Target frequency-based single cavity resonator structure design method
By adopting a single-cavity resonator structure design method based on the target frequency, the problems of long R&D cycle and large prediction error in traditional design are solved, realizing fast and high-precision resonator structure design, which takes into account both physical rationality and engineering feasibility.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA ELECTRONICS TECH GRP NO 26 RES INST
- Filing Date
- 2026-06-30
- Publication Date
- 2026-07-31
AI Technical Summary
Traditional single-cavity resonator design suffers from long development cycles, large prediction errors, and high failure rates in generated structures. Existing reverse design schemes have poor generalization effects at the edge of parameter space and lack physical explanations, failing to effectively take into account engineering constraints such as manufacturing gaps and assembly collisions.
A single-cavity resonator structure design method based on the target frequency is adopted. By defining geometric parameters, constructing a frequency prediction model and a multi-penalty objective function, and combining inverse constraints, a global search is performed to screen high-quality candidate structures, and CST electromagnetic simulation is conducted for verification.
It effectively shortens the R&D cycle of single-cavity resonator structures, reduces the prediction error of extreme structures, and the output scheme takes into account both physical rationality and processing and assembly feasibility, thereby improving prediction accuracy and computational efficiency.
Smart Images
Figure CN122491074A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of cavity resonators, and in particular relates to a single-cavity resonator structure design method based on a target frequency. Background Technology
[0002] In the traditional single-cavity resonator design process, forward performance verification relies on CST electromagnetic simulation for iterative calculations of each dimension. Batch parameter traversal is time-consuming and significantly prolongs the product development cycle. At the same time, the traditional single equivalent circuit model cannot distinguish between four types of electric field coupling mechanisms: screwless, non-penetrating, shallow insertion, and deep insertion. Frequency jumps easily occur at the boundary of operating conditions, and the prediction deviation for deep insertion and small disk screwless structures is significant. Currently, most mainstream reverse design schemes use end-to-end pure black box neural networks without electromagnetic theory constraints to directly fit the geometric and frequency mapping relationship. This not only has poor generalization effect at the parameter space edge and lacks physical interpretability for the output structure, but also fails to take into account engineering constraints such as manufacturing gaps, assembly collisions, and size ratios in the generated candidate geometry, resulting in a high proportion of high-risk unqualified structures. Summary of the Invention
[0003] To address the shortcomings of the prior art, the technical problem to be solved by the present invention is to provide a single-cavity resonator structure design method based on a target frequency.
[0004] To solve the above-mentioned technical problems, the present invention provides the following technical solution: A single-cavity resonator structure design method based on a target frequency includes the following steps: S1. Define the geometric parameters of the single-cavity resonator structure, standardize the geometric parameters, and divide multiple operating conditions according to the geometric parameters; S2. Construct a frequency prediction model based on geometric parameters to predict the frequency of a single-cavity resonator under different working conditions and output the model uncertainty. S3. Input the target frequency and the inverse constraints of each geometric parameter, and search for candidate resonant structures in the whole domain within the range defined by the inverse constraints. S4. Call the frequency prediction model to output the predicted frequency and model uncertainty of all candidate structures. Based on the prediction frequency error, model uncertainty and comprehensive risk value, construct a multi-penalty objective function, calculate the comprehensive penalty value of each candidate structure and output it in order of working conditions. S5. For each working condition, select multiple candidate structures that rank highly as high-quality candidate structures, and output the geometric parameters of each high-quality candidate structure. S6. Perform CST electromagnetic simulation to verify the high-quality candidate structures output, and select the candidate structure parameters that meet the requirements as the parameters of the single-cavity resonator structure.
[0005] Furthermore, the geometric parameters include gap_top, resonant disk height h_xzp1, resonant column height h_xzz1, resonant disk radius r_xzp1, resonant column radius r_xzz1, tuning screw length L_screw1, and cavity radial margin dis; the constraints include upper and lower limit constraints of dimensions, structural proportion constraints, and anti-collision constraints; the method for dividing multiple working conditions is as follows: based on whether there is a tuning screw and the effective insertion depth of the screw, the working conditions are divided into no-screw working condition, non-penetration working condition, shallow insertion working condition, or deep insertion working condition.
[0006] Furthermore, the method for constructing a frequency prediction model includes the following sub-steps: S210. Standardize the geometric parameters of the single-cavity resonator structure, construct a global sample library, and divide it into four sub-libraries based on the operating conditions. S220. Construct a reference electromagnetic equivalent model and obtain the reference theoretical frequency by solving based on the geometric parameters of the cavity; S230. Construct a working condition adaptation correction model, and correct the reference theoretical frequency according to the working condition to obtain the corrected reference frequency. S240. Using the sample library and the benchmark theoretical frequency, corrected reference frequency and correction amount corresponding to each sample, the global residual model and the state residual model corresponding to each working condition are trained. S250. The reference theoretical frequency is predicted based on the geometric parameters of the single-cavity resonator structure under test, and the final predicted frequency is obtained after compensating the reference theoretical frequency with global residual and state residual.
[0007] Furthermore, the predicted frequency error is the absolute difference between the input target frequency and the final predicted frequency of the frequency prediction model in logarithmic space; the global residual model also outputs the global residual uncertainty, and the state residual model also outputs the state residual uncertainty. The model uncertainty is calculated by superimposing the variances of the global residual uncertainty and the state residual uncertainty.
[0008] Furthermore, the comprehensive risk value is obtained by weighted fusion of one or more of the following: extrapolation risk, model consistency risk, boundary geometry risk, and manufacturing process risk.
[0009] Furthermore, step S220 includes the following sub-steps: S221. The equivalent cavity radius is calculated based on the radius of the resonant disk and the radial margin of the cavity; the calculation formula is as follows: r_cav=r_xzp1+0.5dis Where r_cav represents the equivalent cavity radius; r_xzp1 represents the resonant disk radius; and dis represents the cavity radial margin. S222. Based on the coaxial transmission line impedance formula, calculate the equivalent characteristic impedance of the resonant pillar and the equivalent characteristic impedance of the resonant disk in the cavity; the calculation formula is as follows: Z1=60ln(r_cav / r_xzz1); Z2=60ln(r_cav / r_xzp1); Where Z1 represents the equivalent characteristic impedance of the resonant pillar, Z2 represents the equivalent characteristic impedance of the resonant disk; r_xzz1 represents the radius of the resonant pillar; and r_xzp1 represents the radius of the resonant disk. S223. Calculate the equivalent capacitance of the cavity in stages and obtain the total loaded capacitance by weighted fusion. S224. Select the resonance model based on the electrical length of the cavity, and calculate the original theoretical frequency based on the impedance of the resonant pillar, the impedance of the resonant disk, and the total loaded capacitance. S225. A linear correction is made to the original theoretical frequency using a fixed proportionality coefficient and an offset coefficient to obtain the reference theoretical frequency; the correction formula is as follows: f_base=k×f_raw+b In the formula, f_base represents the reference theoretical frequency; f_raw represents the original theoretical frequency; k represents the scaling factor; and b represents the bias factor.
[0010] Furthermore, in step S230, the working condition is corrected by three branches: a normal branch, a deep insertion correction branch, and a small disk capacitance correction branch, based on the working condition label and the radius of the resonant disk as the judgment conditions. For the deep insertion working condition, the deep insertion correction branch is used. For the screwless working condition where the radius of the resonant disk is less than the preset radius threshold, the small disk capacitance correction branch is used. For the non-penetration working condition, the shallow insertion working condition, and the screwless working condition where the radius of the resonant disk is greater than the preset radius threshold, the normal branch is used, and the reference theoretical frequency is directly used as the corrected reference frequency.
[0011] Furthermore, the method of using the deep insertion correction branch for correction is as follows: based on the pre-trained and finalized ridge regression model and fixed coefficients, firstly extract the multi-dimensional geometric features of the cavity, tuning screw and resonant disk under the deep insertion condition to construct feature vectors, and then perform second-order polynomial expansion on the features, then perform standardization processing, and finally call the ridge regression model to calculate, and obtain the corrected reference frequency after logarithmic space transformation; The method of correction using the small disk capacitance correction branch is as follows: define the edge field saturation correction coefficient, radial capacitance suppression coefficient and geometric dynamic scaling coefficient to construct the calculation logic of the small disk equivalent total wall capacitance; replace the disk wall capacitance with the small disk equivalent total wall capacitance and substitute it into the reference electromagnetic equivalent model, and use the output frequency of the reference electromagnetic equivalent model as the corrected reference frequency.
[0012] Furthermore, step S240 includes the following sub-steps: S241. Train labels uniformly in the natural logarithm space; S242. A global residual model is obtained by training the global sample library and the full-dimensional feature set corresponding to the sample. S243. Based on the trained global residual model, generate state residual-specific training labels in the natural logarithm space. S244. Based on the dedicated training labels for state residuals, four sets of state residual models are trained independently using four sub-libraries of operating conditions.
[0013] Furthermore, the following steps are performed: S7. Fill the simulation verification data back into the training set of the frequency prediction model and iteratively optimize the frequency prediction model.
[0014] In this invention, a case-specific reverse design method is adopted, and a residual prediction model with physical constraints is used to replace the full-process CST iterative simulation, which can effectively shorten the R&D cycle of single-cavity resonator structures. Using multiple screw coupling mechanisms for case-specific design can reduce prediction errors for extreme structures; by using multiple penalty objective functions to screen candidates for different cases, the problems of poor generalization and numerous high-risk structures associated with pure black-box models can be avoided, and the output scheme balances physical rationality and manufacturing / assembly feasibility; by backfilling simulation data into the iterative optimization model to form a closed loop, prediction accuracy can be continuously improved, simultaneously considering computational efficiency, multi-case stability, and engineering practicality. Attached Figure Description
[0015] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of an embodiment of the single-cavity resonator structure design method based on the target frequency of the present invention.
[0016] Figure 2 This is a cross-sectional schematic diagram of a single-cavity resonator structure.
[0017] The diagrams in the instruction manual are labeled as follows: Cavity 100; Resonant disk 210; Resonant column 220; Tuning hole 230; Tuning screw 300. Detailed Implementation
[0018] The following specific examples illustrate the implementation of the present invention. The illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.
[0019] Please see Figure 1 , Figure 1This is a flowchart illustrating an embodiment of the single-cavity resonator structure design method based on a target frequency according to the present invention. The single-cavity resonator structure design method based on a target frequency in this embodiment includes the following steps: S1. Define the geometric parameters of the single-cavity resonator structure, standardize the geometric parameters, and divide multiple operating conditions according to the geometric parameters.
[0020] Please see Figure 2 The single-cavity resonator structure includes a cavity 100 and a resonator and a tuning screw 300 disposed within the cavity 100. The resonator includes a resonant disk 210 and a resonant post 220 connecting the resonant disk 210 and the bottom of the cavity. A tuning hole 230 is provided in the resonator, penetrating the resonant disk 210 and the resonant post 220. The geometric parameters may include the top gap (gap_top), resonant disk height (h_xzp1), resonant post height (h_xzz1), resonant disk radius (r_xzp1), resonant post radius (r_xzz1), tuning screw length (L_screw1), and cavity radial margin (dis). Of course, depending on the actual situation, the geometric parameters may also include other parameters required for calculation, such as the tuning hole radius (r_in_kqq1) and the tuning screw radius (r_screw1).
[0021] The method for dividing multiple operating conditions is as follows: based on the presence of the tuning screw 300 and the effective insertion depth of the screw, the conditions are categorized as screwless, non-penetrating, shallow insertion, or deep insertion. The effective insertion depth d_ins is calculated based on the relative position of the tuning screw 300 and the resonant disk 210 in the single-cavity model, using the following formula: d_ins=L_screw1-gap_top The working condition division method is as follows: If L_screw1=0, then the screw 300 is considered untuned and classified as a screwless operating condition; otherwise, the screw 300 is considered tuned and further classified according to the effective insertion depth of the screw. If d_ins≤0, it is classified as a non-penetrating condition; if 0<d_ins≤d0, it is classified as a shallow insertion condition; if d_ins>d0, it is classified as a deep insertion condition. d0 is a preset depth threshold, and in this embodiment, d0=2mm.
[0022] S2. Construct a frequency prediction model based on geometric parameters to predict the frequency of a single-cavity resonator under different operating conditions and output the model uncertainty. This step may include the following sub-steps: S210. Standardize the geometric parameters of the single-cavity resonator structure, construct a global sample library, and divide it into four sub-libraries based on operating conditions. This step may include the following sub-steps: S211. Unify the dimensions of the geometric parameters of the single-cavity resonator structure and set constraints for each geometric parameter to construct a standardized parameter design space. The dimensions of all geometric parameters can be unified to mm. The constraints may include upper and lower limit constraints on dimensions, structural proportion constraints, and collision avoidance constraints.
[0023] S212. Uniform random sampling is performed within the standardized parameter design space to generate multiple combinations of geometric parameters using the multi-combination method, resulting in multiple single-cavity models. These models are then categorized into operating conditions and labeled accordingly. Additionally, boundary transition samples at the junctions of the four operating conditions can be collected. These boundary samples are simultaneously assigned to two adjacent operating condition sub-libraries for subsequent use in eliminating model prediction jumps during operating condition transitions.
[0024] S213. Import each group of single-cavity models into electromagnetic simulation software to carry out automated intrinsic simulation, eliminate invalid samples such as simulation non-convergence and solution error, and extract the simulation true resonant frequency corresponding to each group of valid samples.
[0025] S214. Using the geometric parameters of the single-cavity model, the effective insertion depth of the screw, the operating condition label, and the simulated true frequency as sample features and labels, a global sample library is constructed by integrating effective simulation samples. Based on the operating condition label, the global sample library is further divided into four operating condition sub-libraries. The four operating condition sub-libraries correspond to the screwless operating condition, the non-penetrating operating condition, the shallow insertion operating condition, and the deep insertion operating condition, respectively.
[0026] S220. Construct a reference electromagnetic equivalent model and solve for the reference theoretical frequency based on the cavity's geometric parameters. The reference electromagnetic equivalent model is a globally unified physical calculation model, adaptable to all four types of electromagnetic operating conditions. It can calculate the cavity's equivalent impedance and multi-level equivalent capacitance using coaxial transmission line theory and LC resonant circuit theory. Frequency jumps during operating condition switching are resolved through capacitor smoothing transitions, ultimately outputting the reference theoretical frequency without compensation for errors, providing a unified physical reference for subsequent corrections and residual compensation. This step may include the following sub-steps: S221. The equivalent cavity radius is calculated based on the radius of the resonant disk and the radial margin of the cavity. The following formula can be used for calculation: r_cav=r_xzp1+0.5dis Where r_cav represents the equivalent cavity radius; r_xzp1 represents the resonant disk radius; and dis represents the cavity radial margin; the unit is mm.
[0027] S222. Based on the coaxial transmission line impedance formula, calculate the equivalent characteristic impedances of the two cavity sections, namely the resonant pillar section and the resonant disk section, to characterize the electromagnetic wave transmission characteristics of the cavity. The equivalent characteristic impedances of the resonant pillar and the resonant disk can be calculated using the following formulas: Z1=60ln(r_cav / r_xzz1); Z2=60ln(r_cav / r_xzp1); Where Z1 represents the equivalent characteristic impedance of the resonant pillar, Z2 represents the equivalent characteristic impedance of the resonant disk; r_xzz1 represents the radius of the resonant pillar; and r_xzp1 represents the radius of the resonant disk.
[0028] S223. Calculate the equivalent capacitance of the cavity in stages, and obtain the total loaded capacitance through weighted fusion. This step may include the following sub-steps: S2231. Based on the cavity geometry and vacuum dielectric constant, calculate the cavity's inherent electric field and the corresponding cavity foundation capacitance corresponding to the electric field introduced by the tuning screw 300. The cavity foundation capacitance includes the cavity's axial capacitance C_axial, radial capacitance C_radial, disk wall capacitance C_wall, screw tip edge capacitance C_fringe, screw coaxial capacitance C_coax, and disk surface gap capacitance C_gap. Specifically, the axial capacitance C_axial is the axial electric field energy storage capacitance between the upper surface of the resonant disk 210 and the cavity top plate; the radial capacitance C_radial is the radial electric field energy storage capacitance between the sidewall of the resonant disk 210 and the equivalent cavity wall; and the disk wall capacitance C_wall is the inherent equivalent capacitance between the resonant disk 210 and the inner wall of the cavity, serving as the cavity's foundation energy storage capacitance. The screw tip edge capacitance C_fringe is the equivalent capacitance of the edge electric field generated by the tip of the tuning screw 300 when it does not penetrate deeply into the disk surface of the resonant disk 210, dominating the electric field change during the non-penetration, shallow insertion condition. The coaxial capacitance C_coax of the tuning screw 300 is the equivalent capacitance resulting from the coaxial structure formed between the tuning screw 300 and the cavity after the tuning screw 300 penetrates deep into the resonant disk 210. This capacitance dominates the electric field change during deep insertion. The disk gap capacitance C_gap is the additional electric field capacitance generated by the center gap of the resonant disk 210 after the tuning screw 300 is deeply inserted. This capacitance is an auxiliary capacitance during deep insertion. The axial and radial capacitances are used to calculate the disk wall capacitance. The calculation formulas for the basic capacitance of each cavity are as follows:
[0029] In the formula, It represents the vacuum permittivity.
[0030]
[0031] In the formula, Indicates the equivalent cavity radius.
[0032]
[0033] In the formula, Indicates the edge field magnification factor; Indicates radial capacitance weight; and All are fixed values that do not change with geometric dimensions.
[0034]
[0035] In the formula, This represents the equivalent area directly opposite the tip of the tuning screw 300; delta_factor represents the tip distance correction factor. This means taking the maximum value between d_ins and delta_factor to prevent the denominator from approaching zero and causing abnormal amplification of the capacitance value, thus ensuring calculation stability. In this embodiment, delta_factor = 0.313194 is chosen.
[0036]
[0037] In the formula, β represents the overall calibration coefficient of the coaxial capacitor, which is used to absorb the approximation errors of the three-dimensional field, thread structure, dielectric equivalence, etc. In this embodiment, β = 11.057659 is taken. eff_pen represents the effective insertion length of the tuning screw 300, in meters (which needs to be converted to SI units). It refers to the actual length of the tuning screw 300 that penetrates into the coaxial region of the center of the resonant disk 210 and truly participates in the electric field coupling. It eliminates the invalid segments that do not generate coaxial capacitance.
[0038]
[0039] S gap This represents the equivalent facing area between the root of the tuning screw 300 and the resonant disk 210; gap_total represents the local gap distance between the root of the tuning screw 300 and the disk surface of the resonant disk 210 in the deep insertion region.
[0040] S2232. Calculate the non-penetrating composite capacitance based on the disk wall capacitance and the screw tip edge capacitance, and calculate the deep insertion composite capacitance based on the disk wall capacitance, the screw coaxial capacitance, and the disk surface gap capacitance.
[0041] This embodiment combines the differences in electric field distribution across four operating conditions, categorizing them into two major capacitor systems to accommodate different insertion states of the tuning screw 300. Specifically, the non-penetrating type of integrated capacitor adapts to three operating conditions: no screw, non-penetrating, and shallow insertion. In these conditions, the coaxial capacitance can be ignored; calculation can be performed by simply adding the disk wall capacitance and the screw tip edge capacitance. The calculation formula is as follows: C_above = γ(C_wall + C_fringe) In the formula, C_above represents the overall capacitance of the non-penetrating class; γ represents the non-penetrating class amplification factor pre-calibrated offline; C_wall represents the disk wall capacitance; and C_fringe represents the screw tip edge capacitance.
[0042] The deep insertion type integrated capacitor is adapted for deep insertion conditions, where the tip edge capacitor fails. It can be calculated by superimposing the disk wall capacitance, screw coaxial capacitance, and disk gap capacitance. The calculation formula is as follows: C_deep=γ_insert(C_wall+C_coax+C_gap) In the formula, C_deep represents the deep insertion type composite capacitance; γ_insert represents the offline pre-calibrated non-penetration type amplification factor; C_coax represents the screw coaxial capacitance; and C_gap represents the disk surface gap capacitance.
[0043] S2233. Calculate the transition weight coefficient based on the effective insertion depth of the screw. Use the Sigmoid function to weight and fuse the non-penetrating and deeply inserted composite capacitors according to the transition weight coefficient to obtain the total loaded capacitance. The calculation formula is as follows: C_load = (1-t)C_above + t × C_deep t=sigmoid[(d_ins-1) / trans_width] In the formula, C_load represents the total loaded capacitance; t represents the transition weight coefficient; the Sigmoid function is a continuous S-shaped transition function with an output between 0 and 1. In this embodiment, the Sigmoid function is used to calculate the transition weight coefficient based on the 300 insertion depth of the tuning screw, which can achieve a smooth transition of the comprehensive capacitance corresponding to the two types of working conditions and eliminate the sudden change in capacitance and resonant frequency caused by the switching of working conditions; trans_width is the transition width of the Sigmoid function, which is a fixed value calibrated in advance. For example, trans_width = 1.501mm can be taken.
[0044] When the structure is in the central region of the working condition, the transition weight coefficient t approaches 0 or 1, and the total loaded capacitance is approximately equal to the comprehensive capacitance of the corresponding working condition. When the structure is in the transition region at the boundary of different working conditions, the transition weight coefficient t is between 0 and 1, and the two sets of comprehensive capacitances participate in the weighting, thereby realizing the continuous change of capacitance and resonant frequency and eliminating jump defects.
[0045] S224. Select the resonance model based on the cavity's electrical length, and calculate the original theoretical frequency based on the resonant column impedance, resonant disk impedance, and total loaded capacitance. When the cavity's electrical length is greater than a preset electrical length switching threshold, the cavity is considered a long cavity, and the original theoretical frequency is calculated using the SIR model. Otherwise, the cavity is considered a short cavity, and the original theoretical frequency is calculated using the lumped LC model. Both the SIR and lumped LC models are existing models and will not be elaborated upon here. Electrical length refers to the phase offset corresponding to a certain distance the electromagnetic wave propagates along the transmission line. In this embodiment, the electrical length switching threshold is set to 7.9279°. The method for calculating the original theoretical frequency is existing technology and will not be elaborated upon here.
[0046] S225 uses a fixed proportional coefficient and bias coefficient to perform a linear correction on the original theoretical frequency to obtain the reference theoretical frequency; the correction formula is as follows: f_base=k×f_raw+b In the formula, f_base represents the reference theoretical frequency; f_raw represents the original theoretical frequency; k represents the scaling factor; and b represents the bias factor. The scaling factor k and the bias factor b are obtained through global linear calibration and are used to absorb the overall offset caused by material, boundary, and model simplification. In this embodiment, the scaling factor k = 0.980031 and the bias factor b = 0.074200 are taken.
[0047] S230. Construct a working condition adaptation correction model, and correct the reference theoretical frequency for each working condition to obtain the corrected reference frequency. The reference electromagnetic equivalent model is a universal model, but it has significant inherent errors in deep insertion and small-radius screwless working conditions. Therefore, this embodiment constructs a working condition adaptation correction model, performing physical-layer directional correction for the two types of high-error extreme structures, while directly reusing the reference frequency for conventional structures. This model directly outputs the corrected reference frequency, with the correction amount being the derived difference. At the same time, it integrates all data before and after to construct a full-dimensional feature set, which serves as the sole input to the subsequent residual model.
[0048] In this step, the operating condition label and the radius of the resonant disk are used as the criteria, and the process is divided into three correction branches: the normal branch, the deep insertion correction branch, and the small disk capacitance correction branch, which correct the corresponding operating conditions respectively.
[0049] For deep insertion conditions, a deep insertion correction branch is used for correction. The correction method is as follows: Based on a pre-trained and finalized ridge regression model and fixed coefficients, multi-dimensional geometric features of the cavity, tuning screw 300, and resonant disk 210 under deep insertion conditions are first extracted to construct feature vectors. These features are then expanded using a second-order polynomial, standardized, and finally calculated using the ridge regression model. The corrected reference frequency is obtained after logarithmic space transformation. Specifically, the following steps may be included: S2301, Constructing the basic geometric feature vectors In this embodiment, based on the electric field characteristics under deep insertion conditions, a basic geometric feature vector is constructed consisting of 10 dimensionless, logarithmic features. :
[0050] in, f_base is the natural logarithm of the reference theoretical frequency, used to transmit reference frequency information; The ratio of the insertion depth d_ins to the resonant pillar height h_xzz1 represents the relative insertion amount. The ratio of the top gap_top to the radius r_xzp1 of the resonant disk represents the relative size of the gap; The ratio of the resonant column radius r_xzz1 to the resonant disk radius r_xzp1 represents the difference in column-disk structure. The ratio of the height h_xzp1 to the radius r_xzp1 of the resonant disk represents the disk's shape. The ratio of the equivalent cavity radius r_cav to the resonant disk radius r_xzp1 represents the relative size of the cavity. This is the logarithm of the radial margin dis of the cavity, used to reduce the influence of dimensions; Let r_xzp1 be the logarithm of the ratio of the resonant disk radius r_xzp1 to the tuning screw radius r_screw1, which can be taken as 1.01. The lower limit value; The ratio of the effective insertion depth d_ins to the resonant disk radius r_xzp1; The coupling ratio term is calculated using the following formula:
[0051] S2302, Regarding the fundamental geometric feature vectors A second-order polynomial feature expansion is performed. To characterize the nonlinear coupling relationship between geometric parameters, the fundamental geometric feature vectors are... The second-order expansion yields the following formula:
[0052] In the formula, This represents the eigenvector obtained after expanding the features of a second-order polynomial, with 65 eigenvalues.
[0053] S2303, to The features are standardized to eliminate differences in units and numerical ranges, ensuring stable model training. The standardization formula is as follows:
[0054] In the formula, This represents the feature vector obtained after standardization. This represents the mean vector of features in the training set. This represents the feature scale (standard deviation) vector of the training set.
[0055] S2304. Calculate the logarithmic domain correction frequency using the Ridge model (regression model). The model calculations are performed entirely in logarithmic space, converting absolute error into multiplicative error, which improves extrapolation stability. The formula is as follows:
[0056] In the formula, Indicates the frequency after deep insertion correction; This represents the intercept term of the regression model; This represents the regression coefficient vector.
[0057] S2305. The frequency corrected in the number domain is exponentially restored to obtain the frequency after deep insertion correction. That is:
[0058] f_deep is used as the corrected reference frequency.
[0059] For screwless applications where the resonant disk radius is smaller than a preset radius threshold (e.g., <6.5mm), a small disk capacitance correction branch is used for correction. The correction method is as follows: define the edge field saturation correction coefficient, radial capacitance suppression coefficient, and geometric dynamic scaling coefficient to construct the calculation logic for the small disk's equivalent total wall capacitance; substitute the disk wall capacitance for the small disk's equivalent total wall capacitance in the reference electromagnetic equivalent model, and use the output frequency of the reference electromagnetic equivalent model as the corrected reference frequency. Specifically, this may include the following steps: S2311. Define the dimensionless control quantity for the small disk. In this embodiment, three core geometric ratios are extracted for subsequent correction function calculations, as follows:
[0060]
[0061]
[0062] In the formula, It represents a dimensionless quantity of the upper gap relative to the edge of the disk, characterizing the strength of the edge field. It represents the logarithmic ratio of the radius of the equivalent cavity to that of the resonant disk, and characterizes the radial distance from the disk edge to the cavity wall. The ratio of the height to the radius of the resonant disk 210 represents the thickness and shape of the disk body.
[0063] S2312. Define the design edge field saturation correction coefficient, radial capacitance suppression coefficient, and geometric dynamic scaling coefficient. The formulas are as follows:
[0064]
[0065]
[0066] In the formula, This represents the edge field saturation correction factor for axial capacitance; This represents the fundamental correction coefficient for the edge field (a calibration constant). This represents the saturation suppression coefficient (a calibration constant). This represents the radial capacitance suppression correction factor; This represents the radial suppression coefficient (a calibration constant). This represents the geometric dynamic scaling factor, used to adapt to different small-disk configurations; This represents the baseline value for the scaling of the base capacitance (a calibration constant). , , These are the three geometric correlation correction coefficients obtained through sample calibration.
[0067] S2313. Based on the coefficients obtained in step S312, the axial capacitance and radial capacitance are weighted and combined to obtain the equivalent total wall capacitance of the small disk.
[0068]
[0069] In the formula, This represents the equivalent total wall capacitance of the small disk.
[0070] S2314. Replace the disk wall capacitance with the equivalent total wall capacitance of the small disk and substitute it into the reference electromagnetic equivalent model. Use the output frequency of the reference electromagnetic equivalent model as the corrected reference frequency.
[0071] For non-penetrating conditions, shallow insertion conditions, and screwless conditions where the resonant disk radius is greater than the preset radius threshold, the conventional branch is used without correction, and the reference theoretical frequency is directly used as the corrected reference frequency with a correction amount of 0.
[0072] All formulas and regression coefficients in the working condition adaptation correction model were determined offline in the early stages of the project. During the algorithm's online inference phase, only numerical calculations were performed, with no online parameter training or iterative updates.
[0073] In this step, a full-dimensional feature set can be constructed as the output. The full-dimensional feature set is a standardized input vector connecting the physical calculation module and the machine learning residual module. It integrates all effective information from previous steps to construct the full-dimensional feature set. The output feature dimensions of the three correction branches remain completely consistent, with only the feature values changing with the structural operating conditions. The full-dimensional feature set can include all original structural dimensional features of the cavity, derived geometric features such as the effective insertion depth of the screw, the equivalent cavity radius, and dimensionless proportions of various dimensions, reference electromagnetic features such as the reference theoretical frequency and the logarithmic value of the reference frequency, correction deviation features such as the corrected reference frequency and the logarithmic value of the reference frequency, and state label features such as four types of electromagnetic operating condition coding labels and three types of correction branch coding labels.
[0074] S240. Using the sample library and the corresponding baseline theoretical frequency, corrected reference frequency and correction amount for each sample, the global residual model and the state residual model corresponding to each working condition are trained.
[0075] The physical reference frequency and the working condition corrected reference frequency obtained by the above method still have small nonlinear residual errors that cannot be further eliminated by physical formulas. Therefore, in this embodiment, a two-level compensation network is built, consisting of a global residual model and a working condition-specific residual model. The model does not directly fit the mapping relationship between geometric parameters and frequencies, but only fits the residual errors of the physical model, preserving the overall physical interpretability of the scheme. The entire training process always uses the reference theoretical frequency f_base as the prediction benchmark. The corrected reference frequency output by the working condition adaptation correction model does not directly participate in the final frequency synthesis or replace the reference theoretical frequency. It is only used as a physical enhancement auxiliary feature input to the compensation network to indicate to the model the direction and magnitude of the deviation of the reference theoretical frequency under different working conditions. This step may include the following sub-steps: S241. Unify the training labels in the natural logarithm space to mitigate training errors caused by the frequency range. The formula is as follows: R_global = ln(f_sim) - ln(f_base) In the formula, R_global represents the global residual label; f_sim represents the simulated real frequency; and the training objective is the logarithmic residual between the baseline theoretical frequency and the real frequency.
[0076] S242. A global residual model is trained using a global sample library and the corresponding full-dimensional feature set. This global residual model learns the global systematic residual errors common to the four operating conditions, and outputs a global correction Δglobal to compensate for the fixed bias common to all structures, eliminating the uniform model bias across the entire domain. In this step, the global residual uncertainty σ_global is also output simultaneously to characterize the prediction fluctuation of the uniform systematic bias across all operating conditions, representing the model's reliability in predicting the common fixed errors of all cavities.
[0077] S243. Based on the trained global residual model, generate state residual-specific training labels in the natural logarithm space. The formula is as follows: R_state=ln(f_sim)-ln(f_base)-Δglobal In the formula, R_state represents the residual-specific training label for each working condition.
[0078] S244. Based on the dedicated training labels for state residuals, four sets of state residual models are independently trained using four sub-libraries of operating conditions. The state residual models are used to learn the unique nonlinear residual errors of different operating conditions, and output the local correction amount Δstate of the operating condition to accurately compensate for the differential deviations under different electromagnetic conditions, further suppressing the frequency prediction jump at the operating condition switching position.
[0079] In this step, the state residual uncertainty σ_state is also output synchronously. This uncertainty characterizes the prediction fluctuations of the nonlinear local errors unique to the current operating condition, reflecting only the prediction uncertainty caused by the electric field coupling within this operating condition. The model uncertainty σ_logf can be calculated by combining the global residual uncertainty σ_global and the state residual uncertainty σ_state. For example, the model uncertainty σ_logf can be calculated using variance superposition with the global residual uncertainty σ_global and the state residual uncertainty σ_state, as shown in the following formula:
[0080] Five-fold cross-validation can be used to iteratively train a single BNN network, simultaneously optimizing the mean and variance parameters of the weight distribution within the network. The mean parameter is used to fit the true residuals, while the variance parameter is used to model the model's own prediction uncertainty. Embedding the corrected reference frequencies and correction values from step S3 into the full-dimensional feature set as auxiliary input features for the BNN network helps it quickly distinguish between three types of bias patterns: regular structures, deep insertion correction structures, and small disk correction structures, further improving residual fitting accuracy. Using BNN networks to train global residual models and state residual models has the following advantages: A single model can be used to obtain an integrated global residual model and four sets of state residual models. It can automatically learn common systematic errors across the entire domain, thus achieving the functionality of a global residual model and fitting fixed deviations common to all cavity structures. Furthermore, it can automatically learn nonlinear difference errors under different operating conditions. Relying on the operating condition label features in the feature set, it can autonomously identify the differentiated error patterns of four different electromagnetic operating conditions, thus obtaining the functionality of four independent state residual models for each operating condition, without the need to build separate networks for each type of operating condition.
[0081] S250. Based on the geometric parameters of the single-cavity resonator structure under test, the reference theoretical frequency is predicted. The final predicted frequency is then obtained after compensating for the reference theoretical frequency using global residuals and state residuals. This step may include the following sub-steps: S251. Input the geometric parameters of the single-cavity resonator structure under test, and sequentially complete the parameter verification, operating condition determination, reference electromagnetic equivalent model calculation, and operating condition adaptation correction model calculation to obtain the reference theoretical frequency, corrected reference frequency, and full-dimensional feature set corresponding to the structure under test.
[0082] S252. Input the full-dimensional feature set of the single-cavity resonator structure under test into the global residual model and the state residual model respectively to calculate the global residual and the state residual that matches the current operating condition. After compensating the reference theoretical frequency with the global residual and the state residual, the final predicted frequency is obtained.
[0083] In this embodiment, the final predicted resonant frequency of the single-cavity resonator under test is obtained by superimposing the reference theoretical frequency, global residual, and state residual in logarithmic space, and then restoring the true frequency scale through exponential operations. The specific compensation formula is as follows: f_pred=exp[ln(f_base)+Δglobal+Δstate] In the formula, f_pred represents the final prediction frequency.
[0084] S260. Optimize the model through active learning. Since initial samples were generated using random sampling, active learning can be used to improve training efficiency and data coverage. For example, the trained model can be used to perform batch predictions on unsimulated parameter combinations within the parameter space, actively selecting samples with high model uncertainty σ_logf for targeted supplementary simulations. The supplementary samples are then added back to the global sample library and the corresponding working condition sub-library; subsequently, step S240 is re-executed to complete the training of the global residual model and the state residual models corresponding to each working condition, improving the frequency prediction accuracy under both global and extreme working conditions. By selecting samples, model shortcomings and data blind spots can be compensated for, ineffective simulations can be avoided, sample utilization efficiency can be significantly improved, and model accuracy can be optimized.
[0085] S3. Input the target frequency and the inverse constraints of each geometric parameter, and search for candidate resonant structures across the entire domain within the range defined by the inverse constraints. The target resonant frequency is the target frequency point determined based on product specifications, and serves as the frequency standard for subsequent optimization and matching; it remains fixed throughout the process.
[0086] The inverse constraints on geometric parameters can be categorized into four types to collectively define the legal geometric parameter space. The first type is dimensional boundary constraints, which can include upper and lower limits for all cavity geometric dimensions, thus preventing invalid structures with out-of-bounds dimensions. The second type is operational condition zoning constraints, which divide the space into four independent search sub-intervals based on the effective insertion depth threshold of the screw: no screw, not penetrated, shallow insertion, and deep insertion. Each operational condition separately limits the screw length range to avoid generating hybrid structures that cross operational conditions or do not conform to the electric field coupling mechanism. The third type is structural proportion constraints, such as the radius ratio between the resonant disk and the resonant pillar, the radial clearance ratio between the cavity and the resonant disk, and the ratio between the screw diameter and the tuning hole clearance, used to avoid extreme deformed geometric structures. The fourth type is manufacturing and assembly hard constraints, which can include process constraints such as the minimum safety margin for screw collision prevention, the minimum overhang of the resonant disk, and the minimum machining clearance, avoiding the generation of structures with assembly interference and unmachinable structures.
[0087] After this step is completed, a massive set of compliant resonant geometry candidates will be obtained, stored in four categories of operating conditions. All candidates satisfy all input inverse constraints, with no out-of-bounds errors, no assembly interference, and no illegal structures across operating conditions. These candidates are then fed into the frequency prediction model to complete rapid evaluation and scoring.
[0088] S4. Call the frequency prediction model to output the predicted frequency and model uncertainty of all candidate structures. Based on the prediction frequency error, model uncertainty and comprehensive risk value, construct a multi-penalty objective function, calculate the comprehensive penalty value of each candidate structure and output it in order of working conditions.
[0089] The predicted frequency error is the absolute difference between the input target frequency and the final predicted frequency of the frequency prediction model in logarithmic space. The comprehensive risk value is obtained by weighted fusion of one or more of the following: extrapolation risk, model consistency risk (consistency_gap), boundary geometry risk (risk_score), and manufacturing process risk (mfg_penalty).
[0090] Extrapolation risk is determined based on the distribution deviation score ood_score, which is calculated from the distribution distance between the current sample geometry and the training sample set. It measures the degree to which the geometric features deviate from the distribution of historical simulation samples. When a feature falls entirely within the dense region of the training samples, the distribution deviation score ood_score < 1; when a feature exceeds the boundary of the training sample set, the distribution deviation score ood_score > 1. That is, when the distribution deviation score ood_score < 1, the extrapolation risk is 0; when the distribution deviation score ood_score > 1, the extrapolation risk is [missing value]. .
[0091] The model consistency risk, or consistency_gap, is the absolute difference between the final predicted frequency of the frequency prediction model and the reference theoretical frequency in logarithmic space. If the value of consistency_gap is large, it indicates that the output deviation between the two physical models under the same structure is too large. In this case, the correction logic for this operating condition has poor self-consistency with the reference electromagnetic equivalent model, and there is a significant conflict in the physical modeling.
[0092] The boundary geometric risk score (risk_score) is obtained by summing the scores of the boundary geometric condition risk items. A base score is added when any of the preset boundary geometric condition risk items is met. For example, preset boundary geometric condition risk items might include: the resonant disk radius is less than the small disk threshold, the screw depth is within the critical range of deep and shallow working conditions, the top clearance or cavity radial margin is close to the design upper and lower limits, and the screw insertion depth is close to the structural collision threshold. For extreme structures, more base scores can be added; in the normal intermediate range, risk_score ≈ 0. The reason for setting the boundary geometric risk score (risk_score) is that small gaps, small disks, near-boundary insertion, and insufficient deep insertion margins increase the risk.
[0093] The manufacturing process risk (mfg_penalty) is obtained by accumulating the process risk items. The base score for any preset process risk item is added when it is met. For example, preset process risk items could be: insufficient top clearance, insufficient overhang of the resonant disk relative to the column, insufficient remaining safety collision margin after screw insertion, etc.; if the dimensional margin is sufficient, the score is 0. The reason for setting the manufacturing process risk (mfg_penalty) is that when the clearance is too small, the overhang is too small, or the collision margin is insufficient, there are engineering risks such as interference in structural processing and assembly, and difficulty in processing due to excessively small dimensions.
[0094] Therefore, a multi-penalty objective function can be constructed. as follows:
[0095] In the formula, In this embodiment, the weighting coefficients for the predicted frequency error are taken as follows: =1.0. As the weighting coefficient for model uncertainty, in this embodiment, we take... =0.15. As the weighting coefficient for extrapolation risk, in this embodiment, we take... =0.50. As the weighting coefficient for model consistency risk, in this embodiment, we take... =0.30. As the weighting coefficient for boundary geometric risk, in this embodiment, we take... =0.20. As the weighting coefficient for manufacturing process risk, in this embodiment, we take... =0.10. The sum of the last four terms in the formula is the weighted overall risk value.
[0096] S5. For each working condition, select multiple top-ranked candidate structures as high-quality candidate structures and output the geometric parameters of each high-quality candidate structure.
[0097] In this step, a predetermined number of candidates (e.g., 5 groups per case) are selected from the ranking list for each type of working condition as high-quality candidates for that condition. This method avoids optimization convergence being concentrated on a single working condition and ensures that there are alternative solutions for different tuning characteristic structures such as screwless, shallow insertion, and deep insertion. Afterward, the complete geometric parameters of all high-quality candidates are output in batches. Each set of parameters can be accompanied by relevant indicators, such as predicted resonant frequency, comprehensive penalty value, comprehensive risk value, model uncertainty, and the type of working condition, to provide complete data for subsequent simulation verification.
[0098] S6. After deduplicating the output high-quality candidate structures, perform CST electromagnetic simulation verification and select the candidate structure parameters that meet the requirements as the parameters of the single-cavity resonator structure. This step may include the following sub-steps: S610. Summarize all high-quality candidate structures and perform structure deduplication judgment: compare the geometric dimensions of each group. If the difference between the parameters of the two groups is within the preset small tolerance range, it is judged as an approximately repeated structure. Only the group with a smaller objective function and lower overall risk is retained, and redundant and repeated schemes are eliminated to reduce the amount of subsequent simulation calculations.
[0099] S620. Import all candidate geometric parameters after deduplication into CST electromagnetic simulation software in batches, establish the corresponding three-dimensional model of single-cavity resonator and complete the intrinsic simulation, and extract the actual simulated resonant frequency, miscellaneous mode interference, electric field distribution, screw tuning linear range and other measured electromagnetic performance data for each group of structures.
[0100] S630. The simulation results are evaluated in layers, and unqualified schemes are eliminated layer by layer. The optimal set of geometric parameters with the best overall performance is selected as the final design parameters for the single-cavity resonator structure based on the following four steps; the remaining qualified candidates are considered as backup schemes. Details are as follows: First, verify the error between the simulated resonant frequency and the target frequency, eliminating structures that exceed the engineering allowable error threshold. Second, review the simulation results, removing structures with electromagnetic defects such as miscellaneous modes, electric field distortion, and severe tuning nonlinearity. Third, verify the geometric machining and assembly performance, eliminating high-manufacturing-risk structures with excessively small clearances, insufficient screw collision margins, or difficulty in mass production. Fourth, based on the product's tuning requirements, match the operating conditions among the compliant solutions (select screwless structures for those requiring no tuning, and deep-insertion structures for those requiring a large tuning range).
[0101] S7. Backfill the simulation verification data into the training set of the frequency prediction model, and iteratively optimize the frequency prediction model. This step may include the following sub-steps: In steps S710 and S6, all candidate data from completed CST simulations are organized into standard training samples. Each sample includes: complete cavity geometric parameters, the actual resonant frequency obtained from the simulation, and the corresponding screw operating condition classification. Even structures with substandard simulation performance or large errors are included in the samples to fill data gaps at model boundaries and under extreme operating conditions.
[0102] S720: Add new simulation samples to the existing global simulation sample library, and store them in the corresponding working condition subsets according to the screw working conditions to expand the scale of the original training set of the model, focusing on making up for the previous data shortcomings in OOD distribution and boundary limit size.
[0103] The S730, based on the expanded new training set, is retrained according to the modeling process of the frequency prediction model. It can also expand the sample coverage, reduce the prediction error under extreme sizes and boundary conditions, reduce the risk of OOD domain extrapolation of new structures in subsequent reverse design, and improve the overall accuracy and generalization ability of the frequency prediction model in the next round of reverse search.
[0104] In this embodiment, a frequency prediction model based on a global physical benchmark and residual compensation under different operating conditions replaces the traditional full-process CST simulation iteration, which can significantly shorten the calculation time for parameter traversal and compress the R&D cycle. The frequency prediction model combines the classical electromagnetic equivalent model with residual machine learning algorithms. Through refined calculation of impedance and layered capacitance, and with a smooth fusion strategy, it can accurately restore the electromagnetic characteristics of the cavity under different operating conditions, effectively suppressing the frequency jump problem during operating condition switching. By using the residual model to compensate for the inherent error of the physical model, the frequency prediction accuracy can be greatly improved. Furthermore, by introducing a comprehensive risk value and model uncertainty to construct a multi-penalty objective function, it is possible to achieve hierarchical constraint optimization across the entire domain and select high-quality candidate structures according to different operating conditions. This avoids the shortcomings of pure black-box neural networks, such as lack of electromagnetic theory constraints, poor generalization ability, and a high proportion of high-risk output structures. The output scheme has both physical interpretability and manufacturing and assembly feasibility. At the same time, by backfilling the sample library with simulation data and iteratively updating the prediction model to form a closed-loop optimization, the coverage of training data is continuously expanded, and the model's global generalization and prediction accuracy are improved. This can simultaneously take into account computational efficiency, multi-condition prediction stability, electromagnetic performance accuracy, and engineering manufacturability, providing diverse and reliable design options for the rapid finalization of single-cavity resonators.
[0105] The above embodiments merely illustrate preferred implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention should be determined by the appended claims.
Claims
1. A method for designing a single-cavity resonator structure based on a target frequency, characterized in that, Includes the following steps: S1. Define the geometric parameters of the single-cavity resonator structure, standardize the geometric parameters, and divide multiple operating conditions according to the geometric parameters; S2. Construct a frequency prediction model based on geometric parameters to predict the frequency of a single-cavity resonator under different working conditions and output the model uncertainty. S3. Input the target frequency and the inverse constraints of each geometric parameter, and search for candidate resonant structures in the whole domain within the range defined by the inverse constraints. S4. Call the frequency prediction model to output the predicted frequency and model uncertainty of all candidate structures. Based on the prediction frequency error, model uncertainty and comprehensive risk value, construct a multi-penalty objective function, calculate the comprehensive penalty value of each candidate structure and output it in order of working conditions. S5. For each working condition, select multiple candidate structures that rank highly as high-quality candidate structures, and output the geometric parameters of each high-quality candidate structure. S6. Perform CST electromagnetic simulation to verify the high-quality candidate structures output, and select the candidate structure parameters that meet the requirements as the parameters of the single-cavity resonator structure.
2. The target frequency based single cavity resonator structure design method as claimed in claim 1, wherein, The geometric parameters include top gap (gap_top), resonant disk height (h_xzp1), resonant column height (h_xzz1), resonant disk radius (r_xzp1), resonant column radius (r_xzz1), tuning screw length (L_screw1), and cavity radial margin (dis); the constraints include upper and lower dimensional constraints, structural proportion constraints, and anti-collision constraints; the method for dividing multiple working conditions is as follows: based on whether there is a tuning screw and the effective insertion depth of the screw, the working conditions are divided into no-screw working condition, non-penetration working condition, shallow insertion working condition, or deep insertion working condition.
3. The target frequency based single cavity resonator structure design method as claimed in claim 2, wherein, The method for constructing a frequency prediction model includes the following sub-steps: S210. Standardize the geometric parameters of the single-cavity resonator structure, construct a global sample library, and divide it into four sub-libraries based on the operating conditions. S220. Construct a reference electromagnetic equivalent model and obtain the reference theoretical frequency by solving based on the geometric parameters of the cavity; S230. Construct a working condition adaptation correction model, and correct the reference theoretical frequency according to the working condition to obtain the corrected reference frequency. S240. Using the sample library and the benchmark theoretical frequency, corrected reference frequency and correction amount corresponding to each sample, the global residual model and the state residual model corresponding to each working condition are trained. S250. The reference theoretical frequency is predicted based on the geometric parameters of the single-cavity resonator structure under test, and the final predicted frequency is obtained after compensating the reference theoretical frequency with global residual and state residual.
4. The target frequency based single cavity resonator structure design method as claimed in claim 3, wherein, The predicted frequency error is the absolute difference between the input target frequency and the final predicted frequency of the frequency prediction model in logarithmic space; the global residual model also outputs the global residual uncertainty, and the state residual model also outputs the state residual uncertainty. The model uncertainty is calculated by superimposing the variances of the global residual uncertainty and the state residual uncertainty.
5. The target frequency based single cavity resonator structure design method as claimed in claim 1, wherein, The comprehensive risk value is obtained by weighted fusion of one or more of the following: extrapolation risk, model consistency risk, boundary geometry risk, and manufacturing process risk.
6. The target frequency based single cavity resonator structure design method as claimed in claim 2, wherein, Step S220 includes the following sub-steps: S221. The equivalent cavity radius is calculated based on the radius of the resonant disk and the radial margin of the cavity; the calculation formula is as follows: r_cav=r_xzp1+0.5dis Where r_cav represents the equivalent cavity radius; r_xzp1 represents the resonant disk radius; and dis represents the cavity radial margin. S222. Based on the coaxial transmission line impedance formula, calculate the equivalent characteristic impedance of the resonant pillar and the equivalent characteristic impedance of the resonant disk in the cavity; the calculation formula is as follows: Z1=60ln(r_cav / r_xzz1); Z2=60ln(r_cav / r_xzp1); Where Z1 represents the equivalent characteristic impedance of the resonant pillar, Z2 represents the equivalent characteristic impedance of the resonant disk; r_xzz1 represents the radius of the resonant pillar; and r_xzp1 represents the radius of the resonant disk. S223. Calculate the equivalent capacitance of the cavity in stages and obtain the total loaded capacitance by weighted fusion. S224. Select the resonance model based on the electrical length of the cavity, and calculate the original theoretical frequency based on the impedance of the resonant pillar, the impedance of the resonant disk, and the total loaded capacitance. S225. A linear correction is made to the original theoretical frequency using a fixed proportionality coefficient and an offset coefficient to obtain the reference theoretical frequency; the correction formula is as follows: f_base=k×f_raw+b In the formula, f_base represents the reference theoretical frequency; f_raw represents the original theoretical frequency; k represents the scaling factor; and b represents the bias factor.
7. The target frequency based single cavity resonator structure design method as claimed in claim 6, wherein: In step S230, the working condition is corrected by three correction branches: the normal branch, the deep insertion correction branch, and the small disk capacitor correction branch, based on the working condition label and the radius of the resonant disk as the judgment conditions. For the deep insertion working condition, the deep insertion correction branch is used for correction. For screwless operation where the resonant disk radius is smaller than the preset radius threshold, a small disk capacitor correction branch is used for correction; for screwless operation where there is no penetration, shallow insertion, or resonant disk radius is larger than the preset radius threshold, a conventional branch is used, and the reference frequency is directly used as the corrected reference frequency.
8. The target frequency based single cavity resonator structure design method as claimed in claim 6, wherein, The method of using the deep insertion correction branch is as follows: Based on the pre-trained and finalized ridge regression model and fixed coefficients, the multi-dimensional geometric features of the cavity, tuning screw and resonant disk under the deep insertion condition are first extracted to construct the feature vector, and the features are expanded by second-order polynomials, then standardized, and finally the ridge regression model is called to calculate, and the corrected reference frequency is obtained after logarithmic space transformation. The method of using the small disk capacitance correction branch for correction is as follows: define the edge field saturation correction coefficient, radial capacitance suppression coefficient and geometric dynamic scaling coefficient, and construct the calculation logic of the small disk equivalent total wall capacitance in this way; The equivalent total wall capacitance of the small disk is substituted for the disk wall capacitance in the reference electromagnetic equivalent model, and the output frequency of the reference electromagnetic equivalent model is used as the corrected reference frequency.
9. The target frequency based single cavity resonator structure design method as claimed in claim 6, wherein, Step S240 includes the following sub-steps: S241. Train labels uniformly in the natural logarithm space; S242. A global residual model is obtained by training the global sample library and the full-dimensional feature set corresponding to the sample. S243. Based on the trained global residual model, generate state residual-specific training labels in the natural logarithm space. S244. Based on the dedicated training labels for state residuals, four sets of state residual models are trained independently using four sub-libraries of operating conditions.
10. The design method of a target frequency based single cavity resonator structure according to any one of claims 1 to 9, wherein, Also perform the following steps: S7. Fill the simulation verification data back into the training set of the frequency prediction model and iteratively optimize the frequency prediction model.