Method and system for optimizing high-dimensional parameters of a klystron

Abstract

The application provides a kind of klystron high-dimensional parameter optimization method and system, comprising: using klystron one-dimensional large signal simulation software KlyH, the input design parameter is simulated and calculated, and initial data set containing design parameter and corresponding output parameter is generated;Regression prediction model of design parameter to output parameter is constructed, the normalized output change rate of design parameter is calculated based on regression prediction model, and the sensitivity of each design parameter to output parameter is determined according to the normalized output change rate;According to the sensitivity, the range of each design parameter is dynamically adjusted, the optimization search interval of each design parameter is obtained, and multi-objective optimization algorithm is used to optimize and solve in the optimization search interval, and the optimal solution set is obtained.The dimensionality reduction and search space compression of klystron design parameter are realized, the calculation efficiency and search quality are further improved, and reliable support can be provided for intelligent optimization design of high-performance klystron.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of high-power microwave and computer science, and particularly relates to a method and system for optimizing high-dimensional parameters of a klystron. BACKGROUND

[0002] A relativistic klystron amplifier (RKA) is a typical high-power microwave vacuum electron device. Due to its high peak power, high gain, high efficiency, and frequency and phase stability, the RKA has a wide application prospect in the fields of particle accelerators, pulse radars, and power synthesis. With the development of high-power microwave technology, the RKA has achieved a terawatt to gigawatt level output power in the L-band to Ka-band, which is of great significance to promote the engineering application of high-power microwave systems.

[0003] The design of the RKA involves a large number of coupled parameters such as multi-cavity resonant structure, drift tube length, beam parameters, and external quality factor. The design space is high-dimensional and highly nonlinear. In order to obtain a high-efficiency and compact klystron, it is necessary to globally optimize these parameters under multiple objectives and constraints.

[0004] In the prior art, part of the design work still relies on engineers to perform a trial-and-error cycle of "simulation-manual adjustment-re-simulation" based on physical intuition and previous experience. This method not only has a long cycle and strong subjectivity, but also easily falls into a local optimal solution, and it is difficult to systematically find a global design scheme with better performance in the vast high-dimensional design space. The existing method lacks an effective tool for quickly and quantitatively analyzing the sensitivity of all design parameters in the high-dimensional space. Users cannot clearly identify which parameters are key parameters affecting performance and which parameters are relatively insensitive secondary parameters, resulting in low parameter optimization efficiency and waste of huge computing resources.

[0005] Therefore, the prior art still needs further development. SUMMARY

[0006] The present application aims to overcome the above technical deficiencies and provide a method and system for optimizing high-dimensional parameters of a klystron to solve the problems existing in the prior art.

[0007] To achieve the above technical purpose, according to a first aspect of the present application, a method for optimizing high-dimensional parameters of a klystron is provided, comprising:

[0008] S100, using a one-dimensional large signal simulation software KlyH of the klystron, performing simulation calculation on input design parameters to generate an initial data set containing the design parameters and corresponding output parameters;

[0009] S200, constructing a regression prediction model of the design parameters to the output parameters according to the initial data set, calculating a normalized output change rate of the design parameters based on the regression prediction model, and determining the sensitivity of each design parameter to the output parameter according to the normalized output change rate;

[0010] S300, dynamically adjusting the range of each design parameter according to the sensitivity to obtain an optimized search interval of each design parameter, and performing optimization solving in the optimized search interval by using a multi-objective optimization algorithm to obtain an optimal solution set.

[0011] Specifically, the regression prediction model of the design parameters to the output parameters is constructed according to the initial data set, including:

[0012] The design parameters in the initial data set are taken as input features, the output parameters in the initial data set are taken as prediction targets, and a random forest regression model is used to construct the regression prediction model of the design parameters to the output parameters.

[0013] Specifically, the normalized output change rate of the design parameters is calculated, and the sensitivity of each design parameter to the output parameter is determined according to the normalized output change rate, including:

[0014] Based on the regression prediction model, positive and negative perturbations are applied to each design parameter, the change amount of the corresponding output parameter is calculated by using the regression prediction model, the change amount of the output parameter is normalized to obtain the normalized output change rate of each design parameter, and the sensitivity of each design parameter to the output parameter is determined according to the normalized output change rate of each design parameter.

[0015] Specifically, the calculation method of the normalized output change rate of each design parameter includes:

[0016] The positive and negative perturbations are applied to each design parameter, the change amount of the corresponding output parameter is calculated by using the regression prediction model, and the change amount of the output parameter is normalized, and the specific calculation formula is as follows:

[0017] ;

[0018] Wherein, represents the normalized output change rate of each design parameter, x represents the value of the design parameter, represents the perturbation amplitude, , respectively represent the maximum value and the minimum value of the output parameter in the initial data set.

[0019] Specifically, the sensitivity of each design parameter to the output parameter is determined according to the normalized output change rate of each design parameter, including:

[0020] The mean and variance of the normalized output change rate of each design parameter are calculated, and the sensitivity of a single design parameter is the sum of the mean and variance of the normalized output change rate, and the specific calculation formula is:

[0021] ;

[0022] wherein, sensitivity of a single design parameter, the mean of the normalized output change rate of a single design parameter, the variance of the normalized output change rate of a single design parameter.

[0023] Specifically, the range of each design parameter is dynamically adjusted to obtain an optimized search interval of each design parameter, which comprises:

[0024] First, the initial search interval of the design parameter is defined according to the engineering constraint principle, then a dynamic scaling factor is set for each design parameter according to the sensitivity of each design parameter to the output parameter, and then the initial search interval of each design parameter is adaptively adjusted according to the dynamic scaling factor to obtain the optimized search interval.

[0025] Specifically, the calculation method of the dynamic scaling factor is as follows:

[0026] ;

[0027] wherein, the dynamic scaling factor of a single design parameter, sensitivity of a single design parameter, and respectively represent the minimum and maximum of the sensitivity of all design parameters, preset minimum scaling ratio, ∈(0,1).

[0028] Specifically, the calculation method of the optimized search interval comprises:

[0029] The initial search interval of each design parameter is adaptively adjusted according to the dynamic scaling factor to obtain the optimized search interval, and the specific calculation method is as follows:

[0030] ;

[0031] wherein, the dynamic scaling factor of a single design parameter, the minimum value of the optimized search interval of a single design parameter, the maximum value of the optimized search interval of a single design parameter, the minimum value of the initial search interval of a single design parameter, represent a maximum value of an initial search interval of a single design parameter.

[0032] Specifically, the multi-objective optimization algorithm is used to perform optimization solving in the optimization search interval to obtain an optimal solution set, including:

[0033] The multi-objective particle swarm optimization algorithm is used to perform multi-objective optimization on the design parameters in the optimization search interval to obtain a Pareto front solution set, and the optimal solution set is screened according to the target optimization parameters.

[0034] According to a second aspect of the present application, a high-dimensional parameter optimization system of a klystron is provided, including:

[0035] The data generation module is configured to perform simulation calculation on the input design parameters by using one-dimensional large-signal simulation software KlyH of the klystron to generate an initial data set containing the design parameters and corresponding output parameters.

[0036] The sensitivity analysis module is configured to construct a regression prediction model of the design parameters to the output parameters according to the initial data set, calculate a normalized output change rate of the design parameters based on the regression prediction model, and determine the sensitivity of each design parameter to the output parameter according to the normalized output change rate.

[0037] The multi-objective optimization module is configured to dynamically adjust the range of each design parameter to obtain an optimization search interval of each design parameter, and use a multi-objective optimization algorithm to perform optimization solving in the optimization search interval to obtain an optimal solution set.

[0038] Beneficial effects:

[0039] The present application provides a high-dimensional parameter optimization method and system of a klystron, constructs a regression prediction model of the design parameters to the output parameters according to the generated initial data set containing the design parameters and corresponding output parameters, calculates a normalized output change rate of the design parameters, and determines the sensitivity of each design parameter to the output parameter according to the normalized output change rate, dynamically adjusts the range of each design parameter to obtain an optimization search interval of each design parameter, and uses a multi-objective optimization algorithm to perform optimization solving in the optimization search interval to obtain an optimal solution set, which realizes dimension reduction and search space compression of the design parameters of the klystron, significantly improves the calculation efficiency and search quality, greatly reduces the calculation cost, improves the convergence speed and global optimization ability of the multi-objective optimization, has strong flexibility, high analysis accuracy, and can provide reliable support for intelligent optimization design of high-performance klystrons, and provides a new idea for intelligent design of high-power microwave devices such as klystrons. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1is a flow chart of the high-dimensional parameter optimization method of the klystron provided in the specific embodiment of the present application;

[0041] Figure 2 is a system composition schematic diagram of the high-dimensional parameter optimization system of the klystron provided in the specific embodiment of the present application;

[0042] Figure 3 is a flow chart of the sensitivity analysis based on random forest and NOV provided in the specific embodiment of the present application;

[0043] Figure 4 is a sensitivity mean analysis result graph provided in the specific embodiment of the present application;

[0044] Figure 5 is a sensitivity variance analysis result graph provided in the specific embodiment of the present application;

[0045] Figure 6 is a flow chart of the OMOPSO multi-objective optimization algorithm provided in the specific embodiment of the present application;

[0046] Figure 7 is a Pareto front graph of the OMOPSO multi-objective optimization algorithm provided in the specific embodiment of the present application. DETAILED DESCRIPTION

[0047] In order to make the person skilled in the art better understand the technical solutions of the present application, the technical solutions of the present application will be described clearly and completely below in combination with the drawings of the present application. Based on the embodiments in the present application, other similar embodiments obtained by the person skilled in the art without creative labor should all belong to the protection scope of the present application. In addition, the direction words mentioned in the following embodiments, such as “up”, “down”, “left”, “right” and the like, are only the directions of the drawings, therefore, the direction words used are used for illustration but not for limiting the present application.

[0048] The present application will be further described below in combination with the drawings and preferred embodiments.

[0049] Embodiment One

[0050] Please refer to Figure 1The embodiment provides a method for optimizing high-dimensional parameters of a klystron, which comprises the following steps: performing simulation calculation on input design parameters by using one-dimensional large-signal simulation software KlyH of the klystron to generate an initial data set containing the design parameters and corresponding output parameters; constructing a regression prediction model of the design parameters to the output parameters according to the initial data set, calculating a normalized output change rate of the design parameters based on the regression prediction model, and determining the sensitivity of each design parameter to the output parameter according to the normalized output change rate; dynamically adjusting the range of each design parameter according to the sensitivity to obtain an optimization search interval of each design parameter, and performing optimization solving in the optimization search interval by using a multi-objective optimization algorithm to obtain an optimal solution set.

[0051] It can be understood that, by adopting the technical scheme, the technical problem that the existing method lacks an effective tool capable of performing fast and quantitative sensitivity analysis on all design parameters in a high-dimensional space is solved, the high cost of experiments and three-dimensional simulation is effectively reduced, dimension reduction and search space compression of the design parameters of the klystron are realized, the calculation efficiency and search quality are significantly improved, and reliable support can be provided for engineering fast iterative design.

[0052] Referring to Figure 1 The implementation process of the method for optimizing high-dimensional parameters of the klystron is as follows:

[0053] S100, performing simulation calculation on input design parameters by using one-dimensional large-signal simulation software KlyH of the klystron to generate an initial data set containing the design parameters and corresponding output parameters;

[0054] Further, the embodiment proposes a simulation data generation framework of the relativistic klystron based on KlyH, wherein KlyH adopts a one-dimensional large-signal disc model, can output key indexes such as electron efficiency, interaction length, gain and bandwidth, and has a faster calculation speed than three-dimensional particle simulation. KlyH serves as a generation interface of simulation results of the relativistic klystron, quickly generates large-scale sample data by inputting design parameters such as electron beam parameters, cavity geometric parameters and resonant cavity modulation parameters, needs to remove non-convergent or invalid samples, and has a design variable dimension of 33, thereby providing high-quality basic data for subsequent machine learning model training and sensitivity analysis. The method can effectively reduce the high cost of experiments and three-dimensional simulation, and provides reliable support for engineering fast iterative design.

[0055] Preferably, in the present embodiment, KlyH is a one-dimensional large-signal simulation software of klystron, based on input data including calculation parameters (number of disc, number of pushing disc per high frequency period, maximum number of iterations, initial value of total number of pushing disc), electron beam parameters (beam voltage, beam current, beam radius, drift tube radius), input microwave parameters (input microwave power, input microwave frequency), modulation parameters of each resonant cavity (resonant frequency of resonant cavity, position of resonant cavity in axial direction, characteristic impedance of resonant cavity, gap width, harmonic number), etc., the output efficiency of the klystron is calculated, and the sample number is 60000, including 33 design parameters such as working frequency, beam voltage, beam current, output cavity external quality factor, 6 drift tube lengths and 7 resonant cavity frequencies, data cleaning is performed, and data that does not converge is filtered, and finally the sample number is 57097.

[0056] S200, according to the initial data set, a regression prediction model of design parameters to output parameters is constructed, based on the regression prediction model, the normalized output change rate of the design parameters is calculated, and the sensitivity of each design parameter to the output parameter is determined according to the normalized output change rate.

[0057] Specifically, in the present embodiment, the regression prediction model of design parameters to output parameters is constructed according to the initial data set, including:

[0058] The design parameters in the initial data set are taken as input features, and the output parameters in the initial data set are taken as prediction targets, a random forest regression model is used to construct a regression prediction model of design parameters to output parameters, to learn the nonlinear mapping relationship between the design parameters and the output parameters.

[0059] Preferably, in the present embodiment, the random forest model adopts the configuration of 100 decision trees and a maximum node number of 100, and can process nonlinear and high-dimensional parameter features. The model input is each parameter value, and the output is the corresponding efficiency prediction. The model can use cross-validation method to adjust hyperparameters, to improve the prediction accuracy and avoid overfitting.

[0060] It should be noted that, in view of the characteristics of high dimension and strong nonlinearity of the klystron design variables, the random forest regression model is used for performance prediction modeling in the present embodiment, a large-scale sample generated by KlyH is taken as training data, multi-dimensional design parameters are input, and efficiency prediction values are output, so that fast fitting and high-precision prediction of the performance of the klystron are realized. The random forest model has significant advantages in processing high-dimensional nonlinear features and avoiding overfitting, and can output variable importance indicators at the same time, which is convenient for subsequent sensitivity calculation and optimization range control. Compared with traditional optimization methods based on multivariate linear or simple proxy models, the present method improves the prediction accuracy and generalization ability, and provides a reliable foundation for sensitivity analysis.

[0061] In the embodiment, the normalized output change rate of the design parameter is calculated, and the sensitivity of each design parameter to the output parameter is determined according to the normalized output change rate, comprising:

[0062] Based on the regression prediction model, positive and negative perturbations are applied to each design parameter, the change amount of the corresponding output parameter is calculated by using the regression prediction model, and the change amount of the output parameter is normalized to obtain the normalized output change rate of each design parameter, and the sensitivity of each design parameter to the output parameter is determined according to the normalized output change rate of each design parameter.

[0063] The positive and negative perturbations are applied to each design parameter, the change amount of the corresponding output parameter is calculated by using the regression prediction model, and the change amount of the output parameter is normalized, and the specific calculation formula is as follows:

[0064] ;

[0065] Wherein, The normalized output change rate of each design parameter is represented by x, the value of the design parameter is represented by x, The perturbation amplitude is represented by x, , The maximum and minimum values of the output parameter in the initial data set are represented by x and x respectively.

[0066] It can be understood that in the embodiment, the perturbation amplitude can be set to 10%, that is, ±10% perturbation is applied to each design parameter between its minimum value and maximum value, the difference between the predicted output parameter after perturbation and the original output parameter before perturbation is calculated, the difference value is normalized to the overall output parameter range to obtain the normalized output change rate (NOV), and the sensitivity level of each parameter to the output parameter is comprehensively evaluated by statistics of the mean and variance of NOV in the full sample range, and the sensitivity analysis result is used as the basis for decision of subsequent optimization variable screening and range scaling.

[0067] Further, the mean and variance of the normalized output change rate of each design parameter are calculated, and the sensitivity of a single design parameter is the sum of the mean and variance of the normalized output change rate, and the specific calculation formula is as follows:

[0068] ;

[0069] Wherein, The sensitivity of a single design parameter is represented by x, The mean of the normalized output change rate of a single design parameter is represented by x, The variance of the normalized output change rate of a single design parameter is represented by x.

[0070] It can be understood that the embodiment introduces a normalized output variation rate (NOV) as a core index of sensitivity analysis, calculates the predicted output parameter variation and performs normalization processing by applying positive and negative perturbations to each design parameter, and obtains the NOV mean and variance of each design parameter. The above technical solution can quantify the influence strength and stability of each design parameter on the output parameter in a high-dimensional design space, avoids the problem of large calculation overhead of traditional variance method or Sobol method, and the NOV sensitivity analysis can identify key parameters and reveal the change trend of parameter interaction, thereby providing a quantitative basis for subsequent optimization.

[0071] S300, according to the sensitivity, dynamically adjusting the range of each design parameter, obtaining the optimization search interval of each design parameter, and using a multi-objective optimization algorithm to optimize and solve in the optimization search interval to obtain an optimal solution set.

[0072] Further, in the embodiment, the dynamic adjustment of the range of each design parameter to obtain the optimization search interval of each design parameter comprises:

[0073] First, the initial search interval of the design parameter is defined according to the engineering constraint principle, then a dynamic scaling factor is set for each design parameter according to the sensitivity of each design parameter to the output parameter, and then the initial search interval of each design parameter is adaptively adjusted according to the dynamic scaling factor to obtain the optimization search interval. The calculation method of the dynamic scaling factor is as follows:

[0074] ;

[0075] wherein, denotes the dynamic scaling factor of a single design parameter, denotes the sensitivity of a single design parameter, and denote the minimum value and the maximum value of the sensitivity among all design parameters, denotes a preset minimum scaling ratio, ∈(0,1), in the embodiment, is set to 0.9, that is, to ensure that all parameter ranges are reduced by at most 10%.

[0076] The calculation method of the optimization search interval comprises: adaptively adjusting the initial search interval of each design parameter according to the dynamic scaling factor to obtain the optimization search interval, and the specific calculation method is as follows:

[0077] ;

[0078] wherein, denotes the dynamic scaling factor of a single design parameter, denotes the minimum value of the optimization search interval of a single design parameter, represents a maximum value of the initial search interval of the single design parameter, represents a minimum value of the initial search interval of the single design parameter, represents a maximum value of the initial search interval of the single design parameter.

[0079] It should be noted that the above scheme first defines the initial search interval of the design parameter according to the engineering constraint principle, that is, the principle of meeting the physical feasibility, that is, under the premise of maintaining the physical feasibility, the value range of all design parameters is reduced to accelerate the optimization process and improve the final efficiency. For parameters with low sensitivity, the change has little effect on the efficiency, so a smaller scaling factor is used to reduce the parameter search range, and for parameters with high sensitivity, a larger scaling factor is used to increase the parameter search range, leaving more optimization space to fully explore potential efficient solutions. In the scaling ratio setting, the minimum scaling ratio is fixed at 0.9 to ensure that all design parameter ranges are reduced by at most 10%, and the maximum scaling ratio is dynamically calculated by the NOV mean and standard deviation as input to achieve adaptive coupling of sensitivity and optimization search space. Through this technical scheme, the final optimization search space not only meets the engineering feasibility constraints, but also retains the necessary exploration degree on key parameters, further improving the optimization convergence speed and efficiency index.

[0080] Further, the multi-objective optimization algorithm is used to optimize and solve in the optimization search interval to obtain an optimal solution set, comprising:

[0081] The optimal solution multi-objective particle swarm optimization algorithm is used to perform multi-objective optimization on the design parameters in the optimization search interval to obtain a Pareto front solution set, and the optimal solution set is selected according to the target optimization parameters.

[0082] It can be understood that the optimal solution multi-objective particle swarm optimization algorithm (OMOPSO) is used for multi-objective optimization in this embodiment, the target optimization parameters include the maximum efficiency of the klystron and the minimum interaction length performance indicators, the selection of key optimization parameters is derived from the sensitivity analysis results, and the optimization range is strictly limited based on the sensitivity calculation to ensure that the design scheme is implementable and physically reasonable. The final Pareto front solution set is selected by non-dominated sorting, and in terms of algorithm configuration, the parameters of 15 iterations, 2000 seeds, and 0.07 mutation probability are used, the initial population is randomly generated, and sampling is performed within the sensitivity constraint range, thereby ensuring coverage of the global parameter space.

[0083] Referring to Figures 3-7 The working principle of the present application will be described below by taking the parameter optimization of an X-band seven-cavity single-gap klystron as an example:

[0084] Step 1: First, build a klyH-based one-dimensional large-signal simulation software simulation data generation framework. In the data generation stage, this example is based on a X-band seven-cavity single-gap klystron instance. By inputting design parameters including beam pressure, beam current, beam radius, drift tube geometric parameters, resonant cavity harmonic parameters, input microwave power, and operating frequency, etc., KlyH is driven to perform batch simulation calculation;

[0085] To obtain sufficient sample data covering the design space, this example adopts a strategy combining parameter random sampling and engineering boundary constraints: random sampling ensures coverage of the global parameter space, enabling the machine model to learn global nonlinear relationships and more stable and reliable sensitivity ranking; engineering boundary constraints are based on physical principles to ensure that the generated data are engineering feasible. The selected parameters and their physical boundaries are shown in Table 1.

[0086] Table 1 Design parameters and initial ranges of X-band seven-cavity single-gap klystron

[0087]

[0088] KlyH automatically completes iterative convergence determination during calculation, outputs various performance indicators, and organizes the results into a unified format sample data set, providing data support for subsequent sensitivity analysis and machine learning model training. Through this framework, klystron performance data sets covering multi-dimensional design parameters can be efficiently generated, providing a foundation for rapid modeling and optimization.

[0089] Step 2: Use the Random Forest (RF) algorithm to build a klystron performance prediction model to realize fast mapping from high-dimensional design parameters to output efficiency indicators;

[0090] This method divides the data set generated by KlyH simulation into training and validation sets, and realizes random forest model training through JAVA Smile 3.0.1 framework. The core steps include:

[0091] (1) Construct DataFrame, map parameter vector to feature column, and output efficiency to target column;

[0092] (2) Set random forest parameters, including 100 trees, maximum node number 100, and minimum leaf node sample number, etc., to ensure that the model can capture nonlinear relationships and has good generalization performance;

[0093] (3) Use the training set to fit the model and evaluate the prediction accuracy through the validation set;

[0094] (4) Save the trained model as a callable module for fast prediction of objective function values in sensitivity analysis and optimization processes, avoiding repeated calls to high-time-consuming physical simulations.

[0095] Compared to directly using KlyH simulation, the above-mentioned random forest prediction model can significantly reduce computational overhead while maintaining high prediction accuracy, providing a rapid evaluation tool for sensitivity analysis and algorithm optimization.

[0096] Step 3: After the random forest model is built, the Normalized Rate of Change (NOV) sensitivity analysis method is introduced to quantify the influence of each parameter on the output efficiency. Combined with engineering constraints, the optimization range is dynamically adjusted. The overall process is as follows: Figure 3 As shown, the NOV index is calculated by applying positive and negative perturbations to a single parameter, observing the magnitude of change in output efficiency, and then performing normalization. Its formula is:

[0097] ;

[0098] in, This represents the normalized output rate of change of each design parameter, where x represents the value of the design parameter. Indicates the magnitude of the disturbance. , These represent the maximum and minimum values ​​of the output parameters in the initial dataset, respectively. This method yields the mean and standard deviation of the sensitivity for each parameter, which are then used for sorting and grading to obtain the sensitivity results for each design parameter. Figure 4 and Figure 5 As shown, Figure 4 The mean sensitivity (NOV) of the design parameters is shown, displaying the mean sensitivity for different design parameters. The horizontal axis represents the mean sensitivity, ranging from 0.00 to 0.03, and the vertical axis lists the different design parameters. Figure 5 The sensitivity variance (NOV) of the design parameters is shown, displaying the sensitivity variance for different design parameters. The horizontal axis represents the sensitivity variance, with values ​​ranging from 0.00 to 0.04, and the vertical axis lists the different design parameters.

[0099] Step 4: Propose an optimization range control strategy based on the synergistic effect of sensitivity analysis and engineering constraints to dynamically adjust the initial search interval of the high-dimensional parameters of the klystron and obtain the optimization search interval;

[0100] First, the NOV index is used to calculate the sensitivity of each design parameter to output efficiency. The mean and variance of the sensitivity are then used to comprehensively evaluate the influence of the design parameter on the output efficiency. The higher the sensitivity of the design parameter, the more significant its impact on the output efficiency, requiring a more refined search to obtain the best optimization effect. Conversely, the range of output parameters with lower sensitivity can be narrowed during the optimization process to reduce search costs. The specific implementation method is as follows:

[0101] Firstly, the initial parameter range, i.e. the initial search interval of the design parameters, is defined by the engineering constraint principle, i.e. physical feasibility; then, according to the sensitivity calculation results of each design parameter, a dynamic scaling factor is set for each design parameter, and the calculation formula of the scaling factor is:

[0102]

[0103] wherein, , represents the sensitivity of a single design parameter, represents the mean of the normalized output change rate of a single design parameter, represents the variance of the normalized output change rate of a single design parameter, represents the dynamic scaling factor of a single design parameter, represents the sensitivity of a single design parameter, and represent the minimum and maximum values of the sensitivity among all design parameters, respectively, ∈(0,1) is a minimum scaling ratio set artificially, and in this example, =0.90. According to , the optimization interval of each design parameter is adaptively adjusted:

[0104]

[0105] wherein, represents the dynamic scaling factor of a single design parameter, represents the minimum value of the optimization search interval of a single design parameter, represents the maximum value of the optimization search interval of a single design parameter, represents the minimum value of the initial search interval of a single design parameter, represents the maximum value of the initial search interval of a single design parameter, and the final optimization interval , can reflect the influence degree of each design parameter on the objective function. Through sensitivity analysis and actual engineering experience, the optimization design parameters and their optimization intervals are selected as shown in Table 2.

[0106] Table 2 Design parameters and their optimization ranges based on the modified NOV sensitivity

[0107]

[0108] Step 5: The design parameters and the optimization search interval obtained by optimization are brought into the OMOPSO algorithm, and the algorithm flow is as follows: Figure 6 ​​As shown: After the algorithm starts, it first initializes the particle swarm (each particle represents a potential solution), the individual optimal position (pBest) of each particle, and the representative solution set (rep set) for storing non-dominated solutions, and sets the current iteration number G to 1. Then, it initializes the adaptive network to prepare for subsequent dynamic search adjustments. In each iteration, the algorithm first selects the global guiding solution gBest from the current population, which provides the search direction for the particle swarm. Next, it updates the velocity and position of all particles based on gBest and pBest, and introduces random mutations to enhance population diversity, while updating the historical optimal position pBest of each particle. Then, the algorithm updates the representative solution set (rep set) to include newly discovered non-dominated solutions to maintain the tracking of leading solutions. The adaptive network is updated according to the current search state to more effectively guide the search process. The system determines whether the rep set exceeds its capacity limit: if overflow occurs, a truncation operation is performed to remove redundant or highly similar solutions, retaining the most representative non-dominated solutions to ensure the diversity and quality of the solution set. After completing the above steps, the algorithm checks whether the current iteration number G is less than the preset maximum iteration number MaxG. If the condition is met, G is incremented by 1 and the process returns to continue the next iteration; otherwise, the iteration terminates. Finally, when the termination condition is met, the algorithm ends and outputs the optimal solution set obtained after multiple rounds of optimization, which is the optimized design parameters and their corresponding performance. The entire process achieves efficient optimization in complex multi-objective spaces through particle swarm cooperative search, adaptive mechanism and elite solution set maintenance.

[0109] Based on the above method, its Pareto front is obtained as follows: Figure 7 As shown, Figure 7 The horizontal axis represents the klystron interaction length in centimeters (cm), ranging from 12cm to 20cm. The vertical axis represents the output efficiency in percentage (%), ranging from 20% to 80%. The graph is dotted with numerous small gray dots, representing different solution sets, i.e., the solution space. These dots indicate the efficiency changes at different lengths. The large blue dots represent the Pareto Front, which is the solution with the best efficiency at a given length. Based on the target optimization design requirements of output efficiency and klystron interaction length, the optimal solution set that simultaneously satisfies output efficiency and klystron interaction length can be selected from the Pareto solution set and then verified in three dimensions and implemented in engineering.

[0110] It should be noted that the embodiment provides a high-dimensional parameter optimization method of a klystron, an initial data set containing design parameters and corresponding output parameters is generated, a regression prediction model of the design parameters to the output parameters is constructed, a normalized output change rate of the design parameters is calculated, and the sensitivity of each design parameter to the output parameter is determined according to the normalized output change rate, the range of each design parameter is dynamically adjusted, the optimization search interval of each design parameter is obtained, and a multi-objective optimization algorithm is used for optimization solving in the optimization search interval to obtain an optimal solution set, which realizes dimension reduction and search space compression of the klystron design parameters, significantly improves the calculation efficiency and search quality, greatly reduces the calculation cost, and provides a new idea for intelligent design of high-power microwave devices such as klystrons.

[0111] Embodiment two

[0112] Please refer to Figure 2 The embodiment provides a high-dimensional parameter optimization system of a klystron, and the system comprises:

[0113] The data generation module 100 is configured to perform simulation calculation on the input design parameters by using the one-dimensional large signal simulation software KlyH of the klystron, and generate an initial data set containing the design parameters and corresponding output parameters;

[0114] The sensitivity analysis module 200 is configured to construct a regression prediction model of the design parameters to the output parameters according to the initial data set, calculate a normalized output change rate of the design parameters based on the regression prediction model, and determine the sensitivity of each design parameter to the output parameter according to the normalized output change rate.

[0115] The multi-objective optimization module 300 is configured to dynamically adjust the range of each design parameter according to the sensitivity, obtain an optimization search interval of each design parameter, and use a multi-objective optimization algorithm to perform optimization solving in the optimization search interval to obtain an optimal solution set.

[0116] It should be noted that the embodiment provides a high-dimensional parameter optimization system of a klystron, which comprises a data generation module 100, a sensitivity analysis module 200 and a multi-objective optimization module 300, an initial data set containing design parameters and corresponding output parameters is generated, a regression prediction model of the design parameters to the output parameters is constructed, a normalized output change rate of the design parameters is calculated, and the sensitivity of each design parameter to the output parameter is determined according to the normalized output change rate, the range of each design parameter is dynamically adjusted, the optimization search interval of each design parameter is obtained, and a multi-objective optimization algorithm is used for optimization solving in the optimization search interval to obtain an optimal solution set, which realizes dimension reduction and search space compression of the klystron design parameters, significantly improves the calculation efficiency and search quality, greatly reduces the calculation cost, and provides a new idea for intelligent design of high-power microwave devices such as klystrons.

[0117] It should be noted that the terms "first", "second", and the like, used in the description and the claims of the present application as well as above-described accompanying drawings, are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the data thus used can be interchanged, where appropriate, so that the embodiments of the present application described herein can be carried out in other sequences than the one illustrated or described herein. Furthermore, the terms "comprise" and "have", and any variations thereof, are intended to cover non-exclusive inclusions, for example, a process, method, system, product, or apparatus that comprises a list of steps or units is not necessarily limited to those steps or units that are clearly listed, but can include other steps or units that are not clearly listed or inherent to such processes, methods, products, or apparatuses.

[0118] The technical features described above can be combined arbitrarily. Although all possible combinations of the technical features are not described, any combination of the technical features should be considered to be covered by the present specification, as long as there is no contradiction in such a combination.

[0119] The specific embodiments of the present application described above do not constitute a limitation of the protection scope of the present application. Any various other corresponding changes and modifications made according to the technical concept of the present application should be included in the protection scope of the claims of the present application.

Claims

1. A method for optimizing high-dimensional parameters of a velocity modulation tube, characterized in that, The method comprises the following steps: S100, using a one-dimensional large signal simulation software KlyH of a klystron to simulate and calculate input design parameters to generate an initial data set containing the design parameters and corresponding output parameters; The design parameters include calculation parameters, electron beam parameters, input microwave parameters, and modulation parameters of each resonant cavity; S200, constructing a regression prediction model of the design parameters to the output parameters according to the initial data set, calculating a normalized output change rate of the design parameters based on the regression prediction model, and determining the sensitivity of each design parameter to the output parameter according to the normalized output change rate; The calculation of the normalized output change rate of the design parameters and the determination of the sensitivity of each design parameter to the output parameter based on the normalized output change rate comprise: Based on the regression prediction model, positive and negative perturbations are applied to each design parameter, the change amount of the corresponding output parameter is calculated by using the regression prediction model, the change amount of the output parameter is normalized to obtain the normalized output change rate of each design parameter, and the sensitivity of each design parameter to the output parameter is determined according to the normalized output change rate of each design parameter; The calculation method of the normalized output change rate of each design parameter comprises: Positive and negative perturbations are applied to each design parameter, the change amount of the corresponding output parameter is calculated by using the regression prediction model, and the change amount of the output parameter is normalized, and the specific calculation formula is as follows: ； wherein, represents the normalized output variation rate of each design parameter, x represents the value of the design parameter, represents the perturbation amplitude, , respectively represent the maximum and minimum values of the output parameter in the initial data set; The determination of the sensitivity of each design parameter to the output parameter according to the normalized output change rate of each design parameter comprises: The mean and variance of the normalized output change rate of each design parameter are calculated, and the sensitivity of a single design parameter is the sum of the mean and variance of the normalized output change rate, and the specific calculation formula is as follows: ； wherein, sensitivities of individual design parameters, mean values of normalized output change rates of individual design parameters, variances of normalized output change rates of individual design parameters; S300, according to the sensitivity, dynamically adjusting the range of each design parameter to obtain an optimized search interval of each design parameter, and using a multi-objective optimization algorithm to perform optimization solving in the optimized search interval to obtain an optimal solution set.

2. The method of claim 1, wherein, The construction of the regression prediction model of the design parameters to the output parameters according to the initial data set comprises: The design parameters in the initial data set are used as input features, the output parameters in the initial data set are used as prediction targets, a random forest regression model is used to construct the regression prediction model of the design parameters to the output parameters.

3. The method of claim 1, wherein, The dynamic adjustment of the range of each design parameter to obtain the optimized search interval of each design parameter comprises: First, the initial search interval of the design parameter is defined according to the engineering constraint principle, then a dynamic scaling factor is set for each design parameter according to the sensitivity of each design parameter to the output parameter, and then the initial search interval of each design parameter is adaptively adjusted according to the dynamic scaling factor to obtain the optimized search interval.

4. The method of claim 3, wherein, The calculation method of the dynamic scaling factor is as follows: ； wherein denotes a dynamic scaling factor for an individual design parameter, denotes a sensitivity for an individual design parameter, and denote the minimum and maximum of the sensitivities among all design parameters, respectively, denotes a preset minimum scaling ratio, ∈(0,1).

5. The method of claim 4, wherein, The calculation method of the optimized search interval comprises: The initial search interval of each design parameter is adaptively adjusted according to the dynamic scaling factor to obtain the optimized search interval, and the specific calculation method is as follows: ； wherein, represents a dynamic scaling factor for an individual design parameter, represents a minimum value of an optimization search interval for an individual design parameter, represents a maximum value of an optimization search interval for an individual design parameter, represents a minimum value of an initial search interval for an individual design parameter, represents a maximum value of an initial search interval for an individual design parameter.

6. The method of claim 1, wherein The optimization solving in the optimized search interval by using the multi-objective optimization algorithm to obtain the optimal solution set comprises: The optimal solution multi-objective particle swarm algorithm is used to perform multi-objective optimization on the design parameters in the optimized search interval, to obtain a Pareto front solution set, and to screen an optimal solution set according to the target optimization parameters.

7. A system for optimizing high-dimensional parameters of a klystron, characterized in that, The system comprises the high-dimensional parameter optimization method of the klystron according to any one of claims 1 to 6. The data generation module is configured to perform simulation calculation on the input design parameters by using one-dimensional large-signal simulation software KlyH of the klystron, and to generate an initial data set containing the design parameters and corresponding output parameters; The sensitivity analysis module is configured to construct a regression prediction model of the design parameters to the output parameters according to the initial data set, to calculate a normalized output change rate of the design parameters based on the regression prediction model, and to determine the sensitivity of each design parameter to the output parameter according to the normalized output change rate; The multi-objective optimization module is configured to dynamically adjust the range of each design parameter according to the sensitivity, to obtain an optimized search interval of each design parameter, and to perform optimization solving in the optimized search interval by using a multi-objective optimization algorithm, to obtain an optimal solution set.

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