Method and system for optimizing high-dimensional parameters of klystron

Abstract

The invention provides a klystron high-dimensional parameter optimization method and system, and the method comprises the steps: carrying out the simulation calculation of an input design parameter through the one-dimensional large-signal simulation software KlyH of a klystron, and generating an initial data set containing the design parameter and a corresponding output parameter; constructing a regression prediction model from the design parameters to the output parameters, calculating the 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 parameters according to the normalized output change rate; and 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 solution in the optimization search interval by adopting a multi-objective optimization algorithm to obtain an optimal solution set. Dimensionality reduction of klystron design parameters and search space compression are achieved, the calculation efficiency and the search quality are further improved, and reliable support can be provided for intelligent optimization design of a high-performance klystron.

Description

Technical Field

[0001] This invention relates to the fields of high-power microwave and computer science technology, specifically to a method and system for optimizing high-dimensional parameters of a klystron. Background Art

[0002] The relativistic klystron amplifier (RKA) is a typical high-power microwave vacuum electronic device. Its advantages, including high peak power, high gain, high efficiency, and frequency and phase stability, make it widely applicable in fields such as particle accelerators, pulse radar, and power combining. With the development of high-power microwave technology, RKAs have achieved output power ranging from hundreds of megawatts to several gigawatts in the L-band to Ka-band, which is of great significance for promoting the engineering application of high-power microwave systems.

[0003] The design of an RKA involves numerous coupled parameters, including multi-cavity resonant structures, drift tube length, beam parameters, and appearance quality factors. Its design space is high-dimensional and highly nonlinear. To obtain a high-efficiency, compact klystron, these parameters must be globally optimized under multiple objectives and constraints.

[0004] In existing technologies, a portion of the design work still relies on engineers engaging in a trial-and-error cycle of "simulation-manual adjustment-re-simulation" based on physical intuition and past experience. This method is not only time-consuming and highly subjective, but also prone to getting trapped in local optima, making it difficult to systematically discover better-performing global design solutions in the vast high-dimensional design space. Existing methods lack effective tools for rapid, quantitative sensitivity analysis of all design parameters in high-dimensional space. Users cannot clearly identify which parameters are critical to performance and which are relatively insensitive secondary parameters, leading to low parameter optimization efficiency and a huge waste of computational resources.

[0005] Therefore, existing technologies still need further development. Summary of the Invention

[0006] The purpose of this invention is to overcome the above-mentioned technical deficiencies and provide a method and system for optimizing high-dimensional parameters of a klystron, so as to solve the problems existing in the prior art.

[0007] To achieve the above-mentioned technical objectives, according to a first aspect of the present invention, the present invention provides a method for optimizing high-dimensional parameters of a klystron, comprising: S100. Using the one-dimensional large-signal simulation software KlyH for klystrons, the input design parameters are simulated and calculated to generate an initial dataset containing the design parameters and corresponding output parameters. S200. Based on the initial dataset, construct a regression prediction model from design parameters to output parameters. Based on the regression prediction model, calculate the normalized output change rate of the design parameters, and determine the sensitivity of each design parameter to the output parameters based on the normalized output change rate. S300. Based on the sensitivity, dynamically adjust the range of each design parameter to obtain the optimization search interval of each design parameter, and use a multi-objective optimization algorithm to optimize and solve within the optimization search interval to obtain the optimal solution set.

[0008] Specifically, constructing a regression prediction model from design parameters to output parameters based on the initial dataset includes: Using the design parameters in the initial dataset as input features and the output parameters in the initial dataset as prediction targets, a random forest regression model is used to construct a regression prediction model from the design parameters to the output parameters.

[0009] Specifically, 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 parameters based on the normalized output change rate, includes: Based on the regression prediction model, positive and negative perturbations are applied to each design parameter, and the change in the corresponding output parameter is calculated using the regression prediction model. The change in the output parameter is then normalized to obtain the normalized output change rate of each design parameter. The sensitivity of each design parameter to the output parameter is determined based on the normalized output change rate of each design parameter.

[0010] Specifically, the calculation method for the normalized output change rate of each design parameter includes: Positive and negative perturbations are applied to each design parameter, and the changes in the corresponding output parameters are calculated using a regression prediction model. The changes in the output parameters are then normalized. The specific calculation formula is as follows: ; 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.

[0011] Specifically, determining the sensitivity of each design parameter to the output parameter based on the normalized output change rate of each design parameter includes: Calculate the mean and variance of the normalized output change rate for each design parameter. The sensitivity of a single design parameter is the sum of the mean and variance of the normalized output change rate. The specific calculation formula is as follows: ; in, Indicates the sensitivity of a single design parameter. This represents the mean of the normalized output rate of change for a single design parameter. The variance represents the normalized output rate of change of a single design parameter.

[0012] Specifically, the dynamic adjustment of the range of each design parameter to obtain the optimization search interval for each design parameter includes: First, the initial search range of the design parameters is defined according to the engineering constraint principle. Then, based on the sensitivity of each design parameter to the output parameter, a dynamic scaling factor is set for each design parameter. Subsequently, the initial search range of each design parameter is adaptively adjusted according to the dynamic scaling factor to obtain the optimized search range.

[0013] Specifically, the dynamic scaling factor is calculated as follows: ; in, This represents the dynamic scaling factor for a single design parameter. Indicates the sensitivity of a single design parameter. and These represent the minimum and maximum values ​​of sensitivity among all design parameters, respectively. This indicates the preset minimum scaling ratio. ∈(0,1).

[0014] Specifically, the method for calculating the optimized search interval includes: The initial search interval for each design parameter is adaptively adjusted based on the dynamic scaling factor to obtain the optimized search interval. The specific calculation method is as follows: ; in, This represents the dynamic scaling factor for a single design parameter. This represents the minimum value of the search range for optimizing a single design parameter. This represents the maximum value of the optimization search range for a single design parameter. This represents the minimum value of the initial search range for a single design parameter. This represents the maximum value of the initial search range for a single design parameter.

[0015] Specifically, the step of employing a multi-objective optimization algorithm to perform optimization within the optimization search interval to obtain the optimal solution set includes: The optimal solution multi-objective particle swarm optimization algorithm is used to perform multi-objective optimization of the design parameters within the optimization search interval, obtain the Pareto front solution set, and select the optimal solution set according to the objective optimization parameters.

[0016] According to a second aspect of the present invention, a system for optimizing high-dimensional parameters of a klystron is provided, comprising: Data generation module: Used to perform simulation calculations on the input design parameters using the one-dimensional large-signal simulation software KlyH for klystrons, and generate an initial dataset containing the design parameters and corresponding output parameters; Sensitivity analysis module: used to construct a regression prediction model from design parameters to output parameters based on the initial dataset, calculate the 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 parameters based on the normalized output change rate. Multi-objective optimization module: It is used to dynamically adjust the range of each design parameter according to the sensitivity, obtain the optimization search interval of each design parameter, and use a multi-objective optimization algorithm to optimize and solve within the optimization search interval to obtain the optimal solution set.

[0017] Beneficial effects: This invention provides a method and system for optimizing high-dimensional parameters of a klystron. Based on an initial dataset containing design parameters and corresponding output parameters, a regression prediction model from design parameters to output parameters is constructed. The normalized output change rate of the design parameters is calculated, and the sensitivity of each design parameter to the output parameter is determined based on the normalized output change rate. The range of each design parameter is dynamically adjusted to obtain the optimization search interval for each design parameter. A multi-objective optimization algorithm is then used to optimize and solve within the optimization search interval to obtain the optimal solution set. This achieves dimensionality reduction and search space compression of the klystron design parameters, significantly improving computational efficiency and search quality, greatly reducing computational costs, and enhancing the convergence speed and global optimization capability of multi-objective optimization. It offers high flexibility and high analytical accuracy, providing reliable support for the intelligent optimization design of high-performance klystrons and offering a new approach for the intelligent design of high-power microwave devices such as klystrons. Attached Figure Description

[0018] Figure 1 This is a flowchart of the method for optimizing high-dimensional parameters of a klystron provided in a specific embodiment of the present invention; Figure 2 This is a schematic diagram of the system composition of the klystron high-dimensional parameter optimization system provided in a specific embodiment of the present invention; Figure 3 This is a flowchart of sensitivity analysis based on random forest and NOV provided in a specific embodiment of the present invention; Figure 4 This is a graph showing the sensitivity mean analysis results provided in a specific embodiment of the present invention; Figure 5 This is a graph showing the results of sensitivity variance analysis provided in a specific embodiment of the present invention; Figure 6This is a flowchart of the OMOPSO multi-objective optimization algorithm provided in a specific embodiment of the present invention; Figure 7 This is the Pareto front plot of the OMOPSO multi-objective optimization algorithm provided in a specific embodiment of the present invention. Detailed Implementation

[0019] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Based on the embodiments in this application, other similar embodiments obtained by those skilled in the art without creative effort should all fall within the scope of protection of this application. Furthermore, directional terms mentioned in the following embodiments, such as "up," "down," "left," and "right," are only for reference to the directions in the accompanying drawings; therefore, the directional terms used are for illustrative purposes and not for limiting the invention.

[0020] The present invention will be further described below with reference to the accompanying drawings and preferred embodiments.

[0021] Example 1 Please see Figure 1 This embodiment provides a method for optimizing high-dimensional parameters of a klystron, comprising: using the one-dimensional large-signal simulation software KlyH for klystrons to perform simulation calculations on the input design parameters, generating an initial dataset containing the design parameters and corresponding output parameters; constructing a regression prediction model from the design parameters to the output parameters based on the initial dataset; calculating the 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 parameters based on the normalized output change rate; dynamically adjusting the range of each design parameter based on the sensitivity to obtain the optimization search interval of each design parameter, and using a multi-objective optimization algorithm to optimize and solve within the optimization search interval to obtain the optimal solution set.

[0022] It is understood that by adopting the above-mentioned technical solution, this invention solves the technical problem that existing methods lack effective tools for rapid and quantitative sensitivity analysis of all design parameters in high-dimensional space, effectively reduces the high cost of experiments and three-dimensional simulations, realizes dimensionality reduction and search space compression of klystron design parameters, significantly improves computational efficiency and search quality, and can provide reliable support for rapid iterative design in engineering.

[0023] See Figure 1 The implementation process of the optimization method for the high-dimensional parameters of the klystron in this embodiment is as follows: S100. Using the one-dimensional large-signal simulation software KlyH for klystrons, the input design parameters are simulated and calculated to generate an initial dataset containing the design parameters and corresponding output parameters. Furthermore, this embodiment proposes a KlyH-based framework for generating relativistic klystron simulation data. KlyH employs a one-dimensional large-signal disk model, capable of outputting key indicators such as electron efficiency, interaction length, gain, and bandwidth, and its computational speed is faster than three-dimensional particle simulation. As the interface for generating relativistic klystron simulation results, KlyH rapidly generates large-scale sample data by inputting design parameters such as electron beam parameters, cavity geometry parameters, and resonant cavity modulation parameters. This data requires cleaning and removing non-convergent or invalid samples, and the design variables reach 33 dimensions, providing high-quality foundational data for subsequent machine learning model training and sensitivity analysis. This method effectively reduces the high costs of experiments and three-dimensional simulations, providing reliable support for rapid iterative engineering design.

[0024] Preferably, in this embodiment, KlyH is a one-dimensional large-signal simulation software for klystrons. Based on the input data, including calculation parameters (number of disks, number of disk pushes per high-frequency cycle, maximum number of iterations, initial value of total number of disk pushes), electron beam parameters (beam voltage, beam current, beam radius, drift tube radius), input microwave parameters (input microwave power, input microwave frequency), and modulation parameters of each resonator (resonant frequency of the resonator, position of the resonator in the axial direction, characteristic impedance of the resonator, gap width, harmonic order), the output efficiency of the klystron is calculated, resulting in a sample size of 60,000. This sample size includes 33 design parameters such as operating frequency, beam voltage, beam current, output cavity appearance quality factor, length of 6 drift tubes, and frequency of 7 resonators. After data cleaning and filtering of non-convergent data, the final sample size is 57,097.

[0025] S200. Based on the initial dataset, construct a regression prediction model from design parameters to output parameters. Based on the regression prediction model, calculate the normalized output change rate of the design parameters, and determine the sensitivity of each design parameter to the output parameters based on the normalized output change rate.

[0026] Specifically, in this embodiment, constructing a regression prediction model from design parameters to output parameters based on the initial dataset includes: Using the design parameters in the initial dataset as input features and the output parameters in the initial dataset as prediction targets, a random forest regression model is used to construct a regression prediction model from design parameters to output parameters, so as to learn the nonlinear mapping relationship between design parameters and output parameters.

[0027] Preferably, in this embodiment, the random forest model uses a configuration of 100 decision trees and a maximum number of nodes of 100, which can handle nonlinear and high-dimensional parameter features. The input of the model is the parameter values, and the output is the corresponding efficiency prediction. The model can use cross-validation to adjust the hyperparameters to improve the prediction accuracy and avoid overfitting.

[0028] It should be noted that, considering the high dimensionality and strong nonlinearity of the klystron design variables, this embodiment uses a random forest regression model for performance prediction modeling. By using a large-scale sample generated by KlyH as training data, inputting multidimensional design parameters, and outputting efficiency prediction values, a rapid fitting and high-precision prediction of the klystron performance is achieved. The random forest model has significant advantages in handling high-dimensional nonlinear features and avoiding overfitting. It can simultaneously output variable importance indicators, which facilitates subsequent sensitivity calculation and optimization range adjustment. Compared with traditional optimization methods based on multiple linear or simple surrogate models, this method improves prediction accuracy and generalization ability, providing a reliable foundation for sensitivity analysis.

[0029] In this embodiment, calculating the normalized output change rate of the design parameters and determining the sensitivity of each design parameter to the output parameters based on the normalized output change rate includes: Based on the regression prediction model, positive and negative perturbations are applied to each design parameter, and the change in the corresponding output parameter is calculated using the regression prediction model. The change in the output parameter is then normalized to obtain the normalized output change rate of each design parameter. The sensitivity of each design parameter to the output parameter is determined based on the normalized output change rate of each design parameter.

[0030] Positive and negative perturbations are applied to each design parameter, and the changes in the corresponding output parameters are calculated using a regression prediction model. The changes in the output parameters are then normalized. The specific calculation formula is as follows: ; 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.

[0031] Understandably, in this embodiment, the perturbation amplitude can be set to 10%, that is, a ±10% perturbation is applied to each design parameter between its minimum and maximum values. The difference between the predicted output parameter after perturbation and the original output parameter before perturbation is calculated. This difference is normalized to the overall output parameter range to obtain the normalized output change rate (NOV). By statistically analyzing the mean and variance of the NOV of each parameter in the full sample range, its sensitivity level to the output parameter is comprehensively evaluated. The sensitivity analysis results are used as the basis for subsequent optimization variable selection and range scaling decisions.

[0032] Furthermore, the mean and variance of the normalized output change rate for each design parameter are calculated. The sensitivity of a single design parameter is the sum of the mean and variance of the normalized output change rate, calculated using the following formula: ; in, Indicates the sensitivity of a single design parameter. This represents the mean of the normalized output rate of change for a single design parameter. The variance represents the normalized output rate of change of a single design parameter.

[0033] Understandably, this embodiment introduces the Normalized Rate of Change in Output (NOV) as the core indicator for sensitivity analysis. By applying positive and negative perturbations to each design parameter, the changes in the predicted output parameters are calculated and normalized to obtain the mean and variance of NOV for each design parameter. The above technical solution can quantify the influence intensity and stability of each design parameter on the output parameter in a high-dimensional design space, avoiding the problem of high computational overhead in traditional variance methods or Sobol methods. Moreover, NOV sensitivity analysis can identify key parameters and reveal the changing trend of parameter interactions, providing a quantitative basis for subsequent optimization.

[0034] S300. Based on the sensitivity, dynamically adjust the range of each design parameter to obtain the optimization search interval of each design parameter, and use a multi-objective optimization algorithm to optimize and solve within the optimization search interval to obtain the optimal solution set.

[0035] Furthermore, in this embodiment, the dynamic adjustment of the range of each design parameter to obtain the optimization search interval of each design parameter includes: First, an initial search interval for the design parameters is defined based on engineering constraints. Then, a dynamic scaling factor is set for each design parameter according to its sensitivity to the output parameters. Finally, the initial search interval for each design parameter is adaptively adjusted based on the dynamic scaling factor to obtain an optimized search interval. The calculation method for the dynamic scaling factor is as follows: ; in, This represents the dynamic scaling factor for a single design parameter. Indicates the sensitivity of a single design parameter. and These represent the minimum and maximum values ​​of sensitivity among all design parameters, respectively. This indicates the preset minimum scaling ratio. ∈(0,1), this embodiment will Setting it to 0.9 ensures that the range of all parameters is reduced by at most 10%.

[0036] The method for calculating the optimized search interval includes: adaptively adjusting the initial search interval of each design parameter based on the dynamic scaling factor to obtain the optimized search interval. The specific calculation method is as follows: ; in, This represents the dynamic scaling factor for a single design parameter. This represents the minimum value of the search range for optimizing a single design parameter. This represents the maximum value of the optimization search range for a single design parameter. This represents the minimum value of the initial search range for a single design parameter. This represents the maximum value of the initial search range for a single design parameter.

[0037] It's important to note that the above scheme first defines the initial search range of design parameters based on engineering constraints. These constraints satisfy the principle of physical feasibility, meaning that while maintaining physical feasibility, the range of values ​​for all design parameters is narrowed to accelerate the optimization process and improve final efficiency. For parameters with low sensitivity, their changes have little impact on efficiency; therefore, a smaller scaling factor is used to narrow the parameter search range. Conversely, for parameters with high sensitivity, a larger scaling factor is used to increase the parameter search range, preserving a larger optimization space to fully explore potential efficient solutions. Regarding the scaling ratio, the minimum scaling ratio is fixed at 0.9, ensuring that the range of all design parameters is reduced by at most 10%. The maximum scaling ratio is dynamically calculated using a formula with the mean and standard deviation of NOV as input, achieving adaptive coupling between sensitivity and the optimization search space. Through this technical solution, the final optimization search space satisfies engineering feasibility constraints while retaining necessary exploration for key parameters, further improving the optimization convergence speed and efficiency indicators.

[0038] Furthermore, the step of employing a multi-objective optimization algorithm to perform optimization within the optimization search interval to obtain the optimal solution set includes: The optimal solution multi-objective particle swarm optimization algorithm is used to perform multi-objective optimization of the design parameters within the optimization search interval, obtain the Pareto front solution set, and select the optimal solution set according to the objective optimization parameters.

[0039] It is understood that this embodiment uses the Optimal Solution Multi-Objective Particle Swarm Optimization (OMOPSO) algorithm for multi-objective optimization. The objective optimization parameters include two performance indicators: maximizing klystron efficiency and minimizing interaction length. The selection of key optimization parameters is derived from the sensitivity analysis results and strictly follows the engineering constraints and the optimization range based on sensitivity calculations to ensure the feasibility and physical rationality of the design scheme. Finally, the Pareto front solution set is selected through non-dominated sorting. In terms of algorithm configuration, this embodiment uses parameter settings of 15 iterations, 2000 seeds, and a mutation probability of 0.07. By randomly generating the initial population and sampling within the sensitivity constraints, the coverage of the global parameter space is guaranteed.

[0040] See Figures 3-7The working principle of this invention will be explained below using the parameter optimization of an X-band seven-cavity single-gap klystron as an example: Step 1: First, construct a klystron simulation data generation framework based on KlyH one-dimensional large signal simulation software. In the data generation stage, this example is based on an X-band seven-cavity single-gap klystron instance. By inputting design parameters including beam voltage, beam current, beam radius, drift tube geometric parameters, resonant cavity harmonic parameters, input microwave power and operating frequency, KlyH is driven to perform batch simulation calculations. To obtain sufficient sample data to cover the design space, this example adopts a strategy that combines random parameter sampling with engineering boundary constraints: random sampling ensures coverage of the global parameter space, enabling the machine model to learn global nonlinear relationships and making the sensitivity ranking more stable and reliable; engineering boundary constraints are based on physical principles to ensure that the generated data are all engineering feasible, and the selected parameters and their physical boundaries are shown in Table 1.

[0041] Table 1. Design parameters and initial range of X-band seven-cavity single-gap klystron. KlyH automatically completes the iterative convergence determination during the calculation process, outputs various performance indicators, and organizes the results into a sample dataset in a unified format, providing data support for subsequent sensitivity analysis and machine learning model training. Through this framework, klystron performance datasets covering multi-dimensional design parameters can be generated efficiently, providing a foundation for rapid modeling and optimization.

[0042] Step 2: Construct a klystron performance prediction model using the Random Forest (RF) algorithm to achieve a fast mapping from high-dimensional design parameters to output efficiency indicators; This method divides the dataset generated by KlyH simulation into training and validation sets, and uses the JAVA Smile 3.0.1 framework to train a random forest model. The core steps include: (1) Construct a DataFrame, map the parameter vector to the feature column, and map the output efficiency to the target column; (2) Set the random forest parameters, including the number of trees (100), the maximum number of nodes (100), and the minimum number of leaf node samples, to ensure that the model can capture nonlinear relationships and has good generalization performance. (3) Fit the model using the training set and evaluate the prediction accuracy using the validation set; (4) After the model training is completed, it is saved as a callable module for rapid prediction of the objective function value during sensitivity analysis and optimization, avoiding repeated calls to time-consuming physical simulation.

[0043] 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.

[0044] 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: ; 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.

[0045] 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; 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: First, define the initial parameter range, i.e., the initial search interval for the design parameters, determined by engineering constraints, i.e., physical feasibility. Then, based on the sensitivity calculation results of each design parameter, set a dynamic scaling factor for each design parameter. The formula for calculating the scaling factor is: ; in, , Indicates the sensitivity of a single design parameter. This represents the mean of the normalized output rate of change for a single design parameter. The variance representing the normalized output rate of change of a single design parameter. This represents the dynamic scaling factor for a single design parameter. Indicates the sensitivity of a single design parameter. and These represent the minimum and maximum values ​​of sensitivity among all design parameters, respectively. ∈(0,1) is the minimum scaling factor set manually; in this example, it is taken as... =0.90. According to The optimization range for each design parameter is adaptively adjusted: ; in, This represents the dynamic scaling factor for a single design parameter. This represents the minimum value of the search range for optimizing a single design parameter. This represents the maximum value of the optimization search range for a single design parameter. This represents the minimum value of the initial search range for a single design parameter. This represents the maximum value of the initial search interval for a single design parameter, and the final optimized interval. , The parameters can reflect the degree of influence of each design parameter on the objective function. Based on sensitivity analysis and practical engineering experience, the selected optimization design parameters and their optimization ranges are shown in Table 2.

[0046] Table 2. Design parameters and their optimization range based on modified NOV sensitivity. Step 5: Input the optimized design parameters and optimization search interval into the OMOPSO algorithm. The algorithm flow is as follows: Figure 6As 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.

[0047] 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. It should be noted that this embodiment provides a method for optimizing high-dimensional parameters of a klystron. Based on an initial dataset containing design parameters and corresponding output parameters, a regression prediction model from design parameters to output parameters is constructed. The normalized output change rate of the design parameters is calculated, and the sensitivity of each design parameter to the output parameter is determined based on the normalized output change rate. The range of each design parameter is dynamically adjusted to obtain the optimization search interval for each design parameter. A multi-objective optimization algorithm is then used to optimize and solve the problem within the optimization search interval to obtain the optimal solution set. This method achieves dimensionality reduction and search space compression of the klystron design parameters, significantly improves computational efficiency and search quality, and greatly reduces computational costs. It provides a new approach for the intelligent design of high-power microwave devices such as klystrons.

[0048] Example 2 Please see Figure 2 This embodiment provides an optimization system for high-dimensional parameters of a klystron, the system comprising: Data generation module 100: Used to perform simulation calculations on the input design parameters using the one-dimensional large-signal simulation software KlyH for klystrons, and generate an initial dataset containing the design parameters and corresponding output parameters; Sensitivity analysis module 200: Used to construct a regression prediction model from design parameters to output parameters based on the initial dataset, calculate the 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 parameters based on the normalized output change rate. Multi-objective optimization module 300: It is used to dynamically adjust the range of each design parameter according to the sensitivity, obtain the optimization search interval of each design parameter, and use a multi-objective optimization algorithm to optimize and solve within the optimization search interval to obtain the optimal solution set.

[0049] It should be noted that this embodiment provides an optimization system for high-dimensional parameters of a klystron, including a data generation module 100, a sensitivity analysis module 200, and a multi-objective optimization module 300. Based on the generated initial dataset containing design parameters and corresponding output parameters, a regression prediction model from design parameters to output parameters is constructed. The normalized output change rate of the design parameters is calculated, and the sensitivity of each design parameter to the output parameter is determined based on the normalized output change rate. The range of each design parameter is dynamically adjusted to obtain the optimization search interval of each design parameter. A multi-objective optimization algorithm is then used to optimize and solve within the optimization search interval to obtain the optimal solution set. This achieves dimensionality reduction and search space compression of the klystron design parameters, significantly improves computational efficiency and search quality, and greatly reduces computational costs, providing a new approach for the intelligent design of high-power microwave devices such as klystrons.

[0050] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0051] The technical features described above can be combined arbitrarily. Although not all possible combinations of these technical features are described, any combination of these technical features should be considered to be covered by this specification, provided that such combination does not contain contradictions.

[0052] The specific embodiments of the present invention described above do not constitute a limitation on the scope of protection of the present invention. Any other corresponding changes and modifications made in accordance with the technical concept of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for optimizing high-dimensional parameters of a klystron, characterized in that, include: S100. Using the one-dimensional large-signal simulation software KlyH for klystrons, the input design parameters are simulated and calculated to generate an initial dataset containing the design parameters and corresponding output parameters. S200. Based on the initial dataset, construct a regression prediction model from design parameters to output parameters. Based on the regression prediction model, calculate the normalized output change rate of the design parameters, and determine the sensitivity of each design parameter to the output parameters based on the normalized output change rate. S300. Based on the sensitivity, dynamically adjust the range of each design parameter to obtain the optimization search interval of each design parameter, and use a multi-objective optimization algorithm to optimize and solve within the optimization search interval to obtain the optimal solution set.

2. The method for optimizing high-dimensional parameters of a klystron according to claim 1, characterized in that, The step of constructing a regression prediction model from design parameters to output parameters based on the initial dataset includes: Using the design parameters in the initial dataset as input features and the output parameters in the initial dataset as prediction targets, a random forest regression model is used to construct a regression prediction model from the design parameters to the output parameters.

3. The method for optimizing high-dimensional parameters of a klystron according to claim 1, characterized in that, 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 parameters based on the normalized output change rate, includes: Based on the regression prediction model, positive and negative perturbations are applied to each design parameter, and the change in the corresponding output parameter is calculated using the regression prediction model. The change in the output parameter is then normalized to obtain the normalized output change rate of each design parameter. The sensitivity of each design parameter to the output parameter is determined based on the normalized output change rate of each design parameter.

4. The method for optimizing high-dimensional parameters of a klystron according to claim 3, characterized in that, The calculation method for the normalized output change rate of each design parameter includes: Positive and negative perturbations are applied to each design parameter, and the changes in the corresponding output parameters are calculated using a regression prediction model. The changes in the output parameters are then normalized. The specific calculation formula is as follows: ； 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.

5. The method for optimizing high-dimensional parameters of a klystron according to claim 3, characterized in that, The determination of the sensitivity of each design parameter to the output parameter based on the normalized output change rate of each design parameter includes: Calculate the mean and variance of the normalized output change rate for each design parameter. The sensitivity of a single design parameter is the sum of the mean and variance of the normalized output change rate. The specific calculation formula is as follows: ； in, Indicates the sensitivity of a single design parameter. This represents the mean of the normalized output rate of change for a single design parameter. The variance represents the normalized output rate of change of a single design parameter.

6. The method for optimizing high-dimensional parameters of a klystron according to claim 1, characterized in that, The dynamic adjustment of the range of each design parameter to obtain the optimization search interval of each design parameter includes: First, the initial search range of the design parameters is defined according to the engineering constraint principle. Then, based on the sensitivity of each design parameter to the output parameter, a dynamic scaling factor is set for each design parameter. Subsequently, the initial search range of each design parameter is adaptively adjusted according to the dynamic scaling factor to obtain the optimized search range.

7. The method for optimizing high-dimensional parameters of a klystron according to claim 6, characterized in that, The dynamic scaling factor is calculated as follows: ； in, This represents the dynamic scaling factor for a single design parameter. Indicates the sensitivity of a single design parameter. and These represent the minimum and maximum values ​​of sensitivity among all design parameters, respectively. This indicates the preset minimum scaling ratio. ∈(0,1).

8. The method for optimizing high-dimensional parameters of a klystron according to claim 7, characterized in that, The method for calculating the optimized search interval includes: The initial search interval for each design parameter is adaptively adjusted based on the dynamic scaling factor to obtain the optimized search interval. The specific calculation method is as follows: ； in, This represents the dynamic scaling factor for a single design parameter. This represents the minimum value of the search range for optimizing a single design parameter. This represents the maximum value of the optimization search range for a single design parameter. This represents the minimum value of the initial search range for a single design parameter. This represents the maximum value of the initial search range for a single design parameter.

9. The method for optimizing high-dimensional parameters of a klystron according to claim 1, characterized in that, The method employs a multi-objective optimization algorithm to optimize within the optimization search interval, obtaining the optimal solution set, including: The optimal solution multi-objective particle swarm optimization algorithm is used to perform multi-objective optimization of the design parameters within the optimization search interval, obtain the Pareto front solution set, and select the optimal solution set according to the objective optimization parameters.

10. A system for optimizing high-dimensional parameters of a klystron, characterized in that, include: Data generation module: Used to perform simulation calculations on the input design parameters using the one-dimensional large-signal simulation software KlyH for klystrons, and generate an initial dataset containing the design parameters and corresponding output parameters; Sensitivity analysis module: used to construct a regression prediction model from design parameters to output parameters based on the initial dataset, calculate the 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 parameters based on the normalized output change rate. Multi-objective optimization module: It is used to dynamically adjust the range of each design parameter according to the sensitivity, obtain the optimization search interval of each design parameter, and use a multi-objective optimization algorithm to optimize and solve within the optimization search interval to obtain the optimal solution set.

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