Superconducting cavity cooling structure optimization method based on multi-task learning agent model
By optimizing the cooling structure of the conduction-cooled superconducting cavity using a multi-task learning surrogate model, the problem of balancing thermal stability and thermal uniformity in the conduction-cooled superconducting cavity is solved, achieving efficient optimization under given assembly and manufacturing constraints.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- INST OF HIGH ENERGY PHYSICS CHINESE ACAD OF SCI
- Filing Date
- 2026-04-07
- Publication Date
- 2026-05-12
AI Technical Summary
The thermal stability and thermal uniformity of conductive cooling superconducting cavities are difficult to optimize under given assembly and manufacturing constraints. Existing methods are computationally expensive and cannot achieve multi-objective thermal performance optimization.
A multi-task learning surrogate model is adopted, which combines Morris sensitivity screening and the multi-task learning surrogate model. By defining the transient isothermal index STI and the steady-state margin index HMI, key parameters are screened, the multi-task learning surrogate model is trained, and the cooling structure is optimized.
While reducing the number of thermal simulation calculations, the cooling structure is optimized to improve thermal stability and thermal uniformity, making it suitable for vertical testing, horizontal modules, and various heat leakage conditions.
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Figure CN122021345A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of thermal design and structural optimization of superconducting cavity conductive cooling structures, and relates to a method for optimizing superconducting cavity cooling structures based on a multi-task learning surrogate model. This method is applicable to optimizing cooling structure parameters of superconducting cavities under vertical testing, horizontal module conditions, and various non-uniform heat leakage conditions. Background Technology
[0002] Radio frequency (RF) superconducting modules with conduction-cooled superconducting cavities at their core are considered a key technology for promoting the application of RF superconducting technology in industrial accelerators (such as electron beam irradiation, medical sterilization, and environmental remediation). Their core advantage lies in avoiding the complex facilities and maintenance costs of large liquid helium cryogenic systems, and further enhancing the miniaturization and modularity of superconducting particle accelerators. However, constrained by factors such as the limited cooling capacity of small cryogens and the non-uniform heat leakage distribution of the module, the thermal stability and thermal uniformity of the superconducting cavity often become key bottlenecks in conduction-cooling schemes. This manifests in two main ways: firstly, during transient cooling across the superconducting transition temperature region, if the temperature difference on the cavity surface is too large, it may induce a thermal current and form an additional magnetic field, increasing the risk of magnetic flux trapping, thereby leading to an increase in residual resistance and a decrease in the quality factor; secondly, during steady-state operation, excessively high local hot spot temperatures can compress the thermal stability margin, increasing the risk of quenching failure. Therefore, optimizing the geometric parameters of the cooling structure under given assembly and manufacturing constraints to balance thermal uniformity and thermal stability is a key issue in the engineering design of conduction-cooled superconducting cavities. The main solutions for conductive cooling structures are: (1) Copper hoop type, which uses a high thermal conductivity copper clamp on the surface of the superconducting cavity to remove heat; (2) Surface spraying type, which forms a cold ring on the surface of the superconducting cavity by electroplating or cold spraying copper; (3) Welded niobium ring type, which welds niobium material as a cold ring at the equator and bundle tube of the superconducting cavity.
[0003] Welded niobium ring cooling structures, with equatorial and bundled tube cold rings at their core, have been widely used in vertical testing and horizontal modules due to their simple structure, easy fabrication, and controllable thermal resistance. For vertical testing environments with relatively uniform static heat loads, a simplified, symmetrically arranged cold ring structure can be used. However, in horizontal modules, the non-uniformity of heat leakage at input couplers, supports, and one side of the bundled tube is significantly enhanced, necessitating re-optimization of the cold ring arrangement and geometric parameters for the specific application scenario. Relying solely on empirical iteration or brute-force full-parameter scanning is not only computationally expensive but also makes it difficult to simultaneously achieve multi-objective thermal performance optimization. Therefore, a more efficient and streamlined cooling structure optimization method, guided by quantifiable indicators, is urgently needed to obtain a geometric scheme with superior thermal stability and uniformity under given mechanical and thermal boundary constraints. Summary of the Invention
[0004] To address the problems existing in the prior art, the present invention aims to provide a method for optimizing the cooling structure of a superconducting cavity based on a multi-task learning surrogate model. This method fully considers the evaluation indicators of cooling effect, and combines Morris sensitivity screening, a multi-task learning surrogate model, and an optimization method to obtain the cooling structure with the optimal cooling effect.
[0005] This invention proposes an optimization method for conductive cooling structures, which involves "index definition → parameter screening → proxy modeling → model optimization". Specifically, it is as follows: (1) Construct the transient isothermal index STI and the steady-state margin index HMI. STI is used to measure the control energy of the temperature difference on the superconducting cavity when it crosses the superconducting transition temperature region (such as Nb3Sn about 18K). HMI is used to measure the magnitude of the highest temperature of the superconducting cavity under steady state and the margin of the relative quench limit. For any set of geometric parameter vectors x, a unique superconducting cavity cooling structure model can be obtained after parameterization modeling. Transient thermal simulation and steady-state thermal simulation are performed under the unified thermal boundary conditions, and the STI(x) and HMI(x) corresponding to the parameter vector can be calculated. Both are dimensionless and can be compared across schemes. (2) The Morris sensitivity screening method is used to identify a small number of key parameters that have a significant impact among multiple geometric parameters, reducing the dimension of subsequent optimization and saving simulation computing power. (3) STI and HMI are obtained by batch sampling and transient / steady-state thermal simulation. The dataset is used to train a shared trunk-dual task head multi-task learning surrogate model to simultaneously approximate two responses, and further obtain the prediction uncertainty for adaptive addition of points to improve the reliability of the surrogate model; (4) Based on the surrogate model, a target function Y containing weighted terms and Chebyshev terms is defined, and the minY is solved by a combination of Sobol coarse sweep and Nelder-Mead local refinement. Finally, the optimal parameter vector x* corresponding to the minimum value of the target function is output through continuous iteration, thereby obtaining the optimal conduction cooling structure under given thermal boundary and assembly constraints. This invention can significantly reduce the number of high-cost thermal simulations while ensuring thermal stability and thermal uniformity, and is suitable for the design optimization of conduction cooling structures under vertical testing, horizontal modules and different heat leakage conditions. Among them, the multi-task learning surrogate model is not limited to MLP.
[0006] The technical solution of this invention is as follows: A method for optimizing the cooling structure of a superconducting cavity based on a multi-task learning surrogate model, comprising the following steps: The initial structural parameters of the superconducting cavity cooling structure were adjusted, and a superconducting cavity cooling structure model was constructed based on each set of structural parameters. The transient isothermal index STI and steady-state margin index HMI corresponding to the set of structural parameters were obtained through simulation calculation. Based on the degree of influence of each parameter on the transient isothermal index STI and the steady-state margin index HMI, a set of key parameters are selected from the initial structural parameters. The training sample set is generated based on this set of key parameters to train and optimize the multi-task learning agent model; each training sample includes a set of key parameter values and their corresponding transient isothermal index STI and steady-state margin index HMI; Using these key parameters as optimization variables, the optimized multi-task learning surrogate model is used to determine a set of optimal parameter values as the structural parameters of the superconducting cavity cooling structure.
[0007] Preferably, the transient isothermal index STI is used to measure the control energy of the temperature difference on the superconducting cavity when it crosses the superconducting transition temperature region, and the steady-state margin index HMI is used to measure the magnitude of the highest temperature of the superconducting cavity in steady state and the margin relative to the upper limit of quenching.
[0008] Preferably, the multi-task learning agent model includes an input module, a shared trunk, and a dual-task output head; the method for generating a training sample set based on this set of key parameters to train and optimize the multi-task learning agent model is as follows: N candidate sample points are generated in d-dimensional space using Sobol low-discrepancy sequences, and a feasibility judgment is performed on each candidate sample point. The candidate sample points that meet the feasibility criteria are taken as valid sample points. Each candidate sample point corresponds to a set of normalized key parameter values, where d is the number of parameters in the set of key parameters. For each valid sample point, the transient isothermal index STI and steady-state margin index HMI corresponding to the simulation calculation under the same thermal boundary conditions are used as the label of the valid sample point to form a training sample set; The input module receives a set of key parameters from the training samples and sends them to the shared trunk. The shared trunk extracts intermediate features h(x) that are commonly related to the transient isothermal index STI and the steady-state margin index HMI based on these key parameters. The first task head outputs the predicted value of the transient isothermal index STI based on the intermediate features h(x), and the second task head outputs the predicted value of the steady-state margin index HMI based on the intermediate features h(x). Then, the transient isothermal index loss and the steady-state margin index loss are calculated based on the predicted values and the labels of the training samples. The multi-task learning agent model is optimized based on the loss values.
[0009] Preferably, the shared trunk uses a two-layer fully connected network, each layer containing 64 hidden units and employing the ReLU activation function; the task output head uses a fully connected layer containing 32 hidden units and a linear output layer.
[0010] Preferably, the transient isothermal index STI and steady-state margin index HMI corresponding to each candidate sample point are calculated and substituted into the objective function Y, based on the mean of the comprehensive objective function Y. with standard deviation Constructing a confidence lower bound criterion A is a constant; in the candidate sample point set, the point that minimizes LCB(x) is selected as the new simulation point.
[0011] Preferably, the Sobol sampling method is used to generate multiple sample points in k-dimensional space, where k is the number of key parameters; then, based on the objective function Y, the transient isothermal index STI and steady-state margin index HMI corresponding to each sample point are calculated using a multi-task learning surrogate model and substituted into the objective function Y to calculate the objective function value; several sample points with the smallest objective function value, as well as the center point and 1-2 corner points among the sample points, are selected as the starting point for local optimization, and the Nelder-Mead method is used for local optimization to determine a set of optimal parameter values as the structural parameters of the superconducting cavity cooling structure.
[0012] Preferably, the initial structural parameters of the superconducting cavity cooling structure are adjusted using the Morris sensitivity analysis method to screen out a set of key parameters.
[0013] A superconducting cavity cooling structure optimization system based on a multi-task learning agent model is characterized by comprising an index calculation module, a parameter screening module, a model training module, and an optimization module. The index calculation module is used to construct a superconducting cavity cooling structure model based on each set of structural parameters of the superconducting cavity cooling structure and to simulate and calculate the transient isothermal index STI and steady-state margin index HMI corresponding to the set of structural parameters. The parameter filtering module is used to filter a set of key parameters from the structural parameters based on the degree of influence of each parameter on the transient isothermal index STI and the steady-state margin index HMI. The model training module is used to generate a training sample set based on the set of key parameters to train and optimize the multi-task learning agent model; wherein each training sample includes a set of key parameter values and their corresponding transient isothermal index STI and steady-state margin index HMI; The optimization module is used to take the set of key parameters as optimization variables and use the optimized multi-task learning surrogate model to determine a set of optimal parameter values as the structural parameters of the superconducting cavity cooling structure.
[0014] A computing device, characterized in that it comprises: a processor and a memory storing a computer program, wherein the computer program, when run by the processor, executes the method described above.
[0015] A computer-readable storage medium, characterized in that it stores instructions that, when executed on a computer, cause the computer to perform the above-described method.
[0016] The advantages of this invention are as follows: This invention addresses the conductive cooling structure of a superconducting cavity composed of an equatorial cold ring and a bundled tube cold ring. Under vertical / horizontal testing and various heat leakage conditions, it proposes a general approach and method to obtain the optimal geometric scheme through "defining indicators—sensitivity analysis—multi-task learning surrogate modeling—optimization based on the surrogate model," including the following points: 1) Establish a dimensionless index system for transient and steady-state conditions: STI is used to measure isothermal performance across the 18 K range, providing criteria for meeting standards and requiring optimization; HMI is used to measure the margin of steady-state hotspot distance from the upper limit, also with a grading standard. The setting of these two indices reflects the effectiveness of the cooling structure and facilitates horizontal comparisons between different geometric schemes; 2) Morris method for parameter selection and dimensionality reduction: Considering the complex heat load distribution within the module, direct optimization of all parameters is prone to falling into the curse of dimensionality. First, the geometric parameters are normalized to [0,1]. Based on the STI and HMI obtained from transient / steady-state simulations, all geometric parameters are sorted according to the Morris basic effects and statistics. The key dominant parameters are retained for subsequent optimization, which significantly reduces complexity and computing cost. 3) Data acquisition and multi-task MLP model construction: Sobol is used to generate samples and supplement boundary points. STI and HMI datasets are obtained based on unified thermal boundary conditions. Then, a multi-task MLP model with shared trunk and dual task heads is trained, and the empirical uncertainty is given by Deep Ensemble to achieve adaptive point addition based on LCB criterion. 4) Optimal selection based on global coarse scanning combined with local optimization: using... Using the objective function, a general strategy of Sobol coarse sweep and Nelder-Mead local optimization is performed on the MLP model, and the outputs x1, x2, x3 corresponding to minY are used as the optimized cooling structure parameters. Attached Figure Description
[0017] Figure 1 Flowchart of the method for optimizing conductive cooling structures.
[0018] Figure 2 This is a diagram of a 1.3GHz single-cell superconducting cavity and its cooling structure.
[0019] Figure 3 This is a schematic diagram of the multi-task learning agent model structure.
[0020] Figure 4 This is a system diagram of the present invention. Detailed Implementation
[0021] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
[0022] This invention aims to provide an optimization method for superconducting cavity conductive cooling structures based on a multi-task learning surrogate model. Through a process of "index—parameter screening—surrogate—optimization," it achieves a geometric scheme with better thermal stability and thermal uniformity while satisfying geometric / assembly constraints and thermal boundary conditions, and reduces the number of thermal simulation calculations. The optimization method process adopted in this invention is as follows: Figure 1 As shown.
[0023] The key steps will be explained in detail below.
[0024] I. Geometric Parameters The cooling ring of a conductive cooling superconducting cavity typically consists of an equatorial cooling ring and a bundle tube cooling ring, such as... Figure 2 As shown, the 1.3GHz single-cell cavity, a commonly used cavity type for conductive cooling superconducting cavities, is taken as an example.
[0025] To describe its geometric layout and dimensions, the following parametric geometric variables are established: the ring radius R1 of the equatorial cold ring; the ring radius R2 of the left bundle tube cold ring; the ring radius R3 of the right bundle tube cold ring; the thickness T1 of the equatorial cold ring; the thickness T2 of the left bundle tube cold ring; the characteristic thickness T3 of the right bundle tube cold ring; the relative position dimension L12 between the equatorial cold ring and the left bundle tube cold ring; and the relative position dimension or thermal bridge installation distance L13 between the equatorial cold ring and the right bundle tube cold ring. These parameters may correspond to geometric quantities such as cold ring radius, width, thickness, axial position, and connection position with thermal bridges in different implementations. As long as they are used to parametrically describe the cooling structure and participate in subsequent thermal performance optimization, they fall within the protection scope of this invention.
[0026] Let the original design variable vector be p = (R1, R2, R3, T1, T2, T3, L12, L13). Based on manufacturing constraints, assembly constraints, and geometric non-interference constraints, upper and lower limits are set for each variable. Furthermore, the variables involved in the calculation are normalized to the [0,1] interval through linear mapping, resulting in the normalized design variable vector x = (x1,…,x…). d ), where d is the number of variables entering the current analysis stage; in the initial complete parameter space, d can be 8; after sensitivity screening, d can be reduced to 3 or other preset values. In the following text, x without subscripts represents a vector consisting of a set of design parameters, and x with subscripts... iThis represents the i-th parameter component in the vector.
[0027] II. Two key evaluation indicators Superconducting cavities operate at low temperatures, and their thermal stability and thermal uniformity directly affect their superconducting performance. Particularly for Nb3Sn superconducting cavities, the temperature difference across the superconducting transition temperature region (approximately 18K) drives thermocurrents and induces additional magnetic fields, which are then trapped by magnetic flux during the superconducting transition, leading to increased residual resistance and a decreased Q0 value. Therefore, achieving isothermal crossing of 18K during the transient cooling phase and suppressing hotspots from approaching the allowable upper limit during steady-state operation are key factors in improving the performance of Nb3Sn superconducting cavities. For any given parameter vector x, parametric modeling is first performed according to this parameter vector to obtain the corresponding cooling structure geometry model; then, thermal simulation is performed under uniform boundary conditions, material parameters, and contact thermal resistance. The dependence of the temperature field on the geometric parameters obtained from the simulation can be denoted as T(x). s ,t;x) or T(x s ;x), where x s Let x represent the spatial position on the cavity surface, and let x represent the design parameter vector. Therefore, although parameters such as R1 and R2 are not explicitly written in the following index formulas, the geometric parameters are implicitly included in the index definition through the temperature field. Thus, both STI and HMI can be regarded as response functions of the design parameter vector x.
[0028] 1. STI (Superconducting Transition Index) To suppress the thermocurrent generated in Nb3Sn superconducting cavities during transient cooling exceeding 18K, it is necessary to minimize the temperature difference across the cavity. In engineering, 0.2K is often considered a good standard for this temperature difference. To compare the temperature difference control capabilities of different cooling structures across 18K, a dimensionless transient isothermal index (STI) is defined: Wherein, let the surface of the cavity be S, and the instantaneous temperature field be S. average surface temperature ; Time window ; Temperature control target ;P99() represents all Use the 99th percentile to avoid the influence of occasional numerical spikes caused by abnormal grid patterns or other reasons.
[0029] Therefore, when STI≤1, the temperature control target is achieved or better; when 1<STI≤2, the cooling structure is considered to be effective; when STI>2, the cooling structure is considered to need optimization.
[0030] 2. HMI (Hotspot Margin Index) When the superconducting cavity operates under steady state conditions, it is necessary to pay attention to the distance between the "hot spot" (the highest temperature) and the "risk point" (quench temperature). The closer they are, the greater the risk of quenching. Therefore, the HMI value is defined as an evaluation index: Among them, assuming the steady-state temperature field is , P99(T) is the 99th percentile of the surface temperature T of the superconducting cavity (to prevent occasional numerical spikes), is the upper limit of the allowable highest temperature, taking the quench temperature of Nb, 9.2K; Take the cold-end temperature applied in the simulation.
[0031] Therefore, when HMI ≤ 0.5, it is considered that the operating state is good and the margin is high at this time; when 0.5 < HMI ≤ 0.8, it is considered that the cooling structure needs to be optimized and warning is required; when HMI > 0.8, it is considered that the risk of quenching is very high.
[0032] Thus, for each set of parameter vectors x that satisfy the constraints, a set of definite response values STI(x) and HMI(x) can be obtained under the unified thermal simulation settings.
[0033] III. Morris Sensitivity Analysis Although the performance of the cooling structure is determined by 8 geometric parameters simultaneously, due to the complexity of the structure and thermal load distribution within the module, there may be some parameters that have limited influence on the structure performance; in addition, if multiple variables are optimized simultaneously, it will lead to the curse of dimensionality. Therefore, it is very necessary to evaluate the influence degree of different geometric parameters on the structure performance and select a small number of key geometric parameters. Here, the Morris sensitivity analysis method is used to screen the key geometric parameters. The Morris method is a global sensitivity analysis method based on the one-at-a-time perturbation trajectory. The English expression of the one-at-a-time perturbation trajectory is One-At-a-Time, abbreviated as OAT. Its core idea is to construct several trajectories in the normalized design space, change only one variable each time, and examine the influence amplitude of the change of this variable on the response function.
[0034] Assume that the current normalized design variable vector participating in the sensitivity analysis is x = (x1,..., x d ), and d is the number of variables participating in the analysis. Each variable is discretized into p levels (p ≥ 4, which can be set according to requirements), and the step size is taken as ; assume that a total of r OAT trajectories are generated. For a certain reference point x (j) on the jth trajectory, denote e iLet be the unit vector in the i-th coordinate direction. For any response o, o∈{STI,HMI}, the basic effect of the i-th variable on the j-th trajectory is defined as: Where, when o=STI, This represents the basic effect of the i-th variable on the STI response; when o = HMI, This represents the basic effect of the i-th variable on the HMI response.
[0035] We can further calculate the statistic corresponding to the i-th variable: Used to measure the overall influence of the i-th variable on the response o; the larger the value, the more important the variable. Since both STI and HMI are defined dimensionless indicators, they can be directly combined for weighting. default , The weighting values can be adjusted as needed.
[0036] The result Sort the variables from largest to smallest, retain the top three corresponding geometric parameters as variables for subsequent optimization, and set the others as constants. This reduces the dimensionality of the eight variables to be optimized to three, focusing on the key variables while saving computational resources and time for subsequent optimization. The number of variables, d, to be reduced can be selected based on specific requirements.
[0037] IV. Neural Networks 1. Sampling method: First, linearly scale the key variables selected through Morris sensitivity analysis to [0,1]. d Then, N candidate sample points are generated in this d-dimensional space using Sobol low-discrepancy sequences: , Each candidate sample point Both represent a complete set of key parameter values, rather than generating N values independently for each parameter. A Sobol sequence is a sequence that can be defined in the range [0,1]. d A quasi-random point set is generated internally, belonging to a low-discrepancy sequence, which covers the space more uniformly than pure randomness. Then, multiple boundary points are added at the boundaries to supplement the data and enhance the boundary learning ability. After generating candidate sample points, a feasibility judgment is performed on each candidate point. Only samples that meet the feasibility requirements are retained. The constraint categories are selected as needed, and the main categories are: (1) geometric non-interference constraints; (2) manufacturing constraints, such as the upper and lower limits of cold ring thickness; (3) assembly constraints, such as the thermal bridge installation distance L.12 L 13 Assembly range, etc.
[0038] Only retain those that meet the requirements. The true sample points are used as valid design samples. Transient / steady-state thermal simulations are performed on each valid sample point under the same thermal boundary conditions, and its value is calculated using the aforementioned formula. and This results in a supervised learning dataset: , where N eff The number of valid samples to meet feasibility constraints.
[0039] 2. Multi-task learning agent model (MLP model) Based on the aforementioned dataset, a multi-task learning surrogate model will be built to jointly fit the two responses, STI and HMI. This surrogate model includes an input module, a shared trunk, and a dual-task output head, with the following structure: Figure 3 As shown.
[0040] The input module receives the key geometric parameter vector x, filtered by Morris sensitivity analysis, and organizes it into a network input vector according to a preset parameter order. The vector is then normalized to [0,1]. d The parameter vectors undergo consistency checks and dimension assembly to obtain standardized input. The input vector is then fed into the shared trunk.
[0041] The shared trunk is used to extract intermediate features that are commonly related to the two types of thermal performance indicators, denoted as h(x); the shared trunk consists of a two-layer fully connected network, and its mapping process is written as: The first task header receives h(x) and outputs the predicted value of STI; the second task header receives h(x) and outputs the predicted value of HMI. Therefore, they can be written as follows: Where 𝜃 represents all parameters of the model, which can be further decomposed into: in, To share trunk road mapping, For STI task headers, For HMI task headers, , and These represent the training parameters for the corresponding modules. The shared trunk uses a two-layer fully connected network, each layer containing 64 hidden units and employing the ReLU activation function; each task output head can use a fully connected layer with 32 hidden units and a linear output layer. Let the number of training samples be N. eff The STI task loss and HMI task loss are defined as follows: in, The Huber function can be written as: r is the prediction error. As the segmentation threshold, this invention takes .
[0042] The total loss from multitasking is: in As the task weight, this invention takes .
[0043] The optimizer uses Adam (initial learning rate 10). -3 Early stopping: stop if there is no improvement after 50 rounds on the validation set; regularization includes L2 weight decay (10 -4 ) with Light Dropout (0.05-0.1).
[0044] 3. Prediction uncertainty and adaptive point addition To improve the reliability of the surrogate model in critical regions and sparse sample regions, the Deep Ensemble method can be used to estimate the prediction uncertainty. Specifically, M surrogate models with different initializations or different data perturbations are trained independently, and the prediction of the m-th model for candidate point x is denoted as Z. m (x), where: Where Z can represent STI, HMI, or a combined objective function Y formed by combining the two. For any candidate point x, the predicted mean and predicted standard deviation are defined as follows: in, This represents the average value predicted for that point. It indicates the degree of divergence between models and can reflect empirical uncertainty.
[0045] To determine the most worthy sample points for the next round of realistic thermal simulation. It can be based on the mean of the comprehensive objective function Y. with standard deviation Constructing a confidence lower bound criterion: Where A>0 is a constant, taking values between 1.0 and 2.0. In the candidate sample point set, the point that minimizes LCB(x) is selected as the new simulation point; that is, the model is adaptively added points using the LCB criterion. x new Perform simulations to obtain the true values, add them to the sample library, and retrain the model. Repeat the above steps until the convergence criterion is met. One point can be added per round, or multiple points can be added in batches. Perform realistic thermal simulations on the newly added points to calculate their... and Then add it to dataset D and retrain the surrogate model. Repeat the above steps until convergence criteria are met, such as the improvement in validation error after adding new samples being less than a threshold, or the optimal value no longer changing significantly within several rounds.
[0046] V. Optimization Algorithm Define the objective function Y for optimization: Where x = (x1, x2, x3) is within the given range; , The weighting values can be adjusted as needed; It is Chebyshev's term. This avoids situations where individual outliers are offset by another item.
[0047] The optimization strategy involves first performing a global coarse scan, followed by local optimization, balancing accuracy and efficiency. The Sobol sampling method is used to randomly generate N=200 sample points. For each point, Y is calculated (using a trained multi-task MLP model). The Top-5 (the 5 points with the smallest Y) are selected as starting points for local optimization, along with the center point and 1-2 corner points (for enhanced robustness), for a total of 7-8 starting points. Local optimization employs the Nelder-Mead method, a derivative-free local optimization algorithm belonging to the simplex search class. It does not rely on the gradient information of the objective function; instead, it iteratively adjusts a set of vertices by comparing function values, approximating the optimal solution. This method is well-suited for non-smooth objective functions (such as functions containing a max). Finally, the optimization of minY is completed, yielding the corresponding values of x1, x2, and x3, representing the optimized conductive cooling structure.
[0048] like Figure 4 As shown, an optional embodiment of the present invention provides a superconducting cavity cooling structure optimization system based on a multi-task learning agent model, characterized in that it includes an index calculation module, a parameter screening module, a model training module, and an optimization module; The index calculation module is used to construct a superconducting cavity cooling structure model based on each set of structural parameters of the superconducting cavity cooling structure and to simulate and calculate the transient isothermal index STI and steady-state margin index HMI corresponding to the set of structural parameters. The parameter filtering module is used to filter a set of key parameters from the structural parameters based on the degree of influence of each parameter on the transient isothermal index STI and the steady-state margin index HMI. The model training module is used to generate a training sample set based on the set of key parameters to train and optimize the multi-task learning agent model; wherein each training sample includes a set of key parameter values and their corresponding transient isothermal index STI and steady-state margin index HMI; The optimization module is used to take the set of key parameters as optimization variables and use the optimized multi-task learning surrogate model to determine a set of optimal parameter values as the structural parameters of the superconducting cavity cooling structure.
[0049] An optional embodiment of the present invention provides a computing device, characterized in that it includes: a processor and a memory storing a computer program, wherein the computer program is executed by the processor to perform the above-described method.
[0050] An optional embodiment of the present invention provides a computer-readable storage medium, characterized in that it stores instructions that, when executed on a computer, cause the computer to perform the above-described method.
[0051] The above are preferred embodiments of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for optimizing the cooling structure of a superconducting cavity based on a multi-task learning surrogate model, comprising the following steps: The initial structural parameters of the superconducting cavity cooling structure were adjusted, and a superconducting cavity cooling structure model was constructed based on each set of structural parameters. The transient isothermal index STI and steady-state margin index HMI corresponding to the set of structural parameters were obtained through simulation calculation. Based on the degree of influence of each parameter on the transient isothermal index STI and the steady-state margin index HMI, a set of key parameters are selected from the initial structural parameters. Based on this set of key parameters, a training sample set is generated to train and optimize the multi-task learning agent model. Each training sample includes a set of key parameter values and their corresponding transient isothermal index STI and steady-state margin index HMI; Using these key parameters as optimization variables, the optimized multi-task learning surrogate model is used to determine a set of optimal parameter values as the structural parameters of the superconducting cavity cooling structure.
2. The method according to claim 1, characterized in that, The transient isothermal index STI is used to measure the control energy of the temperature difference in the superconducting cavity when it crosses the superconducting transition temperature region, and the steady-state margin index HMI is used to measure the magnitude of the highest temperature of the superconducting cavity in steady state and the margin relative to the upper limit of quenching.
3. The method according to claim 1, characterized in that, The multi-task learning agent model includes an input module, a shared trunk, and a dual-task output head; the method for generating a training sample set based on this set of key parameters to train and optimize the multi-task learning agent model is as follows: N candidate sample points are generated in d-dimensional space using Sobol low-discrepancy sequences, and a feasibility judgment is performed on each candidate sample point. The candidate sample points that meet the feasibility criteria are taken as valid sample points. Each candidate sample point corresponds to a set of normalized key parameter values, where d is the number of parameters in the set of key parameters. For each valid sample point, the transient isothermal index STI and steady-state margin index HMI corresponding to the simulation calculation under the same thermal boundary conditions are used as the label of the valid sample point to form a training sample set; The input module receives a set of key parameters from the training samples and sends them to the shared trunk. The shared trunk extracts intermediate features h(x) that are commonly related to the transient isothermal index STI and the steady-state margin index HMI based on these key parameters. The first task head outputs the predicted value of the transient isothermal index STI based on the intermediate features h(x), and the second task head outputs the predicted value of the steady-state margin index HMI based on the intermediate features h(x). Then, the transient isothermal index loss and the steady-state margin index loss are calculated based on the predicted values and the labels of the training samples. The multi-task learning agent model is optimized based on the loss values.
4. The method according to claim 3, characterized in that, The shared trunk uses a two-layer fully connected network, each layer containing 64 hidden units and employing the ReLU activation function; the task output head uses a fully connected layer containing 32 hidden units and a linear output layer.
5. The method according to claim 3, characterized in that, Calculate the transient isothermal index STI and steady-state margin index HMI for each candidate sample point and substitute them into the objective function Y. Then, calculate the mean of the comprehensive objective function Y. with standard deviation Constructing a confidence lower bound criterion A is a constant; in the candidate sample point set, the point that minimizes LCB(x) is selected as the new simulation point.
6. The method according to claim 1, characterized in that, Multiple sample points are generated in k-dimensional space using the Sobol sampling method, where k is the number of key parameters. Then, based on the objective function Y, the transient isothermal index STI and steady-state margin index HMI corresponding to each sample point are calculated using a multi-task learning surrogate model and substituted into the objective function Y to obtain the objective function value. Several sample points with the smallest objective function value, as well as the center point and 1-2 corner points among the sample points, are selected as the starting point for local optimization. The Nelder-Mead method is used for local optimization to determine a set of optimal parameter values as the structural parameters of the superconducting cavity cooling structure.
7. The method according to claim 1, characterized in that, The initial structural parameters of the superconducting cavity cooling structure were adjusted using the Morris sensitivity analysis method, and a set of key parameters were selected.
8. A superconducting cavity cooling structure optimization system based on a multi-task learning surrogate model, characterized in that, It includes an indicator calculation module, a parameter selection module, a model training module, and an optimization module; The index calculation module is used to construct a superconducting cavity cooling structure model based on each set of structural parameters of the superconducting cavity cooling structure and to simulate and calculate the transient isothermal index STI and steady-state margin index HMI corresponding to the set of structural parameters. The parameter filtering module is used to filter a set of key parameters from the structural parameters based on the degree of influence of each parameter on the transient isothermal index STI and the steady-state margin index HMI. The model training module is used to generate a training sample set based on the set of key parameters to train and optimize the multi-task learning agent model. Each training sample includes a set of key parameter values and their corresponding transient isothermal index STI and steady-state margin index HMI; The optimization module is used to take the set of key parameters as optimization variables and use the optimized multi-task learning surrogate model to determine a set of optimal parameter values as the structural parameters of the superconducting cavity cooling structure.
9. A computing device, characterized in that, include: A processor, a memory storing a computer program, wherein the computer program, when executed by the processor, performs the method as described in any one of claims 1 to 7.
10. A computer-readable storage medium, characterized in that, A storage instruction that, when executed on a computer, causes the computer to perform the method as described in any one of claims 1 to 7.