection layer thickness; S3: a plurality of first sample data sets are obtained by sampling based on the parameter range of the design variables, each first sample data set comprising coil box thickness data and protection layer thickness data obtained by sampling; and coupling analysis is performed on the finite element simulation model to obtain a first stress result corresponding to each first sample data set, the first stress result comprising a first coil box maximum stress, a first protection layer maximum stress and a first insulation layer maximum stress; S4: a response surface model is constructed based on the plurality of first sample data sets and the first stress result corresponding to each first sample data set. The response surface model comprises: a first response surface model constructed based on the coil box thickness data and the protection layer thickness data and the corresponding first coil box maximum stress; a second response surface model constructed based on the coil box thickness data and the protection layer thickness data and the corresponding first protection layer maximum stress; and a third response surface model constructed based on the coil box thickness data and the protection layer thickness data and the corresponding first insulation layer maximum stress; S5: based on the response surface model, an optimization equation is defined and the protection structure is structurally optimized to obtain a final protection structure optimization scheme, with the first stress result being less than or equal to a preset allowable stress as a constraint condition and the sum of the stress margins being maximized as an optimization target, wherein the preset allowable stress comprises a coil box allowable stress, a protection layer allowable stress and an insulation layer allowable stress.

[0006] By adopting the technical scheme, in step S1, the finite element simulation model of the protection structure is automatically generated by parameterized modeling according to the geometric model of the protection structure in software, which facilitates subsequent direct acquisition of the parameters of the design variables on the basis of the finite element simulation model, and the parameters of the design variables can be directly modified in the finite element simulation model without repeated modeling. In step S2, the parameter range of the design variables is determined to limit the value range of the to-be-optimized parameters (the coil box thickness and the protection layer thickness), so that the design variables are optimized within the range in which the protection structure can normally play a protection role, and invalid optimization results or results deviating from the actual application scenario are avoided. 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 practicability of the sampling results, and compared with the traditional exhaustive method and orthogonal method, the data amount is smaller, and the calculation cost can be greatly reduced. Since the coil box thickness and the protection layer thickness in the protection structure directly affect the coil box stress, the protection layer stress and the insulation layer stress, the first stress result corresponding to each first sample data set can be obtained by coupling analysis on the finite element simulation model. In step S4, a response surface model is constructed to reflect the relationship between the coil box thickness data, the protection layer thickness data and the corresponding first coil box maximum stress, the first protection layer maximum stress and the first insulation layer maximum stress. In step S5, the first stress result less than or equal to the preset allowable stress is taken as a constraint condition to avoid invalid optimization results, and the sum of the maximum stress margins is taken as an optimization target, so that the far stress safety redundancy is maximally reserved within the range of ensuring the safety and stability of the protection structure, and the safety, stability and risk resistance of the protection structure are maximized.

[0007] In summary, the structure optimization method of the protection structure of the superconducting cable provided by the application has the beneficial effects of high optimization efficiency, the ability to cover the global optimization in a complex optimization scene with multiple design variables and multiple constraint conditions, and improved optimization result accuracy.

[0008] According to another specific embodiment of the application, the structure optimization method of the protection structure of the superconducting cable disclosed in the embodiments of the application has the optimization equation in step S5 as follows:

[0009]

[0010] wherein M sum is the sum of the stress margins, σ 线圈盒 is the first coil box maximum stress; σ 保护层 is the first protection layer maximum stress; τ 绝缘层 is the first insulation layer maximum stress.

[0011] According to another specific embodiment of the present application, the method for optimizing the structure of the protection structure of the superconducting cable disclosed by the embodiments of the present application further comprises the following steps after the step S4 of constructing the response surface model based on the plurality of first sample data sets and the first stress results corresponding to each first sample data set: extracting a plurality of second sample data sets from the finite element simulation model, each second sample data set comprising the coil box thickness data and the protection 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 a second stress result corresponding to each second sample data set, the second stress result comprising a second coil box maximum stress, a second protection layer maximum stress and a second insulation layer maximum stress; and extracting a response surface stress result corresponding to each second sample data set in the plurality of second sample data sets from the response surface model, the response surface stress result comprising a response surface coil box stress corresponding to each second sample data set extracted from the first response surface model, a response surface protection layer stress corresponding to each second sample data set extracted from the second response surface model, and a response surface insulation layer stress corresponding to each second sample data set extracted from the third response surface model; calculating a stress error value corresponding to the plurality of second sample data sets according to the response surface stress result and the second stress result corresponding to each second sample data set; wherein, if the stress error values of the plurality of second sample data sets are greater than a preset error, the response surface accuracy verification fails, the plurality of second sample data sets are added to the plurality of first sample data sets, and the step S3 is returned to; if the stress error values of the plurality of second sample data sets are less than or equal to the preset error, the response surface accuracy verification passes, and the step S5 is continued.

[0012] By performing the response surface accuracy verification, it is determined whether the response surface model can reliably replace the geometric model of the original protection structure, the step S5 is continued in the case that the response surface accuracy verification passes, so as to ensure the reliability and stability of the optimization result and improve the accuracy of the optimization result.

[0013] According to another specific embodiment of the present application, the stress error value comprises a root mean square error and / or a mean absolute error.

[0014] The calculation formula of the root mean square error is as follows:

[0015]

[0016] The calculation formula of the root mean square error is as follows: i is the response surface stress result corresponding to the i-th second sample data set; is the second stress result corresponding to the i-th second sample data set.

[0017] The calculation formula of the average absolute error is:

[0018]

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

[0020] By using the above technical scheme, one or both of the root mean square error and the average absolute error are combined to calculate the stress error value, and the deviation is quantified into a specific error value through mathematical calculation, so that the precision judgment is changed from subjective feeling to objective standard, and the actual degree of the response surface model deviation is clearly defined.

[0021] According to another specific embodiment of the present application, the structure optimization method of the protection structure of the superconducting cable disclosed by the embodiments of the present application further comprises: obtaining an optimal sample data set by using a multi-island genetic algorithm on 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 is obtained; if the accuracy of the optimal sample data set does not meet the requirements, return 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 application, the structure optimization method of the protection structure of the superconducting cable disclosed by the embodiments of the present application, in step S2: the parameter range of the coil box thickness is 28mm~40mm; the parameter range of the protection layer thickness is 2.4mm~4.6mm.

[0023] According to another specific embodiment of the present application, the structure optimization method of the protection structure of the superconducting cable disclosed by the embodiments of the present application, the number of the first sample data set is 30~70, and the number of the second sample data set is 3~15.

[0024] According to another specific embodiment of the present application, the structure optimization method of the protection structure of the superconducting cable disclosed by the embodiments of the present application, the coil box and the protection layer are made of metal materials, and the insulation layer is made of glass fiber and epoxy resin composite material.

[0025] The embodiment of the present application further discloses a protection structure of a superconducting cable, which comprises a protection layer, an insulation layer and a coil box which are sequentially wrapped on the outer periphery of the superconducting cable from inside to outside, and the protection structure is subjected to structure optimization by using the structure optimization method of the protection structure of the superconducting cable.

[0026] The embodiment of the present application further discloses a superconducting coil, which comprises a superconducting cable and a protection structure of the superconducting cable. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 It is a structural schematic diagram of an existing superconducting coil;

[0028] Figure 2 It is a flow chart of one specific embodiment of the structure optimization method of the protection structure of the superconducting cable provided in the embodiment 1 of the present application;

[0029] Figure 3 It is one specific case of the first response surface model constructed in the step S4 of the structure optimization method of the protection structure of the superconducting cable provided in the embodiment 1 of the present application;

[0030] Figure 4 It is one specific case of the second response surface model constructed in the step S4 of the structure optimization method of the protection structure of the superconducting cable provided in the embodiment 1 of the present application;

[0031] Figure 5 It is one specific case of the third response surface model constructed in the step S4 of the structure optimization method of the protection structure of the superconducting cable provided in the embodiment 1 of the present application;

[0032] Figure 6 It is a stress distribution schematic diagram of one specific protection structure when the protection structure in the embodiment 1 of the present application is not subjected to structure optimization; Figure 1

[0033] Figure 7 It is a stress distribution schematic diagram of the protection structure after the final protection structure optimization scheme is adopted in the structure optimization method of the protection structure of the superconducting cable provided in the embodiment 1 of the present application in one specific implementation process;

[0034] Figure 8 It is a stress distribution schematic diagram of one specific coil box when the protection structure in the embodiment 1 of the present application is not subjected to structure optimization; Figure 1

[0035] Figure 9 It is a stress distribution schematic diagram of the coil box after the final protection structure optimization scheme is adopted in the structure optimization method of the protection structure of the superconducting cable provided in the embodiment 1 of the present application in one specific implementation process;

[0036] Figure 10 It is a stress distribution schematic diagram of one specific coil box when the protection structure in the embodiment 1 of the present application is not subjected to structure optimization;​​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 outside the superconducting cable 10, and the cross section thereof is generally circular or square, the protective layer 110 can be made of a metal material, for example, 316LN stainless steel; the insulating layer 111 is used for insulation between adjacent superconducting cables 10 and the superconducting cable 10, and the insulating layer 111 can be made of glass fiber and epoxy resin composite (G10); the coil box 112 is a structure wrapped outside the superconducting cable 10, and provides support for the superconducting cable 10, and the coil box 112 can be made of a metal material, for example, 316LN stainless steel.

[0047] Specifically, as shown in Figure 2 The structure optimization method of the protective structure of the superconducting cable includes the following steps S1-S5.

[0048] S1: According to the geometric model of the protective structure, parameterized modeling is performed to obtain a finite element simulation model of the protective structure.

[0049] Specifically, the finite element simulation model of the protective structure is automatically generated by performing parameterized modeling in the modeling software according to the geometric model of the actual protective structure, which facilitates subsequent direct acquisition of 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 the need to repeatedly establish the model.

[0050] S2: Determine the parameter range of the design variable, the design variable including the coil box thickness and the protective layer thickness.

[0051] In order to ensure the insulation performance of the insulating layer, the size of the insulating layer is not involved in the optimization design. Under this premise, the protective structure can be optimized by optimizing the thickness of the coil box and the protective layer, so the thickness of the coil box and the protective layer is taken as the design variable. 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 length of the side of the cross section of the outer protective layer - the diameter of the inner circular superconducting cable) / 2, that is, the thickness of the thinnest part of the protective layer.

[0052] In step S2, the parameter range of the design variable is determined in order to limit the value range of the to-be-optimized parameters (the thickness of the coil box and the thickness of the protective layer), so as to ensure that the design variable is optimized under the premise of ensuring the normal protection of the protective structure, and to avoid invalid optimization results or deviating from the actual application scenario.

[0053] In one of the specific embodiments of the present application, the parameter range of the coil box thickness is 28mm-40mm; the parameter range of the protective layer thickness is 2.4mm-4.6mm. Preferably, the parameter range of the coil box thickness can be set to 29mm-39mm; the parameter range of the protective layer thickness can be set to 2.5mm-4.5mm.

[0054] S3: sample to obtain a plurality of first sample data sets based on the parameter range of the design variable, each first sample data set comprising the sampled coil box thickness data and the protective layer thickness data. It should be noted that the Latin hypercube sampling (LHS) method can be selected for stratified sampling to ensure uniform sample distribution and cover the entire global range.

[0055] In another specific embodiment of the application, the number of first sample data sets is 30-70. Preferably, 40 first sample data sets can be extracted for optimization design in this embodiment.

[0056] And, the finite element simulation model is coupled for analysis to obtain a first stress result corresponding to each first sample data set, the first stress result comprising a first coil box maximum stress, a first protective layer maximum stress, and a first insulation layer maximum stress.

[0057] In step S3, the first sample data set obtained by sampling can uniformly cover the parameter range of the design variable, ensuring the reliability and engineering practicability of the sampling result, and compared with the traditional exhaustive method and orthogonal method, the data amount is less, which can greatly reduce the calculation cost. Since the coil box thickness and the protective layer thickness in the protective structure directly affect the coil box stress, the protective layer stress and the insulation layer stress, the finite element simulation model is coupled for analysis to obtain a first stress result corresponding to each first sample data set.

[0058] It should be noted that the finite element simulation model can be used for thermal-electromagnetic-structure multi-physical field coupling analysis. The first coil box maximum stress in the first stress result refers to the local maximum yield stress of the coil box, the first protective layer maximum stress refers to the local maximum yield stress of the protective layer, and the first insulation layer maximum stress refers to the local maximum shear stress of the insulation layer.

[0059] S4: 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. It should be noted that the Kriging interpolation method can be used to construct the response surface model.

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

[0061] According to another specific embodiment of the present application, the method for optimizing the structure of the protection structure of the superconducting cable disclosed by the embodiment of the present application further comprises, after the step S4 of constructing the response surface model based on the plurality of first sample data sets and the first stress result corresponding to each first sample data set: extracting a plurality of second sample data sets from the finite element simulation model, each second sample data set comprising the coil box thickness data and the protection layer thickness data extracted from the finite element simulation model. In another specific embodiment of the present application, the number of the second sample data sets is 3-15. Preferably, 5 second sample data sets can be extracted in the present embodiment.

[0062] And, performing coupling analysis on the finite element simulation model based on the second sample data sets to obtain a second stress result corresponding to each second sample data set, the second stress result comprising a second coil box maximum stress, a second protection layer maximum stress and a second insulation layer maximum stress. And, extracting a response surface stress result corresponding to each second sample data set from the plurality of second sample data sets from the response surface model, the response surface stress result comprising a response surface coil box stress corresponding to each second sample data set extracted from the first response surface model, a response surface protection layer stress corresponding to each second sample data set extracted from the second response surface model, and a response surface insulation layer stress corresponding to each second sample data set extracted from the third response surface model. Calculating a stress error value corresponding to the plurality of second sample data sets according to the response surface stress result and the second stress result corresponding to each second sample data set; wherein, if the stress error value of the plurality of second sample data sets is greater than a preset error, the response surface accuracy verification fails, the plurality of second sample data sets are added to the plurality of first sample data sets, and the step S3 is returned; if the stress error value of the plurality of second sample data sets is less than or equal to the preset error, the response surface accuracy verification passes, and the step S5 is continued.

[0063] Based on the step S4 described above, the response surface model can be determined whether it can reliably replace the geometric model of the original protection structure by performing the response surface accuracy verification, the reliability and stability of the optimization result are ensured, and the accuracy of the optimization result is improved in the case that the response surface accuracy verification passes and the step S5 is continued.

[0064] According to another specific embodiment of the present application, the stress error value comprises a root mean square error and / or an average absolute error. And, the preset error comprises a preset root mean square error and / or a preset average absolute error, the root mean square error is compared with the preset root mean square error and / or the average absolute error is compared with the preset average absolute error to determine whether the response surface accuracy verification passes.

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

[0066] The calculation formula of the root mean square error is:

[0067]

[0068] The calculation formula of the root mean square error is: i The response surface stress result corresponding to the i th second sample data group is yi; The second stress result corresponding to the i th second sample data group is yi.

[0069] It should be noted that since the response surface stress result corresponding to each second sample data group includes the response surface coil box stress, the response surface protection layer stress and the response surface insulation layer stress, and the second stress result corresponding to each second sample data group includes the second coil box maximum stress, the second protection layer maximum stress and the second insulation layer maximum stress, therefore, when calculating the root mean square error, the coil box stress root mean square error value corresponding to multiple second sample data groups is calculated according to the response surface coil box stress and the second coil box maximum stress corresponding to each second sample data group, the protection layer stress root mean square error value corresponding to multiple second sample data groups is calculated according to the response surface protection layer stress and the second protection layer maximum stress corresponding to each second sample data group, and the insulation layer stress root mean square error value corresponding to multiple second sample data groups is calculated according to the response surface insulation layer stress and the second insulation layer maximum stress corresponding to each second sample data group, when the root mean square error is used for response surface accuracy verification, the maximum value of the coil box stress root mean square error value, the protection layer stress root mean square error value and the insulation layer stress root mean square error value is compared, and the maximum value is taken as the root mean square error corresponding to multiple second sample data groups, and the root mean square error is compared with the preset root mean square error, when the root mean square error is less than or equal to the preset root mean square error, it is judged that the response surface accuracy verification is passed.

[0070] The calculation formula of the mean absolute error is:

[0071]

[0072] The calculation formula of the mean absolute error is: i The response surface stress result corresponding to the i th second sample data group is yi; The second stress result corresponding to the i th second sample data group is yi.

[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 with the increase of the coil box thickness, the first coil box stress first increases and then decreases; with the increase of the protection layer thickness, the first coil box stress gradually decreases. The third response surface model is a response surface model constructed based on the coil box thickness data and the protection layer thickness data and the corresponding first insulation layer maximum stress, according to Figure 4 It can be concluded that with the increase of the coil box thickness, the first protection layer maximum stress first increases and then decreases; with the increase of the protection layer thickness, the first protection layer maximum stress gradually decreases. The third response surface model is a response surface model constructed based on the coil box thickness data and the protection layer thickness data and the corresponding first insulation layer maximum stress, according to Figure 5 It can be concluded that with the increase of the coil box thickness, the first insulation layer maximum stress gradually decreases; with the increase of the protection layer thickness, the first insulation layer maximum stress gradually decreases.

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

[0077] In step S5, the first stress result less than or equal to the preset allowable stress is taken as a constraint condition to avoid invalid optimization results, and the sum of the maximum stress margins is taken as an optimization target, so as to maximize the stress safety redundancy within the range of ensuring the safety and stability of the protection structure, and maximize the safety, stability and risk resistance of the protection structure.

[0078] According to another specific embodiment of the present application, the structural optimization method of the protection structure of the superconducting cable disclosed in the embodiment of the present application, the optimization equation in step S5 is:

[0079]

[0080] Wherein, M sum is the sum of the stress margins, σ 线圈盒 is the first coil box maximum stress; σ 保护层 is the first protection layer maximum stress; τ 绝缘层 is the first insulation layer maximum stress.

[0081] It should be noted that, since the first stress result includes the first coil box maximum stress, the first protective layer maximum stress and the first insulation layer maximum stress, the corresponding preset allowable stress includes the coil box allowable stress, the protective layer allowable stress and the insulation layer allowable stress. The yield strength of the coil box at a 4K temperature environment is 900Mpa, which is taken as the coil box allowable stress; the yield strength of the protective layer at a 4K temperature environment is 900Mpa, which is taken as the protective layer allowable stress; and the shear strength of the insulation layer at a 4K temperature environment is 68.6Mpa, which is taken as the insulation layer allowable stress. 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 application, the method for optimizing the structure of the protection structure of the superconducting cable disclosed in the embodiments of the present application further comprises: obtaining an optimal sample data set by using a multi-island genetic algorithm on 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 is obtained; if the accuracy of the optimal sample data set does not meet the requirements, returning to step S4 to increase the number of the second sample data set to optimize the response surface model.

[0083] In summary, the method for optimizing the structure of the protection structure of the superconducting cable provided in the present embodiment has the beneficial effects of high optimization efficiency, being able to cover the global optimization in a complex optimization scenario with multiple design variables and multiple constraint conditions, thereby improving the accuracy of the optimization result. Moreover, the dependence on physical tests is greatly reduced through finite element simulation, the cost and period are reduced, the problem of long period and time-consuming of the traditional optimization method is solved, thereby shortening the iteration period of the optimization design. The response surface model can greatly improve the optimization speed by approximately reflecting the mapping relationship between the coil box thickness, the protective layer thickness and the stress through limited sample data. The response surface model can approximately fit the global trend of the design space, and can jump out of the "local trap" of the experience and trial method through the global optimization algorithm (such as the genetic algorithm), so as to find a better design scheme. Multiple design variables and constraint conditions are simultaneously introduced into the optimization equation during the optimization process, and all conditions are automatically satisfied through the optimization equation, thereby avoiding the performance deterioration caused by single variable optimization. The optimized scheme can be verified again through the finite element model (i.e., "the optimal solution is substituted into the finite element simulation model to verify whether the performance meets the requirements"), thereby ensuring the reliability of the result.

[0084] In order to intuitively understand the effect of the method for optimizing the protection structure of the superconducting cable provided in the present embodiment, the stress distribution diagram obtained in a specific test process is taken as an example for comparison and illustration. Figures 6-13 Figure 6 , Figure 8 ,​Figure 10 and Figure 12 are stress distribution diagrams of the protection structure and components when the protection structure in Figure 1 is not structurally optimized; Figure 7 , Figure 9 , Figure 11 and Figure 13 are stress distribution diagrams of the protection structure and components after the protection structure is optimized using the structural optimization method of the protection structure of the superconducting cable provided in the embodiment.

[0085] As shown in Figure 6 , the overall maximum stress of the protection structure when the protection structure in Figure 1 is not structurally optimized is about 822 MPa, as shown in Figure 7 , the overall maximum stress of the protection structure after optimization is about 468 MPa, that is, the overall maximum stress of the protection structure after optimization decreases by about 43%.

[0086] As shown in Figure 8 , the maximum stress of the coil box before optimization is about 322 MPa, as shown in Figure 9 , the maximum stress of the coil box after optimization is about 210 MPa, that is, the maximum stress of the coil box after optimization decreases by about 35%.

[0087] As shown in Figure 10 , the maximum stress of the protection layer before optimization is about 822 MPa, as shown in Figure 11 , the maximum stress of the protection layer after optimization is about 468 MPa, that is, the maximum stress of the protection layer after optimization decreases by about 43%.

[0088] As shown in Figure 12 , the maximum stress of the insulation layer before optimization is about 45 MPa, as shown in Figure 13 , the maximum stress of the insulation layer after optimization is about 34 MPa, that is, the maximum stress of the insulation layer after optimization decreases by about 18%.

[0089] That is, the optimization scheme obtained by the optimization method of the protection structure of the superconducting cable provided in the embodiment can reduce the stress of each part after redesigning the thickness of the coil box and the protection layer of the protection structure, thereby maximizing the stress margin to improve the structural safety and reliability.

[0090] Embodiment 2

[0091] The embodiment provides a protection structure of a superconducting cable, as shown in Figure 1As shown, the protection structure 11 includes a protection layer 110, an insulation layer 111 and a coil box 112 which are sequentially wrapped outside the superconducting cable 10, and it should be noted that the protection layer 110 can be an armored structure which integrates the functions of mechanical support, electromagnetic shielding, thermal protection, insulation protection and the like. The structure optimization method of the protection structure of the superconducting cable provided in Embodiment 1 is used to optimize the structure of the protection structure 11.

[0092] Embodiment 3

[0093] The embodiment provides a superconducting coil, which comprises a superconducting cable and a protection structure of the superconducting cable. Figure 1 As shown, the superconducting coil 1 comprises the superconducting cable 10 and the protection structure of the superconducting cable provided in Embodiment 2, and the superconducting coil 1 can be combined by a plurality of superconducting cables 10, and the specific number of the superconducting cables 10 can be set according to the use scene requirements of the superconducting coil 1, for example, two, three, four or more, as long as the outer periphery of each superconducting cable 10 is wrapped with the protection layer 110, and the adjacent protection layers 110 are separated by the insulation layer 111, and the outermost side of the insulation layer 111 is wrapped with the coil box 112. It should be noted that, in order to ensure that the superconducting cable 10 has sufficient magnetic field restraining capability when used in a magnetic confinement device, or has sufficient power transmission capability when used for power transmission, the size of the superconducting cable 10 is not involved in the optimization design.

[0094] It should be further noted that the superconducting coil 1 can be used in a stellarator device, and the gap between adjacent superconducting coils of the stellarator superconducting coil is small due to the special shape, so it is very important to improve the space utilization of the protection structure of the superconducting coil. The optimization scheme obtained by the optimization method of the protection structure of the superconducting cable provided in the present application can reasonably optimize the thickness of the coil box and the thickness of the protection layer, and reasonably set the thickness of the coil box and the thickness of the protection layer in the limited space, so as to ensure the safe and stable operation of the superconducting coil. The protection layer of the superconducting coil for the stellarator generally adopts an armored structure.

[0095] It should be noted that, in addition to the specific embodiments of the present application described above, other advantages and effects of the present application can be easily understood by those skilled in the art from the disclosure. Although the description of the present application will be introduced in combination with the preferred embodiments, this does not mean that the features of the present application are limited to this embodiment. On the contrary, the purpose of introducing the present application in combination with the embodiment is to cover other options or modifications which can be extended based on the claims of the present application. In order to provide a deep understanding of the present application, many specific details will be included in the following description. The present application can also be implemented without using these details. In addition, in order to avoid confusion or obscure the focus of the present application, some specific details will be omitted in the description. It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0096] It should be noted that in the present specification, similar reference numbers and letters represent similar items in the following drawings, thus, once an item is defined in one drawing, it need not be further defined and explained in subsequent drawings.

[0097] In the description of the present embodiments, it should be noted that the terms "upper", "lower", "inner", "bottom", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship in which the product of the present application is usually placed, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application.

[0098] The terms "first", "second", etc. are only used for differentiation in description, and cannot be understood as indicating or implying relative importance.

[0099] In the description of the present embodiments, it should also be noted that, unless otherwise explicitly specified and limited, the terms "provided", "connected", "connected" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the communication inside two elements. For those skilled in the art, the specific meaning of the above terms in the present embodiments can be understood according to the specific circumstances.

[0100] Although the present application has been illustrated and described with reference to certain preferred embodiments thereof, it should be understood that the above is further detailed description of the present application in combination with specific embodiments, and cannot be considered as limiting the specific implementation of the present application to these descriptions. Those skilled in the art can make various changes in form and details, including making a number of simple deductions or substitutions, without departing from the spirit and scope of the present application.

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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