Application method and system of intelligent electromagnetic simulation data

Abstract

The invention discloses an application method and system of intelligent electromagnetic simulation data, and relates to the technical field of data processing. The method comprises the following steps: step 1, constructing a virtual mirror image electromagnetic space of a multi-source electromagnetic space; in the virtual mirror image electromagnetic space; calculating the difference between the characteristic decomposition result and the simulation characteristic decomposition result; 2, a test target object is placed in the multi-source electromagnetic space, and a multi-layer electromagnetic scattering interface is arranged around the test target object by taking the test target object as the center; calculating an interface propagation characteristic coefficient of the multi-source electromagnetic space according to the electromagnetic scattering characteristic; and step 3, calculating the corrected space-time electromagnetic field tensor at each time and each position in the multi-source electromagnetic space. According to the method, the high-precision space-time electromagnetic field tensor is generated through the technologies of virtual mirror image electromagnetic space construction, characteristic decomposition correction, multi-layer interface propagation modeling and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and in particular to an application method and system for intelligent electromagnetic simulation data. Background Art

[0002] The dynamic distribution characteristics of electromagnetic fields are the core content of research in the field of modern electromagnetic technology, involving multiple directions such as communications, radar, electronic countermeasures, radio wave propagation, antenna design and imaging. Especially in complex multi-source electromagnetic environments, the distribution of electromagnetic fields is not only affected by the characteristics of the field sources, but also by the common constraints of the spatial environment, medium properties and interactions between field sources. Therefore, how to accurately describe and dynamically update the spatiotemporal distribution of electromagnetic fields, and then obtain a spatiotemporal electromagnetic field tensor that can uniformly characterize the spatial position and time evolution laws, has become a key scientific issue in electromagnetic simulation and optimization. However, existing technologies have obvious deficiencies in computational efficiency, accuracy and dynamic adaptability, and cannot meet the needs of complex application scenarios.

[0003] At present, the method for describing the spatiotemporal distribution of electromagnetic fields mainly uses numerical calculation methods based on physical modeling. Numerical calculation methods based on physical modeling rely on solving the basic theoretical model of electromagnetic fields, such as Maxwell's equations, and combining specific numerical algorithms to simulate the distribution of electromagnetic fields. Typical methods include finite element method (FEM), finite difference time domain method (FDTD) and multi-layer fast multipole method (MLFMM). The finite element method (FEM) discretizes the electromagnetic field space, divides the continuous medium into a finite number of small units, and uses the variational method to solve the distribution of electric and magnetic fields. This method has high accuracy in regular geometric shapes and homogeneous media, but when dealing with complex geometric structures or multi-source field environments, it is necessary to refine the grid, resulting in a significant increase in computational complexity. The finite difference time domain method (FDTD) directly numerically solves the Maxwell equations in the time domain and can describe the time evolution law of the electromagnetic field. However, the FDTD method is limited by the grid size in terms of spatial resolution, and the computational efficiency drops sharply with the increase of the number of field sources and spatial complexity. In addition, the limitation of the time step further increases the computational burden for high-frequency electromagnetic waves or long-term simulations. The multi-layer fast multipole method (MLFMM) reduces the spatial complexity of the calculation by expanding the multipole of the electromagnetic field. This method has good computational efficiency for the far-field propagation of a single source, but it still faces limitations in the scattering calculation of multiple sources and complex media. Summary of the invention

[0004] In view of this, the present invention provides an application method and system for intelligent electromagnetic simulation data, which generates a high-precision space-time electromagnetic field tensor by constructing a virtual mirror electromagnetic space, characteristic decomposition correction, multi-layer interface propagation modeling and other technologies. This tensor realizes a unified description of the spatial distribution and time evolution law of the electromagnetic field in a complex multi-source electromagnetic environment, and significantly improves the simulation accuracy through a dynamic correction mechanism. Compared with the prior art, the present invention overcomes the problems of nonlinear coupling of multi-source fields, poor adaptability to dynamically changing environments, and insufficient space-time consistency.

[0005] The technical solution adopted by the present invention is as follows:

[0006] An application method of intelligent electromagnetic simulation data, the method comprising:

[0007] Step 1: construct a virtual mirror electromagnetic space of the multi-source electromagnetic space; in the virtual mirror electromagnetic space, generate a mirror electromagnetic field source corresponding to each electromagnetic field source in the multi-source electromagnetic space; obtain the electromagnetic field components generated by the electromagnetic field source at each sampling point in the multi-source electromagnetic space at each time, and construct the space-time electromagnetic field tensor of the multi-source electromagnetic space; similarly, construct a corresponding simulated space-time electromagnetic field tensor in the virtual mirror electromagnetic space; perform eigendecomposition on the space-time electromagnetic field tensor and the simulated space-time electromagnetic field tensor, respectively, and obtain eigendecomposition results and simulation eigendecomposition results, respectively; calculate the difference between the eigendecomposition result and the simulation eigendecomposition result;

[0008] Step 2: Place a test target in the multi-source electromagnetic space, with the test target as the center, and set multiple layers of electromagnetic scattering interfaces around the test target, with each layer of electromagnetic scattering interface being equidistant from the adjacent electromagnetic scattering interface; calculate the electromagnetic scattering characteristics of the test target in the multi-source electromagnetic space; and calculate the interface propagation characteristic coefficient of the multi-source electromagnetic space based on the electromagnetic scattering characteristics;

[0009] Step 3: Based on the difference between the characteristic decomposition result and the simulation characteristic decomposition result, as well as the interface propagation characteristic coefficient of the multi-source electromagnetic space, calculate the corrected space-time electromagnetic field tensor at each time and each position in the multi-source electromagnetic space.

[0010] Furthermore, in step 1, the electromagnetic field components include: electric field, magnetic field and magnetic induction intensity.

[0011] Furthermore, in step 1, the space-time electromagnetic field tensor is expressed using the following formula.

[0012]

[0013] in, Indicates that at time t, the position The space-time electromagnetic field tensor at ; N represents the number of electromagnetic field sources in the multi-source electromagnetic space; i is an integer subscript index; Vi represents the radiation space range of the i-th electromagnetic field source; V' is the spatial integral differential element; It means that the position of the i-th electromagnetic field source at time t is At , the electric field is generated along the X-axis direction; It means that the position of the i-th electromagnetic field source at time t is At , the electric field is generated along the Y axis; It means that the position of the i-th electromagnetic field source at time t is At , the electric field is generated along the Z axis; It means that the position of the i-th electromagnetic field source at time t is At , the magnetic field generated along the X-axis direction; It means that the position of the i-th electromagnetic field source at time t is At , the magnetic field generated along the Y axis; It means that the position of the i-th electromagnetic field source at time t is At , the magnetic field generated along the Z axis; It means that the position of the i-th electromagnetic field source at time t is The time rate of change of the magnetic induction intensity generated along the X-axis direction; It means that the position of the i-th electromagnetic field source at time t is The time rate of change of the magnetic induction intensity generated along the Y-axis direction; It means that the position of the i-th electromagnetic field source at time t is The time rate of change of the magnetic induction intensity generated along the Z axis is: μ0 is the vacuum permeability; j is the imaginary sign; k is the wave number; let the corresponding simulated space-time electromagnetic field tensor constructed in the virtual mirror electromagnetic space be:

[0014] Furthermore, in step 1, the characteristic decomposition result Λ is obtained by the following formula: EM :

[0015]

[0016] in, set up The dimension is m×n; U is an m×m orthogonal matrix; Σ is an m×n diagonal matrix; V is an n×n orthogonal matrix; T is a transpose operator; Indicates that at time t, the position The divergence of the electric field at ; Indicates that at time t, the position The divergence of the magnetic field at ; It means that the position of the i-th electromagnetic field source at time t is The curl of the electric field at ; It means that the position of the i-th electromagnetic field source at time t is The curl of the magnetic field at ; ||·|| 2 Indicates the calculation of the square of the modulus; represents the variance of the divergence; represents the variance of the curl; let the simulation characteristic decomposition result be Λ SIM .

[0017] Furthermore, in step 1, the difference Δ between the characteristic decomposition result and the simulation characteristic decomposition result is calculated by the following formula: ES :

[0018]

[0019] Among them, ||·|| F is the F-norm.

[0020] Furthermore, in step 2, the electromagnetic scattering characteristic σ of the test target in the multi-source electromagnetic space is calculated by the following formula: RCS :

[0021]

[0022] Where, R is the distance from the surface of the test target; l is a surface distance threshold, which is a set value; is the scattered electric field generated by the i-th electromagnetic field source on the surface of the test target; is the incident electric field generated by the i-th electromagnetic field source on the surface of the test target; ∈ r is the relative dielectric constant of the test object; μ r is the relative magnetic permeability of the test object; α loss is the material loss coefficient of the test object, which is the set value; θ i is the azimuth of the scattered electric field generated by the i-th electromagnetic field source on the surface of the test target; β i is the azimuth angle of the incident electric field generated by the i-th electromagnetic field source on the surface of the test target; φ i is the pitch angle of the scattered electric field generated by the i-th electromagnetic field source on the surface of the test target; α i is the pitch angle of the incident electric field generated by the i-th electromagnetic field source on the surface of the test target; |·| represents the determinant operation of the matrix.

[0023] Furthermore, in step 2, the interface propagation characteristic coefficient of the multi-source electromagnetic space is calculated by the following formula:

[0024]

[0025] Where M is the number of electromagnetic scattering interfaces; P iis the power of the i-th electromagnetic field source; D is the average distance from all electromagnetic field sources to the test target; d is the distance between the electromagnetic scattering interface and the adjacent electromagnetic scattering interface; α(s) is the attenuation function; k is an integer subscript index; Γ k is the interface scattering coefficient of the kth electromagnetic scattering interface; s is the attenuation function variable, ranging from 0 to d; ds is the integral differential element.

[0026] Furthermore, the decay function α(s) is an exponential decay function or a Gaussian decay function.

[0027] Furthermore, in step 3, the space-time electromagnetic field tensor after correction at each time and each position in the multi-source electromagnetic space is calculated by the following formula:

[0028]

[0029] in, Indicates location The average distance from all electromagnetic field sources.

[0030] An application system for intelligent electromagnetic simulation data, the system comprising: a mirror simulation difference calculation part, used to construct a virtual mirror electromagnetic space of a multi-source electromagnetic space; in the virtual mirror electromagnetic space, a mirror electromagnetic field source corresponding to each electromagnetic field source in the multi-source electromagnetic space is generated; the electromagnetic field component generated by the electromagnetic field source at each sampling point in the multi-source electromagnetic space at each time is obtained to construct a space-time electromagnetic field tensor of the multi-source electromagnetic space; similarly, a corresponding simulated space-time electromagnetic field tensor is constructed in the virtual mirror electromagnetic space; characteristic decomposition is performed on the space-time electromagnetic field tensor and the simulated space-time electromagnetic field tensor respectively, and characteristic decomposition results and simulation characteristic decomposition results are obtained respectively; characteristic decomposition results are calculated The method comprises the following steps: a propagation characteristic calculation part, which is used to place a test target in the multi-source electromagnetic space, set multiple layers of electromagnetic scattering interfaces around the test target with the test target at the center, and each layer of electromagnetic scattering interface is equidistant from the adjacent electromagnetic scattering interface; calculate the electromagnetic scattering characteristics of the test target in the multi-source electromagnetic space; and calculate the interface propagation characteristic coefficients of the multi-source electromagnetic space based on the electromagnetic scattering characteristics; a correction part, which is used to calculate the space-time electromagnetic field tensor after correction at each time and each position in the multi-source electromagnetic space based on the difference between the characteristic decomposition result and the simulation characteristic decomposition result and the interface propagation characteristic coefficients of the multi-source electromagnetic space.

[0031] By adopting the above technical scheme, the present invention produces the following beneficial effects: the present invention successfully solves the problem of insufficient description of multi-source field coupling effect in the prior art by constructing virtual mirror electromagnetic space and space-time electromagnetic field tensor. Multi-source electromagnetic space usually has complex field source distribution and dynamic space-time evolution characteristics. The traditional linear superposition model is difficult to reflect the nonlinear interaction between field sources. The present invention generates mirror field sources corresponding to real field sources in mirror space, and constructs a complete mapping relationship of multi-source electromagnetic space based on the symmetry and equivalence of mirror field. The introduction of this virtual mirror electromagnetic space not only reduces the difficulty of handling nonlinear complexity in the actual electromagnetic field environment, but also provides a more intuitive and mathematically rigorous tool for coupling analysis of multi-source fields. The present invention significantly improves the computational efficiency of electromagnetic simulation data through mathematical modeling and optimization design. The construction of virtual mirror space reduces the computational complexity of multi-source nonlinear interaction, and the dynamic correction method based on eigendecomposition avoids repeated solution of the full space tensor. This distributed correction mechanism can quickly respond to changes in the local environment while ensuring the consistency of global characteristics. In addition, the integration and accumulation operations used in the formula are flexible to adapt to a variety of electromagnetic field distribution patterns, such as uniform distribution, multi-source superposition, and local heterogeneous environments, so that the present invention can achieve efficient calculations in different scenarios. . The present invention introduces the characteristic decomposition technology to dynamically correct the space-time electromagnetic field tensor, thereby solving the problem of deviation between the electromagnetic field model and the actual distribution in a complex environment. The characteristic decomposition technology can extract the main mode information contained in the tensor, and quantitatively calculate the difference between the actual characteristic decomposition result and the simulation characteristic decomposition result. This difference is further combined with the interface propagation characteristic coefficient of the multi-source electromagnetic space to correct the initial tensor point by point, thereby effectively compensating for the errors caused by non-ideal field sources, noise and dynamic changes in the environment. This dynamic correction method based on characteristic differences significantly improves the accuracy of the space-time electromagnetic field tensor, enabling it to maintain a high degree of adaptability and consistency in a complex and changeable electromagnetic environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a flow chart of the application method of intelligent electromagnetic simulation data in an embodiment of the present invention. DETAILED DESCRIPTION

[0033] All features disclosed in this specification, or steps in all methods or processes disclosed, except mutually exclusive features and / or steps, can be combined in any manner.

[0034] Any feature disclosed in this specification (including any additional claims and abstract), unless otherwise stated, may be replaced by other equivalent or alternative features having similar purposes. That is, unless otherwise stated, each feature is only an example of a series of equivalent or similar features.

[0035] Example 1, reference Figure 1 :An application method of intelligent electromagnetic simulation data, the method comprising:

[0036] Step 1: construct a virtual mirror electromagnetic space of the multi-source electromagnetic space; in the virtual mirror electromagnetic space, generate a mirror electromagnetic field source corresponding to each electromagnetic field source in the multi-source electromagnetic space; obtain the electromagnetic field components generated by the electromagnetic field source at each sampling point in the multi-source electromagnetic space at each time, and construct the space-time electromagnetic field tensor of the multi-source electromagnetic space; similarly, construct a corresponding simulated space-time electromagnetic field tensor in the virtual mirror electromagnetic space; perform eigendecomposition on the space-time electromagnetic field tensor and the simulated space-time electromagnetic field tensor, respectively, and obtain eigendecomposition results and simulation eigendecomposition results, respectively; calculate the difference between the eigendecomposition result and the simulation eigendecomposition result;

[0037] The basic principle of virtual mirror electromagnetic space is to establish a symmetric relationship through mirror theory, so that each real electromagnetic field source has a corresponding mirror field source in the mirror space. This mirror relationship is not a simple geometric symmetry, but the result of precise calculation based on the boundary conditions and field distribution laws in electromagnetic theory. In a physical sense, this mirror process can be regarded as a virtual field extension, so that the originally complex field distribution problem can be processed by simplified mathematical methods in a larger symmetric space. In this process, the field source characteristics in the real electromagnetic space, such as intensity, direction, phase, etc., will be mapped to the mirror space according to preset rules to form a mirror field source. This mapping not only retains the basic properties of the field source in the real space, but also introduces a mathematical supplement, making the joint analysis of the two spaces possible. While constructing the virtual mirror electromagnetic space, the system needs to sample data from the actual multi-source electromagnetic space. This process decomposes the dynamic changes of the electromagnetic field into a series of discrete time and space points by discretizing the time and space dimensions of the electromagnetic field. At each sampling point, the spatial components and time changes of the electromagnetic field are fully recorded. The advantage of this sampling method is that it can simultaneously capture detailed information about the electromagnetic field at different locations and times, thus providing a basis for subsequent modeling and analysis. After sampling, these data will be integrated into a multidimensional data structure to represent the electromagnetic field distribution in the entire multi-source electromagnetic space.

[0038] At the same time, in the virtual mirror electromagnetic space, the system generates a set of corresponding data based on the simulation model, which has a one-to-one correspondence with the data in the actual space. In this way, the field distribution in the mirror space becomes a mapping of the real space, which makes subsequent comparison and analysis possible. After the data of the actual and mirror spaces are prepared, the system will extract features from them. The core of this feature extraction is to find the main patterns and laws in the field distribution through mathematical methods, thereby simplifying the complexity of the original data. In order to achieve feature extraction, the system will use a decomposition method to decompose the multidimensional data into several relatively independent feature patterns. These feature patterns can be regarded as the main components of the field distribution, and each pattern reflects the change law of the electromagnetic field in a certain direction, frequency or time scale. Through this decomposition method, the originally complex electromagnetic field data is converted into several feature patterns with clear physical meanings. The data in the virtual mirror space will be processed in the same way to obtain a set of corresponding feature patterns. This pair of feature pattern extraction and decomposition enables the distribution law of complex electromagnetic fields to be expressed in a simpler and clearer way. After completing the feature extraction, the system will compare the feature results of the actual space and the mirror space. Since the mirror space is constructed based on the theoretical model, its field distribution characteristics should be highly consistent with the real space under ideal conditions. However, in the actual electromagnetic environment, due to factors such as nonlinear interference between field sources and external noise, the characteristic results of the real space often differ from those of the mirror space. By calculating and analyzing this difference, the system can identify the main factors affecting the electromagnetic field distribution and provide a basis for subsequent corrections. The key principle of the entire step is that by introducing the virtual mirror electromagnetic space, the system effectively simplifies the complex multi-source electromagnetic field distribution problem in the actual space into two sub-problems with a symmetrical relationship. In the mirror space, the field distribution generated by the theoretical model and simulation method can provide a reference at a low computational cost, while the field distribution in the real space reflects the actual state of the electromagnetic field through actual sampling and feature extraction. After comparing the two, the complexity introduced by the actual environment can be effectively separated, and the subsequent electromagnetic field distribution can be corrected based on these differences.

[0039] Step 2: Place a test target in the multi-source electromagnetic space, with the test target as the center, and set multiple layers of electromagnetic scattering interfaces around the test target, with each layer of electromagnetic scattering interface being equidistant from the adjacent electromagnetic scattering interface; calculate the electromagnetic scattering characteristics of the test target in the multi-source electromagnetic space; and calculate the interface propagation characteristic coefficient of the multi-source electromagnetic space based on the electromagnetic scattering characteristics;

[0040] The purpose of placing a test target in a multi-source electromagnetic space is to introduce a physical entity that can interact with the external electromagnetic field and thus affect the surrounding field distribution. The test target can be any object with electromagnetic scattering capabilities, such as a metal ball, a dielectric body with a complex shape, or a target object in other application scenarios. By studying the response of the target to the electromagnetic field, the electromagnetic scattering characteristics of the object can be extracted from it. The electromagnetic scattering characteristics are important physical manifestations of the object under the action of electromagnetic waves, which can reflect information such as the material, geometric structure, and position of the target. After placing the target, in order to more comprehensively describe the electromagnetic scattering effect, the system designs a series of equidistantly distributed multi-layer electromagnetic scattering interfaces around the target. The role of these interfaces is to capture the scattering laws of electromagnetic waves at different distances in a layered manner, so that the electromagnetic effects of the target in the entire space can be more accurately quantified. The relative position relationship between the multi-layer electromagnetic scattering interface and the target is carefully designed, and the distance between each layer and its adjacent interface is consistent. This setting ensures that the sampling of the scattering effect at different distances is consistent and comparable. In the process of interaction between electromagnetic waves and the test target and the scattering interface, different electromagnetic phenomena such as reflection, refraction, and scattering will occur on the interface. These phenomena are essentially caused by the change of boundary conditions when electromagnetic waves encounter physical interfaces during propagation, such as the discontinuity of the medium's refractive index or the wavefront distortion caused by the geometric characteristics of the target. By analyzing the electromagnetic field distribution on the scattering interface, the response characteristics of the target to incident waves of different bands, directions and intensities can be extracted. These response characteristics are directly related to the physical properties of the target, and are also closely related to the mutual interference of other field sources in the multi-source electromagnetic space.

[0041] After the scattering characteristics are calculated, the system further derives the interface propagation characteristic coefficient, which is the core parameter describing the propagation law of electromagnetic waves between interfaces. The interface propagation characteristic coefficient is a comprehensive indicator containing multiple information. It not only includes the attenuation effect of electromagnetic waves during propagation, but also includes complex phenomena such as phase shift and mode conversion. The attenuation effect describes the law that the energy of electromagnetic waves gradually weakens as the propagation distance increases. This attenuation may be caused by free space propagation loss, interface absorption, and scattering loss of the target object; the phase shift is the phase change caused by the propagation path length, medium characteristics, or target scattering effect; the mode conversion is reflected in the electromagnetic wave during the propagation process. It may change from one field mode (such as plane wave) to another mode (such as spherical wave or cylindrical wave). Through in-depth analysis of the interface propagation characteristic coefficient, we can fully understand the propagation law of the electromagnetic environment around the target, which is crucial for electromagnetic simulation in complex scenes. The entire process of step 2 is a detailed modeling of the electromagnetic environment around the target, which not only describes the interaction between electromagnetic waves and targets from a physical level, but also provides an accurate quantitative description of the interface propagation characteristics from a mathematical level. The significance of this process is that it provides the core environmental parameters for subsequent simulation correction. Especially in multi-source electromagnetic space, interference between field sources, scattering of target objects, and propagation characteristics between interfaces jointly determine the actual distribution of electromagnetic fields, and these factors are analyzed and quantified one by one in step 2. By calculating the scattering characteristics of the target objects and the interface propagation characteristics coefficients, the system can provide accurate input for the correction model in step 3, which ensures that the final correction results can reflect the true characteristics of the actual electromagnetic environment.

[0042] Step 3: Based on the difference between the characteristic decomposition result and the simulation characteristic decomposition result, as well as the interface propagation characteristic coefficient of the multi-source electromagnetic space, calculate the corrected space-time electromagnetic field tensor at each time and each position in the multi-source electromagnetic space.

[0043] The correction process first relies on the results of the eigendecomposition in step 1. These results can be regarded as an abstract expression of the electromagnetic field distribution characteristics of the multi-source electromagnetic space, and the complex multi-dimensional electromagnetic field distribution is compressed into a set of mathematical expressions that best characterize its core characteristics through eigenvalues ​​and eigenvectors. The simulation eigendecomposition results are idealized reference models constructed based on virtual mirror electromagnetic space, so the difference between the two essentially reflects the deviations in the actual electromagnetic environment, including the nonlinear effects of the field source, environmental noise, and other dynamic factors that cannot be ignored. The analysis of the eigendecomposition differences provides a key correction direction, which guides the system on which characteristics and modes should be focused in the subsequent adjustment process. At the same time, the interface propagation characteristic coefficients obtained in step 2 play a bridging role in the correction. These coefficients record the propagation laws of electromagnetic waves when passing through the test target and its surrounding multi-layer scattering interfaces, and reflect the energy transfer and phase change characteristics of the electromagnetic field in space at different times and positions. These laws are not only limited to the local scattering area of ​​the target, but also capture the propagation dynamics in a wider space through multi-layer interfaces. Therefore, the interface propagation characteristic coefficients have become an important basis for adjusting the electromagnetic field distribution during the correction process. During the correction, these coefficients are used to quantitatively compensate for the problems revealed by the characteristic decomposition differences, thereby ensuring that the correction results can not only eliminate the deviation, but also be compatible with the actual propagation characteristics in the complex electromagnetic environment. Specifically, when executing the correction calculation, the system uses a dynamic adjustment mechanism to process the electromagnetic field components at each time point and each spatial position. This adjustment mechanism fully considers the problems reflected by the characteristic decomposition differences, and combines the interface propagation characteristic coefficients for point-by-point correction. During the correction process, the adjustment in the time dimension aims to capture the dynamic change characteristics of the electromagnetic field and ensure that the simulation results can accurately reflect the time-varying behavior of the real field source. The adjustment in the spatial dimension focuses more on the distribution law of the electromagnetic field at different positions, especially the interference and superposition effects between field sources in the multi-source electromagnetic space. Through the joint correction of the time and space dimensions, the system can generate a comprehensive and accurate space-time electromagnetic field tensor.

[0044] Multi-source electromagnetic space is usually a dynamic system formed by multiple different field sources in a complex environment. The distribution of electromagnetic fields is affected by the characteristics of the field sources themselves, the interactions between the field sources, and the properties of the surrounding media. Therefore, it is difficult for simple static or linear models to truly reflect the spatiotemporal evolution laws in this system. The accurate spatiotemporal electromagnetic field tensor can comprehensively characterize the distribution of field components of the electromagnetic field at each moment and each spatial position. This description not only captures the local variation characteristics of the electromagnetic field, but also reveals the global synergy between multi-source fields. Its value lies in providing a physically accurate and dynamically updated basic framework so that complex electromagnetic field behaviors can be effectively understood and predicted. The direct use of this tensor is to support a variety of complex electromagnetic simulation applications. For example, in electromagnetic environment assessment, it can be used to analyze electromagnetic compatibility issues in a specific area and identify potential interference sources or risk areas by accurately predicting the field strength distribution. In antenna design and optimization, the spatiotemporal electromagnetic field tensor can help engineers simulate and optimize the radiation characteristics of antennas to ensure their performance stability in complex environments. In the field of communications, it provides an accurate data basis for wireless channel modeling, thereby improving the design accuracy and reliability of communication systems. In addition, in the electromagnetic shielding design of electronic equipment, this tensor can accurately characterize the propagation path and scattering behavior of electromagnetic waves, providing a scientific basis for the design of shielding structures. More importantly, the role of the space-time electromagnetic field tensor is not limited to the field of traditional electromagnetic simulation. In the intelligent electromagnetic simulation system, the accuracy of this tensor provides the possibility for further application of artificial intelligence and machine learning algorithms. By inputting the corrected electromagnetic field data into the intelligent algorithm, the system can automatically learn the field distribution pattern in a complex environment and further optimize the simulation accuracy. This ability to combine artificial intelligence means that the space-time electromagnetic field tensor is not only a data output, but also the core input of the intelligent system. Its accuracy directly affects the feedback and optimization effect of intelligent simulation. In addition, the accurate space-time electromagnetic field tensor also has unique advantages in dynamic environments. Many electromagnetic field applications need to deal with non-static scenarios, such as real-time channel changes in mobile communication devices, environmental perception of autonomous vehicle sensors, and dynamic electromagnetic environment assessment in the aerospace field. In these scenarios, the electromagnetic field distribution presents highly complex dynamic characteristics with changes in time and spatial position, and traditional methods often cannot provide real-time and high-precision simulation results. The model based on the accurate space-time electromagnetic field tensor can be updated in real time to ensure that the simulation in the dynamic application scenario is highly consistent with the actual situation.

[0045] Embodiment 2: In step 1, the electromagnetic field components include: electric field, magnetic field and magnetic induction intensity.

[0046] First, the electric field is one of the core components of the electromagnetic field, which describes the electric force felt by the charge at each position in space. The existence of the electric field directly determines the propagation characteristics of electromagnetic waves, because in a time-varying electromagnetic field, the changing electric field will induce a magnetic field, thus forming mutually coupled electromagnetic fluctuations. The components of the electric field contain not only intensity information, but also directional characteristics, and its spatial distribution can intuitively reflect the layout and interaction of multi-source field sources. In a multi-source electromagnetic space, the electric field distribution may manifest as complex interference and superposition effects. By accurately sampling and modeling the electric field components, the system can capture these details and provide important support for the construction of the space-time electromagnetic field tensor. The magnetic field is another important component of the electromagnetic field and is closely related to the electric field. The magnetic field describes the magnetic force generated by the current or magnet in space. Especially in a multi-source electromagnetic space, due to the complex magnetic field superposition effect that different field sources may produce, its distribution and change law are often difficult to predict intuitively. By collecting magnetic field components, the system can identify the magnetic characteristics of different field sources and their impact on the surrounding space. This information is crucial in many application scenarios. For example, when analyzing the efficiency of wireless charging systems, the magnetic field component can directly reflect the strength of magnetic coupling in the power transfer path, thus providing a basis for optimizing the design. Magnetic induction intensity is an important parameter for describing the characteristics of the magnetic field. It reflects the magnetic flux generated by the magnetic field per unit area and directly reflects the spatial intensity distribution of the magnetic field. The introduction of magnetic induction intensity allows the system to more comprehensively describe the intensity characteristics of the magnetic field, especially in complex electromagnetic environments, where different materials and structures may have a significant impact on the magnetic induction intensity. By introducing this component, the system can more carefully analyze the magnetic response characteristics at different locations and provide more accurate input data for subsequent correction steps.

[0047] Example 3: In step 1, the space-time electromagnetic field tensor is expressed using the following formula.

[0048]

[0049]

[0050] in, Indicates that at time t, the position The space-time electromagnetic field tensor at ; N represents the number of electromagnetic field sources in the multi-source electromagnetic space; i is an integer subscript index; V i represents the radiation space range of the i-th electromagnetic field source; V' is the spatial integral differential element; It means that the position of the i-th electromagnetic field source at time t is At , the electric field is generated along the X-axis direction; It means that the position of the i-th electromagnetic field source at time t is At , the electric field is generated along the Y axis; It means that the position of the i-th electromagnetic field source at time t is At , the electric field is generated along the Z axis; It means that the position of the i-th electromagnetic field source at time t is At , the magnetic field generated along the X-axis direction; It means that the position of the i-th electromagnetic field source at time t is At , the magnetic field generated along the Y axis direction; It means that the position of the i-th electromagnetic field source at time t is At , the magnetic field generated along the Z axis; It means that the position of the i-th electromagnetic field source at time t is The time rate of change of the magnetic induction intensity generated along the X-axis direction; It means that the position of the i-th electromagnetic field source at time t is The time rate of change of the magnetic induction intensity generated along the Y-axis direction; It means that the position of the i-th electromagnetic field source at time t is The time rate of change of the magnetic induction intensity generated along the Z axis is: v0 is the vacuum permeability; j is the imaginary number; k is the wave number; let the corresponding simulated space-time electromagnetic field tensor constructed in the virtual mirror electromagnetic space be

[0051] Specifically, the core of the formula is to describe the electromagnetic field distribution at each position and time in a unified way through spatial integration and multi-source accumulation. Indicates at location The field strength at time t is expressed as a whole, where the contribution of each source i is summed up through the integral term to form a global electromagnetic field description. represents any position within the radiation range of each field source, and the integral operation reflects the continuous influence of the field source on the entire space. This description fully reflects the superposition effect of field strength in space, that is, the radiation characteristics of each field source will affect the spatial field distribution with different intensities and directions within its range of action, and the comprehensive effect of multi-source fields is displayed through superposition. In the formula, the distance term in the denominator is The formula describes the attenuation law of the radiation intensity of the field source with the spatial distance. This design strictly follows the inverse attenuation characteristics of point source radiation in classical electromagnetic theory. As the distance increases, the field strength will show a decay trend, thus reflecting the energy dispersion effect of the radiation field in the far field area. By introducing this distance factor, the formula can effectively simulate the distribution characteristics of the field strength in multi-source electromagnetic space and ensure the physical rationality of the calculation results. The exponential term in the formula It is the key part to describe the phase change of electromagnetic waves. During the propagation process, electromagnetic waves not only attenuate in intensity, but also experience periodic changes in phase. The exponential term includes the imaginary number j and the propagation path length. The dynamic propagation behavior of the wave is fully described. This form of description can reflect the interference and phase superposition effects between multiple source fields, and is an important supplement to the propagation characteristics of electromagnetic waves. By combining the exponential term and the distance factor, the formula can simultaneously express the amplitude and phase information of the field strength in the same framework, providing a highly accurate tool for the dynamic description of the electromagnetic field in space and time.

[0052] When describing the components of the electromagnetic field, the formula uses a matrix form to uniformly represent the time rate of change of the electric field, magnetic field, and magnetic induction intensity as multi-dimensional components. Each column of the matrix corresponds to the time derivative of the electric field intensity, magnetic field intensity, and magnetic induction intensity in a certain direction. These components reflect the spatial distribution and time variation of the electromagnetic field. For example, the three components of the electric field are Describes the electric force generated by the field source in different directions, and the corresponding components of the magnetic field It reflects the magnetic force. The time rate of change of magnetic induction intensity It captures the core characteristics of dynamic changes in the electromagnetic field. The joint expression of these components enables the space-time electromagnetic field tensor to fully reflect the complex changing characteristics of the field strength in different directions, at different times and at different locations. The cumulative term in the formula This further reflects the comprehensive effect of multi-source electromagnetic fields. The electromagnetic radiation of each source is calculated separately through independent integral terms, and the total contribution of the multi-source field is integrated by accumulation. This hierarchical calculation method can well adapt to the multi-source distribution characteristics in actual complex electromagnetic environments. For example, in a multi-antenna system, the radiation characteristics of different antennas may vary significantly. The formula can model the characteristics of each antenna separately, and then superimpose the effects of all antennas to generate a global electromagnetic field distribution.

[0053] Example 4: In step 1, the characteristic decomposition result Λ is obtained by the following formula: EM :

[0054]

[0055] in, set up The dimension is m×n; U is an m×m orthogonal matrix; Σ is an m×n diagonal matrix; V is an n×n orthogonal matrix; T is a transpose operator; Indicates that at time t, the position The divergence of the electric field at ; Indicates that at time t, the position The divergence of the magnetic field at ; It means that the position of the i-th electromagnetic field source at time t is The curl of the electric field at ; It means that the position of the i-th electromagnetic field source at time t is The curl of the magnetic field at ; ||·|| 2 Indicates the calculation of the square of the modulus; represents the variance of the divergence; represents the variance of the curl; let the simulation characteristic decomposition result be Λ SIM .

[0056] Specifically, the formula first transforms the space-time electromagnetic field tensor based on the classical characteristic decomposition theory Represented as three matrices U, Σ, and V T The decomposition form allows complex tensor data to be represented in a more concise way. At the same time, the extraction of eigenvalues ​​and eigenvectors also provides tools for further analysis of the local and global characteristics of the electromagnetic field. In order to more deeply describe the physical properties of the electromagnetic field, the formula introduces weighting factors for divergence and curl. The divergence of the electric field and the divergence of the magnetic field They respectively reflect the intensity of the influence of the field source on the electromagnetic field. According to Gauss's law, the divergence of the electric field is directly related to the charge density of the field source, while the divergence of the magnetic field is always zero in classical electromagnetic theory. This relationship provides a physical constraint on the continuity and consistency of the field distribution. In the formula, the divergence is used as a weight factor to perform a weighted correction on the eigenvalue through an exponential attenuation function. The exponential denominator of the correction term contains the variance of the divergence This design aims to balance the contribution of divergence data in global and local features. Specifically, when the divergence changes slightly, the weighting factor has less impact on the eigenvalue, whereas when the divergence changes significantly, the impact of the weight is significantly enhanced, thereby highlighting the dominant role of the field source in the electromagnetic field distribution. Similarly, the curl characteristic is introduced through another part of the correction term. The curl of the electric field and the curl of the magnetic field are important parameters for describing the dynamic characteristics of electromagnetic waves. They are closely related to the rate of change of the magnetic field and the rate of change of the electric field. In the formula, the square of the curl is used to measure the inhomogeneity of the field distribution. The curl variance in the exponential term is It plays a smoothing role. When the amplitude of the curl component changes slightly, the system tends to maintain the stability of the eigenvalue; when the curl changes significantly, the system emphasizes the local disturbance characteristics of the electromagnetic wave by adjusting the eigenvalue. By multiplying the curl of all field sources, the formula can capture the coupling and interference effects between multi-source fields, thereby more comprehensively revealing the internal laws of the complex field environment.

[0057] In the formula, by combining the weighted correction of divergence and curl with eigendecomposition, a deep fusion of physical meaning and mathematical expression is achieved. This method plays an important role in intelligent electromagnetic simulation systems. On the one hand, it provides higher accuracy and reliability for the feature extraction of space-time electromagnetic field tensors, so that the eigendecomposition results can not only characterize the main characteristics of the electromagnetic field, but also reflect its detailed changes in local areas; on the other hand, it dynamically adjusts the weights of eigenvalues ​​through variance analysis of divergence and curl, so that the system can adapt to the dynamic changes of complex field sources and environments. The final eigendecomposition result Λ EM It is a multi-level expression of the electromagnetic field in space and time. It contains both global information, such as the overall distribution characteristics of the field source and the field strength trend, and local details, such as interference, superposition, and dynamic change laws. This result not only provides a key basis for feature comparison in the subsequent correction steps, but can also be directly used in application scenarios such as electromagnetic environment assessment, wireless communication modeling, and complex electromagnetic system optimization. At the same time, the simulation feature decomposition result Λ SIM The introduction of provides a reference for the difference analysis between actual characteristics and theoretical models. By comparing the two, the system can accurately identify the source of errors and perform dynamic corrections, thereby improving the accuracy and applicability of the entire intelligent electromagnetic simulation system.

[0058] Example 5: In step 1, the difference Δ between the characteristic decomposition result and the simulation characteristic decomposition result is calculated by the following formula: ES :

[0059]

[0060] Among them, ‖·|| F is the F-norm.

[0061] Specifically, the first part of the formula ||Λ EM -Λ SIM || F It is the core of the difference calculation and uses the F-norm to quantify the global difference between the two eigendecomposition results. The F-norm, also known as the Frobenius norm, is the square root of the sum of the squares of all elements of the matrix and is used to measure the overall deviation between matrices. In this formula, ||Λ EM -Λ SIM || F It reflects the degree of deviation between the actual electromagnetic field characteristic decomposition results and the simulation results in the overall characteristic space. This part of the calculation ensures that the formula can capture the global consistency difference of the characteristic decomposition results, thereby providing basic data for subsequent corrections. The second part of the formula refines the difference through the weights of curl and divergence. Describes the dynamic characteristics of the field source. The curl of the electric and magnetic fields is a key parameter that reflects the dynamic characteristics of electromagnetic waves. Especially in multi-source electromagnetic space, the interaction between field sources will significantly affect the size of the curl component. By multiplying the curl weights of each field source, the formula can identify the dynamic differences in local areas in multi-source electromagnetic fields. This approach ensures that the deviation analysis is not limited to global characteristics, but can also go deep into the local behavior of the field source, thereby revealing the source of the problem in more detail. The divergence term corresponding to the curl term describes the static characteristics of the field source distribution. The divergence of the electric field is directly related to the charge density, while the divergence of the magnetic field is usually zero in classical electromagnetic theory, so the divergence deviation can be used as an important indicator to measure whether the field distribution conforms to physical constraints. By introducing the divergence weight, the formula can identify deviations caused by abnormal or discontinuous field source distribution and use it as part of the overall difference analysis. This design is of great significance for the physical consistency analysis in multi-source electromagnetic space. The formula further distinguishes the influence of dynamic and static deviations by comparing the curl weight term and the divergence weight term. The curl weight term reflects the dynamic change characteristics of the local area by multiplying the contributions of all field sources, while the divergence weight term describes the global static distribution characteristics through a single exponential function. The difference between the two is used in the formula to correct the overall deviation measurement, ensuring that the deviation analysis can not only reflect the overall difference in the characteristic decomposition results, but also reveal the deeper source of the problem by comparing the dynamic and static characteristics. This design provides higher sensitivity and adaptability for the intelligent electromagnetic simulation system, enabling the system to achieve more accurate correction in a complex electromagnetic environment. The final calculated Δ ES It is a comprehensive quantitative indicator of the difference between the actual characteristic results and the simulated characteristic results. This result provides key data input for the correction of the space-time electromagnetic field tensor in the subsequent steps. By combining the global characteristic difference, dynamic characteristic deviation and static characteristic deviation, the system can accurately analyze the non-ideality in the actual environment, and then adjust the simulation model to improve its applicability and accuracy. This deviation calculation method is not only applicable to traditional electromagnetic simulation scenarios, but also provides theoretical support for real-time correction and optimization in dynamic electromagnetic environments, enabling intelligent electromagnetic simulation systems to adapt to complex application requirements more efficiently.

[0062] Example 6: In step 2, the electromagnetic scattering characteristic σ of the test target in the multi-source electromagnetic space is calculated by the following formula: RCS :

[0063]

[0064] Where, R is the distance from the surface of the test target; l is a surface distance threshold, which is a set value; is the scattered electric field generated by the i-th electromagnetic field source on the surface of the test target; is the incident electric field generated by the i-th electromagnetic field source on the surface of the test target; ∈ r is the relative dielectric constant of the test object; μ r is the relative magnetic permeability of the test object; α loss is the material loss coefficient of the test object, which is the set value; θ i is the azimuth of the scattered electric field generated by the i-th electromagnetic field source on the surface of the test target; β i is the azimuth angle of the incident electric field generated by the i-th electromagnetic field source on the surface of the test target; φ i is the pitch angle of the scattered electric field generated by the i-th electromagnetic field source on the surface of the test target; α i is the pitch angle of the incident electric field generated by the i-th electromagnetic field source on the surface of the test target; |·| represents the determinant operation of the matrix.

[0065] Specifically, the basic framework of the formula is based on 4πR 2 is the scale normalization factor, which is directly related to the growth law of the radiation spherical area. According to classical electromagnetic theory, when electromagnetic waves propagate in the form of spherical waves, their energy distribution will spread evenly on a larger sphere as the distance increases. Through this normalized design, the formula ensures that the calculation results of the scattering cross-sectional area can exclude the distance effect caused by spatial propagation, thereby reflecting the inherent scattering characteristics of the target object. This part lays the theoretical foundation for the formula, enabling it to maintain consistency and reliability of the results within different distance ranges. The core content of the formula is the ratio of the scattered electric field to the incident electric field, that is, For the i-th field source, this ratio reflects the responsiveness of the target surface to the incident electric field. The scattered electric field is a reflected wave or scattered wave generated by the interaction between the incident electric field and the target. Its intensity and direction are jointly affected by the material properties, geometric shape and surface electromagnetic properties of the target. This ratio indicates the scattering efficiency of the target to the incident wave. The larger the value, the stronger the scattering ability of the target in this direction. By accumulating the contributions of all field sources, the formula can integrate the global scattering characteristics of the target in a multi-field source environment. This design makes the formula not only suitable for simple scattering analysis of a single field source, but also can accurately characterize the scattering behavior in a complex multi-source environment. In the geometric description of the scattering direction, the formula uses a matrix containing the relationship between the azimuth and elevation angles. The determinant |·| reflects the degree of spatial deviation between the scattering and incident directions. The matrix is ​​composed of θ i ,φ i ,α i ,β iThe determinant is composed of angular parameters such as the angle parameter, which respectively describe the angular characteristics of the scattered electric field and the incident electric field in specific directions. The geometric characteristics of the target directly affect these angular relationships. For example, a smooth surface usually results in a smaller deviation between the scattering direction and the incident direction, while a rough surface or a complex geometric shape may cause a significant change in the scattering direction. By calculating the size of the determinant, the formula can quantify the impact of this angular relationship on the scattering intensity, and further reveal the role of the surface characteristics of the target in the scattering behavior. This part is particularly important because the stealth design of the target often relies on the control of the scattering direction, and the formula provides a mathematical description of this key characteristic.

[0066] Material properties through ∈ r ,μ r ,α loss The parameters such as dielectric constant and permeability are integrated into the formula to reflect the influence of the target's dielectric properties, magnetic permeability properties and material loss properties on the scattering behavior. r It shows the polarization ability of the material to the electric field, while the relative magnetic permeability μ r It reflects the material's response to the magnetic field. The square root of the two Describes the modulation effect of the material on the propagation speed of electromagnetic waves, which directly affects the scattering pattern of the target. loss It is the core parameter for evaluating the material's ability to absorb electromagnetic wave energy. These material properties are quantified as modulation factors of the scattering intensity. When the material loss is high, more electromagnetic wave energy is absorbed rather than reflected, resulting in a significant reduction in the scattering cross-sectional area; conversely, for low-loss materials, more energy is returned in the form of scattering, thereby increasing the scattering cross-sectional area. The design of this part enables the formula to distinguish the scattering characteristics of different materials, providing a theoretical basis for material selection and optimization design. The limit operation lim in the formula R→l It is a limitation on the calculation range of the scattering cross-sectional area. The set distance threshold l is usually selected as a fixed radius outside the surface of the target object to ensure that the evaluation of the scattered field intensity is concentrated within a range of greater practical significance. This setting not only avoids the abnormal increase of local field intensity due to too close distance, but also eliminates the error influence caused by the weakening of the scattering field intensity at too long distance, thereby ensuring the physical meaning and accuracy of the calculation results. In general, the formula forms a comprehensive quantitative analysis of the scattering behavior of the target object through a comprehensive description of the multi-source field effect, directional geometric characteristics and material characteristics.

[0067] Embodiment 7: In step 2, the interface propagation characteristic coefficient of the multi-source electromagnetic space is calculated by the following formula:

[0068]

[0069] Where M is the number of electromagnetic scattering interfaces; P i is the power of the i-th electromagnetic field source; D is the average distance from all electromagnetic field sources to the test target; d is the distance between the electromagnetic scattering interface and the adjacent electromagnetic scattering interface; α(s) is the attenuation function; k is an integer subscript index; Γ k is the interface scattering coefficient of the kth electromagnetic scattering interface; s is the attenuation function variable, ranging from 0 to d; ds is the integral differential element.

[0070] Specifically, the core idea of ​​the formula is to decompose the propagation characteristics of electromagnetic waves into multiple independent but interrelated physical factors, and express them uniformly as an overall propagation coefficient through cumulative effects. In this part, the formula combines the power distribution of the multi-source field with the distance characteristics, reflecting the energy contribution of different field sources around the test target. i It is the direct factor that determines the intensity of electromagnetic waves, while the average distance D reflects the uniformity of spatial distribution. When the field source is densely distributed and the power is large, this item will significantly increase P rec , and vice versa. This design ensures that the formula can adapt to the energy distribution characteristics under different field source configurations. The formula then introduces the inverse square relationship between the wavelength λ and the path distance d, through It expresses the law of electromagnetic wave propagation in space. This part strictly follows the classical radiation theory, that is, the intensity of point source radiation decreases with the inverse square of the propagation distance, and the increase of wavelength will reduce the attenuation of radiation energy. This description ensures the physical rationality of the formula in practical application, especially when dealing with high-frequency or long-wave electromagnetic wave propagation, it can give realistic predictions. Electromagnetic scattering characteristics σ RCS is another key component of the formula, which is used to describe the scattering ability of the target to the incident wave. By incorporating the radar scattering cross-section area of ​​the target into the calculation of the propagation coefficient, the formula can reflect the significant impact of the test target on the propagation of electromagnetic waves. When the target has a complex geometry or the surface material has strong reflective properties, σ RCS will increase significantly, thereby improving the interface propagation characteristic coefficient. This part is closely related to the formula of Example 6, and further enhances the adaptability of the system in a multi-layer scattering environment. The role of the multi-layer interface is through The scattering coefficient Γ of each interface is precisely characterized. k describes the ability of the interface to reflect incident waves, while It represents the energy transfer efficiency through the interface. By multiplying the transfer efficiency of all interfaces, the formula can comprehensively describe the overall loss characteristics of electromagnetic waves after multiple reflections and transmissions in multi-layer interfaces. Such a design is particularly suitable for complex multi-layer structures, such as composite materials, layered media or multi-layer shielding, and can accurately quantify the contribution of each layer to electromagnetic wave propagation. The formula also uses the exponential attenuation term Describes the energy loss of electromagnetic waves on the propagation path. This term combines the absorption effect of the material medium, the path length, and the attenuation characteristics of the external environment. The attenuation function α(s) is a dynamic variable that can reflect the loss intensity of the electromagnetic wave at different positions as the path s changes, and the integral operation accumulates the attenuation effect on the entire propagation path. The set value l is used as a benchmark to allow the system to adjust the propagation coefficient according to different loss models. The design of this part ensures that the formula can flexibly adapt to a variety of propagation environments. For example, in high-loss media, the exponential term will significantly reduce the propagation coefficient, while in low-loss media, a high energy transfer efficiency is maintained.

[0071] Embodiment 8: The attenuation function α(s) is an exponential attenuation function or a Gaussian attenuation function.

[0072] Specifically, when the decay function takes the form of exponential decay, its expression can usually be written as α(s) = α0e -κs , where α0 is the initial attenuation intensity and κ is the attenuation rate. This form reflects the exponentially decreasing relationship between the energy loss in the medium and the propagation path, and is widely applicable to the propagation of highly absorbent media or electromagnetic waves in a highly dissipative environment. For example, in a metal shield or highly conductive material, the energy of an electromagnetic wave will decay rapidly with the propagation distance, and the exponential decay function can accurately capture this characteristic. In addition, when the absorption characteristics of the medium are uniform and there is no significant spatial variation, the exponential decay form can provide a simple and effective loss description. The advantage of this function form is its high computational efficiency and its ability to adapt well to the common uniform medium attenuation model. In contrast, the Gaussian attenuation function is more suitable for describing local loss characteristics or the propagation characteristics of inhomogeneous media, and its expression can be written as Where α0 is the attenuation amplitude, s0 is the center position, and σ is the standard deviation of the control attenuation range. The characteristic of the Gaussian attenuation function is that its attenuation intensity reaches the maximum at the center of the path (i.e., s0) and gradually weakens at positions far away from the center. This form is particularly suitable for describing energy loss phenomena with strong localization, such as the most significant absorption of electromagnetic waves by a specific layer in a multilayer medium, or energy dissipation caused by local scattering and interference in complex geometric structures. In practical applications, the Gaussian attenuation form can accurately capture the energy loss in certain key areas on the propagation path and provide a more refined propagation characteristic analysis for intelligent electromagnetic simulation systems. The choice of the two attenuation function forms not only reflects the adaptability to different propagation environments, but also provides the possibility for flexible modeling of the system. In intelligent electromagnetic simulation systems, the propagation environment is usually complex and changeable, and the medium may present different uniformity characteristics, and there may even be areas with significant spatial changes. The combination of the simplicity of the exponential attenuation function and the local characteristics of the Gaussian attenuation function enables the system to dynamically adjust the attenuation model according to actual conditions. For example, in some sections of the propagation path, the electromagnetic wave may be dissipated by a uniform medium. In this case, the exponential decay function can well describe the law of energy loss; in other sections, if the medium characteristics show obvious inhomogeneity, the Gaussian decay function can be used to more finely characterize the local characteristics. In addition, these two forms of decay functions have different effects on the integral term in the formula. The calculation of the propagation coefficient also has different effects. When the exponential decay function is used, the integral result is usually expressed as a simple exponential form, which makes the calculation of the propagation coefficient more efficient and suitable for scenarios that require rapid evaluation of energy loss. When the Gaussian decay function is used, the integral result can reflect the influence of the attenuation center position and its range on the propagation coefficient, providing higher accuracy for local loss evaluation in complex scenarios. This diverse design ensures that the system can achieve a dynamic balance between efficiency and accuracy.

[0073] Example 9: In step 3, the space-time electromagnetic field tensor after correction at each time and each position in the multi-source electromagnetic space is calculated by the following formula:

[0074]

[0075] in, Indicates location The average distance from all electromagnetic field sources.

[0076] Specifically, the starting point of the formula is the initial space-time electromagnetic field tensor This tensor is constructed by the previous steps and represents the electromagnetic field distribution at each time and position in the multi-source electromagnetic space. However, non-ideal factors in the actual electromagnetic field environment, such as interference, noise, and non-uniform medium characteristics, may cause It cannot fully reflect the real field distribution. Therefore, the corrected space-time electromagnetic field tensor The calculation of becomes a key step in the intelligent electromagnetic simulation system, which aims to minimize the deviation between the theoretical model and the actual environment by introducing a series of correction factors. In the formula, the correction factor P rec It is the interface propagation characteristic coefficient of the multi-source electromagnetic space. It integrates the energy loss, scattering characteristics and transmission efficiency of the multi-layer interface into a comprehensive factor through the calculation of the previous steps. rec By introducing the correction formula, the system can consider the specific impact of multilayer interfaces on electromagnetic wave propagation at each location. For example, in a high-loss interface, P rec The value of will be significantly reduced, thereby reducing the strength of the correction tensor, reflecting the energy loss of electromagnetic waves during propagation. The addition of this factor makes the correction result closer to the multi-layer transmission characteristics in the real electromagnetic environment, ensuring the physical rationality of the correction process. Characteristic decomposition difference Δ ES is another important correction factor in the formula, used to quantize the initial tensor The deviation between Δ ES Incorporating the formula, the correction process can modify the initial tensor according to the direction and magnitude of the difference in the eigendecomposition. For example, when the difference at certain positions is large, the formula will significantly adjust the correction value at that position, thereby enhancing the consistency of the corrected tensor in the spatial and temporal dimensions. This correction method based on eigendecomposition improves the system's ability to analyze complex electromagnetic field characteristics and ensures that the final correction result can more accurately reflect the actual characteristics of the field source. The integral term in the formula The influence of spatial distance on electromagnetic field distribution is further considered. Indicates the target location The average distance from all field sources reflects the field source coverage of the target location and the overall length of the propagation path. During the integration process, the introduction of the variable c simulates the energy accumulation effect of electromagnetic waves during propagation. By calculating the energy accumulation from the starting point to the target position, the formula can describe the spatial distribution law of the electromagnetic field in more detail. The design of this integral term is particularly suitable for situations where field sources are unevenly distributed in complex environments with multiple sources. For example, some locations may be strongly affected by multiple near-field sources, while other locations are mainly contributed by far-field sources. Through the adjustment of the integral term, the formula can better capture these spatial differences. Finally, the formula integrates the initial tensor, propagation characteristic coefficients, characteristic decomposition difference, and spatial distance effects into a whole, and constructs the corrected space-time electromagnetic field tensor in the form of a product.

[0077] Embodiment 10: An application system for intelligent electromagnetic simulation data, the system comprising: a mirror simulation difference calculation part, used to construct a virtual mirror electromagnetic space of a multi-source electromagnetic space; in the virtual mirror electromagnetic space, generate a mirror electromagnetic field source corresponding to each electromagnetic field source in the multi-source electromagnetic space; obtain the electromagnetic field component generated by the electromagnetic field source at each sampling point in the multi-source electromagnetic space at each time, and construct a space-time electromagnetic field tensor of the multi-source electromagnetic space; similarly, construct a corresponding simulated space-time electromagnetic field tensor in the virtual mirror electromagnetic space; perform feature decomposition on the space-time electromagnetic field tensor and the simulated space-time electromagnetic field tensor respectively, and obtain feature decomposition results and simulation feature decomposition results respectively; calculate the feature The method comprises the following steps: a propagation characteristic calculation part, which is used to place a test target in the multi-source electromagnetic space, set a plurality of electromagnetic scattering interfaces around the test target with the test target at the center, and each layer of electromagnetic scattering interface is equidistant from the adjacent electromagnetic scattering interface; calculate the electromagnetic scattering characteristics of the test target in the multi-source electromagnetic space; and calculate the interface propagation characteristic coefficients of the multi-source electromagnetic space based on the electromagnetic scattering characteristics; a correction part, which is used to calculate the space-time electromagnetic field tensor after correction at each time and each position in the multi-source electromagnetic space based on the difference between the feature decomposition result and the simulation feature decomposition result and the interface propagation characteristic coefficients of the multi-source electromagnetic space.

[0078] The present invention is not limited to the above-mentioned specific embodiments, but extends to any new features or any new combination disclosed in this specification, as well as any new method or process steps or any new combination disclosed.

Claims

1. An application method of intelligent electromagnetic simulation data, characterized in that: The method comprises: Step 1: construct a virtual mirror electromagnetic space of the multi-source electromagnetic space; in the virtual mirror electromagnetic space, generate a mirror electromagnetic field source corresponding to each electromagnetic field source in the multi-source electromagnetic space; obtain the electromagnetic field components generated by the electromagnetic field source at each sampling point in the multi-source electromagnetic space at each time, and construct the space-time electromagnetic field tensor of the multi-source electromagnetic space; similarly, construct a corresponding simulated space-time electromagnetic field tensor in the virtual mirror electromagnetic space; perform eigendecomposition on the space-time electromagnetic field tensor and the simulated space-time electromagnetic field tensor, respectively, and obtain eigendecomposition results and simulation eigendecomposition results, respectively; calculate the difference between the eigendecomposition result and the simulation eigendecomposition result; Step 2: Place a test target in the multi-source electromagnetic space, with the test target as the center, and set multiple layers of electromagnetic scattering interfaces around the test target, with each layer of electromagnetic scattering interface being equidistant from the adjacent electromagnetic scattering interface; calculate the electromagnetic scattering characteristics of the test target in the multi-source electromagnetic space; and calculate the interface propagation characteristic coefficient of the multi-source electromagnetic space based on the electromagnetic scattering characteristics; Step 3: Based on the difference between the characteristic decomposition result and the simulation characteristic decomposition result, as well as the interface propagation characteristic coefficient of the multi-source electromagnetic space, calculate the corrected space-time electromagnetic field tensor at each time and each position in the multi-source electromagnetic space.

2. The application method of intelligent electromagnetic simulation data according to claim 1, characterized in that: In step 1, the electromagnetic field components include: electric field, magnetic field and magnetic induction intensity.

3. The application method of intelligent electromagnetic simulation data according to claim 2, characterized in that: In step 1, the space-time electromagnetic field tensor is expressed using the following formula. in, Indicates that at time t, the position The space-time electromagnetic field tensor at ; N represents the number of electromagnetic field sources in the multi-source electromagnetic space; i is an integer subscript index; V i represents the radiation space range of the i-th electromagnetic field source; V' is the spatial integral differential element; It means that the position of the i-th electromagnetic field source at time t is At , the electric field is generated along the X-axis direction; It means that the position of the i-th electromagnetic field source at time t is At , the electric field is generated along the Y axis; It means that the position of the i-th electromagnetic field source at time t is At , the electric field is generated along the Z axis; It means that the position of the i-th electromagnetic field source at time t is At , the magnetic field generated along the X-axis direction; It means that the position of the i-th electromagnetic field source at time t is At , the magnetic field generated along the Y axis direction; It means that the position of the i-th electromagnetic field source at time t is At , the magnetic field generated along the Z axis; It means that the position of the i-th electromagnetic field source at time t is The time rate of change of the magnetic induction intensity generated along the X-axis direction; It means that the position of the i-th electromagnetic field source at time t is The time rate of change of the magnetic induction intensity generated along the Y-axis direction; It means that the position of the i-th electromagnetic field source at time t is The time rate of change of the magnetic induction intensity generated along the Z axis is: μ0 is the vacuum permeability; j is the imaginary sign; k is the wave number; let the corresponding simulated space-time electromagnetic field tensor constructed in the virtual mirror electromagnetic space be:

4. The application method of intelligent electromagnetic simulation data according to claim 3, characterized in that: In step 1, the characteristic decomposition result Λ is obtained by the following formula EM : in, set up The dimension is m×n; U is an m×m orthogonal matrix; Σ is an m×n diagonal matrix; V is an n×n orthogonal matrix; T is a transpose operator; Indicates that at time t, the position The divergence of the electric field at ; Indicates that at time t, the position The divergence of the magnetic field at ; It means that the position of the i-th electromagnetic field source at time t is The curl of the electric field at ; It means that the position of the i-th electromagnetic field source at time t is The curl of the magnetic field at ; ||·|| 2 Indicates the calculation of the square of the modulus; represents the variance of the divergence; represents the variance of the curl; let the simulation characteristic decomposition result be Λ SIM .

5. The application method of intelligent electromagnetic simulation data according to claim 4, characterized in that: In step 1, the difference Δ between the eigendecomposition result and the simulation eigendecomposition result is calculated by the following formula: ES : Among them, ||·|| F is the F-norm.

6. The method for applying intelligent electromagnetic simulation data according to claim 5, characterized in that: In step 2, the electromagnetic scattering characteristics σ of the test target in the multi-source electromagnetic space are calculated by the following formula: RCS : Where, R is the distance from the surface of the test target; l is a surface distance threshold, which is a set value; is the scattered electric field generated by the i-th electromagnetic field source on the surface of the test target; is the incident electric field generated by the i-th electromagnetic field source on the surface of the test target; ∈ r is the relative dielectric constant of the test object; φ r is the relative magnetic permeability of the test object; α loss is the material loss coefficient of the test object, which is the set value; θ i is the azimuth of the scattered electric field generated by the i-th electromagnetic field source on the surface of the test target; β i is the azimuth angle of the incident electric field generated by the i-th electromagnetic field source on the surface of the test target; φ i is the pitch angle of the scattered electric field generated by the i-th electromagnetic field source on the surface of the test target; α i is the pitch angle of the incident electric field generated by the i-th electromagnetic field source on the surface of the test target; |·| represents the determinant operation of the matrix.

7. The method for applying intelligent electromagnetic simulation data according to claim 6, characterized in that: In step 2, the interface propagation characteristic coefficient of the multi-source electromagnetic space is calculated by the following formula: Where M is the number of electromagnetic scattering interfaces; P i is the power of the i-th electromagnetic field source; D is the average distance from all electromagnetic field sources to the test target; d is the distance between the electromagnetic scattering interface and the adjacent electromagnetic scattering interface; α(s) is the attenuation function; k is an integer subscript index; Γ k is the interface scattering coefficient of the kth electromagnetic scattering interface; s is the attenuation function variable, ranging from 0 to d; ds is the integral differential element.

8. The method for applying intelligent electromagnetic simulation data according to claim 7, characterized in that: The decay function α(s) is an exponential decay function or a Gaussian decay function.

9. The method for applying intelligent electromagnetic simulation data according to claim 8, characterized in that: In step 3, the corrected space-time electromagnetic field tensor at each time and each position in the multi-source electromagnetic space is calculated by the following formula: in, Indicates location The average distance from all electromagnetic field sources.

10. An application system for intelligent electromagnetic simulation data for implementing the method according to any one of claims 1 to 9, characterized in that: The system comprises: a mirror simulation difference calculation part, which is used to construct a virtual mirror electromagnetic space of a multi-source electromagnetic space; in the virtual mirror electromagnetic space, a mirror electromagnetic field source corresponding to each electromagnetic field source in the multi-source electromagnetic space is generated; the electromagnetic field component generated by the electromagnetic field source at each sampling point in the multi-source electromagnetic space at each time is obtained to construct a space-time electromagnetic field tensor of the multi-source electromagnetic space; similarly, a corresponding simulation space-time electromagnetic field tensor is constructed in the virtual mirror electromagnetic space; characteristic decomposition is performed on the space-time electromagnetic field tensor and the simulation space-time electromagnetic field tensor respectively, and characteristic decomposition results and simulation characteristic decomposition results are obtained respectively; the characteristic decomposition results and the simulation characteristic decomposition results are calculated and compared. The method comprises the following steps: a propagation characteristic calculation part, which is used to place a test target in the multi-source electromagnetic space, set a plurality of electromagnetic scattering interfaces around the test target with the test target at the center, and each layer of electromagnetic scattering interface is equidistant from the adjacent electromagnetic scattering interface; calculate the electromagnetic scattering characteristics of the test target in the multi-source electromagnetic space; and calculate the interface propagation characteristic coefficients of the multi-source electromagnetic space based on the electromagnetic scattering characteristics; a correction part, which is used to calculate the space-time electromagnetic field tensor after correction at each time and each position in the multi-source electromagnetic space based on the difference between the characteristic decomposition result and the simulation characteristic decomposition result and the interface propagation characteristic coefficients of the multi-source electromagnetic space.

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