An ultra-electric large platform time domain electromagnetic environment and electromagnetic interference simulation and prediction method

Abstract

The application discloses a kind of super electrical big platform time domain electromagnetic environment and electromagnetic interference simulation prediction method, comprising the following steps: Fourier transform is carried out to time domain excitation signal, and the frequency spectrum curve corresponding to periodic time domain excitation signal is obtained;The obtained frequency spectrum curve is dispersed based on transmission path tracking, and the specific discrete frequency point to be calculated is obtained;Super electrical big platform is decomposed, and full-wave frequency domain electromagnetic environment and electromagnetic interference are solved in parallel;Frequency domain electromagnetic environment and electromagnetic interference are simulated, and simulation data are corrected, and the sampling frequency point electromagnetic environment and electromagnetic interference simulation data are obtained;The sampling frequency point electromagnetic environment and electromagnetic interference simulation data of the obtained super electrical big platform are multiplied with the corresponding frequency point of the frequency spectrum data of excitation source time domain signal, then inverse Fourier transform is carried out, and the super electrical big platform time domain electromagnetic environment and electromagnetic interference coupling signal are obtained.The method provided in the application solves the super electrical big platform time domain electromagnetic environment simulation prediction problem.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic compatibility and protection technology, and in particular relates to a simulation and prediction method for time-domain electromagnetic environment and electromagnetic interference of ultra-large electric platforms. Background Technology

[0002] With the increasing integration of electronic information systems, the electromagnetic environment faced by ultra-large electric platforms (ships, aircraft, vehicles, etc.) is becoming increasingly complex. On the one hand, the platform integrates multiple radio frequency systems such as communication, navigation, and radar. These systems form complex electromagnetic interference networks through antenna coupling, cable crosstalk, and other paths, and the electromagnetic environment in sensitive areas is too large, leading to prominent electromagnetic compatibility issues. On the other hand, pulse source signals have the characteristics of steep rise edges, extremely wide spectral coverage, and extremely high peak field strength, which may couple into the equipment through the "front door" (antenna) and "back door" (cables, gaps, etc.), causing instantaneous failure or permanent damage to electronic components. Therefore, in the design phase of ultra-large electric platforms, there is an urgent need for efficient simulation methods that can accurately calculate the transient electromagnetic environment distribution in sensitive areas of the platform and the current coupled at antenna ports within a wide frequency band.

[0003] Traditional time-domain numerical methods, such as the finite-difference time-domain (FDTD) and finite-element time-domain (FETD) methods, directly start from Maxwell's equations and perform time-stepping iterations. These methods have clear physical concepts and can obtain a wide-bandwidth response in one step, but they face severe challenges when applied to ultra-electric large platforms: First, to ensure numerical stability, the time step is limited by the minimum mesh size. For ultra-electric large platforms, the number of meshes is huge and detailed simulation of local structures is required, resulting in extremely small time steps and the number of iterations can reach hundreds of thousands or even millions, making the computation time unacceptable. Second, FDTD uses structured meshes, which produce stepped approximation errors when fitting complex surfaces, while FETD, although it can use unstructured meshes, further increases the computational overhead per step by solving its mass matrix.

[0004] In contrast, frequency domain methods transform Maxwell's equations into frequency domain integral equations, with unknowns distributed only on the platform surface. Combined with multi-level fast multipole acceleration, the computational complexity can be reduced to O(NlogN), demonstrating a significant advantage in ultra-large electrical problems. However, conventional frequency domain methods only obtain the steady-state response at a single frequency in a single solution. If broadband characteristics are obtained by scanning frequency-by-frequency point, the efficiency problem of too many full-wave calculations arises. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a simulation and prediction method for the time-domain electromagnetic environment and electromagnetic interference of ultra-electric large platforms, solving the problem of simulation and prediction of the time-domain electromagnetic environment of ultra-electric large platforms and providing efficient and reliable data support for electromagnetic compatibility and protection simulation of ultra-electric large platforms.

[0006] The objective of this invention is achieved through the following technical solution: a method for simulating and predicting the time-domain electromagnetic environment and electromagnetic interference of an ultra-large electric platform, comprising the following steps: Step 1: Perform a Fourier transform on the time-domain excitation signal to obtain the spectrum curve corresponding to the periodic time-domain excitation signal; Step 2: Discretize the spectrum curve obtained in Step 1 based on transmission path tracing to obtain the specific discrete frequency points to be calculated; In step 2, the spectral discrete interval is obtained based on the shortest sampling time length of the time-domain electromagnetic environment. Based on this spectral discrete interval, the specific discrete frequency points to be calculated are obtained. The shortest sampling time length is calculated using the following formula: =

[0007] In the formula, Let be the shortest time sampling length of the electromagnetic environment in the time domain to be determined. L The longest transmission path length between the excitation signal source and the observation point of the simulation object. τ The pulse width of the excitation source signal. c The speed of light; In step 2, a ray tracing algorithm is used to obtain the longest transmission path length from the excitation signal source to the observation point of the simulated object. Ray tracing is used to obtain the direct, reflected, and diffracted transmission paths from the excitation signal to each observation point of the simulated object. The longest path length is then selected from all paths as the longest path length. L The possible values ​​of ; Step 3: Decompose the super-electric large platform into regions and solve the full-wave frequency domain electromagnetic environment and electromagnetic interference in parallel. The solution frequency points are the discrete frequency points obtained in Step 2. Step 4: Simulate the frequency domain electromagnetic environment and electromagnetic interference, and correct the simulation data to obtain the electromagnetic environment and electromagnetic interference simulation data of the sampling frequency of the super-electric platform. Step 5: Align and multiply the electromagnetic environment and electromagnetic interference simulation data of the sampling frequency point of the ultra-electric large platform obtained in Step 4 with the corresponding frequency points of the spectrum data of the excitation source time-domain signal obtained in Step 2, and then perform inverse Fourier transform to obtain the time-domain electromagnetic environment and electromagnetic interference coupling signal of the ultra-electric large platform.

[0008] Preferably, in step 1, the time-domain signal radiated by the antenna from the excitation source in an open area is used as the time-domain excitation signal.

[0009] Preferably, in step 3, electromagnetic environment or electromagnetic interference data is obtained using a parallel full-wave frequency domain electromagnetic environment and electromagnetic interference solution method based on domain decomposition. The domain decomposition includes at least the antenna region and the platform region, and the full-wave frequency domain electromagnetic environment and electromagnetic interference solution process includes at least the following steps: Step 3.1: Solve for the differential of the antenna region; Step 3.2: Solve for the platform region by integration; Step 3.3: Establish a data exchange mechanism at the interface between the antenna region and the platform region, and use a coupling strategy based on the Huygens equivalence principle to tightly couple the antenna region and the platform region.

[0010] Preferably, in step 3, the electromagnetic environment and electromagnetic interference are solved by frequency sweeping based on the interpolation algorithm. Specifically, a frequency sweeping strategy based on the interpolation algorithm is used to perform full-wave numerical solutions on some "sample frequency points" to obtain the electromagnetic environment or electromagnetic interference data of the corresponding frequency points, and the data of the remaining frequency points are reconstructed by cubic spline interpolation algorithm.

[0011] Preferably, in step 3.1, a finite element-based differential algorithm is used to solve the differential problem of the antenna region, and in step 3.2, a multi-layer fast multipole-based integral algorithm is used to solve the integral problem of the platform region.

[0012] Preferably, in step 3.3, at the boundary of the domain decomposition, the antenna region is equivalent to a current source and a magnetic current source, radiating towards the platform region; conversely, the scattered field of the platform region at the interface is used as an external excitation and applied to the antenna region; the solution result of the finite element subdomain is transformed into the incident field of the multilayer fast multipole subdomain by establishing the boundary integral equation; let the interface be... Then the field radiated from the antenna region to the platform region can be expressed as:

[0013] in, This refers to the electric field radiated from the antenna region to the platform region through the interface. This is the common interface between the antenna and the platform. As an equivalent current source, As an equivalent magnetic current source, The curl of the Green's function is given; the coupling relationship between the antenna region and the platform region forms a differential-integral hybrid method, which naturally extends to multi-region parallelism under the domain decomposition framework: each region independently solves its own matrix equation, and the coupling between regions is updated iteratively through boundary conditions until convergence.

[0014] Preferably, the steps for solving the electromagnetic environment and electromagnetic interference frequency sweep based on the interpolation algorithm include: S1. Frequency sampling: Within the frequency sweep range, samples are taken at equal intervals. The frequency sweep range is evenly divided into multiple sub-intervals, and the endpoints or midpoints of each sub-interval are selected as sample frequency points. S2. At the selected sample frequency points, the electromagnetic environment or electromagnetic interference data is obtained by using the parallel full-wave frequency domain electromagnetic environment and electromagnetic interference solution method of region decomposition. S3. For other sampling frequency points within the sweep frequency range, the cubic spline interpolation method is used to solve the problem.

[0015] Preferably, in S3, an error evaluation mechanism is embedded in the cubic spline interpolation process. During the adaptive sampling process, some initial sample points outside the frequency range are used as a validation set. The full-wave solution is calculated and compared with the interpolation result. When the error between the interpolation result of the validation set and the full-wave solution is within a preset range, the requirement is met. If not, new sample points are inserted for the sub-intervals that do not meet the accuracy requirements, and the full-wave calculation and cubic spline interpolation are performed again until the full frequency band meets the requirements.

[0016] Preferably, step 4 includes at least the following steps: Step 4.1: Select a portion of the sampling frequencies and conduct simulation tests to obtain electromagnetic environment and electromagnetic interference data; Step 4.2: Calculate the electromagnetic environment or electromagnetic interference value for simulation correction, and calculate the simulation correction value for the frequency point. Correct the simulation data in step 4.1 based on the simulation correction value.

[0017] Preferably, in step 5, the spectrum data within the sampling frequency is completed, and then the completed spectrum data is subjected to discrete inverse Fourier transform to obtain the time-domain electromagnetic environment and electromagnetic interference coupling signal of the UPC platform.

[0018] The beneficial effects of this invention are as follows: As can be seen from the above scheme, the present invention provides a simulation and prediction method for the time-domain electromagnetic environment and electromagnetic interference of an ultra-electric large platform. It breaks through the grid and step limitations of the time-domain method, transforms the transient problem of the ultra-electric large platform into frequency domain sampling and inverse transformation reconstruction, avoids the extremely small time step and huge grid volume caused by the stability conditions of the time-domain method, significantly reduces memory requirements and computation time, and makes time-domain simulation of ultra-electric large platforms possible.

[0019] This invention balances broadband accuracy with computational efficiency. It leverages the near-linear complexity advantage of frequency domain full-wave algorithms in ultra-large electrical problems and combines interpolation techniques to reduce the number of frequency points to be solved in the full-wave solution. While ensuring broadband response accuracy, it shortens the total computation time by 1-2 orders of magnitude, providing efficient and reliable data support for electromagnetic compatibility and protection simulations.

[0020] After obtaining a small amount of full-wave frequency domain response data, this invention uses an interpolation algorithm to obtain frequency domain response data that meets the required sampling frequency points. Then, it uses experimental data to correct the accuracy of the simulated frequency domain response data. Finally, it combines inverse Fourier transform to obtain the time-domain electromagnetic environment and electromagnetic interference coupling current of the ultra-electric large platform, providing a new technical method for electromagnetic compatibility and protection simulation of the ultra-electric large platform. Attached Figure Description

[0021] Figure 1This is a flowchart of a time-domain electromagnetic environment and electromagnetic interference simulation and prediction method for an ultra-large electric platform according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the time-domain waveform of the test excitation signal in an embodiment of the present invention; Figure 3 This is a schematic diagram of the spectrum curve corresponding to the test excitation signal in an embodiment of the present invention; Figure 4 This is a schematic diagram of the ray tracing process in an embodiment of the present invention; Figure 5 This is a schematic diagram of the longest transmission path considering multipath effects in an embodiment of the present invention; Figure 6 This is a schematic diagram comparing electromagnetic environment data after test data correction in an embodiment of the present invention; Figure 7 This is a schematic diagram comparing electromagnetic interference data after test data correction in an embodiment of the present invention; Figure 8 This is a schematic diagram of the discrete Fourier transform of an aperiodic discrete signal in an embodiment of the present invention; Figure 9 This is a schematic diagram of the data completion method within the sampling frequency range in an embodiment of the present invention; Figure 10 This is a schematic diagram of the time-domain electromagnetic environment distribution at time 41ns in an embodiment of the present invention; Figure 11 This is a schematic diagram of the time-domain electromagnetic environment distribution at 83ns in an embodiment of the present invention; Figure 12 This is a schematic diagram of the time-domain current curve of the receiving antenna port coupling in an embodiment of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in this embodiment will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0023] like Figure 1 As shown, the technical solution of the present invention provides a method for simulating and predicting the time-domain electromagnetic environment and electromagnetic interference of an ultra-large electric platform, comprising the following steps: Step 1: Perform a Fourier transform on the time-domain excitation signal to obtain the spectrum curve corresponding to the periodic time-domain excitation signal; Step 2: Discretize the spectrum curve obtained in Step 1 based on transmission path tracing to obtain the specific discrete frequency points to be calculated; Step 3: Decompose the super-electric large platform into regions and solve the full-wave frequency domain electromagnetic environment and electromagnetic interference in parallel. The solution frequency points are the discrete frequency points obtained in Step 2. Step 4: Simulate the frequency domain electromagnetic environment and electromagnetic interference, and correct the simulation data to obtain the electromagnetic environment and electromagnetic interference simulation data of the sampling frequency of the super-electric platform. Step 5: Align and multiply the electromagnetic environment and electromagnetic interference simulation data of the sampling frequency point of the ultra-electric large platform obtained in Step 4 with the corresponding frequency points of the spectrum data of the excitation source time-domain signal obtained in Step 2, and then perform inverse Fourier transform to obtain the time-domain electromagnetic environment and electromagnetic interference coupling signal of the ultra-electric large platform.

[0024] In one embodiment of the present invention, in step 1, a fast simulation method for the time-domain electromagnetic environment of an ultra-large electric platform based on frequency domain + Fourier transform is adopted. This method requires performing Fourier transform on the time-domain signal of the excitation source to obtain the spectrum curve corresponding to the time-domain excitation signal, which lays the foundation for subsequently determining the discrete frequency point set for calculating the frequency domain field.

[0025] The spectral curve of the time-domain excitation signal is calculated using the Fourier transform correlation formula. Formula (1) gives the periodic time-domain excitation signal. ( t The Fourier series expansion expression of the periodic time-domain excitation signal can be derived from this expression. ( t Discrete spectrum The expression is given. The spectral curve corresponding to the periodic time-domain excitation signal is obtained using formula (2).

[0026]

[0027] In the formula, ( t () is a periodic time-domain excitation signal. For the nth discrete spectral component, A periodic function ( t An expression for a period of time. Angular frequency, T The period of the time-domain excitation signal, For a periodic time-domain excitation signal, i For complex units, n Indicates the first n One. Considering that the signal waveform of the excitation source will change after being theoretically designed and then amplified by the excitation source module, this embodiment collects the time-domain signal of the excitation source radiated by the antenna in an open area, thereby obtaining the time-domain excitation signal characteristics of the excitation source with high precision. For example... Figure 2As shown, this is the time-domain signal curve measured after the broadband excitation source is radiated by the antenna; Figure 3 The figure shows the spectrum curve of the time-domain signal tested.

[0028] In one embodiment of the present invention, in step 2, spectrum discretization is performed based on transmission path tracing to obtain the specific discrete frequency points to be calculated. Specifically, the spectrum discretization interval is reasonably set according to the relative relationship between the excitation signal source and the simulation object. The spectrum discretization interval is related to the time sampling length of the electromagnetic environment in the time domain to be determined. Closely related, the time sampling length must be sufficient to reflect the entire signal; for transient signals, it should include the entire transient process. The sampling length needs to be long enough to allow sufficient attenuation of the current and radiation field contained in the excitation pulse. However, to reduce computational load, the sampling length should not be too long. Assume the longest transmission path length between the excitation signal source and the observation point of the simulated object is... L The pulse width of the excitation source signal is Then, the shortest time sampling length of the electromagnetic environment in the time domain to be determined is... It should be: = (4) In the formula, Let be the shortest time sampling length of the electromagnetic environment in the time domain to be determined. L The longest transmission path length between the excitation signal source and the observation point of the simulation object. τ The pulse width of the excitation source signal. c It is the speed of light.

[0029] For ultra-electric large-size targets, typically L / c Much larger Therefore, the shortest time sampling length of the electromagnetic environment in the time domain needs to be determined. It should be: ≈ (5) Based on the shortest time sampling length of the time-domain electromagnetic environment The discrete interval of the spectrum can be obtained as follows: (6) As can be seen from the formula above, L Determine the discrete interval of the spectrum Size, L An excessively long timeframe would result in too many discrete frequency points, leading to excessively long calculation times for the electromagnetic environment at each frequency point. L If the signal is too short, the excitation signal transmission field will not decay sufficiently at the observation point, resulting in a large error in the calculation of the electromagnetic environment in the time domain.

[0030] In one embodiment of the present invention, in step 2, in order to accurately obtain the longest transmission path length between the excitation signal source and the observation point of the simulation object, L A ray tracing algorithm is employed to obtain the transmission paths (direct, reflected, diffracted, etc.) from the excitation signal to the observation points of each simulated object. The longest path length is then selected from all paths. L The value of is determined by the following. The basic process of the ray tracing algorithm is as follows: First, based on the object of calculation, determine the size of the virtual aperture surface of the excitation signal source. Then, divide the virtual aperture surface into a two-dimensional matrix composed of ray tubes. To ensure calculation accuracy, the ray density must be guaranteed. Taking a cavity structure as an example, such as... Figure 4 As shown, a virtual aperture surface is constructed at a certain distance from the cavity structure, and a matrix of ray tubes is created. Ray tubes start from the virtual aperture surface, enter the cavity structure, and are tracked. Each ray tube is traversed, visiting all surfaces in the scene to determine the intersection points between the ray tubes and objects, and the intersection information and paths are saved. New reflecting and refracting ray tubes are then generated, and they are tracked again. If they intersect with an object, the intersection is calculated again; otherwise, the ray tube is discarded. This process is recursively repeated until all ray tubes leave the scene, their energy decays to a certain threshold, or the maximum number of bounces is reached (this is the most common choice), thus completing the tracking of all ray tubes. To describe this process, a binary tree-like data structure called a RayTree can be constructed. The RayTree is used to store the paths and intersection information of all ray tubes.

[0031] When a light ray intersects the surface of an object, both the reflected and refracted rays obey Snell's Law. Therefore, the direction of reflection can be determined using the following formula. r and p Direction of refraction:

[0032] (7) In the formula, The direction of the incident ray. The unit normal vector of the object's surface at the reflection point. and These are the refractive indices of the upper and lower media, respectively.

[0033] when When the denominator is an imaginary number, it is total internal reflection. The path of the ray is determined by the equation of the ray: (8) In the formula, s is the position vector of the ray. It is the starting point of the light. It is the direction of wave propagation. For example... Figure 5As shown, given the transmission path between the radiation source and the observation point, the longest transmission path between the radiation source and the observation point is selected as... L The value of is used to calculate the discrete interval of the spectrum. .

[0034] In one embodiment of the present invention, step 3 involves the parallel full-wave frequency domain electromagnetic environment and electromagnetic interference solution based on region decomposition: Based on the frequency domain curve obtained from the Fourier transform of the excitation source signal, the low-frequency and high-frequency points in the frequency domain are determined according to the spectral amplitude threshold (generally 0.1). Then, based on the previously mentioned spectral discrete interval, the set of frequency points for simulation calculation using electromagnetic numerical methods can be obtained. Addressing the challenge of mixed calculations involving multi-material antennas and ultra-electric large metal platform structures in the frequency domain electromagnetic environment and electromagnetic interference solution of ultra-electric large platforms, a parallel full-wave frequency domain electromagnetic environment and electromagnetic interference solution method based on region decomposition is proposed. This method divides the overall solution region into antenna and platform regions based on differences in physical structure and electromagnetic characteristics, employs appropriate numerical algorithms for each, and achieves efficient coupling through region decomposition. Finally, it accelerates the full-wave solution by leveraging the parallel computing base. Specifically, the method includes the following steps: Step 3.1: Solve for the differential of the antenna region; Antenna regions typically contain intricate structures such as dielectric substrates, metal patches, and hybrid dielectric-metal feed sections, exhibiting complex geometry and varying materials. This region is well-suited for finite element-based differential algorithms. Finite element methods, based on variational principles, are naturally adaptable to complex geometries and diverse materials, enabling accurate simulation of electromagnetic coupling, surface wave propagation, and radiation characteristics in the near-field of antennas. Its frequency-domain Maxwell equations can be reduced to vector wave equations concerning the electric field: (9) In the formula, E is the electric field strength. Relative permeability For free space wavenumber, The relative permittivity, Angular frequency, The permeability of free space, For the applied excitation current density, This represents the Del operator.

[0035] The equivalent variational form is obtained through the Galerkin weighted residual method, and then discretized into a sparse linear system of equations. To further adapt to the problem of solving large array antennas, domain decomposition is applied again within the antenna region, dividing the array antenna into multiple subdomains. Each subdomain is independently discretized using finite element methods, and information is exchanged through Robin transmission conditions at the subdomain interfaces, thereby reducing the matrix size of a single solution.

[0036] Step 3.2: Solve for the platform region by integration; Platforms (such as ships, aircraft, and vehicles) are typically made of pure metal and have extremely large electrical dimensions, but their geometric complexity is much lower than that of the antenna region. This region is suitable for integration algorithms based on multilayer fast multipoles. Integration algorithms solve the electric field integral equation (EFIE) or mixed field integral equation (CFIE) for metallic surfaces, where the unknowns are distributed only on the surface, and the dimensionality is much lower than that of volume discretization. Taking EFIE as an example, on the surface S of an ideal conductor, the following holds: (10) in m The surface unit outward normal vector, The incident electric field strength is... The induced current density on the conductor surface, For free space Green's function, coordinates of the origin gradient operator, Let be the vacuum permittivity, and j be the complex unit; S represents the ideal conductor surface, and S' represents a local part of the ideal conductor surface. For ultra-large electric platforms, multilayer fast multipole can reduce the computational complexity to... The memory requirements are greatly reduced, and it can efficiently calculate the induced current and far-field radiation field on the platform surface.

[0037] Step 3.3: To achieve tight coupling between the antenna region and the platform region, a data exchange mechanism needs to be established at their interface. A coupling strategy based on the Huygens equivalence principle is adopted. At the boundary of the domain decomposition, the antenna region is equivalent to a current source and a magnetic current source, radiating towards the platform region; conversely, the scattered field of the platform region at the interface is applied to the antenna region as an external excitation. Mathematically, the solution results of the finite element subdomain are transformed into the incident field of a multilayer fast multipole subdomain by establishing boundary integral equations. Let the interface be... Then the field radiated from the antenna region to the platform region can be expressed as:

[0038] in, This refers to the electric field radiated from the antenna region to the platform region through the interface. This is the common interface between the antenna and the platform. As an equivalent current source, As an equivalent magnetic current source, Let be the curl of the Green's function. This coupling relationship forms a hybrid differential-integral method, which naturally extends to multi-region parallelism within the domain decomposition framework: each region independently solves its own matrix equations, and the coupling between regions is updated iteratively through boundary conditions until convergence. In this embodiment, an efficient parallel acceleration method is adopted, and the full-wave frequency domain solution ultimately reduces to solving a large-scale linear algebra system. To improve efficiency, algorithm-level parallelism and load balancing and acceleration techniques are employed. Regarding algorithm-level parallelism, regions are naturally decoupled, and the matrix equations of each region can be assigned to different process groups for independent solution. The iterative process of region coupling uses asynchronous communication to reduce waiting time. Regarding load balancing and acceleration techniques, the antenna region has fewer unknowns but complex matrix filling, while the platform region has more unknowns but mature acceleration algorithms. Through a dynamic load balancing strategy, CPU resources are rationally allocated to improve parallel computing efficiency.

[0039] In one embodiment of the present invention, in step 3, a fast frequency sweep solution for electromagnetic environment and electromagnetic interference based on interpolation algorithms is proposed. For the need for rapid assessment of the electromagnetic environment or electromagnetic interference of broadband excitation source signals, traditional methods require full-wave numerical solutions for each frequency point after frequency discretization, resulting in huge computational overhead. Therefore, a fast frequency sweep strategy based on interpolation algorithms is proposed, which performs full-wave numerical solutions only on a small number of "sample frequency points" to obtain the electromagnetic environment or electromagnetic interference data for the corresponding frequency points. Then, the data for the remaining frequency points is reconstructed using a cubic spline interpolation algorithm, thereby significantly reducing the total solution time. This method includes a frequency sampling strategy, full-wave numerical solution, cubic spline interpolation solution, error assessment, and adaptive refinement. In this embodiment, the steps for the frequency sweep solution for electromagnetic environment and electromagnetic interference based on interpolation algorithms include: S1, Frequency sampling, frequency sweep range Within this context, the electromagnetic environment or electromagnetic interference effect function obtained through full-wave analysis is typically a smoothed function of frequency (except at resonant points). Therefore, the strategy employed must balance accuracy and efficiency. This embodiment selects equally spaced sampling, uniformly dividing the frequency sweep range into... Each sub-interval has an endpoint or midpoint as a sample frequency point.

[0040] S2, at the selected sample frequency points The electromagnetic environment or electromagnetic interference data is obtained by using the parallel full-wave frequency domain electromagnetic environment and electromagnetic interference solution method of the above-mentioned region decomposition.

[0041] S3. For other sampling frequency points within the sweep frequency range, the cubic spline interpolation method is used to solve the problem, as follows: Frequency sweep range For other sampling frequency points, cubic spline interpolation is used to solve the problem. This method ensures the continuity of the first and second derivatives of the interpolation curve, which physically conforms to the smooth variation of electromagnetic response with frequency. Let the sample frequency point be... , , ..., The corresponding electromagnetic environment and electromagnetic interference response value is , , ..., (Can be complex or amplitude / phase). In each subinterval [ Construct a cubic polynomial above: (12) Where f is the frequency variable. For the i-th sample frequency point, ( f In subinterval The cubic spline interpolation function is used to approximate the real electromagnetic environment and electromagnetic interference response R(f). , , and The coefficients are undetermined and are uniquely determined by the interpolation and continuity conditions. For the complex response to electromagnetic environment and electromagnetic interference, cubic spline interpolation is performed on the real and imaginary parts respectively to synthesize the complex number.

[0042] In the above embodiments, error assessment and adaptive refinement need to be considered. To ensure the reliability of cubic spline interpolation, an error assessment mechanism must be embedded. During the adaptive sampling process, some initial sample points outside the frequency range are used as a validation set (not participating in interpolation construction). The full-wave solution is calculated and compared with the interpolation result. The requirement is met when the error between the interpolation result of the validation set and the full-wave solution is within a certain range; if not, new sample points are inserted for the sub-intervals that do not meet the accuracy requirements, and the full-wave calculation and cubic spline interpolation are re-performed until the requirements are met across the entire frequency band.

[0043] In one embodiment of the present invention, step 4, the frequency domain electromagnetic environment and electromagnetic interference simulation data correction driven by test data, includes at least the following steps: To improve the simulation accuracy of electromagnetic environment and electromagnetic interference (EMI) at the sampling frequencies, a simulation accuracy correction method based on measured data is adopted. A subset of frequencies are selected from the sampling frequencies to obtain EMI data. Regarding the selection of test frequencies, when the EMI changes relatively smoothly with frequency, equally spaced frequencies are chosen; in frequency bands where the EMI changes drastically with frequency, the number of test frequencies can be increased.

[0044] Let the sample frequency be , , ..., The corresponding electromagnetic environment and electromagnetic interference response value is , , ..., If every other sampling frequency is selected as the test frequency, i.e., the sample frequency... , , …If tests are conducted at the same frequency points, the simulated electromagnetic environment or electromagnetic interference value will be:

[0045]

[0046]

[0047] in , , These are the 2m-2, 2m-1, and 2m frequency points, respectively. This is the simulation correction value for the 2m-1th frequency point. This is the simulated value for the 2m-1th frequency point. The simulation error at the 2m-2 frequency point is... The simulation error at the 2m-th frequency point is... This is the test value at the 2m-2 frequency point. This is the simulated value for the 2m-2th frequency point. This is the test value at the 2m frequency point. This is the simulated value for the 2mth frequency point.

[0048] Taking the electromagnetic environment of a shortwave antenna as an example, the sampling frequencies are 3MHz, 4MHz, ... 30MHz, with a frequency interval of 1MHz. Among these sampling frequencies, test data at frequencies of 3MHz, 5MHz, ... 29MHz, with a frequency interval of 2MHz, are selected as calibration data. Using the simulation calibration formula above, the calibrated data is as follows... Figure 6 As shown in the figure, after correction using test data from some of the sampled frequency points, the simulation correction data and the test data generally match well, greatly improving the accuracy of the simulation data.

[0049] Taking electromagnetic interference from a shortwave antenna as an example, the sampling frequencies are 9MHz, 10MHz, ... 30MHz, with a frequency interval of 1MHz. Among these sampling frequencies, test data at frequencies of 9MHz, 11MHz, ... 29MHz, with a frequency interval of 2MHz, are selected as calibration data. Using the simulation calibration formula above, the calibrated data is as follows. Figure 7 As shown in the figure, after correction with test data from some of the sampled frequency points, the simulation verification data and the test data generally match well, greatly improving the accuracy of the simulation data.

[0050] In one embodiment of the present invention, step 5, which involves solving for the time-domain electromagnetic environment and electromagnetic interference based on frequency domain and inverse Fourier transform, is as follows: After obtaining the electromagnetic environment and electromagnetic interference data at the sampling frequency of the ultra-large electric power platform, it is necessary to align and multiply it with the corresponding frequency points of the spectrum data of the excitation source time-domain signal obtained in step 2, and then perform an inverse Fourier transform. For example... Figure 8 As shown, according to the knowledge of Discrete Fourier Transform, when a time-domain aperiodic discrete signal is subjected to Discrete Fourier Transform, its spectrum will undergo periodic extension. Figure 8 The transformation from a time-domain signal to a frequency-domain signal is described using variables. In the left graph, the horizontal axis represents time, and since it does not involve specific numerical values, it has no specific time unit. The vertical axis of the left graph represents a physical quantity (such as voltage, current, or energy), and it also has no specific unit. In the right graph, the horizontal axis represents angular frequency, and since it does not involve specific numerical values, it has no specific angular frequency unit. The vertical axis of the right graph represents a physical quantity (such as voltage, current, or energy), and it also has no specific unit.

[0051] (16) in The amplitude of the spectrum. The amplitude of the time-domain signal, Ω is the angular frequency variable, T is the sampling time interval, and n represents the nth point. In reality, the frequency-domain electromagnetic environment and electromagnetic interference data obtained from electromagnetic calculations are located at 0 < Ω. f < ( Within the range of sampling frequency, the discrete inverse Fourier transform requires 0 < f < The spectrum data within the range requires completion of the spectrum data within the sampling frequency. Region 1 is the spectrum data obtained by multiplying the spectrum data of the time-domain excitation source signal with the spectrum data obtained from electromagnetic calculation. Region 2 is the supplementary data. The data in Region 1 and Region 2 are related to... Conjugate symmetry, the completed spectrum data distribution is as follows Figure 9 As shown, the time-domain electromagnetic environment and electromagnetic interference coupling signal of the UHVDC platform can be obtained by performing a discrete inverse Fourier transform on the completed spectrum data. Figure 9 The frequency domain signal sampling method is described using variables. The horizontal axis represents frequency, which does not involve specific numerical values, so there is no specific frequency domain unit. The vertical axis represents a physical quantity (such as voltage, current, or energy), and therefore has no specific unit.

[0052] Figure 10 and Figure 11 The time-domain electromagnetic environment distribution diagrams of the broadband excitation source after 41ns and 83ns of transmission are given respectively. The process of electromagnetic wave signal transmission can be clearly seen from the diagrams. Figure 12The time-domain curve of the coupling current at the receiving antenna port 15m directly in front of the broadband excitation source is given. The maximum value of the coupling current occurs at 61.8ns, which is the same time when the electromagnetic wave radiated by the broadband excitation source travels to the receiving antenna.

[0053] The above are preferred embodiments of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A simulation and prediction method for the time-domain electromagnetic environment and electromagnetic interference of an ultra-large electric platform, characterized in that: The method includes the following steps: Step 1: Perform a Fourier transform on the time-domain excitation signal to obtain the spectrum curve corresponding to the periodic time-domain excitation signal; Step 2: Discretize the spectrum curve obtained in Step 1 based on transmission path tracing to obtain the specific discrete frequency points to be calculated; In step 2, the spectral discrete interval is obtained based on the shortest time sampling length of the time-domain electromagnetic environment. Based on the spectral discrete interval, the specific discrete frequency points to be calculated are obtained. The shortest time sampling length is calculated using the following formula: = In the formula, Let be the shortest time sampling length of the electromagnetic environment in the time domain to be determined. L The longest transmission path length between the excitation signal source and the observation point of the simulation object. τ The pulse width of the excitation source signal, c The speed of light; In step 2, a ray tracing algorithm is used to obtain the longest transmission path length from the excitation signal source to the observation point of the simulated object. Ray tracing is used to obtain the direct, reflected, and diffracted transmission paths from the excitation signal to each observation point of the simulated object. Then, the longest path length is selected from all paths as the longest path. L The possible values ​​of ; Step 3: Decompose the super-electric large platform into regions and solve the full-wave frequency domain electromagnetic environment and electromagnetic interference in parallel. The solution frequency points are the discrete frequency points obtained in Step 2. Step 4: Simulate the frequency domain electromagnetic environment and electromagnetic interference, and correct the simulation data to obtain the electromagnetic environment and electromagnetic interference simulation data of the sampling frequency of the super-electric platform. Step 5: Align and multiply the electromagnetic environment and electromagnetic interference simulation data of the sampling frequency point of the ultra-electric large platform obtained in Step 4 with the corresponding frequency points of the spectrum data of the excitation source time-domain signal obtained in Step 2, and then perform inverse Fourier transform to obtain the time-domain electromagnetic environment and electromagnetic interference coupling signal of the ultra-electric large platform.

2. The simulation and prediction method for time-domain electromagnetic environment and electromagnetic interference of a super-electric large platform as described in claim 1, characterized in that: In step 1, the time-domain signal radiated by the antenna from the excitation source in an open area is collected as the time-domain excitation signal.

3. The simulation and prediction method for time-domain electromagnetic environment and electromagnetic interference of a super-electric large platform as described in claim 2, characterized in that: In step 3, electromagnetic environment or electromagnetic interference data is obtained using a parallel full-wave frequency domain electromagnetic environment and electromagnetic interference solution method based on domain decomposition. The domain decomposition includes at least the antenna region and the platform region. The full-wave frequency domain electromagnetic environment and electromagnetic interference solution process includes at least the following steps: Step 3.1: Solve for the differential of the antenna region; Step 3.2: Solve for the platform region by integration; Step 3.3: Establish a data exchange mechanism at the interface between the antenna region and the platform region, and use a coupling strategy based on the Huygens equivalence principle to tightly couple the antenna region and the platform region.

4. The simulation and prediction method for time-domain electromagnetic environment and electromagnetic interference of a super-electric large platform as described in claim 3, characterized in that: In step 3, the electromagnetic environment and electromagnetic interference are solved by frequency sweeping based on the interpolation algorithm. Specifically, the frequency sweeping strategy based on the interpolation algorithm is used to perform full-wave numerical solution on some "sample frequency points" to obtain the electromagnetic environment or electromagnetic interference data of the corresponding frequency points. The data of the remaining frequency points are reconstructed by cubic spline interpolation algorithm.

5. The simulation and prediction method for time-domain electromagnetic environment and electromagnetic interference of an ultra-large electric platform as described in claim 4, characterized in that: In step 3.1, a finite element-based differential algorithm is used to solve the differential problem of the antenna region. In step 3.2, a multi-layer fast multipole-based integral algorithm is used to solve the integral problem of the platform region.

6. The simulation and prediction method for time-domain electromagnetic environment and electromagnetic interference of a super-electric large platform as described in claim 5, characterized in that: In step 3.3, at the boundary of the domain decomposition, the antenna region is equivalent to a current source and a magnetic current source, radiating towards the platform region; conversely, the scattered field of the platform region at the interface is applied to the antenna region as an external excitation; the solution result of the finite element subdomain is transformed into the incident field of the multilayer fast multipole subdomain by establishing the boundary integral equation; let the interface be... Then the field radiated from the antenna region to the platform region can be expressed as: in, This refers to the electric field radiated from the antenna region to the platform region through the interface. This is the common interface between the antenna and the platform. As an equivalent current source, As an equivalent magnetic current source, The curl of the Green's function is given; the coupling relationship between the antenna region and the platform region forms a differential-integral hybrid method, which naturally extends to multi-region parallelism under the domain decomposition framework: each region independently solves its own matrix equation, and the coupling between regions is updated iteratively through boundary conditions until convergence.

7. The simulation and prediction method for time-domain electromagnetic environment and electromagnetic interference of a super-electric large platform as described in claim 6, characterized in that: The steps for solving the electromagnetic environment and electromagnetic interference frequency sweep based on the interpolation algorithm include: S1. Frequency sampling: Within the frequency sweep range, samples are taken at equal intervals. The frequency sweep range is evenly divided into multiple sub-intervals, and the endpoints or midpoints of each sub-interval are selected as sample frequency points. S2. At the selected sample frequency points, the electromagnetic environment or electromagnetic interference data is obtained by using the parallel full-wave frequency domain electromagnetic environment and electromagnetic interference solution method of region decomposition. S3. For other sampling frequency points within the sweep frequency range, the cubic spline interpolation method is used to solve the problem.

8. The simulation and prediction method for time-domain electromagnetic environment and electromagnetic interference of a super-electric large platform as described in claim 7, characterized in that: In step S3, an error evaluation mechanism is embedded in the cubic spline interpolation process. During the sampling process, some initial sample points outside the frequency range are used as a validation set. The full-wave solution is calculated and compared with the interpolation result. When the error between the interpolation result of the validation set and the full-wave solution is within a preset range, the requirement is met. If not, new sample points are inserted for the sub-intervals that do not meet the accuracy requirements, and the full-wave calculation and cubic spline interpolation are performed again until the full frequency band meets the requirements.

9. The simulation and prediction method for time-domain electromagnetic environment and electromagnetic interference of a super-electric large platform as described in claim 8, characterized in that: Step 4 includes at least the following steps: Step 4.1: Select a subset of frequencies from the sampling frequencies and conduct simulation tests to obtain electromagnetic environment and electromagnetic interference data; Step 4.2: Calculate the electromagnetic environment or electromagnetic interference value for simulation correction, and calculate the simulation correction value for the frequency point. Correct the simulation data in step 4.1 based on the simulation correction value.

10. The simulation and prediction method for time-domain electromagnetic environment and electromagnetic interference of an ultra-large electric platform as described in claim 9, characterized in that: In step 5, the spectrum data within the sampling frequency is completed, and then the completed spectrum data is subjected to discrete inverse Fourier transform to obtain the time-domain electromagnetic environment and electromagnetic interference coupling signal of the UPC platform.

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