An Optimization Design Method for Interaction Structures of Space Traveling Wave Tubes

Abstract

This invention belongs to the field of design and optimization methods for space traveling wave tubes, specifically an optimization design method for the interaction structure of a space traveling wave tube. Based on the Kriging surrogate model, this invention obtains initial sample points for constructing the Kriging surrogate model using Latin hypercube, considering both the spatial distribution of the sample points and the numerical distribution of the optimization target. It then applies the addition criterion of subtractive clustering algorithm to add multiple new sample points simultaneously in a single iteration, thereby updating the sample point set and reconstructing the surrogate model. This allows the Kriging model to converge with fewer iterations. The resulting model, meeting accuracy requirements, replaces the calculation process of electromagnetic simulation software, reducing the number of simulation calculations and effectively improving the design efficiency of the interaction structure. This provides guidance for subsequent more accurate optimization designs. It effectively solves the problems of long calculation times and high computational resource consumption associated with existing optimization calculations using electromagnetic simulation software.

Description

Technical Field

[0001] This invention belongs to the field of design and optimization methods for space traveling wave tubes. Specifically, it is an optimization design method for the interaction structure of a space traveling wave tube, based on the Kriging surrogate model. Background Technology

[0002] Traveling wave tubes (TWTs) are specialized tubes used in space applications. Their primary function is to amplify microwave power. They are characterized by high reliability, long lifespan, and high efficiency, making them core components in various application satellites and spacecraft payloads. TWTs can withstand the intense radiation and high vacuum environment of space, ensuring the stable operation of aerospace systems such as communication relay, data transmission, and radar detection.

[0003] The interaction structure is a core component of a space traveling wave tube (TWT), serving as the site for exchanging energy between the electron beam and the high-frequency field, and amplifying electromagnetic waves. The performance of the interaction structure directly affects the TWT's operating frequency, output power, bandwidth, transduction efficiency, and a range of other overall tube performance characteristics. Therefore, designing an interaction structure that meets the required specifications is a crucial step in the development of a space TWT.

[0004] When designing interaction structures, a common method is to use general-purpose 3D electromagnetic simulation software such as HFSS, CST, and MTSS for modeling and simulation, and to scan or optimize various structural parameters within a certain range to find a structure that meets performance requirements. Interaction structures have many dimensional parameters, making the design process complex. The design process consists of two steps: First, for an interaction structure with fixed dimensions, a series of input powers are scanned and calculated at the center frequency to find the input power at which the output power is lowest, called the minimum input power point. Second, using this minimum input power point as the input power, frequency scanning is performed within the operating frequency band, and simulation calculations are conducted to obtain a series of indicators such as the output power and gain of the space traveling wave tube. Because general-purpose 3D electromagnetic simulation software requires a series of steps in interaction structure design, including modeling, mesh generation, numerical calculation, and post-processing analysis, a single simulation calculation consumes a significant amount of time and computer memory. When using optimization techniques such as parameter scanning, a large number of single calculations are required. Therefore, obtaining a traveling wave tube interaction structure with ideal output power, output gain, and other indicators requires a long computation time.

[0005] To address the challenges of time-consuming and resource-intensive design processes for interaction structures, including the inability to quickly and accurately obtain structural dimensions that meet performance requirements, an optimization design method based on the Kriging surrogate model is employed for simulation and optimization design of the interaction structure. The Kriging surrogate model is an interpolation model that provides a good approximation of black-box functions. Since the computational process of electromagnetic simulation cannot be given by specific mathematical expressions, the simulation calculation process can be treated as a black-box function during the optimization design of a space traveling wave tube. A highly accurate Kriging model can replace simulation calculations, directly providing estimates of the performance indicators of the interaction structure of the space traveling wave tube. The flowchart for constructing the Kriging model is shown below. Figure 1 As shown. After the Kriging model is constructed, the model's response output value is used as the optimization objective function, and the optimization result can be obtained quickly.

[0006] Optimization methods based on surrogate models rely heavily on the approximate accuracy of the surrogate model for their optimization performance. Adding a point criterion during model construction can improve accuracy. This criterion creates a mechanism that drives the addition of new sample points based on historical data. During iteration, sample points and their response outputs are continuously added to the optimization parameter design space, reconstructing the model and enriching it with more information. Currently, widely used adding criteria include minimizing the surrogate model's prediction, improving the expected value, and improving the probability. However, these criteria only add a single new sample point per iteration, lengthening the iteration process and making them prone to convergence too quickly or too slowly, leading to insufficient accuracy or excessive computational cost in the surrogate model. Summary of the Invention

[0007] To address the aforementioned problems and shortcomings, and to resolve the issues of time-consuming and resource-intensive numerical electromagnetic simulation software used in the design of space traveling wave tube interaction structures, as well as the difficulty of quickly determining design schemes that meet performance requirements using traditional optimization design techniques such as parameter scanning, this invention proposes an optimization design method for space traveling wave tube interaction structures. This invention obtains initial sample points for constructing a Kriging surrogate model using Latin hypercube, updates the sample point set using a subtractive clustering algorithm, and reconstructs the surrogate model to obtain a model that meets accuracy requirements, replacing the calculation process of electromagnetic simulation software. This effectively improves the design efficiency of interaction structures and provides guidance for subsequent more accurate optimization designs.

[0008] An optimization design method for the interaction structure of a space traveling wave tube includes the following steps:

[0009] Step 1: When performing optimization calculations on the interaction structure, the initial structural parameters of the interaction structure are first needed (such as interaction length, helix radius, pitch, and the lengths of the helix transition and jump segments, etc.). Based on the actual design requirements, one or more of these initial structural parameters are determined as the target optimization parameters. A decision vector x = [x1, x2, ..., x...] is formed from these optimization parameters. m ] T The value range of each component is given, and m is the number of optimization parameters. Then, the decision vector x is used as the input parameter of the Kriging surrogate model.

[0010] Step 2: Determine the response output of the surrogate model. Based on actual requirements, select one or more performance indicators of a space traveling wave tube, perform corresponding mathematical transformations, and use these as the response outputs y1, y2, ..., y n , where n is the number of response outputs.

[0011] Step 3: Using the Latin Hypercube Design of Experiment sampling method, based on full space filling, non-overlapping sampling is performed within the optimization parameter range given in Step 1.

[0012] The number of layers in the Latin hypercube experimental design is determined to be 10m+1. After sampling, a sample point set X with 10m+1 decision vectors is obtained within the parameter range. The dimensions of the traveling wave tube interaction structure are modified according to the values ​​of the sample points in set X. Interaction simulation calculations are performed in electromagnetic simulation software, and a set Y with 10n+1 response outputs is obtained according to the mathematical transformation in step 2. X and Y together form the initial model sample point set S.

[0013] Step 4: Construct the Kriging proxy model using the current sample point set S.

[0014] Step 5: Use the clustering algorithm's point addition criterion to obtain new sampling points, calculate the response output of the new sampling points, and update the sample point set S.

[0015] Within the design space of the input parameters, obtain a sample point set S of size q, and substitute it into the current Kriging model to obtain its predicted output. Then, process the sample points s in the sample point set... i The dimension is defined as m+n, s i = [x1,x2,…,x m ,y1,y2,…,y n ], s i Each component will participate in the density calculation. Subtractive clustering is performed on the sample points in S, and the resulting cluster centers are the new input sample points.

[0016] Step 6: Determine if the iteration termination condition is met. If it is met, obtain the final qualified surrogate model and proceed to Step 7; if it is not met, return to Step 4 and reconstruct the Kriging model using the new sample point set S.

[0017] The average error of the Kriging model The iteration is considered to have reached its termination condition when the following condition is met for w consecutive iterations:

[0018]

[0019] Where: k is the current iteration number, and a is the total number of new sample points added in the current iteration. Let y be the predicted value of the current Kriging model for the i-th newly added sample point. k (x i ) represents the true response output obtained from the simulation of the i-th sample point. ε is the convergence accuracy of the model, determined based on the numerical error of the simulation calculation at the sampling points, and its value ranges from [0.001, 0.01]. w is selected according to actual requirements, with a value range of 3-5.

[0020] Step 7: Select one of the following as the optimization algorithm: genetic algorithm, particle swarm optimization, and Newton's method. Use the decision vector from Step 1 as the decision variable and the output value of the qualified surrogate model response as the objective function to optimize and obtain the optimal space traveling wave tube interaction structure.

[0021] Furthermore, step 4 is specifically described as follows: Calculate the mapping relationship between input sample points and response outputs based on the mathematical expression of the Kriging model, and establish a Kriging surrogate model. The mathematical expression of the Kriging model is:

[0022]

[0023] The expression consists of two parts, the first part Let be a linear regression function for the data, which reflects the change in the process mean through p regressors. The linear regression function is a quadratic function, i.e., ...

[0024]

[0025] f1(x)=1

[0026] f2(x) = x1,…,f m+1 (x)=x m

[0027]

[0028]

[0029]

[0030] Where f j (x) is the j-th regressor, β j Its coefficient.

[0031] The second part, z(x), is a stochastic model built through data observation and the quantification of data correlation. z(x) is a realization of the stochastic process Z(x), and Z(x) has decision vectors x1 and x2 with respect to the h-th and g-th decisions. g The covariance matrix is:

[0032] cov[Z(x h ),Z(x g )]=σ 2 R[<(x1,x g )]

[0033] Where <(x1,x2) is the Gaussian correlation function:

[0034]

[0035] In the formula: θ l Let be the correlation coefficient of the l-th component of the decision vector x.

[0036] Furthermore, step 5 specifically includes:

[0037] Step 5-1: Obtain a sample point set S of size q within the design space of the input parameters, calculate the density of the sample points, and define the data point s. i Density D at that location i for:

[0038]

[0039] Where r a It is a constant, which is half the distance between the middle sample in the sample set and the sample furthest from it.

[0040] Step 5-2: Find the density D among q sample points i The largest point is defined as the cluster center 3. t Its density is D ct L represents the number of iterations of the clustering algorithm, where t = 1.

[0041] Step 5-3: Update the density of each data point:

[0042]

[0043] Where r b It is a constant with a value range of [1, 1r]. a 1.5r aBased on the updated sample point density, find the maximum density D of sample points other than the existing cluster centers. maP Select the next cluster center 3 t+1 .

[0044] Step 5-4: Determine if the following conditions are met:

[0045]

[0046] Where δ is a constant, and δ≥0.5. If this condition is met, proceed to step 5-5; if not, let L=L+1 and return to step 5-3.

[0047] Step 5-5: Use all the obtained cluster centers as new sample points and obtain their response outputs. Add the new sample points and their response outputs to the original sample point set to form a new sample point set S.

[0048] The detailed flowchart of the above steps is as follows: Figure 2 As shown.

[0049] For expensive computations such as simulating traveling wave tubes in space, this invention adopts the point addition criterion of subtractive clustering, which considers both the spatial distribution of sample points and the numerical distribution of the optimization target. Furthermore, multiple new sample points can be added simultaneously in a single iteration, reducing the number of simulation calculations and enabling the Kriging model to converge with fewer iterations.

[0050] In summary, this invention leverages the advantage of surrogate models, which can establish responses from a small number of sample points to represent the actual responses in the computational space. This solves the problems of long computation time and high computational resource consumption associated with optimization calculations using electromagnetic simulation software during the design of interaction structures in space traveling wave tubes. Furthermore, the Kriging model-based optimization method proposed in this invention is also applicable to the optimization design of interaction sections and other components of space traveling wave tubes. Attached Figure Description

[0051] Figure 1 This is a flowchart of the construction process of the Kriging model.

[0052] Figure 2 This is a flowchart of the spatial traveling wave tube interaction structure optimization method based on the Kriging model of the present invention.

[0053] Figure 3 This is a schematic diagram of the interaction structure parameters of the L-band traveling wave tube in the embodiment.

[0054] Figure 4 This describes the construction process of the L-band traveling wave tube output power proxy model in the embodiment.

[0055] Figure 5The example shows the actual response output curve obtained by electromagnetic simulation software at the optimal size predicted by the Kriging model. Detailed Implementation

[0056] The present invention will now be described in further detail with reference to the embodiments and accompanying drawings.

[0057] This embodiment employs an optimization design method for the interaction structure of a space traveling wave tube proposed in this invention to optimize the design of an L-band helical traveling wave tube. The three-segment design with positive jump and negative gradient is relatively common in the interaction structure design of L-band traveling wave tubes, and its interaction structure is illustrated below. Figure 3 In this embodiment, the inner diameter of the helix of the L-band traveling wave tube is 2.15 mm, and the pitch is 1.2 mm. Based on the operating frequency range of the L-band traveling wave tube, the minimum operating frequency is determined. min =1.5GHz, maximum operating frequency fre maP =1.7 GHz, number of sampling frequency points in the frequency band Q = 11, step size Δfre = 0.04 GHz.

[0058] Step 1: Set the basic dimensional parameters of the interaction structure to be optimized in the space traveling wave tube interaction structure, and determine the optimization parameters and their range. For example... Figure 3 As shown, the structural variables that need to be optimized are l1, l 20 ,l 21 The number of design variables is m=3. The value range of each optimization parameter satisfies: 160≤l1≤170mm, 170 <l 20 <180mm, 15 <l 21 <16mm.

[0059] Step 2: Determine the response output of the Kriging model. To ensure that the output power of the space traveling wave tube is as high as possible at each frequency point within a given frequency band, the point with the lowest output power within the frequency band is selected as the response output y.

[0060]

[0061] In the formula, fre min ,fre max For the minimum and maximum frequencies, fre i P is the sampling frequency. not (x,fre i ) indicates the sampling frequency point fre i The corresponding output power is the input parameter x and the frequency fre. i The function outputs the minimum output power within the frequency band. If the minimum value meets the design specifications, then the output power within the frequency band will also meet the specifications.

[0062] Step 3: Determine the number of layers in the Latin hypercube experimental design. In this embodiment, the number of design variables is m=3, and the number of layers in the Latin hypercube experimental design is set to 10m+1, which generates 31 three-dimensional vectors within the design range, forming the initial set of sampling points X. Based on the values ​​of the current sample points, the interaction structure dimensions of the L-band traveling wave tube are modified, and the output power within the operating frequency band is calculated using electromagnetic simulation software. The point with the lowest output power within the band is selected as the response output, obtaining the set of response outputs Y. X and Y together form the initial sample point set S.

[0063] Step 4: Construct the Kriging proxy model based on the current sample point set S.

[0064] Step 5: Use the clustering algorithm's point addition criterion to obtain new sampling points, obtain the response output in the manner of Step 2, and update the sample point set S.

[0065] Step 6: Determine if the optimization termination condition is met; if yes, proceed to step 7; if no, go back to step 4.

[0066] Optimization termination condition: the average error of the Kriging model An iteration can terminate when the following condition is met for three consecutive iterations, where k is the current iteration number:

[0067]

[0068] ε = 0.005

[0069] Step 7: Using the particle swarm optimization algorithm, the interaction structure variables l1, l 20 ,l 21 As a decision variable, the output response of the Kriging model is used as the objective function to optimize the interaction structure when the output power is maximized.

[0070] like Figure 4 As shown, in this embodiment, the Kriging model for output power converges after 16 iterations. The output power P in the frequency band obtained after optimization based on this model is... out Curves Figure 5 As shown, Figure 5 The graph shows the actual response output curve obtained by electromagnetic simulation software under the optimal size predicted by the Kriging model in this embodiment. Within the given optimization range, the maximum in-band output power was obtained.

[0071] As can be seen from the above embodiments, this invention, based on the Kriging surrogate model, employs the addition criterion of subtractive clustering. It obtains the initial sample points for constructing the Kriging surrogate model using Latin hypercube, while considering both the spatial distribution of the sample points and the numerical distribution of the optimization objective. The subtractive clustering algorithm allows multiple new sample points to be added simultaneously in a single iteration, thereby updating the sample point set and reconstructing the surrogate model. This enables the Kriging model to converge with fewer iterations. Ultimately, a model meeting the required accuracy is obtained, replacing the computation process of electromagnetic simulation software. This reduces the number of simulation calculations, effectively improves the design efficiency of interaction structures, and provides guidance for subsequent more accurate optimization designs. It effectively solves the problems of long computation time and high computational resource consumption associated with existing electromagnetic simulation software optimization calculations.

Claims

1. A method for the optimized design of a spatially growing wave tube interaction structure, characterized in that, The method comprises the following steps: Step 1, according to the actual design requirements, one or several of the initial structure parameters of the interaction structure are determined as the target optimization parameters; the decision vector x = [x1, x2, …, xn] composed of each optimization parameter is determined, and the value range of each component is given, and m is the number of optimization parameters; m ] T , Then the decision vector x is taken as an input parameter of the Kriging surrogate model; Step 2, determining the response output of the agent model, selecting one or more performance indicators of the spatial traveling wave tube according to actual requirements, and performing corresponding mathematical transformation to serve as the response output y1, y2, …, y n n is the number of response outputs; Step 3, a Latin hypercube sampling method is adopted to perform non-overlapping sampling in the optimization parameter range given in step 1 based on full space filling; The number of layers of the Latin hypercube experimental design is determined, and the number of layers is 10m+1; after sampling, a sample point set X with 10m+1 decision vectors is obtained in the parameter range; the size of the interaction structure of the traveling wave tube is modified according to the numerical value of the sample point in the set X, interaction simulation calculation is performed in the electromagnetic simulation software, and a set Y with 10n+1 response outputs is obtained according to the mathematical transformation of step 2; X and Y together constitute an initial model sample point set S; Step 4, a Kriging surrogate model is constructed through the current sample point set S; Step 5, a new sampling point is obtained by using the adding point criterion of the clustering algorithm, the response output of the new sampling point is calculated, and the sample point set S is updated; Obtain a sample point set S of size q within the design space of the input parameters, and substitute it into the current Kriging model to obtain its predicted output; then, convert the sample points s in the sample point set... i The dimension is defined as m+n, s i =[x1,x2,…,x m ,y1,y2,...,y n ], s i Each component will participate in the calculation of its density; subtractive clustering is performed on the sample points in S, and the obtained cluster centers are the new input sample points; Step 6, whether the iteration termination condition is met is judged, if the iteration termination condition is met, a final qualified surrogate model is obtained, and step 7 is entered; if the iteration termination condition is not met, step 4 is returned, and the Kriging model is reconstructed by using the new sample point set S; Average error of the Kriging model The iteration termination condition is considered to be reached when the following condition is satisfied for a consecutive w number of iterations: wherein: k is the current iteration number, a is the total number of new sample points in the current iteration, is the predicted value of the i-th new sample point by the current Kriging model, y k (x i ) is the true response output of the i-th sample point obtained by simulation. ε is the convergence precision of the model, which is determined according to the numerical error of the simulation calculation of the sampling points, and the value range is [0.001, 0.01]; the value range of w is 3-5; Step 7, one of a genetic algorithm, a particle swarm algorithm and a Newton method is selected as an optimization algorithm, the decision vector in step 1 is taken as a decision variable, and the response output value of the qualified surrogate model is taken as an objective function, so that the optimal space traveling wave tube interaction structure is obtained.

2. The method for optimized design of a space-traveling-wave tube interaction structure according to claim 1, wherein: The initial structure parameters are interaction length, helix radius, pitch and lengths of helix gradual change section and jump section.

3. The method of claim 1, wherein the space-charge wave interaction structure is a space-charge wave interaction structure of a traveling wave tube. The step 4 is specifically described as: The mapping relationship between the input sample points and the response outputs is calculated according to the mathematical expression of the Kriging model, the Kriging surrogate model is established, and the mathematical expression of the Kriging model is: The expression is composed of two parts, the first part is a linear regression function of the data, which reflects the variation of the process mean through p regressors; the linear regression function is chosen to be a quadratic function, i.e. f1(x)=1 f2(x) = x1,..., f m+1 (x) = x m where f j (x) is the jth regressor, β j is its coefficient; The second part z(x) is a stochastic model built by the observation of data and the quantification of data correlation. z(x) is an implementation of the stochastic process Z(x) with respect to the hth and gth decision vectors x1and x g The covariance matrix is: cov[Z(x h ),Z(x g )] = σ 2 R[<(x h ,x g )] where <(x h ,x g ) is a Gaussian correlation function: where: θ A is the correlation coefficient for the / th component of the decision vector x.

4. The method of claim 1, wherein the space-charge wave interaction structure is a space-charge wave interaction structure of a traveling wave tube. The step 5 is specifically described as: Step 5-1, obtain a sample point set S with a number of q within the design space of input parameters, calculate the density of sample points, define the density D of data points s at i i D =​ where r a is a constant, taken as half the distance between the sample in the middle of the sample set and the sample farthest from it; Step 5 - 2, find density D in q sample points i The largest point is defined as the cluster center 3 t , whose density is D ct L is the number of iterations of the clustering algorithm, at this time t = 1; Step 5-3, the density of each data point is updated: wherein r b is a constant, and the value range is [1.1r a , 1.5r a ]; according to the updated sample point density, the maximum density D maP of the sample points except the existing cluster center is found, and the next cluster center 3 t+1 is selected; Step 5-4, whether the following condition is met is judged: Wherein δ is a constant, and δ≥0.5; if the condition is met, step 5-5 is entered; if the condition is not met, L=L+1 is set, and step 5-3 is returned; Step 5-5, all the clustering centers obtained are taken as new sample points, the response outputs thereof are obtained; the new sampling points and the response outputs thereof are added to the original sample point set, and a new sample point set S is formed.

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