A wideband electromagnetic simulation adaptive frequency sweeping method and system based on a hybrid interpolation model, an electronic device and a readable storage medium

Abstract

The application discloses a wideband electromagnetic simulation adaptive frequency sweeping method and system based on a hybrid interpolation model, electronic equipment and a readable storage medium. The method obtains initial frequency point S parameters of a target frequency band, maps physical frequency to a Chebyshev domain, adopts Chebyshev orthogonal bases combined with singular value decomposition to construct a global rational function model, simultaneously constructs a cubic spline local interpolation model, locates a frequency response sharp change area through a double model heterogeneous response deviation, adopts a minimum frequency interval constraint collision detection greedy sampling to supplement new sampling points, and reconstructs a full frequency band electromagnetic simulation result after iterative convergence. The application solves the problems of false convergence of a traditional adaptive frequency sweeping, numerical instability of high-order fitting, and sampling dead loop, greatly improves efficiency while ensuring simulation accuracy, and is suitable for wideband electromagnetic simulation of radio frequency microwave components, high-speed interconnection channels and multi-port networks.

Description

Technical Field

[0001] This invention belongs to the field of computational electromagnetics and numerical simulation analysis technology, specifically relating to an adaptive frequency sweep method and system for broadband electromagnetic simulation based on a hybrid interpolation model, and particularly to a fast reconstruction and modeling technique for frequency response based on a heterogeneous model verification of global rational functions and local spline interpolation. Background Technology

[0002] With the rapid evolution of 5G / 6G wireless communication and high-speed digital circuit technologies, the operating frequencies and bandwidths of RF microwave passive components, high-speed interconnect channels, and large-scale multi-port networks are continuously increasing. Broadband electromagnetic simulation has become a crucial part of modern electronic design and signal integrity analysis. Electromagnetic scattering parameters (S-parameters), as core indicators characterizing the frequency domain characteristics of high-frequency passive networks, have a significant impact on device design, system simulation, and performance verification due to the accuracy and efficiency of their broadband response acquisition.

[0003] Traditional discrete frequency sweeping methods require calling the full-wave electromagnetic field solver point by point, resulting in extremely high computational costs and time consumption when simulating thousands of frequency points. To improve efficiency, model-based adaptive frequency sweeping technology has become the mainstream solution in the industry, but existing technologies still face three major technical bottlenecks: 1. The problem of spurious convergence is prominent: Existing technologies mostly adopt isomorphic rational model self-verification or isomorphic geometric verification of pure spline interpolation. For example, Chinese invention patent with publication number CN115795765A discloses an adaptive sampling transmission scattering parameter interpolation frequency sweeping method, which determines the sampling point by calculating the difference between the integrals of two fitting functions within a sub-interval; Chinese invention patent with publication number CN112232002A discloses a method and system for determining the electromagnetic response of integrated circuits based on error estimation. The sparse sampling stage of this scheme is prone to non-physical oscillations, omission of high Q value resonance peaks, and inability to eliminate spurious poles and Runge phenomenon. 2. Poor numerical stability of high-order fitting: Broadband deep resonance scenarios require high-order fitting. Traditional monomial basis is prone to matrix ill-conditioning. In the prior art, such as the Chinese invention patent with patent publication number CN114139372A, a broadband electromagnetic simulation method using efficient adaptive frequency scanning is disclosed. It adopts a vector fitting method based on partial fractions, which depends on the selection of initial poles and is prone to divergence or getting trapped in local optima. The accuracy is difficult to guarantee in broadband multi-pole scenarios. 3. The sampling strategy has the risk of deadlock: The existing greedy sampling collision-free detection mechanism is prone to infinitely increasing sampling near the high Q value resonance point, which leads to iteration deadlock and simulation time increases instead of decreasing, seriously reducing the design efficiency of complex systems.

[0004] In summary, existing adaptive frequency sweeping techniques for broadband electromagnetic simulation cannot simultaneously achieve high precision, high stability, and high efficiency, making it difficult to meet the simulation requirements of ultra-wideband, deep resonant, and multi-port complex electromagnetic systems. Summary of the Invention

[0005] For modern complex electromagnetic systems such as RF front-ends, high-speed interconnects, and three-dimensional heterogeneous packaging, traditional discrete frequency sweeping is inefficient when extracting broadband S-parameters. Existing adaptive frequency sweeping algorithms are prone to problems such as false convergence, unstable high-order fitting values, and matrix singularities and deadlocks caused by repeated sampling. This invention provides a broadband electromagnetic simulation adaptive frequency sweeping method and system based on a hybrid interpolation model, which solves the problems of false convergence, unstable high-order fitting values, and sampling dead loops in traditional techniques, and achieves high-precision, high-stability, high-efficiency, and rapid reconstruction of broadband electromagnetic responses.

[0006] In a first aspect, this invention proposes an adaptive frequency sweeping method for broadband electromagnetic simulation based on a hybrid interpolation model, which includes the following steps: S1. Obtain the electromagnetic scattering S-parameters corresponding to the initial frequency point within the target frequency band; S2. Map the physical frequency domain to the Chebyshev computational domain, and construct a global rational function model using a Chebyshev orthogonal polynomial basis combined with singular value decomposition (SVD). S3. Construct a cubic spline local interpolation model based on the initial frequency point S-parameters, and locate the region of drastic frequency response change by the heterogeneous response deviation between the global rational function model and the cubic spline local interpolation model. S4. Greedy sampling with collision detection and minimum frequency interval constraint is adopted to determine new sampling points and update the dual model in the rapidly changing region; S5. After iterating until the model converges, reconstruct the model based on the global rational function model and output the full-band electromagnetic simulation results.

[0007] By constructing a core adaptive frequency sweeping process and using a collaborative design of "heterogeneous model + orthogonal basis + anti-collision sampling", the three major pain points of false convergence, numerical instability and sampling dead loop are solved simultaneously, thereby achieving a coordinated improvement in the accuracy, efficiency and stability of broadband electromagnetic simulation.

[0008] Preferably, in step S2, the mapping formula from the physical frequency to the Chebyshev computational domain is: ,in, Physical frequency, These are the upper and lower limits of the target frequency band. This represents the Chebyshev domain normalized frequency. By normalizing the physical frequencies to the Chebyshev standard interval, the condition number of the linear system matrix is ​​reduced, thus improving the numerical stability of higher-order fitting.

[0009] Preferably, in step S2, a high-density physical scan point set is generated across the entire frequency band. For any frequency point to be measured Normalization Its rational function response value is Then the global rational function model is expressed as: ,in, , For Chebyshev orthogonal polynomials, , These are the model coefficients. By employing Chebyshev orthogonal basis vectors to construct a global physical model, the wideband multi-pole frequency domain response of the electromagnetic system is accurately characterized.

[0010] Preferably, in step S3, the formula for the total heterogeneous error across all ports is: ,in, The response is a rational function model. The response of the cubic spline interpolation model, Modular operation for complex numbers.

[0011] Further optimization involves traversing the entire frequency band scan point set. Finding errors The highest frequency point is used as the new interpolation point. ,but By using full-port quantization of the dual-model response deviation, resonance characteristics are avoided from being missed during single-channel error verification, thus accurately locating regions of dramatic frequency response changes.

[0012] Preferably, in step S4, the formula for the relative L2 error of model iteration convergence for the entire frequency band and the entire port is: ,in, Indicates the first iteration This represents the updated rational function model response. This represents the model response of the previous iteration. This is a preset global tolerance. By accurately locating the frequency point with the maximum error and selectively supplementing sampling points, sampling efficiency and model convergence speed are significantly improved. Convergence is judged based on global relative error, ensuring the simulation accuracy of multi-port systems across the entire frequency band and avoiding misleading results from local convergence.

[0013] A further preferred approach employs a closed-loop iterative mechanism; if the calculated relative L2 error... Less than the preset global tolerance If the interpolation result converges, the iteration stops, and the final result is output. The parameter interpolation result is used; otherwise, the iteration continues until the error converges. This achieves automated closed-loop control of the iterative process, balancing simulation accuracy and computation time, and improving engineering practicality.

[0014] In a second aspect, embodiments of the present invention provide a broadband electromagnetic simulation adaptive frequency sweeping system based on a hybrid interpolation model, used to implement the broadband electromagnetic simulation adaptive frequency sweeping method as described in any of the implementations in the first aspect, including: The data acquisition module is used to acquire the electromagnetic scattering S-parameters corresponding to the initial frequency point within the target frequency band; The global model module is used for Chebyshev domain mapping, Chebyshev basis construction, and SVD solving to generate a global rational function model. The local model module is used to construct local interpolation models for cubic splines; The error verification module is used to calculate the heterogeneous response deviation of the two models and locate the region of dramatic change. The sampling iteration module is used to perform greedy sampling for collision detection and update the model; The convergence output module is used to output the full-band simulation results after iterative convergence.

[0015] The system integrates core algorithms in a modular fashion, can be directly embedded into electromagnetic simulation software, stably executes adaptive frequency sweeping, and has strong versatility.

[0016] Thirdly, embodiments of the present invention provide an electronic device, including: one or more processors; and a storage device for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the broadband electromagnetic simulation adaptive frequency sweep method as described in any implementation of the first aspect.

[0017] Fourthly, embodiments of the present invention provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the broadband electromagnetic simulation adaptive frequency sweep method as described in any of the implementations in the first aspect.

[0018] Fifthly, embodiments of this application provide a computer program product, wherein the computer program product includes a non-transitory computer-readable storage medium storing a computer program operable to cause a computer to perform some or all of the steps described in the first aspect of embodiments of this application. The computer program product may be a software installation package.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) By constructing a heterogeneous dual-model error criterion of "global rational function" and "local spline interpolation", spurious convergence in broadband frequency sweeping is effectively avoided. Unlike existing technologies that rely on recursive convergence of isomorphic models, this invention introduces local cubic spline interpolation as a reference benchmark. By utilizing the smoothing characteristics of spline functions on local data, the Runge phenomenon that may occur in undersampled regions by rational functions is forcibly verified and prevented. This mechanism is equivalent to introducing "third-party supervision", which solves the problem of spurious convergence caused by the failure of self-consistency verification of a single model while ensuring the high Q-value resonance capture accuracy.

[0020] (2) By applying Chebyshev orthogonal polynomial basis combined with singular value decomposition (SVD) to solve linear systems, the numerical stability bottleneck of high-order fitting is overcome. This differs from traditional methods that use monomial basis. Alternatively, relying on vector fitting based on initial pole selection, this invention maps the frequency domain response to the Chebyshev domain to construct the coefficient matrix and solves it using SVD decomposition. This method significantly reduces the condition number of the system matrix by utilizing the orthogonality of the basis functions, enabling the algorithm to maintain extremely high numerical robustness and computational accuracy when dealing with ultra-wideband and high-order complex systems covering DC to terahertz frequencies.

[0021] (3) A sampling strategy with a "collision detection" mechanism is adopted to eliminate redundant calculations and ensure numerical safety. Unlike the traditional sampling method that simply finds the maximum error, this invention introduces a minimum frequency interval constraint. Once the distance between a candidate point and a known point is less than a preset threshold (i.e., a "collision" occurs), the algorithm will determine that the point is an invalid redundant point and automatically backtrack to search for the second largest error point. This mechanism ensures that each newly added sampling point is valid and distinct, which not only fundamentally prevents the risk of system matrix singularity caused by repeated sampling, but also avoids invalid calls to the electromagnetic field solver, significantly improving the automated operation efficiency of the algorithm. Attached Figure Description

[0022] The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments and, together with the description, serve to explain the principles of the invention. Other embodiments and many anticipated advantages of the embodiments will be readily recognized as they become better understood through reference to the following detailed description. Elements in the drawings are not necessarily to scale. The same reference numerals refer to corresponding similar parts.

[0023] Figure 1 This is an exemplary system architecture diagram in which an embodiment of the present invention can be applied; Figure 2This is a flowchart illustrating the adaptive frequency sweeping method for broadband electromagnetic simulation based on a hybrid interpolation model, according to an embodiment of the present invention. Figure 3 This is a schematic diagram of the adaptive rational function interpolation frequency sweep process according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the geometric model of a dual-band filtered antenna array according to an embodiment of the present invention; Figure 5 This is a comparison chart of interpolation and discretization results from an embodiment of the present invention; Figure 6 This is a graph showing the relative error between interpolation and discrete frequency sweep S-parameters in an embodiment of the present invention. Figure 7 This is a schematic diagram of the architecture of a broadband electromagnetic simulation adaptive frequency sweeping system based on a hybrid interpolation model, according to an embodiment of the present invention. Figure 8 This is a schematic diagram of the structure of a computer device suitable for implementing electronic devices according to embodiments of the present invention. Detailed Implementation

[0024] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0025] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0026] Figure 1 An exemplary system architecture 100 is shown, which can be applied to the broadband electromagnetic simulation adaptive frequency sweep method based on the hybrid interpolation model or the broadband electromagnetic simulation adaptive frequency sweep system based on the hybrid interpolation model of the present invention.

[0027] like Figure 1 As shown, system architecture 100 may include terminal devices 101, 102, and 103, a network 104, and a server 105. Network 104 serves as the medium for providing communication links between terminal devices 101, 102, and 103 and server 105. Network 104 may include various connection types, such as wired or wireless communication links, or fiber optic cables, etc.

[0028] Users can use terminal devices 101, 102, and 103 to interact with server 105 via network 104 to receive or send messages, etc. Various communication client applications can be installed on terminal devices 101, 102, and 103, such as web browser applications, shopping applications, search applications, instant messaging tools, email clients, social media platform software, etc.

[0029] Terminal devices 101, 102, and 103 can be either hardware or software. When terminal devices 101, 102, and 103 are hardware, they can be various electronic devices, including but not limited to smartphones, tablets, laptops, and desktop computers. When terminal devices 101, 102, and 103 are software, they can be installed in the electronic devices listed above. They can be implemented as multiple software programs or software modules (e.g., software programs or software modules used to provide distributed services) or as a single software program or software module. No specific limitations are imposed here.

[0030] Server 105 can be a server that provides various services, such as a background information processing server that processes verification request information sent by terminal devices 101, 102, and 103. The background information processing server can analyze and process the received verification request information and obtain the processing results.

[0031] It should be noted that the broadband electromagnetic simulation adaptive frequency sweeping method based on a hybrid interpolation model provided in this embodiment of the invention is generally executed by server 105. Correspondingly, the broadband electromagnetic simulation adaptive frequency sweeping system based on a hybrid interpolation model is generally set in server 105. Furthermore, the broadband electromagnetic simulation adaptive frequency sweeping method based on a hybrid interpolation model provided in this embodiment of the invention is generally executed by terminal devices 101, 102, and 103. Correspondingly, the broadband electromagnetic simulation adaptive frequency sweeping system based on a hybrid interpolation model is generally set in terminal devices 101, 102, and 103.

[0032] It should be noted that a server can be either hardware or software. When the server is hardware, it can be implemented as a distributed server cluster consisting of multiple servers, or as a single server. When the server is software, it can be implemented as multiple software programs or software modules (for example, to provide distributed services), or as a single software program or multiple software modules; no specific limitations are made here.

[0033] It should be understood that Figure 1 The number of terminal devices, networks, and servers shown is merely illustrative. Depending on implementation needs, any number of terminal devices, networks, and servers can be included. If the data being processed does not need to be retrieved remotely, the above system architecture may exclude the network and only require servers or terminal devices.

[0034] In a first aspect, embodiments of the present invention disclose a broadband electromagnetic simulation adaptive frequency sweeping method based on a hybrid interpolation model, such as... Figure 2 As shown, this embodiment of the invention constructs a core adaptive frequency sweeping process, employing a collaborative design of "heterogeneous model + orthogonal basis + anti-collision sampling" to simultaneously address three major pain points: spurious convergence, numerical instability, and sampling dead loops, thereby achieving a synergistic improvement in the accuracy, efficiency, and stability of broadband electromagnetic simulation. The method includes the following steps: S1. Obtain the electromagnetic scattering S-parameters corresponding to the initial frequency point within the target frequency band.

[0035] S2. Map the physical frequency domain to the Chebyshev computational domain, and construct a global rational function model using a Chebyshev orthogonal polynomial basis combined with singular value decomposition (SVD).

[0036] Specifically, in this step: the mapping formula from physical frequency to Chebyshev computational domain is: ,in, Physical frequency, These are the upper and lower limits of the target frequency band. This represents the Chebyshev domain normalized frequency. By normalizing the physical frequencies to the Chebyshev standard interval, the condition number of the linear system matrix is ​​reduced, thus improving the numerical stability of higher-order fitting.

[0037] Generate a high-density physical scan point set across the entire frequency band. For any frequency point to be measured Normalization Its rational function response value is Then the global rational function model is expressed as: ,in, , For Chebyshev orthogonal polynomials, , These are the model coefficients. By employing Chebyshev orthogonal basis vectors to construct a global physical model, the wideband multi-pole frequency domain response of the electromagnetic system is accurately characterized.

[0038] S3. Construct a cubic spline local interpolation model based on the initial frequency point S-parameters, and locate the region of dramatic frequency response changes by the heterogeneous response deviation between the global rational function model and the cubic spline local interpolation model.

[0039] Specifically, in this step: the formula for the total port cumulative heterogeneous error is: ,in, The response is a rational function model. The response of the cubic spline interpolation model, Modular operation for complex numbers.

[0040] Traversing the full-band scan point set Finding errors The highest frequency point is used as the new interpolation point. ,but By using full-port quantization of the dual-model response deviation, resonance characteristics are avoided from being missed during single-channel error verification, thus accurately locating regions of dramatic frequency response changes.

[0041] S4. Greedy sampling with collision detection and minimum frequency interval constraint is adopted to determine new sampling points in the rapidly changing region and update the dual model.

[0042] Specifically, in this step: the formula for the relative L2 error of the model iteration convergence for the full-band, full-port model is: ,in, Indicates the first iteration This represents the updated rational function model response. This represents the model response of the previous iteration. This is the preset global tolerance.

[0043] By accurately locating the frequency point with the maximum error and selectively supplementing sampling points, sampling efficiency and model convergence speed are significantly improved. Convergence is judged based on global relative error, ensuring the simulation accuracy of multi-port systems across the entire frequency band and avoiding misleading results from local convergence.

[0044] S5. After iterating until the model converges, reconstruct the model based on the global rational function model and output the full-band electromagnetic simulation results.

[0045] By employing a closed-loop iterative mechanism, if the calculated relative L2 error... Less than the preset global tolerance If the interpolation result converges, the iteration stops, and the final result is output. The parameter interpolation result is used; otherwise, the iteration continues until the error converges. This achieves automated closed-loop control of the iterative process, balancing simulation accuracy and computation time, and improving engineering practicality.

[0046] This invention discloses a method that addresses the problems of spurious convergence, numerical instability in high-order fitting, and low sampling efficiency in broadband and deep resonance simulations caused by traditional interpolation frequency sweep algorithms. It achieves high-precision and rapid prediction of the original complex electromagnetic system across the entire frequency band by constructing a dual heterogeneous verification model of "global rational function - local spline interpolation". First, the method maps discrete S-parameter sampling points in the physical frequency domain to the Chebyshev computational domain. It then uses a Chebyshev orthogonal polynomial basis combined with singular value decomposition (SVD) to solve the linear system, constructing a highly robust global rational function model. Next, a cubic spline is introduced as a local reference benchmark, and the frequency response abrupt change region is located by calculating the response deviation between the global and local models. Finally, a greedy sampling strategy with minimum frequency interval constraints (collision detection) is used to complete the iterative calculation and reconstruction of the frequency domain response while ensuring that physical features are not lost.

[0047] This method can significantly reduce the number of electromagnetic solver calls and computation time while maintaining broadband simulation accuracy. It has good numerical stability and convergence reliability, and is suitable for signal integrity analysis of RF microwave passive components and high-speed interconnect channels, as well as broadband electromagnetic characteristic extraction and high-fidelity modeling of large-scale multi-port networks.

[0048] The method of this invention employs a basis construction method based on Chebyshev orthogonal polynomials, combined with singular value decomposition (SVD) to solve high-order linear systems, thus overcoming numerical ill-conditioning. Simultaneously, a heterogeneous dual-model error criterion of "global rational function - local spline interpolation" is constructed, utilizing the smoothing characteristics of the local model to verify the global model. Furthermore, a greedy sampling strategy with deadlock detection is introduced to optimize frequency distribution, achieving adaptive reconstruction of the full-band response. Broadband electromagnetic simulation based on this method not only effectively avoids the risks of spurious convergence and infinite loops, but also maintains extremely high numerical stability and significantly shortens simulation time when dealing with deep resonance and multi-port complex systems.

[0049] This invention addresses the challenges of traditional discrete frequency sweeping in extracting broadband S-parameters for modern complex electromagnetic systems such as RF front-ends, high-speed interconnects, and three-dimensional heterogeneous packaging. These challenges include low efficiency, susceptibility to false convergence, instability in higher-order fitting values, and matrix singularities and deadlocks caused by repeated sampling. The invention proposes a broadband electromagnetic simulation adaptive frequency sweeping method based on a hybrid interpolation model, applicable to S-parameter extraction for RF microwave devices, high-speed interconnect circuits, and antenna arrays.

[0050] The following is combined with Figure 3The flowchart illustrates the embodiments of the present invention in further detail. The implementation method includes the entire adaptive frequency sweep process: initial sampling frequency point selection → full-wave electromagnetic field solution → construction of heterogeneous prediction model (rational function interpolation model + cubic spline interpolation model) → full-band error scanning → anti-collision criterion → iterative convergence / new sampling.

[0051] The core steps of the adaptive interpolation frequency sweep proposed in this invention are threefold: First, constructing a broadband rational interpolation function model based on Chebyshev orthogonal basis and SVD regularization; second, heterogeneous dual-model error verification; and third, greedy sampling with anti-collision mechanism.

[0052] Core Step 1: Construct a broadband rational interpolation function model based on Chebyshev orthogonal basis and SVD regularization.

[0053] Based on microwave network theory, the frequency domain response of an electromagnetic system is essentially determined by the system's complex poles and residues. Therefore, broadband scattering parameters... It can be accurately characterized by a rational function model in the frequency domain: ; in: and These are the numerator and denominator polynomials, respectively. For frequency, To find the coefficients, and These are the orders of the numerator and denominator, respectively. Let be the selected basis functions. To solve the above nonlinear approximation problem, it needs to be transformed into a linearized equation: .

[0054] Traditional interpolation methods (such as the Cauchy method) typically select monomial bases. The choice of basis function can lead to matrix ill-conditioning and numerical stability issues in solving higher-order coefficients. To address this problem, this embodiment employs an orthogonal basis based on Chebyshev polynomials to construct the linear system and utilizes the right singular vectors of singular value decomposition (SVD) to solve for the coefficients. Since the orthogonality property of Chebyshev polynomials is defined in the standard interval... Above, while the actual physical frequency range of electromagnetic simulation is .

[0055] To ensure numerical stability, we first establish a value from the physical frequency. to normalized variables Linear mapping relationship: ; For discrete sampling point set The above formula maps them one by one to a normalized point set. .

[0056] In this embodiment, the basis function Replaced with Chebyshev polynomials Basis vectors are generated using the trinomial recurrence property of Chebyshev polynomials: .

[0057] Based on the above recursive relationship, for the normalized sampling point set Each sample point in (in ) and their corresponding S-parameters Substitute it into the linearized equation Expanding, we get: .

[0058] To solve for the unknown coefficients and All By simultaneously solving the constraint equations of the sampling points, a homogeneous linear system of equations is constructed. Among them, the coefficient vector to be determined Defined as: .

[0059] System Matrix Its block structure is shown below: ; Due to the number of sampling points The coefficients are usually much larger than the total number of coefficients, making the above system of equations overdetermined. To avoid zero solutions and find the optimal solution in the least squares sense, this embodiment does not perform matrix inversion; instead, it uses singular value decomposition (SVD) to decompose the matrix. Decompose: ; in, It is a left singular vector matrix. It is a diagonal singular value matrix. For the conjugate transpose of the right singular vector matrix, choose the matrix corresponding to... The right singular vector (i.e., matrix) with the minimum singular value The last column) is used as the optimal solution vector. Thus, the coefficients are determined. and This method utilizes the truncation property of SVD to effectively filter out high-frequency measurement noise and numerical calculation errors, thereby achieving regularized solution of coefficients.

[0060] Using the solved coefficients, a rational function model is reconstructed across the entire frequency band. A high-density set of physical scan points is then generated across the entire frequency band. For any frequency point to be measured Normalization Its rational function response value is: .

[0061] This process completes the mathematical reconstruction from sparse sampling points to a high-precision model in the high-frequency band.

[0062] This step constructs a broadband rational interpolation model based on Chebyshev orthogonal basis and SVD regularization. It solves the matrix ill-conditioning problem in broadband simulation by using frequency mapping and Chebyshev orthogonal basis, and uses SVD technology to filter out numerical noise, thereby improving the stability and robustness of the solution.

[0063] Core Step Two: Heterogeneous Dual-Model Error Verification.

[0064] The global rational function model is obtained through the first core step. Next, it is necessary to determine whether the current model accurately approximates the true physical response. Existing techniques typically employ a "homogeneous model comparison" strategy (e.g., comparing...). Rank and While the model is a rational function of order 1, in the initial stage when sampling points are sparse, the isomorphic model is prone to generating similar non-physical oscillations in the unsampled region, leading to spurious convergence. To address this issue, this embodiment introduces a local cubic spline interpolation model with completely different mathematical properties as a reference benchmark, constructing a heterogeneous verification mechanism between the "global physical model" and the "local geometric model".

[0065] For including The microwave network under test has 10 ports, for each specific response channel. (where port index) Based on the current set of discrete sampling points and their corresponding S-parameter response values Construct a cubic spline interpolation model Spline interpolation is defined in each adjacent physical frequency sub-interval. Above (of which) ). No. Piecewise function of subintervals Defined as about frequency cubic polynomial: ; In the formula, , , , For the first The coefficients of the undetermined set of intervals. To uniquely determine these coefficients, the spline interpolation model must simultaneously satisfy multiple mathematical constraints: ① Interpolation constraints: Ensure that the curve strictly passes through all known physical sampling points, i.e., satisfy... .

[0066] ② Smoothness constraint: at each internal node At a given point, the first and second derivatives of adjacent polynomials with respect to frequency must be continuous.

[0067] ③ Boundary constraints: at the beginning and end points of the frequency band ( and Use non-node (Not-a-Knot) or natural boundary conditions.

[0068] By solving the above system of linear equations, a geometric reference standard based on physical frequency is obtained across the entire frequency band. .

[0069] To comprehensively evaluate the convergence accuracy of the system and avoid the situation where a good fit in a single transmission channel masks the loss of resonance in the reflection channel, this embodiment defines a full-port cumulative error function. Generate a high-density physical scan point set across the entire frequency band. For any test frequency Calculate the rational function model response generated in core step one. Response of the spline interpolation model generated in this step The difference in the complex modulus between them.

[0070] Weighted summation of the squared errors of all port combinations: ; In the formula, Modular operations on complex numbers are represented. The aggregation method using the sum of squared errors significantly amplifies the weight of local maximum errors compared to simple linear summation, ensuring the system remains highly sensitive to minor oscillations or pole loss.

[0071] Traversing the full-band scan point set Finding errors The highest frequency point is used as the new interpolation point. : .

[0072] This step introduces a heterogeneous dual-model error verification mechanism that combines a "global theoretical model" and a "local geometric model". It uses cubic spline interpolation, which has a different mathematical nature, as a reference to effectively overcome the pseudo-convergence phenomenon in the sparse sampling stage and ensure accurate capture of subtle resonance peaks and lost poles.

[0073] Core Step 3: Greedy Sampling and Iterative Updates with Collision Avoidance Mechanism.

[0074] In the second core step, the candidate frequency point was located by maximizing the full-port cumulative error function. However, as it approaches high... When extreme points or numerical noise exist in the system, greedy algorithms tend to repeatedly select extreme points near already sampled points. If a new sampled point is too close to a known point in physical space, it not only fails to provide effective information increments but also causes linear dependence of row vectors in the Chebyshev system matrix in the core step one, leading to matrix singularities or even solution collapse. To address this, this embodiment designs a collision-avoiding iterative selection mechanism based on "residual suppression" to ensure the effectiveness of the physical distribution of newly added sampled points and the robustness of the algorithm.

[0075] Set minimum physical resolution interval threshold The global maximum error point output from core step two is set as the initial candidate point. And obtain the currently existing physical sample set. Enter the filtering loop and calculate the current candidate points. With sampling set The set of Euclidean distances to all points : ; Extract the minimum distance between candidate points and known samples. .

[0076] like Determine the current candidate point Meeting the physical resolution requirements, this constitutes an effective new sampling point. .like A "frequency collision" has occurred. This means that the current maximum error peak originates from local noise in the numerical calculation or invalid subdivisions near poles, rather than a lack of actual physical characteristics. To escape the deadlock, residual suppression is performed. The cumulative error function is applied across all ports. In the middle, the current collision point is forcibly changed. The error value at that point is set to zero, i.e. Subsequently, the second largest global error peak is searched again on the corrected error function surface and used as a new candidate point. : ; After updating the candidate points, return to the beginning of this step and repeat the distance calculation and collision detection until a valid point that meets the conditions is found or all error peaks are suppressed.

[0077] During the iterative selection process described above, if the global maximum value of the corrected error function approaches zero, meaning all potential error peaks have been detected as collision points and suppressed, then the current model is determined to have reached the limit of numerical accuracy. The adaptive sampling process is then forcibly terminated, and the current model is output as the final result. If valid sampling points are successfully selected... Call the full-wave electromagnetic field solver to calculate the frequency. The truth of the place Parameter response The new frequency points and responses will then be added to the dataset. .

[0078] Return to core step one, reconstruct a higher-order Chebyshev rational function model using the updated dataset, and repeat the subsequent steps until the global convergence condition is met.

[0079] The adaptive interpolation frequency sweep method described in this embodiment employs a closed-loop iterative mechanism. To ensure the numerical stability of the final output model and prevent premature termination, the algorithm introduces a global convergence criterion based on the relative L2 norm of model evolution. This criterion evaluates the convergence state of the system by quantifying the overall impact of adding new sampling points on the overall response vector of the full-band model.

[0080] In the After the next iteration, among For each of the current adaptive sampling rounds, obtain the updated rational function model response. Model response compared to the previous iteration Define the relative L2 error of the full-band, full-port model: ; If the calculated relative L2 error Less than the preset global tolerance If the interpolation result converges, the iteration stops, and the final result is output. The parameter interpolation result. Otherwise, continue iterating until the error converges.

[0081] This step employs an adaptive greedy sampling strategy with a "residual suppression" collision avoidance mechanism. It avoids matrix linearity caused by excessively dense sampling points by using a minimum physical resolution threshold, maximizing information increment while preventing numerical computational crashes and optimizing point distribution. This is achieved by establishing a model evolution-based relative... The full-band closed-loop convergence criterion of norm is used to evaluate the system convergence state by utilizing the response difference between adjacent iterations, and multi-port is achieved with a very small number of adaptive sampling points. High-fidelity parameter reconstruction significantly improves electromagnetic simulation efficiency.

[0082] To verify the effectiveness of the proposed method, this embodiment selects a complex dual-frequency filtered antenna array model for simulation verification, the specific structure of which is as follows: Figure 4 As shown. This model uses 2 The double-row symmetrical layout of 6, with a total of 12 radiating elements arranged on a dielectric substrate with sidewall reflectors, adopts lumped port excitation, has 12 lumped ports, and has 8,516,846 degrees of freedom.

[0083] In a preferred example, the initial number of frequency points is set to 5, with a global tolerance. Full-band scanning point set The quantity is 251, and the adaptive interpolation sweep frequency parameters are as follows: , 5 initial frequency points in They are equidistantly distributed within the range.

[0084] During the iteration process, the algorithm performs full-port cumulative error evaluation using a heterogeneous dual model (rational function model and cubic spline interpolation model), and adaptively calls the electromagnetic field full-wave solver to add samples at the frequency points with the largest errors, under the constraint of the anti-collision mechanism. As the adaptive iteration deepens, when the global relative L2 error of the interpolation model increases... Converge to preset global tolerance When the preset convergence criterion is met, the termination mechanism is automatically triggered, and a high-precision full-band S-parameter reconstruction response is output.

[0085] Figure 5 The model is shown in A comparison of the results of S-parameter interpolation frequency sweep and discrete frequency sweep within the frequency band. Considering the large number of model ports... Figure 5 Eight representative response curves are presented, including those from the reflection channel (e.g., , ), strongly coupled channels (such as , , ) and the far-end weakly coupled channel reflecting numerical stability (such as , , ).exist Figure 5 In each sub-figure, the blue solid dots are interpolation points, the black solid lines are discrete frequency sweep results, and the red dashed lines are interpolation results using the method of this invention.

[0086] Depend on Figure 5The comparative analysis shows that the algorithm of this invention accurately captures all the resonant details in the passband and the deep nulls in the stopband of the dual-frequency filtered antenna array using only 26 interpolation points. The interpolation sweep results and the discrete sweep results maintain a high degree of consistency across the entire frequency band. Thanks to the good orthogonality of the Chebyshev basis and the elimination of numerical noise by SVD, even at amplitudes lower than... In the weakly coupled channel, the interpolation curve remains smooth, without the Runge phenomenon or non-physical spikes commonly seen in traditional interpolation methods. Analysis of the data in Table 1 shows that, compared to the traditional discrete frequency sweep method (which requires calculating 251 frequency points), the interpolation method proposed in this invention significantly reduces computation time by 84.75% while maintaining the same accuracy, increasing computational efficiency to 6.56 times the original, and significantly reducing the simulation cost of complex multi-port electromagnetic models.

[0087] Table 1 Comparison of solution efficiency between the interpolation sweep frequency method and the discrete sweep frequency method proposed in this invention. ; This embodiment achieves the simulation accuracy of the traditional 251 uniform sampling points with only 26 sampling points, with a maximum relative error of ≤0.16% across the entire frequency band, a simulation time reduction of 84.75%, no false spikes in the weakly coupled channel, and accurate capture of all resonance characteristics, fully meeting the requirements of engineering applications.

[0088] Figure 6 The diagram shows the relative error curve between the reconstructed multi-port scattering parameter matrix using the adaptive interpolation algorithm proposed in this invention and the discrete frequency sweep result. This error is obtained by calculating the relative L2 difference between the interpolation model response and the actual physical response set across the entire frequency band. Figure 6 Data analysis shows that, Within the entire frequency band, the maximum relative error of the entire system's scattering parameter matrix is ​​strictly controlled within... Within this range, and in most of the non-resonant smooth intervals, the relative error remains within a certain range. The following are extremely low levels. It can be observed that, although the error curve is within the device's strong resonant frequency band (such as...), as well as The S-parameter amplitude and phase characteristics show a slight bulge and local peak in the vicinity (near the [specific range]), which is due to the extremely drastic changes in the S-parameter amplitude and phase characteristics within this range; however, the overall response remains highly smooth and continuous, and the peak error is far below what is permissible for engineering applications. Error threshold.

[0089] In summary, the adaptive frequency sweeping method for broadband electromagnetic simulation based on a hybrid interpolation model proposed in this invention significantly improves simulation efficiency and reconstruction accuracy for multi-port RF devices with complex multi-resonance characteristics. By constructing a rational function model based on Chebyshev orthogonal basis and singular value decomposition (SVD) regularization, and combining it with a heterogeneous dual-model error verification mechanism, high-fidelity mathematical reconstruction of high-dimensional scattering parameter matrices can be achieved with a small number of adaptive sampling points. This successfully solves the technical challenge of balancing accuracy, efficiency, and stability in broadband simulation of complex multi-port systems, and has extremely high engineering application and scientific research reference value.

[0090] Further reference Figure 7 As an implementation of the methods shown in the above figures, this application provides an embodiment of a broadband electromagnetic simulation adaptive frequency sweeping system based on a hybrid interpolation model. This system embodiment is similar to... Figure 2 and Figure 3 Corresponding to the method embodiments shown, the system can be specifically applied to various electronic devices.

[0091] Secondly, embodiments of the present invention also disclose a broadband electromagnetic simulation adaptive frequency sweeping system based on a hybrid interpolation model, used to implement the aforementioned broadband electromagnetic simulation adaptive frequency sweeping method, such as... Figure 7 As shown, it includes: a data acquisition module 71, a global model module 72, a local model module 73, an error verification module 74, a sampling iteration module 75, and a convergence output module 76.

[0092] In one specific embodiment, the data acquisition module 71 is used to acquire the electromagnetic scattering S-parameters corresponding to the initial frequency point within the target frequency band; the global model module 72 is used for Chebyshev domain mapping, Chebyshev basis construction and SVD solution to generate a global rational function model; and the local model module 73 is used to construct a cubic spline local interpolation model.

[0093] Error verification module 74 is used to calculate the heterogeneous response deviation of the two models and locate the region of dramatic change; sampling iteration module 75 is used to perform collision detection greedy sampling and update the model; convergence output module 76 is used to output the full-band simulation results after iterative convergence.

[0094] The system integrates core algorithms in a modular fashion, can be directly embedded into electromagnetic simulation software, stably executes adaptive frequency sweeping, and has strong versatility.

[0095] The functions and methods of the above modules correspond to each other, and will not be repeated here.

[0096] The following is for reference. Figure 8 It illustrates an electronic device suitable for implementing embodiments of the present invention (e.g., Figure 1The diagram shows the structure of a computer device 800 (a server or terminal device). Figure 8 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of the present invention.

[0097] like Figure 8 As shown, the computer device 800 includes a central processing unit (CPU) 801 and a graphics processing unit (GPU) 802, which can perform various appropriate actions and processes according to programs stored in read-only memory (ROM) 803 or programs loaded from storage section 809 into random access memory (RAM) 804. The RAM 804 also stores various programs and data required for the operation of the device 800. The CPU 801, GPU 802, ROM 803, and RAM 804 are interconnected via a bus 805. An input / output (I / O) interface 806 is also connected to the bus 805.

[0098] The following components are connected to I / O interface 806: an input section 807 including a keyboard, mouse, etc.; an output section 808 including a liquid crystal display (LCD) and speakers, etc.; a storage section 809 including a hard disk, etc.; and a communication section 810 including a network interface card such as a LAN card and a modem, etc. The communication section 810 performs communication processing via a network such as the Internet. A drive 811 may also be connected to I / O interface 806 as needed. A removable medium 812, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on drive 811 as needed so that computer programs read from it can be installed into storage section 809 as needed.

[0099] In particular, according to the embodiments disclosed in this invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments disclosed in this invention include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication section 810, and / or installed from removable medium 812. When the computer program is executed by central processing unit (CPU) 801 and graphics processing unit (GPU) 802, the functions defined in the methods of this invention are performed.

[0100] It should be noted that the computer-readable medium described in this invention can be a computer-readable signal medium, a computer-readable medium, or any combination thereof. A computer-readable medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this invention, a computer-readable medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In this invention, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media can also be any computer-readable medium other than a computer-readable medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0101] Computer program code for performing the operations of this invention can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as "C" or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0102] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of apparatus, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using dedicated hardware-based devices that perform the specified functions or operations, or using a combination of dedicated hardware and computer instructions.

[0103] The modules described in the embodiments of the present invention can be implemented in software or in hardware. The described modules can also be located in a processor.

[0104] In another aspect, the present invention also provides a computer-readable medium, which may be included in the electronic device described in the above embodiments; or it may exist independently and not assembled into the electronic device. The computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to: acquire the electromagnetic scattering S-parameters corresponding to the initial frequency point within the target frequency band; map the physical frequency domain to the Chebyshev computational domain, and construct a global rational function model using a Chebyshev orthogonal polynomial basis combined with singular value decomposition (SVD); construct a cubic spline local interpolation model based on the initial frequency point S-parameters, and locate the frequency response abrupt change region through the heterogeneous response deviation between the global rational function model and the cubic spline local interpolation model; employ collision detection greedy sampling with minimum frequency interval constraints to determine new sampling points in the abrupt change region and update the dual model; iterate until the model converges, and reconstruct and output the full-band electromagnetic simulation results based on the global rational function model.

[0105] The above description is merely a preferred embodiment of the present invention and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention is not limited to the specific combination of the above-described technical features, but also includes other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in this invention.

Claims

1. A broadband electromagnetic simulation adaptive frequency sweep method based on a hybrid interpolation model, characterized in that, The method includes the following steps: S1. Obtain the electromagnetic scattering S-parameters corresponding to the initial frequency point within the target frequency band; S2. Map the physical frequency domain to the Chebyshev computational domain, and construct a global rational function model using a Chebyshev orthogonal polynomial basis combined with singular value decomposition (SVD). S3. Construct a cubic spline local interpolation model based on the initial frequency point S-parameters, and locate the region of drastic frequency response change by the heterogeneous response deviation between the global rational function model and the cubic spline local interpolation model. S4. Greedy sampling with collision detection and minimum frequency interval constraint is adopted to determine new sampling points and update the dual model in the rapidly changing region; S5. After iterating until the model converges, reconstruct the model based on the global rational function model and output the full-band electromagnetic simulation results.

2. The broadband electromagnetic simulation adaptive frequency sweep method according to claim 1, characterized in that, In step S2, the mapping formula from the physical frequency to the Chebyshev computational domain is: ,in, Physical frequency, These are the upper and lower limits of the target frequency band. This is the Chebyshev domain normalized frequency.

3. The broadband electromagnetic simulation adaptive frequency sweep method according to claim 1, characterized in that, In step S2, a high-density physical scan point set is generated across the entire frequency band. For any frequency point to be measured Normalization Its rational function response value is Then the global rational function model is expressed as: ,in, , For Chebyshev orthogonal polynomials, , These are the model coefficients.

4. The broadband electromagnetic simulation adaptive frequency sweep method according to claim 1, characterized in that, In step S3, the formula for the total heterogeneous error across all ports is: ,in, The response is a rational function model. The response of the cubic spline interpolation model Modular operation for complex numbers.

5. The broadband electromagnetic simulation adaptive frequency sweep method according to claim 4, characterized in that, Traversing the full-band scan point set Finding errors The highest frequency point is used as the new interpolation point. ,but .

6. The broadband electromagnetic simulation adaptive frequency sweep method according to claim 1, characterized in that, In step S4, the formula for the relative L2 error of model iteration convergence for the full frequency band and full port is: ,in, Indicates the first iteration This represents the updated rational function model response. This represents the model response of the previous iteration. This is the preset global tolerance.

7. The broadband electromagnetic simulation adaptive frequency sweep method according to claim 6, characterized in that, Using a closed-loop iterative mechanism, if the calculated relative L2 error... Less than the preset global tolerance If the interpolation result converges, the iteration stops, and the final result is output. Check the parameter interpolation result; otherwise, continue iterating until the error converges.

8. A broadband electromagnetic simulation adaptive frequency sweeping system based on a hybrid interpolation model, characterized in that, The method for implementing the broadband electromagnetic simulation adaptive frequency sweep method as described in any one of claims 1-7 includes: The data acquisition module is used to acquire the electromagnetic scattering S-parameters corresponding to the initial frequency point within the target frequency band; The global model module is used for Chebyshev domain mapping, Chebyshev basis construction, and SVD solving to generate a global rational function model. The local model module is used to construct local interpolation models for cubic splines; The error verification module is used to calculate the heterogeneous response deviation of the two models and locate the region of dramatic change. The sampling iteration module is used to perform greedy sampling for collision detection and update the model; The convergence output module is used to output the full-band simulation results after iterative convergence.

9. An electronic device, characterized in that, include: One or more processors; Storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the broadband electromagnetic simulation adaptive frequency sweep method as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the broadband electromagnetic simulation adaptive frequency sweep method as described in any one of claims 1 to 7.

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