Method, device and equipment for equivalent source reconstruction based on spatial boundary constraint

Abstract

This application provides an equivalent source reconstruction method, apparatus, and device based on spatial boundary constraints. The method includes: acquiring near-field magnetic field amplitude data and the geometric boundary generated by sub-scheme one; initializing the population according to the boundary, so that the position coordinates of each equivalent dipole are randomly generated within its corresponding boundary, and the dipole moment parameter is randomly generated across the entire range. During iteration, the new individuals generated by mutation and crossover are subject to boundary validity judgment, and coordinates exceeding the boundary are corrected to within the boundary to ensure that all individuals satisfy the spatial constraints. Finally, excellent individuals are selected through fitness evaluation, and iterative optimization is performed until convergence, outputting the optimal equivalent dipole model that satisfies all boundary constraints. This scheme deeply embeds spatial constraints into the entire differential evolution algorithm process, achieving precise compression of the search space from the entire plane to local high-radiation regions, avoiding invalid searches and physically unreasonable local optima, and improving the convergence speed of a single optimization by more than an order of magnitude.

Description

Technical Field

[0001] This application relates to the field of electromagnetic compatibility prediction, and in particular to an equivalent source reconstruction method, apparatus and equipment based on spatial boundary constraints. Background Technology

[0002] With the rapid development of electronic information technology, the integration level and switching frequency of printed circuit boards (PCBs) and integrated circuits (ICs) continue to rise. The resulting electromagnetic interference (EMI) and electromagnetic compatibility (EMC) issues have become core challenges restricting the reliability of complex electronic systems. In fields such as automotive electronics, consumer electronics, communication equipment, and industrial control systems, the analysis and prediction of the radiation characteristics of devices under test (DUTs) are crucial for ensuring product compliance. For example, in automotive electronics R&D, electromagnetic radiation from vehicle controllers, radar modules, or communication modules may interfere with the normal operation of other electronic components; in the consumer electronics field, EMI issues in smartphones and wearable devices may affect signal transmission quality or pose health risks to users. Traditional EMC testing requires a 3-meter or 10-meter far-field environment, relying on large semi-anechoic chambers (SACs) to simulate a free-space environment. However, such testing places extremely high demands on site, equipment, and maintenance costs, especially for small and medium-sized enterprises or in the early stages of R&D, where the economic burden of frequent testing is unbearable.

[0003] In the existing technology, far-field radiation prediction for EMC testing mainly relies on two schemes: traditional far-field measurement and near-field reconstruction based on dynamic differential evolution (DDE) algorithm.

[0004] However, the above methods cannot balance cost-effectiveness, computational efficiency, and statistical reliability of prediction results, which limits their application in practical R&D scenarios. Summary of the Invention

[0005] This application provides an equivalent source reconstruction method, apparatus, and device based on spatial boundary constraints to solve the technical problem of how to significantly enhance the convergence stability and physical matching degree of the reconstruction model.

[0006] In a first aspect, embodiments of this application provide an equivalent source reconstruction method based on spatial boundary constraints, comprising:

[0007] Step 1: Obtain the near-field magnetic field strength amplitude data of the device under test as reference field data and the geometric boundary of the spatial cluster. The geometric boundary is generated by a preset method and has the same number of preset equivalent dipoles.

[0008] Step 2: Based on the geometric boundary, initialize the population of the dynamic differential evolution algorithm, so that the position coordinate parameters of each equivalent dipole are randomly generated within their respective geometric boundaries, and the dipole moment parameters of all equivalent dipoles are randomly generated in the entire range, to obtain an initial population that satisfies the geometric boundary constraints, and use the initial population as the current population.

[0009] Step 3: For each target individual in the current population, perform differential mutation operation to generate candidate individuals, and determine the boundary validity of the position coordinate parameters of each equivalent dipole in the candidate individuals. Correct the coordinates that exceed the corresponding geometric boundary to the boundary to obtain mutated individuals that satisfy the geometric boundary constraints.

[0010] Step 4: Perform cross-operation between the target individual and the mutated individual to generate an initial test individual, and perform boundary validity judgment on the position coordinate parameters of each equivalent dipole in the initial test individual. Correct the coordinates that exceed the corresponding geometric boundary to the boundary to obtain a test individual that satisfies the geometric boundary constraints.

[0011] Step 5: Calculate the fitness value of each target individual and the corresponding experimental individual according to the fitness function, select the individual with better fitness value to enter the next generation of the population, obtain the updated population, and use the updated population as the new current population;

[0012] Step 6: Repeat steps 3 to 5 until the preset termination condition is met, and obtain the optimal equivalent dipole model that satisfies all geometric boundary constraints.

[0013] In one possible implementation, the geometric boundaries are generated by a near-field radiation source spatial pre-calibration method based on K-means clustering. Each geometric boundary corresponds to a spatial cluster of concentrated radiation energy, and the geometric boundaries corresponding to different equivalent dipoles are independent and do not overlap.

[0014] In one possible implementation, the boundary validity determination of the position coordinate parameters of each equivalent dipole in the initial test individual includes:

[0015] After generating candidate position parameters, check one by one whether the position coordinates of each equivalent dipole fall within its corresponding geometric boundary.

[0016] If the coordinates exceed the geometric boundary range, the boundary correction strategy is performed using the boundary absorption strategy, the boundary reflection strategy, or the regeneration strategy.

[0017] The boundary absorption strategy involves directly setting the out-of-boundary coordinates to the nearest boundary value; the boundary reflection strategy involves folding the out-of-boundary portion back into the boundary according to reflection rules; and the regeneration strategy involves randomly generating a new legal position within the corresponding geometric boundary to replace the illegal position.

[0018] In one possible implementation, after calculating the fitness value of each target individual and the corresponding experimental individual according to the fitness function, selecting individuals with better fitness values ​​to enter the next generation population, obtaining an updated population, and using the updated population as the new current population, the method further includes:

[0019] Perform geometric boundary compliance verification on the best individual in the current population;

[0020] Individuals whose equivalent dipole positions exceed the corresponding geometric boundaries in the optimal individual are identified as the target optimal individuals.

[0021] Then, a forced boundary correction is performed on the target optimal individual, and the corrected individual is used to replace the target optimal individual in subsequent iterations.

[0022] In one possible implementation, the method further includes:

[0023] During the iterative optimization process, the parameters of the equivalent dipole model are updated one by one, including the position parameter and the dipole moment parameter;

[0024] The update of the position parameter is constrained by the geometric boundary, while the update of the dipole moment parameter is not constrained by the geometric boundary, so as to realize the parallel processing of position optimization and dipole moment optimization.

[0025] In one possible implementation, the preset termination condition includes at least one of the following: reaching a preset maximum number of iterations, the improvement of the population fitness function value being lower than a preset threshold for several consecutive generations, and the fitness function value of the best individual reaching a preset target value.

[0026] In one possible implementation, the preset termination condition includes at least one of the following: reaching a preset maximum number of iterations, the improvement of the population fitness function value being lower than a preset threshold for several consecutive generations, and the fitness function value of the best individual reaching a preset target value.

[0027] In one possible implementation, the optimal equivalent dipole model is used for far-field radiation prediction, and the position coordinates of each equivalent dipole in the optimal equivalent dipole model are constrained within their respective geometric boundaries.

[0028] Secondly, embodiments of this application provide an equivalent source reconstruction device based on spatial boundary constraints, comprising:

[0029] The acquisition module is used to acquire the near-field magnetic field strength amplitude data of the device under test as reference field data and the geometric boundary of the spatial cluster. The geometric boundary is generated by a preset method and has the same number of preset equivalent dipoles.

[0030] An initialization module is used to initialize the population of the dynamic differential evolution algorithm according to the geometric boundary, so that the position coordinate parameters of each equivalent dipole are randomly generated within their respective geometric boundaries, and the dipole moment parameters of all equivalent dipoles are randomly generated in the entire range to obtain an initial population that satisfies the geometric boundary constraints, and the initial population is used as the current population.

[0031] The differential mutation module is used to perform differential mutation operation on each target individual in the current population to generate candidate individuals, and to determine the boundary legality of the position coordinate parameters of each equivalent dipole in the candidate individuals. The coordinates that exceed the corresponding geometric boundary are corrected to be within the boundary to obtain mutated individuals that satisfy the geometric boundary constraints.

[0032] The crossover module is used to perform crossover operations between the target individual and the mutated individual to generate an initial test individual, and to determine the boundary validity of the position coordinate parameters of each equivalent dipole in the initial test individual, correcting the coordinates that exceed the corresponding geometric boundary to within the boundary, thereby obtaining a test individual that satisfies the geometric boundary constraints.

[0033] The calculation module is used to calculate the fitness value of each target individual and the corresponding experimental individual according to the fitness function, select individuals with better fitness values ​​to enter the next generation population, obtain the updated population, and use the updated population as the new current population.

[0034] The iterative module is used to repeatedly execute the above differential mutation operation, crossover operation, and fitness calculation until the preset termination condition is reached, so as to obtain the optimal equivalent dipole model that satisfies all geometric boundary constraints.

[0035] In one possible implementation, the geometric boundaries are generated by a near-field radiation source spatial pre-calibration method based on K-means clustering. Each geometric boundary corresponds to a spatial cluster of concentrated radiation energy, and the geometric boundaries corresponding to different equivalent dipoles are independent and do not overlap.

[0036] In one possible implementation, the differential mutation module includes:

[0037] After generating candidate position parameters, check one by one whether the position coordinates of each equivalent dipole fall within its corresponding geometric boundary.

[0038] If the coordinates exceed the geometric boundary range, the boundary correction strategy is performed using the boundary absorption strategy, the boundary reflection strategy, or the regeneration strategy.

[0039] The boundary absorption strategy involves directly setting the out-of-boundary coordinates to the nearest boundary value; the boundary reflection strategy involves folding the out-of-boundary portion back into the boundary according to reflection rules; and the regeneration strategy involves randomly generating a new legal position within the corresponding geometric boundary to replace the illegal position.

[0040] In one possible implementation, the device further includes:

[0041] The verification module is used to verify the geometric boundary compliance of the best individual in the current population.

[0042] The determination module is used to determine the target optimal individual as the individual in which the equivalent dipole position of the optimal individual exceeds the corresponding geometric boundary.

[0043] The correction module is used to perform forced boundary correction on the target optimal individual and replace the target optimal individual with the corrected individual in subsequent iterations.

[0044] In one possible implementation, the device further includes:

[0045] An update module is used to update the parameters of the equivalent dipole model one by one during the iterative optimization process. The parameters include position parameters and dipole moment parameters.

[0046] The update of the position parameter is constrained by the geometric boundary, while the update of the dipole moment parameter is not constrained by the geometric boundary, so as to realize the parallel processing of position optimization and dipole moment optimization.

[0047] In one possible implementation, the preset termination condition includes at least one of the following: reaching a preset maximum number of iterations, the improvement of the population fitness function value being lower than a preset threshold for several consecutive generations, and the fitness function value of the best individual reaching a preset target value.

[0048] In one possible implementation, the fitness function is the root mean square error between the near-field magnetic field amplitude calculated from the equivalent dipole model and the reference field data, and the equivalent dipole model is driven to approximate the real radiation source distribution by minimizing the root mean square error.

[0049] In one possible implementation, the optimal equivalent dipole model is used for far-field radiation prediction, and the position coordinates of each equivalent dipole in the optimal equivalent dipole model are constrained within their respective geometric boundaries.

[0050] Thirdly, embodiments of this application provide an electronic device, including: a memory and a processor;

[0051] The memory stores computer-executed instructions;

[0052] The processor executes computer execution instructions stored in the memory, causing the processor to perform the first aspect and / or various possible implementations of the first aspect as described above.

[0053] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the first aspect and / or various possible implementations of the first aspect.

[0054] Fifthly, embodiments of this application provide a computer program product, including a computer program that, when executed by a processor, implements the first aspect and / or various possible implementations of the first aspect.

[0055] The equivalent source reconstruction method and device based on spatial boundary constraints provided in this application acquires the near-field magnetic field strength amplitude data of the device under test as reference field data and the geometric boundary of the spatial cluster. Based on the geometric boundary, a population of dynamic differential evolution algorithm is initialized, such that the position coordinate parameters of each equivalent dipole are randomly generated within their respective geometric boundaries. Simultaneously, the dipole moment parameters of all equivalent dipoles are randomly generated across the entire range, resulting in an initial population that satisfies the geometric boundary constraints. This initial population is then used as the current population. For each target individual in the current population, a differential mutation operation is performed to generate candidate individuals. The boundary validity of the position coordinate parameters of each equivalent dipole in the candidate individuals is determined, and individuals exceeding the corresponding geometric boundary are excluded. The coordinates are corrected to within the boundary, resulting in mutant individuals that satisfy the geometric boundary constraints. The target individual and the mutant individuals are then cross-operated to generate initial experimental individuals. The position coordinate parameters of each equivalent dipole in the initial experimental individuals are then checked for boundary validity. Coordinates exceeding the corresponding geometric boundary are corrected to within the boundary, resulting in experimental individuals that satisfy the geometric boundary constraints. The fitness value of each target individual and its corresponding experimental individual is calculated using the fitness function. Individuals with better fitness values ​​are selected to enter the next generation of the population, resulting in an updated population. This updated population is then used as the new current population. The aforementioned steps are repeated until a preset termination condition is reached, resulting in the optimal equivalent dipole model that satisfies all geometric boundary constraints. This method fundamentally avoids invalid searches in non-radiative regions and physically unreasonable local optima, significantly improving convergence speed and reconstruction accuracy. The reconstructed equivalent source model highly matches the actual physical radiation source distribution of the device under test, providing an efficient and reliable reconstruction foundation for large-sample statistical prediction. Attached Figure Description

[0056] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0057] Figure 1 A flowchart illustrating the equivalent source reconstruction method based on spatial boundary constraints provided in this application. Figure 1 ;

[0058] Figure 2 A flowchart illustrating the equivalent source reconstruction method based on spatial boundary constraints provided in this application. Figure 2 ;

[0059] Figure 3 A flowchart illustrating the equivalent source reconstruction method based on spatial boundary constraints provided in this application. Figure 3 ;

[0060] Figure 4 A schematic diagram of the equivalent source reconstruction device based on spatial boundary constraints provided in this application;

[0061] Figure 5 A schematic diagram of the structure of the electronic device provided in this application.

[0062] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0063] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0064] With the rapid development of electronic information technology, the integration level and switching frequency of printed circuit boards (PCBs) and integrated circuits (ICs) have continued to rise. The resulting electromagnetic interference (EMI) and electromagnetic compatibility (EMC) issues have become core challenges restricting the reliability of complex electronic systems. In fields such as automotive electronics, consumer electronics, communication equipment, and industrial control systems, the analysis and prediction of the radiation characteristics of devices under test (DUTs) is a crucial step in ensuring product compliance. For example, in automotive electronics R&D, the electromagnetic radiation from vehicle controllers, radar modules, or communication modules may interfere with the normal operation of other electronic components; in the consumer electronics field, EMI issues in smartphones and wearable devices may affect signal transmission quality or pose health risks to users. Traditional EMC testing requires a 3-meter or 10-meter far-field environment, relying on large semi-anechoic chambers (SACs) to simulate a free-space environment. However, such testing places extremely high demands on site, equipment, and maintenance costs, especially for small and medium-sized enterprises or in the early stages of R&D, where the economic burden of frequent testing is unbearable. In existing technologies, far-field radiation prediction for EMC testing mainly relies on two schemes: traditional far-field measurement and near-field reconstruction based on dynamic differential evolution (DDE) algorithms. However, the above methods cannot balance cost-effectiveness, computational efficiency, and statistical reliability of prediction results, which limits their application in practical R&D scenarios.

[0065] To address the aforementioned issues, this application provides an equivalent source reconstruction method, apparatus, and device based on spatial boundary constraints, significantly enhancing the convergence stability and physical matching degree of the reconstructed model. Specifically, in the prior art, far-field radiation prediction for EMC testing mainly relies on two schemes: traditional far-field measurement and near-field reconstruction based on the Dynamic Differential Evolution (DDE) algorithm. However, these methods cannot simultaneously consider cost-effectiveness, computational efficiency, and statistical reliability of prediction results, limiting their application in practical R&D scenarios. Considering the above problems, the inventors investigated whether spatial boundary constraints could be added. The coordinate position of each magnetic dipole is no longer aimlessly optimized in the global coordinate system, but is strictly limited to the range of its corresponding K-means cluster space. By narrowing the value range of each independent variable, the parameter search space of the algorithm is exponentially compressed. Since the invalid oscillation of dipoles in non-radiative regions is avoided, the reconstructed equivalent source model has a higher matching degree with the actual physical source, significantly improving the reconstruction effect.

[0066] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0067] Figure 1A flowchart illustrating the equivalent source reconstruction method based on spatial boundary constraints provided in this application. Figure 1 ,like Figure 1 As shown, the method includes:

[0068] Step 1: Obtain the near-field magnetic field strength amplitude data of the device under test as reference field data and the geometric boundary of the space cluster.

[0069] In existing technologies, only near-field magnetic field amplitude data is acquired as a reference field, without any spatial constraint boundaries. The position initialization of the equivalent dipole is randomized across the entire scanning plane, without any prior information to guide its distribution. This approach forces the optimization algorithm to blindly search across a vast space across the entire plane, resulting in a huge search space, slow convergence, and a tendency to place the dipole in non-radiative or weakly radiative regions, leading to wasted computational resources and a loss of physical meaning in the model.

[0070] This step obtains two types of basic data required for subsequent optimization: first, measured near-field reference data used to evaluate the accuracy of the equivalent source model; and second, the spatial geometric boundary used to constrain the search range of the equivalent dipole position.

[0071] Specifically, this step acquires two types of data simultaneously. The first type is the near-field magnetic field strength amplitude data of the device under test, which serves as a reference benchmark for subsequent fitness evaluation. The second type is the geometric boundaries of spatial clusters with the same number of preset equivalent dipoles. These geometric boundaries are generated by a near-field radiation source spatial pre-calibration method based on K-means clustering. Each geometric boundary corresponds to a spatial cluster with concentrated radiation energy, and the geometric boundaries corresponding to different equivalent dipoles are independent and do not overlap. Step 1 uses these two types of data as input for the subsequent optimization process, providing a foundation for the position constraint mechanism.

[0072] The geometric boundaries include the center coordinates, the minimum and maximum values ​​along the x-axis, and the minimum and maximum values ​​along the y-axis. These geometric boundaries are stored in an array, where the i-th geometric boundary corresponds to the legal position range of the i-th equivalent dipole.

[0073] Step 2: Based on the geometric boundary, initialize the population of the dynamic differential evolution algorithm so that the position coordinate parameters of each equivalent dipole are randomly generated within their respective geometric boundaries, and the dipole moment parameters of all equivalent dipoles are randomly generated within the entire range to obtain an initial population that satisfies the geometric boundary constraints, and use the initial population as the current population.

[0074] Existing techniques randomly initialize the position coordinates and dipole moment parameters of all equivalent dipoles within the entire scanning plane. This "full-plane random" initialization method results in a large number of individuals in the initial population being distributed in non-radiative or weakly radiative regions. These individuals require multiple generations of iterations to gradually move into high-radiative regions during subsequent optimization, or they may get trapped in local optima due to a lack of gradient information. Furthermore, the position parameters and dipole moment parameters are generated using the same random generation strategy, without considering the differences in their physical meanings.

[0075] This step generates an initial population that satisfies the geometric boundary constraints, providing a starting point for the iterative optimization of the differential evolution algorithm.

[0076] Specifically, a differentiated initialization strategy is adopted. For the position coordinate parameter, the i-th equivalent dipole is forcibly confined to a random generation within the i-th geometric boundary, ensuring that each dipole is located within its corresponding concentrated radiation energy region from the beginning. For the dipole moment parameter, since the dipole moment reflects radiation intensity and is not directly related to spatial location, it is randomly generated across the entire range. After initialization, the resulting population is defined as the initial population and simultaneously used as the current population, preparing for subsequent iterations.

[0077] For example, the population size is set to P, typically between 50 and 200. A larger P value results in stronger search capabilities but also greater computational complexity. The preset number of equivalent dipoles is N, meaning each individual contains the position and dipole moment parameters of N equivalent dipoles.

[0078] For the i-th equivalent dipole in each individual, its position coordinates are initialized as follows: within the i-th geometric boundary, i.e. and Within the rectangular area, randomly generated using a uniform distribution and The numerical value. In specific implementation, a random number r between 0 and 1 is first generated, and then the value is calculated. = + r × ( - ), Similarly.

[0079] For the dipole moment parameter, since the dipole moment reflects the radiation intensity, its numerical range is usually preset according to the radiation level of the device under test, for example, set between 0 and 1, or dynamically determined based on measured data. The dipole moment parameter is generated randomly using a uniform distribution across the entire range. Each dipole contains a complex dipole moment, including a real part and an imaginary part, which are generated independently and randomly.

[0080] Repeat the above process P times to generate an initial population containing P individuals. Define this initial population as the current population for subsequent iterations.

[0081] Step 3: For each target individual in the current population, perform differential mutation operation to generate candidate individuals, and perform boundary validity judgment on the position coordinate parameters of each equivalent dipole in the candidate individuals. Correct the coordinates that exceed the corresponding geometric boundary to the boundary to obtain mutated individuals that satisfy the geometric boundary constraints.

[0082] In existing mutation operations, candidate individuals are generated using the difference vectors of different individuals in the population. The position coordinates of these candidate individuals can appear at any location within the full scan plane. This unconstrained mutation operation easily produces illegal individuals located in non-radioactive regions. These individuals will receive poor scores in subsequent fitness evaluations, but since they are still allowed to participate in selection and iteration, they will interfere with the evolutionary direction of the population and reduce convergence efficiency.

[0083] This step generates candidate individuals through differential mutation operations, introducing population diversity while ensuring that the individuals generated by mutation satisfy geometric boundary constraints.

[0084] Specifically, firstly, a standard difference mutation operation is performed on each target individual in the current population to generate candidate individuals. Then, the position coordinates of each equivalent dipole in the candidate individuals are checked for boundary validity, verifying whether their coordinates fall within the corresponding geometric boundaries. If coordinates exceed the boundaries, a boundary correction operation is performed to correct the illegal positions to within the boundaries. The correction strategy can employ one of three methods: boundary absorption, boundary reflection, or regeneration. After correction, mutated individuals that satisfy the geometric boundary constraints are obtained.

[0085] Specifically, the boundary validity determination of the position coordinate parameters of each equivalent dipole in the candidate individuals includes checking whether the position coordinates of each equivalent dipole fall within its corresponding geometric boundary after generating the candidate position parameters. If the coordinates exceed the geometric boundary range, a boundary absorption strategy, a boundary reflection strategy, or a regeneration strategy is used to correct the boundary.

[0086] For example, for each target individual in the current population, perform the following operations in sequence:

[0087] The first step is to randomly select three distinct individuals from the current population that are different from the target individual, denoted as individual a, individual b, and individual c.

[0088] The second step is to perform a differential mutation operation. For the position coordinate parameters of each equivalent dipole, candidate positions are generated according to the formula: Candidate position = Position of individual a + Scaling factor F × (Position of individual b - Position of individual c). The scaling factor F is usually a constant between 0.5 and 1 to control the influence strength of the difference vector. For the dipole moment parameter, the same mutation formula is used to generate candidate dipole moments.

[0089] The third step is to determine the boundary validity of the generated candidate individuals. This involves checking the position coordinates of each equivalent dipole to see if they satisfy the following conditions: ≤ ≤ and ≤ ≤ If the conditions are met, the candidate position is retained; otherwise, boundary correction is performed.

[0090] There are three possible implementation methods for boundary correction:

[0091] Boundary absorption strategy: If < Then set = ;like > Then set = The same applies to the y-coordinate.

[0092] Boundary reflection strategy: If < Then calculate the excess amount d = - ,set up = + d, if it still exceeds the limit, continue reflecting until it falls within the boundary; if > Then calculate the excess amount d = - ,set up = - d.

[0093] Regeneration strategy: Within the corresponding geometric boundaries, legal positions are randomly regenerated using a uniform distribution to replace illegal positions.

[0094] After boundary correction, mutant individuals that satisfy geometric boundary constraints are obtained.

[0095] Step 4: Perform cross-operation between the target individual and the mutated individual to generate the initial experimental individual, and perform boundary validity judgment on the position coordinate parameters of each equivalent dipole in the initial experimental individual. Correct the coordinates that exceed the corresponding geometric boundary to the boundary to obtain the experimental individual that satisfies the geometric boundary constraints.

[0096] In existing crossover techniques, experimental individuals are generated by randomly combining the parameters of the target individual and the mutant individual. Since the position of the mutant individual may have been corrected in step 3, but the position of the target individual remains within the boundary, the combination of the two may produce a new position outside the boundary. Existing techniques lack a mechanism to handle this, leading to experimental individuals potentially containing illegal position parameters, affecting the accuracy of fitness evaluation and the evolutionary efficiency of the population.

[0097] This step involves cross-combining the target individual with the variant individual to generate experimental individuals, and ensuring that the individuals generated by the cross-combination meet the geometric boundary constraints.

[0098] Specifically, firstly, the mutated individuals generated in step 3 are cross-crossed with their corresponding target individuals to generate initial experimental individuals. Then, the position coordinate parameters of each equivalent dipole in the initial experimental individuals are checked for boundary validity, and the same boundary checking and correction process as in step 3 is performed. After correction, experimental individuals that satisfy the geometric boundary constraints are obtained.

[0099] For example, for each target individual and its corresponding variant individual, a crossover operation is performed to generate experimental individuals. The crossover operation uses a binomial crossover method, specifically implemented as follows:

[0100] First, for each parameter dimension of each equivalent dipole, generate a random number rand between 0 and 1. Set the crossover probability CR, typically a constant between 0.8 and 0.9.

[0101] Then, the parameters for the experimental individuals are generated according to the following rule: if rand ≤ CR or the current dimension is a randomly selected cross dimension, the parameter is inherited from the mutated individual; otherwise, the parameter is inherited from the target individual. This rule ensures that at least one dimension is inherited from the mutated individual to maintain the introduction of mutation.

[0102] After the crossover operation is completed, an initial experimental individual is generated. The same boundary validity determination and boundary correction process as in step 3 is then performed on the initial experimental individual. Each equivalent dipole's position coordinates are checked to ensure they are within the corresponding geometric boundary. If they exceed the boundary, boundary absorption, boundary reflection, or regeneration strategies are used for correction. After correction, an experimental individual that satisfies the geometric boundary constraints is obtained.

[0103] Step 5: Calculate the fitness value of each target individual and the corresponding experimental individual based on the fitness function, select the individual with the better fitness value to enter the next generation of the population, obtain the updated population, and use the updated population as the new current population.

[0104] Existing techniques use root mean square error as the fitness function to calculate the difference between the near field generated by the equivalent source model and the measured near field. However, since existing techniques do not constrain the location parameters, the fitness evaluation may include a large number of illegal individuals located in radiation-free areas. Although the fitness values ​​of these individuals may be poor, their participation will reduce the effectiveness of selection pressure and delay the spread of superior genes.

[0105] This step evaluates the quality of individuals using a fitness function, selects superior individuals to enter the next generation of the population, and achieves population evolution.

[0106] Specifically, the fitness value of each target individual and its corresponding experimental individual is calculated according to the fitness function. The fitness function is the root mean square error between the near-field magnetic field amplitude calculated based on the equivalent dipole model and the reference field data obtained in step 1. Then, individuals with better fitness values ​​are selected to enter the next generation of the population, resulting in an updated population. This updated population is then used as the new current population to prepare for the next iteration.

[0107] The fitness function is the root mean square error between the near-field magnetic field amplitude calculated from the equivalent dipole model and the reference field data. Minimizing this root mean square error drives the equivalent dipole model to approximate the actual radiation source distribution.

[0108] Step 6: Repeat steps 3 to 5 until the preset termination condition is met, and obtain the optimal equivalent dipole model that satisfies all geometric boundary constraints.

[0109] Existing technologies typically use a fixed maximum number of iterations as the termination condition, lacking a judgment on the convergence state. This may lead to the algorithm continuing to calculate even after convergence, wasting resources, or terminating prematurely before fully converging, affecting model accuracy.

[0110] This step controls the iterative process, terminating the optimization when the conditions are met, and outputting the optimal equivalent dipole model that satisfies all geometric boundary constraints.

[0111] Specifically, steps 3 through 5 are repeated until a preset termination condition is met. The termination condition can be reaching a preset maximum number of iterations, the improvement in the population fitness function value being below a preset threshold for several consecutive generations, or the fitness function value of the optimal individual reaching a preset target value. After termination, the output is an optimal equivalent dipole model that satisfies all geometric boundary constraints. The position coordinates of each equivalent dipole in this model are restricted within its corresponding geometric boundary.

[0112] Among them, the optimal equivalent dipole model is used for far-field radiation prediction. The position coordinates of each equivalent dipole in the optimal equivalent dipole model are restricted within their respective geometric boundaries.

[0113] Optionally, in the above iterative process, the method also includes updating the parameters of the equivalent dipole model one by one during the iterative optimization process.

[0114] Existing differential evolution algorithms typically employ a population-level holistic update strategy. This involves performing mutation and crossover operations on all target individuals in each iteration to generate all experimental individuals, followed by unified fitness evaluation and selection to form the next generation population. While this holistic update approach is simple to implement, it suffers from two main drawbacks: first, the algorithm requires storing all experimental individuals simultaneously, resulting in significant memory consumption; second, newly generated high-quality individuals cannot be immediately used to guide the evolution of other individuals in the current generation, reducing information utilization efficiency.

[0115] This step employs a sequential update strategy during the iterative optimization process, enabling parallel optimization of position parameters and dipole moment parameters, reducing algorithm memory usage, and improving convergence efficiency.

[0116] Specifically, a dynamic update mechanism is adopted, updating one by one. During the iterative optimization process, target individuals in the population are processed one by one. After each experimental individual is generated and its fitness is evaluated, the corresponding individual in the population is immediately updated. The specific implementation is as follows: for each target individual in the current population, differential mutation and crossover operations are performed sequentially to generate a corresponding experimental individual. The fitness value of the experimental individual is calculated and compared with the fitness value of the target individual. If the experimental individual is superior, the target individual is immediately replaced. After updating the current individual, the next target individual is processed. This one-by-one update method allows newly discovered superior individuals to immediately participate in the mutation operations of subsequent target individuals, accelerating the spread of superior genes in the population.

[0117] For example, for the current population, processing begins with the first individual and proceeds sequentially. For each target individual, the differential mutation operation and boundary correction in step 3 are executed sequentially to generate a mutated individual; then the crossover operation and boundary correction in step 4 are executed to generate a trial individual; next, the fitness calculation in step 5 is executed, comparing the fitness values ​​of the target individual and the trial individual; if the fitness value of the trial individual is better than that of the target individual, the target individual in the current population is immediately replaced with the trial individual; then the process continues to the next target individual.

[0118] This sequential update approach ensures that by the time the (k+1)th individual is processed, the updates for the previous k individuals have already taken effect. Newly generated high-quality individuals can immediately serve as candidates for mutation operations, participating in the optimization of subsequent individuals, thereby accelerating the spread of superior genes within the population. Simultaneously, since it is not necessary to store all experimental individuals simultaneously, the algorithm's memory usage is reduced by approximately half.

[0119] The equivalent source reconstruction method based on spatial boundary constraints provided in this application obtains the near-field magnetic field strength amplitude data of the device under test as reference field data and the geometric boundary of the spatial cluster. Based on the geometric boundary, a population of dynamic differential evolution algorithm is initialized, such that the position coordinate parameters of each equivalent dipole are randomly generated within its corresponding geometric boundary. Simultaneously, the dipole moment parameters of all equivalent dipoles are randomly generated across the entire range, resulting in an initial population that satisfies the geometric boundary constraints. This initial population is then used as the current population. For each target individual in the current population, a differential mutation operation is performed to generate candidate individuals. The boundary validity of the position coordinate parameters of each equivalent dipole in the candidate individuals is determined, and those exceeding the corresponding geometric boundary are excluded. The target individual is corrected to fit within the boundary, resulting in a mutant individual that satisfies the geometric boundary constraints. A crossover operation is performed between the target individual and the mutant individuals to generate initial experimental individuals. The position coordinates of each equivalent dipole in the initial experimental individuals are then checked for boundary validity. Coordinates exceeding the corresponding geometric boundary are corrected to fit within the boundary, resulting in experimental individuals that satisfy the geometric boundary constraints. The fitness value of each target individual and its corresponding experimental individual is calculated using the fitness function. Individuals with better fitness values ​​are selected for the next generation of the population, resulting in an updated population. This updated population is then used as the new current population. The aforementioned steps are repeated until a preset termination condition is met, resulting in the optimal equivalent dipole model that satisfies all geometric boundary constraints. This method fundamentally avoids invalid searches in non-radiative regions and physically unreasonable local optima, significantly improving convergence speed and reconstruction accuracy. The reconstructed equivalent source model highly matches the actual physical radiation source distribution of the device under test, providing an efficient and reliable reconstruction foundation for large-sample statistical prediction.

[0120] Figure 2 A flowchart illustrating the equivalent source reconstruction method based on spatial boundary constraints provided in this application. Figure 2 ,like Figure 2 As shown, based on the above embodiment, step 3 involves determining the boundary validity of the position coordinate parameters of each equivalent dipole in the initial experimental individual, specifically including:

[0121] S201: After generating candidate position parameters, check one by one whether the position coordinates of each equivalent dipole fall within its corresponding geometric boundary.

[0122] In existing technologies, since the position parameters of equivalent dipoles are freely optimized within the entire scan plane without any geometric boundary constraints, there is no step for determining boundary validity. All position parameters of candidate individuals, regardless of their validity, are directly accepted and participate in subsequent fitness evaluations. This approach leads to a large number of illegal individuals located in non-radiative or weakly radiative regions entering the evaluation stage. These individuals not only waste computational resources but also interfere with the evolutionary direction of the population. For example, an equivalent dipole located at the edge of the scan region produces a very weak near-field contribution, but the algorithm still needs to calculate its complete near-field distribution, consuming a significant amount of computation time. Furthermore, the presence of such an individual dilutes the concentration of superior genes in the population.

[0123] This step verifies the legitimacy of candidate positions generated by mutation or crossover operations, accurately identifying illegal equivalent dipole positions that exceed geometric boundaries, thus providing a basis for subsequent corrections.

[0124] After generating the position parameters of candidate individuals, the boundary validity determination process is immediately initiated. The determination process is performed independently for each equivalent dipole, and the specific implementation is as follows:

[0125] First, obtain the geometric boundary information corresponding to the i-th equivalent dipole, including the minimum value in the x-axis direction. and maximum value and the minimum value in the y-axis direction. and maximum value Each geometric boundary corresponds to a spatial cluster of concentrated radiation energy.

[0126] Then, extract the position coordinates of the i-th equivalent dipole among the candidate individuals. , Then, perform the following four comparisons and judgments one by one:

[0127] judge Is it greater than or equal to?

[0128] judge Is it less than or equal to?

[0129] judge Is it greater than or equal to?

[0130] judge Is it less than or equal to?

[0131] The position coordinates of the equivalent dipole are considered valid, i.e., within the geometric boundary, only when all four conditions are true. If any one condition is false, the position coordinates of the equivalent dipole are considered invalid, i.e., outside the geometric boundary.

[0132] After the determination is completed, the legality status of all equivalent dipoles is recorded as a Boolean array, with legal ones marked as true and illegal ones marked as false, for use in subsequent correction steps.

[0133] S202: If the coordinates exceed the geometric boundary range, the boundary correction strategy is performed using the boundary absorption strategy, the boundary reflection strategy, or the regeneration strategy.

[0134] Existing technologies lack boundary correction mechanisms. Once the position parameters of candidate individuals are generated, they are directly accepted and used in subsequent operations, regardless of their validity. The direct consequence of this approach is that the algorithm allows equivalent dipoles to appear in non-radiative or weakly radiative regions. While these illegal locations may theoretically generate near-field radiation, they are physically unreasonable. For example, an equivalent dipole placed at the edge of the scanning area far from the device under test may contribute negligibly to radiation, but the algorithm may need to compensate by canceling out multiple dipoles to fit the near-field data. This results in a physically unexplainable dipole distribution in the reconstructed model, significantly deviating from the true radiation source location.

[0135] This step corrects the position coordinates of the equivalent dipoles that are deemed illegal, bringing them back to the corresponding geometric boundaries, thus ensuring that all individuals participating in the subsequent optimization process satisfy the spatial constraints.

[0136] Specifically, based on the judgment result of S201, boundary correction is performed on the equivalent dipole position coordinates marked as illegal. This step provides three optional correction strategies, each suitable for different application scenarios, and their specific implementation methods are as follows:

[0137] Implementation of the boundary absorption strategy:

[0138] Boundary absorption is the simplest and most direct correction method. For the i-th equivalent dipole, check if its coordinates exceed the geometric boundary; if so, directly set the coordinates to the nearest boundary value. The specific implementation is as follows:

[0139] like < Then set =

[0140] like > Then set =

[0141] like < Then set =

[0142] like > Then set =

[0143] The advantages of this strategy are its simplicity, speed of computation, and the fact that the corrected position is always on the boundary. The disadvantage is that all candidate positions outside the boundary will be pulled back to the boundary line, potentially leading to a decrease in population diversity, as a large number of individuals may cluster on the boundary.

[0144] Implementation of the boundary reflection strategy:

[0145] The boundary reflection strategy reflects the portion of light that extends beyond the boundary back into the boundary according to reflection rules, similar to the reflection of light on a mirror. The specific implementation is as follows:

[0146] like < Then calculate the excess amount d = - ,set up = + d, if corrected Still greater than Then continue to reflect.

[0147] like > Then calculate the excess amount d = - ,set up = - d, if corrected Still smaller Then continue to reflect.

[0148] The y-coordinate is processed in the same way.

[0149] The advantage of this strategy is that it maintains the continuity of the position distribution; the farther a position is from the boundary, the farther it is from the boundary after reflection, thus preserving the position offset information introduced by the mutation operation. The disadvantage is that the calculation is slightly more complex, requiring handling of multiple reflections.

[0150] How the regeneration strategy is implemented:

[0151] The regeneration strategy completely abandons illegal positions and randomly regenerates legal positions within the corresponding geometric boundaries. Specifically, this is implemented as follows: arrive New randomized distributions are generated within the range using a uniform distribution. ,exist arrive New randomized distributions are generated within the range using a uniform distribution. .

[0152] The advantage of this strategy is that it fully guarantees population diversity because each correction generates entirely new random positions, preventing individuals from clustering at the boundary. The disadvantage is that it discards the positional offset information generated by the mutation operation, which may slow down the convergence speed.

[0153] The choice of the three strategies can be determined based on the actual application scenario: when fast convergence is required, the boundary absorption strategy can be selected; when maintaining the continuity of positional distribution is required, the boundary reflection strategy can be selected; and when population diversity is insufficient, the regeneration strategy can be selected. In practical implementation, the three strategies can also be combined, for example, using the absorption strategy for some illegal individuals and the reflection strategy for others, to balance convergence speed and diversity.

[0154] The equivalent source reconstruction method based on spatial boundary constraints provided in this application, after generating candidate position parameters, checks whether the position coordinates of each equivalent dipole fall within its corresponding geometric boundary. If the coordinates exceed the geometric boundary range, a boundary absorption strategy, a boundary reflection strategy, or a regeneration strategy is used for boundary correction. By strictly limiting the position of the equivalent dipole to the geometric boundary of the high-radiation region pre-calibrated in sub-scheme one, the search space is compressed from the full-scan plane to multiple independent local subspaces. This fundamentally eliminates the possibility of equivalent dipoles appearing in non-radiation or weak-radiation regions, avoiding the problem of multiple dipoles overlapping or being distributed in non-radiation regions, which leads to a loss of physical meaning, as seen in existing technologies. Simultaneously, it allows the computational resources for fitness evaluation to be more focused on meaningful search directions, significantly improving optimization efficiency and the physical reliability of the reconstructed model.

[0155] Figure 3 A flowchart illustrating the equivalent source reconstruction method based on spatial boundary constraints provided in this application. Figure 3 ,like Figure 3 As shown, based on the above embodiments, the method further includes:

[0156] S301: Verify the geometric boundary compliance of the best individual in the current population.

[0157] In existing technologies, due to the lack of geometric boundary constraints, there is no compliance verification step for the optimal individual. The algorithm only focuses on the fitness value; as long as an individual can produce a result that matches the measured near-field well, it is accepted as the optimal solution regardless of whether the distribution of its equivalent dipoles is reasonable. This approach may lead to a serious problem: the equivalent dipoles of the optimal individual may appear in non-radiative or weakly radiative regions, or even multiple dipoles may overlap. However, because these illegal distributions happen to fit the near-field data, the algorithm still outputs them as the final result. This physically uninterpretable optimal solution may produce huge errors in subsequent far-field predictions, because small perturbations in the near-field data may be amplified by the illegal dipole distribution, causing the far-field prediction results to deviate significantly from the true value.

[0158] After each generation iteration, this step involves a special check on the individual with the best fitness value in the current population to verify whether the position coordinates of all its equivalent dipoles strictly satisfy the geometric boundary constraints.

[0159] Specifically, after each iteration, the individual with the best fitness value is first identified from the current population, that is, the individual with the smallest root mean square error among all individuals. Then, compliance verification is performed on this best individual, and the verification process is as follows:

[0160] For each equivalent dipole in the optimal individual, obtain its position coordinates ( , This is then compared with the geometric boundary corresponding to the equivalent dipole. Geometric boundary information includes the minimum value in the x-axis direction. and maximum value and the minimum value in the y-axis direction. and maximum value .

[0161] The verification criteria are as follows:

[0162] Is it greater than or equal to? and less than or equal to

[0163] Is it greater than or equal to? and less than or equal to

[0164] The optimal individual is considered fully compliant only if the position coordinates of all equivalent dipoles satisfy the above conditions. If the coordinates of any equivalent dipole exceed its corresponding geometric boundary, the optimal individual is considered non-compliant.

[0165] S302: Identify the individuals whose equivalent dipole positions exceed the corresponding geometric boundaries as the target optimal individuals.

[0166] Current techniques lack a step for locating specific equivalent dipoles within the optimal individual. When an illegal position exists within the optimal individual, existing techniques either directly accept the individual as the final result or simply discard it. The former leads to a physically uninterpretable output model, while the latter may lose the already optimized excellent fitness value. Neither approach can accurately handle the problem of local illegality within the optimal individual.

[0167] This step identifies equivalent dipoles whose positions exceed geometric boundaries from the optimal individuals, thus clarifying the target objects that require forced correction.

[0168] Specifically, after S301 verification reveals that the optimal individual is non-compliant, this step further identifies the targets that need to be corrected. The specific implementation method is as follows:

[0169] Iterate through each equivalent dipole in the optimal individual, and for the i-th equivalent dipole, check its position coordinates ( , Does it satisfy the geometric boundary constraints? If it does, mark the equivalent dipole as legal and leave it unchanged; if it does not, mark the equivalent dipole as the target optimal dipole and record its index number i and the specific situation of exceeding the boundary.

[0170] Specific situations that exceed the boundary include:

[0171] Beyond the left boundary of the x-axis: <

[0172] Beyond the right boundary of the x-axis: >

[0173] Beyond the lower boundary of the y-axis: <

[0174] Beyond the upper boundary of the y-axis: >

[0175] For cases exceeding multiple boundaries, all directions of deviation are recorded simultaneously. This information will provide a precise basis for subsequent forced corrections. Finally, the set of all equivalent dipoles marked as the target optimal dipole, together with other legitimate equivalent dipoles in the optimal individual, constitutes the target optimal individual that needs correction.

[0176] S303: Perform forced boundary correction on the target optimal individual, and replace the target optimal individual with the corrected individual in subsequent iterations.

[0177] Current technologies lack a mechanism to forcibly correct and replace the optimal individual. When the optimal individual is in an illegal position, existing technologies can only accept the illegal individual or discard it. Accepting an illegal individual will cause subsequent iterations to continue optimizing based on an unreasonable distribution, potentially causing the population to deviate further from a reasonable physical distribution; discarding the optimal individual wastes the already obtained excellent fitness information and reduces convergence efficiency.

[0178] This step forcibly corrects illegal equivalent dipoles in the optimal individual, bringing them back within the geometric boundary. Then, the corrected individual replaces the original individual, ensuring that the optimal individual participating in subsequent iterations always satisfies the spatial constraints.

[0179] Specifically, this step performs forced boundary correction on the target optimal dipole determined in S302. The correction strategy is consistent with the boundary correction in regular iterations, providing three optional methods:

[0180] The implementation of the boundary absorption strategy is as follows: For the target optimal dipole, check whether its coordinates exceed the geometric boundary. If they do, directly set the coordinates to the closest boundary value.

[0181] The boundary reflection strategy works by reflecting any portion of the data that exceeds the boundary back into the boundary according to the reflection rules. If the data still exceeds the boundary after correction, reflection continues until it falls within the boundary.

[0182] The regeneration strategy is implemented by randomly generating legal positions within the corresponding geometric boundaries using a uniform distribution, replacing the original illegal positions.

[0183] After correction, the corrected equivalent dipole coordinates are combined with the other valid equivalent dipole coordinates of the optimal individual to form the fully corrected optimal individual. Then, the fitness value of the corrected optimal individual is calculated. While position correction may worsen the fitness value, this is a necessary cost to ensure physical plausibility. Finally, the original optimal individual in the current population is replaced with the corrected optimal individual, allowing it to participate in subsequent iterative optimization.

[0184] The equivalent source reconstruction method based on spatial boundary constraints provided in this application verifies the geometric boundary compliance of the optimal individual in the current population. Individuals whose equivalent dipole positions exceed the corresponding geometric boundaries are identified as target optimal individuals. Forced boundary correction is performed on the target optimal individuals, and the corrected individuals replace the target optimal individuals in subsequent iterations. This method performs a special review of the optimal individuals outside of regular iterations, accurately locating and correcting any potentially illegal positions, and then replacing the original individuals with corrected individuals in subsequent iterations. This mechanism fundamentally eliminates the existence of illegal positions in the optimal individuals, ensuring that the final output equivalent dipole model is not only optimal in near-field fitting accuracy but also physically reliable. That is, each equivalent dipole is strictly located within the pre-calibrated high-radiation region of sub-scheme one, providing a physically reliable input model for subsequent far-field predictions.

[0185] Figure 4 A schematic diagram of the equivalent source reconstruction device based on spatial boundary constraints provided in this application is shown below. Figure 4 As shown, the equivalent source reconstruction device 400 based on spatial boundary constraints provided in this embodiment specifically includes:

[0186] The acquisition module 401 is used to acquire the near-field magnetic field strength amplitude data of the device under test as reference field data and the geometric boundary of the space cluster. The geometric boundary is generated by a preset method and has the same number of preset equivalent dipoles.

[0187] The initialization module 402 is used to initialize the population of the dynamic differential evolution algorithm according to the geometric boundary, so that the position coordinate parameters of each equivalent dipole are randomly generated within their respective geometric boundaries, and the dipole moment parameters of all equivalent dipoles are randomly generated in the entire range to obtain an initial population that satisfies the geometric boundary constraints, and the initial population is used as the current population.

[0188] The differential mutation module 403 is used to perform differential mutation operation on each target individual in the current population, generate candidate individuals, and perform boundary legality judgment on the position coordinate parameters of each equivalent dipole in the candidate individuals, correcting the coordinates that exceed the corresponding geometric boundary to the boundary, and obtaining mutated individuals that satisfy the geometric boundary constraints.

[0189] The cross module 404 is used to perform cross operations between the target individual and the mutated individual to generate an initial test individual, and to determine the boundary validity of the position coordinate parameters of each equivalent dipole in the initial test individual, correcting the coordinates that exceed the corresponding geometric boundary to the boundary, so as to obtain a test individual that satisfies the geometric boundary constraints.

[0190] The calculation module 405 is used to calculate the fitness value of each target individual and the corresponding experimental individual according to the fitness function, select individuals with better fitness values ​​to enter the next generation of the population, obtain the updated population, and use the updated population as the new current population.

[0191] The iteration module 406 is used to repeatedly execute the above differential mutation operation, crossover operation and fitness calculation until the preset termination condition is reached, so as to obtain the optimal equivalent dipole model that satisfies all geometric boundary constraints.

[0192] In one possible implementation, the geometric boundaries are generated by a near-field radiation source spatial pre-calibration method based on K-means clustering. Each geometric boundary corresponds to a spatial cluster of radiation energy concentration, and the geometric boundaries corresponding to different equivalent dipoles are independent and do not overlap.

[0193] In one possible implementation, the differential mutation module 403 includes:

[0194] After generating candidate position parameters, check one by one whether the position coordinates of each equivalent dipole fall within its corresponding geometric boundary.

[0195] If the coordinates exceed the geometric boundary range, the boundary correction strategy is performed using the boundary absorption strategy, the boundary reflection strategy, or the regeneration strategy.

[0196] Among them, the boundary absorption strategy is to directly set the out-of-boundary coordinates to the nearest boundary value, the boundary reflection strategy is to fold the out-of-boundary part back into the boundary according to the reflection rule, and the regeneration strategy is to randomly generate a new legal position in the corresponding geometric boundary to replace the illegal position.

[0197] In one possible implementation, the equivalent source reconstruction device 400 based on spatial boundary constraints further includes:

[0198] Verification module 407 is used to verify the geometric boundary compliance of the best individual in the current population;

[0199] The determination module 408 is used to determine the target optimal individual as the individual in which the position of the equivalent dipole in the optimal individual exceeds the corresponding geometric boundary.

[0200] The correction module 409 is used to perform forced boundary correction on the target optimal individual and replace the target optimal individual with the corrected individual in subsequent iterations.

[0201] In one possible implementation, the equivalent source reconstruction device 400 based on spatial boundary constraints further includes:

[0202] The update module 410 is used to update the parameters of the equivalent dipole model one by one during the iterative optimization process. The parameters include position parameters and dipole moment parameters.

[0203] The update of the position parameter is constrained by the geometric boundary, while the update of the dipole moment parameter is not constrained by the geometric boundary, so as to realize the parallel processing of position optimization and dipole moment optimization.

[0204] In one possible implementation, the preset termination condition includes at least one of the following: reaching a preset maximum number of iterations, the improvement of the population fitness function value being lower than a preset threshold for several consecutive generations, or the fitness function value of the best individual reaching a preset target value.

[0205] In one possible implementation, the fitness function is the root mean square error between the near-field magnetic field amplitude calculated from the equivalent dipole model and the reference field data. Minimizing this root mean square error drives the equivalent dipole model to approximate the actual radiation source distribution.

[0206] In one possible implementation, the optimal equivalent dipole model is used for far-field radiation prediction, and the position coordinates of each equivalent dipole in the optimal equivalent dipole model are restricted within their respective geometric boundaries.

[0207] The equivalent source reconstruction device based on spatial boundary constraints provided in this embodiment can execute the equivalent source reconstruction method based on spatial boundary constraints provided in the above method embodiment. Its implementation principle and technical effect are similar, and will not be described in detail here.

[0208] Figure 5 A schematic diagram of the structure of the electronic device provided in this application. Figure 5 As shown, the electronic device 500 provided in this embodiment includes at least one processor 501 and a memory 502. Optionally, the electronic device 500 further includes a communication component 503. The processor 501, memory 502, and communication component 503 are connected via a bus 504.

[0209] In a specific implementation, at least one processor 501 executes computer execution instructions stored in memory 502, causing at least one processor 501 to perform the above-described method.

[0210] The specific implementation process of processor 501 can be found in the above method embodiments, and its implementation principle and technical effect are similar. It will not be repeated here.

[0211] In the above embodiments, it should be understood that the processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor.

[0212] The memory may include random access memory (RAM) and may also include non-volatile memory (NVM), such as at least one disk storage device.

[0213] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0214] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0215] This application also provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the above-described method.

[0216] The aforementioned readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer.

[0217] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. Of course, the readable storage medium can also be a component of the processor. The processor and the readable storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and the readable storage medium can exist as discrete components in the device.

[0218] The division of units is merely a logical functional division; in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0219] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0220] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0221] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0222] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0223] Finally, it should be noted that other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein, and is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

Claims

1. A method for equivalent source reconstruction based on spatial boundary constraint, characterized in that, include: Step 1: Obtain the near-field magnetic field strength amplitude data of the device under test as reference field data and the geometric boundary of the spatial cluster. The geometric boundary is generated by a preset method and has the same number of preset equivalent dipoles. Step 2: Based on the geometric boundary, initialize the population of the dynamic differential evolution algorithm, so that the position coordinate parameters of each equivalent dipole are randomly generated within their respective geometric boundaries, and the dipole moment parameters of all equivalent dipoles are randomly generated in the entire range, to obtain an initial population that satisfies the geometric boundary constraints, and use the initial population as the current population. Step 3: For each target individual in the current population, perform differential mutation operation to generate candidate individuals, and determine the boundary validity of the position coordinate parameters of each equivalent dipole in the candidate individuals. Correct the coordinates that exceed the corresponding geometric boundary to the boundary to obtain mutated individuals that satisfy the geometric boundary constraints. Step 4: Perform cross-operation between the target individual and the mutated individual to generate an initial test individual, and perform boundary validity judgment on the position coordinate parameters of each equivalent dipole in the initial test individual. Correct the coordinates that exceed the corresponding geometric boundary to the boundary to obtain a test individual that satisfies the geometric boundary constraints. Step 5: Calculate the fitness value of each target individual and the corresponding experimental individual according to the fitness function, select the individual with better fitness value to enter the next generation of the population, obtain the updated population, and use the updated population as the new current population; Step 6: Repeat steps 3 to 5 until the preset termination condition is met, and obtain the optimal equivalent dipole model that satisfies all geometric boundary constraints.

2. The method of claim 1, wherein, The geometric boundaries are generated by a near-field radiation source spatial pre-calibration method based on K-means clustering. Each geometric boundary corresponds to a spatial cluster of radiation energy concentration, and the geometric boundaries corresponding to different equivalent dipoles are independent and do not overlap.

3. The method of claim 1, wherein, The boundary validity determination of the position coordinate parameters of each equivalent dipole in the initial experimental individual includes: After generating candidate position parameters, check one by one whether the position coordinates of each equivalent dipole fall within its corresponding geometric boundary. If the coordinates exceed the geometric boundary range, the boundary correction strategy is performed using the boundary absorption strategy, the boundary reflection strategy, or the regeneration strategy. The boundary absorption strategy involves directly setting the out-of-boundary coordinates to the nearest boundary value; the boundary reflection strategy involves folding the out-of-boundary portion back into the boundary according to reflection rules; and the regeneration strategy involves randomly generating a new legal position within the corresponding geometric boundary to replace the illegal position.

4. The method of claim 1, wherein, After calculating the fitness value of each target individual and its corresponding experimental individuals according to the fitness function, selecting individuals with better fitness values ​​to enter the next generation of the population, obtaining an updated population, and using the updated population as the new current population, the method further includes: Perform geometric boundary compliance verification on the best individual in the current population; Individuals whose equivalent dipole positions exceed the corresponding geometric boundaries in the optimal individual are identified as the target optimal individuals. Forced boundary correction is performed on the target optimal individual, and the corrected individual is used to replace the target optimal individual in subsequent iterations.

5. The method of claim 1, wherein, The method further includes: During the iterative optimization process, the parameters of the equivalent dipole model are updated one by one, including the position parameter and the dipole moment parameter; The update of the position parameter is constrained by the geometric boundary, while the update of the dipole moment parameter is not constrained by the geometric boundary, so as to realize the parallel processing of position optimization and dipole moment optimization.

6. The method of claim 1, wherein, The preset termination conditions include at least one of the following: reaching the preset maximum number of iterations, the improvement of the population fitness function value being lower than the preset threshold for several consecutive generations, or the fitness function value of the best individual reaching the preset target value.

7. The method of claim 1, wherein, The fitness function is the root mean square error between the near-field magnetic field amplitude calculated based on the equivalent dipole model and the reference field data. By minimizing this root mean square error, the equivalent dipole model is driven to approximate the actual radiation source distribution.

8. The method according to any one of claims 1 to 7, characterized in that, The optimal equivalent dipole model is used for far-field radiation prediction, and the position coordinates of each equivalent dipole in the optimal equivalent dipole model are restricted within their respective geometric boundaries.

9. An equivalent source reconstruction device based on spatial boundary constraint, characterized in that, include: The acquisition module is used to acquire the near-field magnetic field strength amplitude data of the device under test as reference field data and the geometric boundary of the spatial cluster. The geometric boundary is generated by a preset method and has the same number of preset equivalent dipoles. An initialization module is used to initialize the population of the dynamic differential evolution algorithm according to the geometric boundary, so that the position coordinate parameters of each equivalent dipole are randomly generated within their respective geometric boundaries, and the dipole moment parameters of all equivalent dipoles are randomly generated in the entire range to obtain an initial population that satisfies the geometric boundary constraints, and the initial population is used as the current population. The differential mutation module is used to perform differential mutation operation on each target individual in the current population to generate candidate individuals, and to determine the boundary legality of the position coordinate parameters of each equivalent dipole in the candidate individuals. The coordinates that exceed the corresponding geometric boundary are corrected to be within the boundary to obtain mutated individuals that satisfy the geometric boundary constraints. The crossover module is used to perform crossover operations between the target individual and the mutated individual to generate an initial test individual, and to determine the boundary validity of the position coordinate parameters of each equivalent dipole in the initial test individual, correcting the coordinates that exceed the corresponding geometric boundary to within the boundary, thereby obtaining a test individual that satisfies the geometric boundary constraints. The calculation module is used to calculate the fitness value of each target individual and the corresponding experimental individual according to the fitness function, select individuals with better fitness values ​​to enter the next generation population, obtain the updated population, and use the updated population as the new current population. The iterative module is used to repeatedly execute the above differential mutation operation, crossover operation, and fitness calculation until the preset termination condition is reached, so as to obtain the optimal equivalent dipole model that satisfies all geometric boundary constraints.

10. An electronic device, comprising: include: Memory, processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory, causing the processor to perform the method as described in any one of claims 1-8.

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