Method for determining frequency stirring bandwidth of electrically large metal cavity based on small sample

Abstract

The invention discloses an electrically large metal cavity frequency stirring bandwidth determination method based on a small sample, and belongs to the technical field of electromagnetic compatibility test, and the method comprises the following steps: S1, configuring a test system and determining test parameters; s2, calibrating the vector network analyzer, and respectively storing the vector network analyzer as a real part and an imaginary part; s3, calculating to obtain an alternative stirring bandwidth in combination with the frequency in the test frequency band; s4, selecting one broadband value in the step S3, adopting a nonparametric bootstrapping algorithm, carrying out self-sampling on the broadband value to obtain M * N-dimensional samples, and arranging the M * N-dimensional samples to form module values; s5, carrying out AD test on the modulus value, and determining a critical frequency; and S6, obtaining a critical frequency cluster corresponding to the alternative stirring bandwidth in the S3, calculating a standard deviation, and selecting the alternative stirring bandwidth with the minimum standard deviation as a frequency stirring bandwidth. With the adoption of the method, the technical problem that the frequency stirring bandwidth of the electrically large metal cavity is not accurately determined under the small sample condition is solved.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic compatibility testing technology, and in particular to a method for determining the frequency stirring bandwidth of an electrically large metal cavity based on a small sample size. Background Technology

[0002] Currently, the assessment of electromagnetic field distribution in electrically large metallic cavities such as aircraft cabins mainly employs full-wave simulation calculations or mode tuning techniques based on reverberation chambers. Full-wave simulation can theoretically achieve accurate solutions for electromagnetic field distribution, while mode tuning techniques introduce statistical analysis through methods such as mechanical stirring, source stirring, or frequency stirring, effectively improving the problems of long computation time and low computational efficiency of full-wave simulation, making it particularly suitable for assessment scenarios under electronic equipment loading conditions. Among these, frequency stirring, theoretically achieving field homogenization effects comparable to mechanical stirring and source stirring, has become an important technical choice for adapting to some special cavities.

[0003] However, in existing technologies, the determination of stirring bandwidth largely relies on empirical formulas, lacking a scientifically accurate method for bandwidth determination. It requires calculation based on parameters such as cavity quality factor bandwidth and number of independent frequency points, and relies on a large number of test samples for analysis. However, empirical selection can easily lead to problems such as underestimating the peak electromagnetic field due to excessive bandwidth or increasing uncertainty due to insufficient bandwidth. Furthermore, its bandwidth calculation requires a large number of test samples, making it difficult to achieve effective application in small-sample scenarios with limited test conditions. This severely restricts the promotion and accurate implementation of frequency stirring technology in the evaluation of electromagnetic fields in electrically large metal cavities. In addition, full-wave simulation is computationally intensive and time-consuming when facing the complex boundaries brought about by electrically large cavities and internally loaded electronic devices, and may even be unable to complete the solution due to hardware resource limitations. Summary of the Invention

[0004] The purpose of this invention is to provide a method for determining the frequency stirring bandwidth of electrically large metal cavities based on small samples, thereby solving the above-mentioned technical problems.

[0005] To achieve the above objectives, the present invention provides a method for determining the frequency stirring bandwidth of an electrically large metal cavity based on a small sample size, comprising the following steps: S1. Configure the test system and determine the test parameters: Set the transmitting antenna... and receiving antenna The antenna is placed inside the metal cavity of the open university, while the vector network analyzer is placed outside the cavity. The antenna maintains a preset distance from the ground and the metal wall, avoiding line-of-sight transmission. The transmitting antenna... Receiving antenna Connect the two ports of the vector network analyzer using coaxial cables and determine the test frequency band. Frequency step interval ; S2. Calibration and Data Acquisition: Based on the test system configured in S1 and the determined test frequency band. Frequency step interval Calibrate the vector network analyzer and measure the transmitting antenna. With receiving antenna Transmission coefficient between , corresponding to each frequency point Separate the real and imaginary parts, and store them as 1×N dimensional real parts respectively. and the virtual part ; S3. Determine the alternative stirring bandwidth: based on the electrically large metal cavity volume obtained in S1. and the speed of light The constant value, combined with the frequency within the test band Calculations yielded One alternative stirring bandwidth that satisfies the frequency point number relationship , , ..., ; S4. Small sample size expansion: Select one of the bandwidth values ​​from S3. Based on the 1×N dimensional real part collected and stored by S2 and the virtual part For small samples, a nonparametric bootstrapping algorithm is used to self-sample them into M×N dimensional samples to construct an equivalent mechanical stirrer, where M is the number of equivalent mechanical stirring positions and N is the number of frequency points in the test band. The expanded real and imaginary parts are then sorted and formed into modulus values. S5. Determination of critical frequency: Perform Anderson-Darling AD test on the modulus of the expanded sample in S4 to determine the critical frequency; S6. Standard Deviation Calculation and Bandwidth Selection: Based on the equivalent mechanical stirring position number M set in S4 and the preset number of self-sampling times m, repeat the small sample expansion operation in S4 and the critical frequency determination process in S5 m times to obtain the standard deviation and bandwidth selection. For each of the candidate stirring bandwidths corresponding to a critical frequency cluster, calculate the standard deviation of each critical frequency cluster. The candidate stirring bandwidth with the smallest standard deviation was selected as the frequency stirring bandwidth of the electrically powered metal cavity. .

[0006] Preferably, in S1, the antenna is at least 1m away from the ground and any metal wall.

[0007] Preferably, in S3, the candidate stirring bandwidth is determined by the following formula: ; in, It is the speed of light, and ; The volume of the electrically large cavity; For frequency.

[0008] Preferably, in S3, any alternative bandwidth All must satisfy the following relation: ; in, For the first Number of frequency points within the available mixing bandwidth.

[0009] Preferably, in S4, the number of frequency points N in the test frequency band and the test frequency band Frequency step interval The matching relationship is: .

[0010] Preferably, in S4, the expanded real and imaginary parts are respectively sorted into real parts. and the virtual part Specifically: ; ; The resulting modulus is: ; The modulus was tested using the AD method of S5 to determine the critical frequency. .

[0011] Preferably, in S6, the number of self-sampling times m is a preset number of self-sampling times based on the nonparametric bootstrapping algorithm, resulting in m sets of critical frequencies, and thus obtaining the critical frequency cluster as follows: The standard deviation of the critical frequency cluster was calculated. .

[0012] Preferably, it also includes a processing progress judgment step, that is, judging by... and The size, if This indicates that all alternative mixing bandwidths have been processed; if Then execute S4 until the condition is met. .

[0013] Therefore, the present invention employs the above-mentioned method for determining the frequency stirring bandwidth of electrically large metal cavities based on small samples, which has the following beneficial effects: 1. Employing a nonparametric bootstrapping algorithm, subsequent analysis can be completed with only a small 1×N-dimensional sample of data obtained from a single test, eliminating the need for additional test runs or large sample collection. This reduces the workload of data collection during testing, avoids test disruptions due to insufficient samples, and saves significant time and manpower costs associated with sample collection. It can still be stably implemented even in scenarios where testing conditions are limited or multiple repeated tests are not possible, significantly improving testing efficiency and scenario adaptability.

[0014] 2. It fully utilizes the equivalence of frequency stirring and mechanical stirring, and directly constructs a virtual mechanical stirrer by expanding the sample size. It does not require the deployment of any physical mechanical stirring device or special function antenna, nor does it rely on the electromagnetic environment provided by a specific test site. It solves the problem that physical stirring equipment cannot be installed in complex structures or small spaces. It does not require structural modification of the cavity under test, and avoids the deployment costs and operational complexity brought by physical equipment. It has good adaptability to electrically large metal cavities of various sizes and structures, and has a wider range of applications.

[0015] 3. A bandwidth selection mechanism that minimizes the standard deviation of the critical frequency cluster is adopted. Through repeated expansion, Anderson-Darling AD test and standard deviation calculation, the optimal solution is dynamically determined from multiple candidate stirring bandwidths, which gets rid of the limitations of traditional bandwidth selection based on experience. It can accurately match the actual electromagnetic characteristics of the electrically large metal cavity, effectively avoiding the problems of underestimating the peak value due to excessive bandwidth and high uncertainty due to insufficient bandwidth. This significantly improves the accuracy and stability of frequency stirring, and the test results can better reflect the true electromagnetic environment distribution of the cavity, providing reliable technical support for subsequent electromagnetic compatibility assessment.

[0016] 4. The test system corresponding to this method only requires a pair of transmit / receive antennas, a vector network analyzer, and coaxial cables to be set up. The equipment composition is simple and does not require complex phase control modules, multi-element array antennas, or special calibration devices. In the test process, the antenna deployment only needs to meet the basic spacing and line-of-sight avoidance requirements. No additional environmental adjustments or multiple rounds of calibration operations are required. The operation logic is coherent and clear, which greatly reduces the professional skills required of operators and avoids the deployment and maintenance costs caused by complex equipment.

[0017] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] Figure 1 A flowchart of a method for determining the frequency stirring bandwidth of an electrically large metal cavity based on a small sample size, provided by the present invention; Figure 2 A schematic diagram of the test setup for a method for determining the frequency stirring bandwidth of an electrically large metal cavity based on a small sample size, provided by the present invention. Figure 3 The diagram illustrates the principle of determining the frequency stirring bandwidth of a method for determining the frequency stirring bandwidth of an electrically large metal cavity based on a small sample size, as provided by this invention.

[0019] Figure Labels 201. Open University Metal Cavity; 202. Vector Network Analyzer; 203. Transmitting Antenna 204. Receiving Antenna 301. Nonparametric bootstrapping; 302. A / D test; 303. Critical frequency clustering; 304. Standard deviation; 305. Addressing; 306. Stirring bandwidth (BW). Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.

[0021] It should be noted that the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, such as a process, method, system, product, or server that includes a series of steps or units, not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product, or device.

[0022] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0023] Existing technologies for evaluating electromagnetic field distribution and determining frequency stirring bandwidth in electrically large metal cavities have several limitations: while full-wave simulation is theoretically accurate, it is computationally intensive and time-consuming when dealing with electrically large sizes and complex internal boundaries, and is easily limited by hardware resources; mechanical stirring schemes are difficult to implement due to the constraints of cavity structure, such as narrow spaces and complex shapes, and some alternatives require complex hardware such as phased array antennas and phase shifters to construct the stirring environment, increasing equipment deployment costs and operational difficulty; the bandwidth selection of traditional frequency stirring techniques often relies on experience or requires a large number of test samples to calculate the cavity quality factor and the number of independent frequency points, but the nonlinear characteristics of the number of modes and mode density make it difficult to accurately solve the bandwidth, and it is easy to have problems such as underestimating the peak value when the bandwidth is too large, or having high uncertainty when the bandwidth is too small. Overall, there is no efficient, accurate and universally applicable scheme for determining frequency stirring bandwidth under small sample conditions, which cannot meet the practical application needs in scenarios with limited test conditions.

[0024] Based on the above analysis, this invention is designed. (See appendix.) Figure 1-3 A method for determining the frequency stirring bandwidth of an electrically large metal cavity based on a small sample size includes the following steps: S1. Configure the test system and determine the test parameters: Set the transmitting antenna... and receiving antenna The antenna is placed inside the metal cavity of the open university, while the vector network analyzer is placed outside the cavity. The antenna maintains a preset distance from the ground and the metal wall, avoiding line-of-sight transmission. The transmitting antenna... Receiving antenna Connect the two ports of the vector network analyzer using coaxial cables and determine the test frequency band. Frequency step interval ; In S1, the antenna is at least 1 meter away from the ground and any metal wall. This effectively avoids near-field coupling between the antenna and the cavity boundary, reducing the impact of wall reflections and ground spurious signals on the transmission coefficient. The collected interference ensures the transmitting antenna With receiving antenna The stability and purity of signal transmission between them; at the same time, the spacing requirement ensures that the antenna is in the far-field region that meets the test requirements, guaranteeing the acquisition of the 1×N dimensional real part. and the virtual part Small sample sizes accurately reflect the actual distribution characteristics of the electromagnetic field within the electrically powered metal cavity, improving the accuracy of determining the frequency stirring bandwidth (BW). Furthermore, the standardized spacing ensures good standardization and repeatability of the testing process. Regardless of the size or structure of the electrically powered metal cavity, standardized antenna deployment can reduce system errors, guaranteeing the universality of the method and the consistency of the test results.

[0025] For details, see Figure 2 As shown, the transmitting antenna 203 and receiving antenna 204 is placed inside the Open University metal cavity 201, and the vector network analyzer 202 is placed outside the Open University metal cavity 201. Inside the Open University metal cavity 201, the antenna is at least 1m away from the ground and any metal wall, and the transmitting antenna is avoided. 203 and receiving antenna 204 forms line-of-sight transmission, transmitting antenna 203 and receiving antenna 204 is connected to the two ports of the vector network analyzer 202 via coaxial cables.

[0026] S2. Calibration and Data Acquisition: Based on the test system configured in S1 and the determined test frequency band. Frequency step interval Calibrate the vector network analyzer and measure the transmitting antenna. With receiving antenna Transmission coefficient between , corresponding to each frequency point Separate the real and imaginary parts, and store them as 1×N dimensional real parts respectively. and the virtual part .

[0027] S3. Determine the alternative stirring bandwidth: based on the electrically large metal cavity volume obtained in S1. and the speed of light The constant value, combined with the frequency within the test band Calculations yielded One alternative stirring bandwidth that satisfies the frequency point number relationship , , ..., ; In S3, the candidate stirring bandwidth is determined by the following formula: ; in, It is the speed of light, and ; The volume of the electrically large cavity; For frequency.

[0028] In S3, any alternative bandwidth All must satisfy the following relation: ; in, For the first Number of frequency points within the available mixing bandwidth.

[0029] S4. Small sample size expansion: Select one of the bandwidth values ​​from S3. Based on the 1×N dimensional real part collected and stored by S2 and the virtual part For small samples, a nonparametric bootstrapping algorithm is used to self-sample them into M×N dimensional samples to construct an equivalent mechanical stirrer, where M is the number of equivalent mechanical stirring positions and N is the number of frequency points in the test band. The expanded real and imaginary parts are then sorted and formed into modulus values. The principle of the nonparametric bootstrapping algorithm is based on the equivalence of frequency stirring and mechanical stirring in an electrically large metal cavity, using the real part of the 1×N dimensional transfer coefficient obtained from a single test. and the virtual part Based on a small sample size, the samples are expanded to M×N dimensions through repeated self-sampling. The real and imaginary parts of the expanded samples are then organized into corresponding forms and synthesized into complex modulus values. By constructing a virtual equivalent mechanical stirrer, test scenarios with multiple stirring positions can be simulated without relying on physical mechanical stirring devices or complex hardware. This overcomes the limitation of small sample data on analytical accuracy, ensures complete coverage of the electromagnetic field characteristics of the cavity by the sample data, and improves the accuracy and universality of determining the frequency stirring bandwidth under small sample conditions.

[0030] In S4, the number of frequency points N in the test frequency band and the test frequency band Frequency step interval The matching relationship is: .

[0031] In S4, the expanded real and imaginary parts are reorganized into real parts respectively. and the virtual part Specifically: ; ; get Its modulus is: .

[0032] S5. Critical Frequency Determination: The modulus of the expanded sample from S4 is subjected to the Anderson-Darling AD test to determine the critical frequency; the modulus is then tested using the AD method in S5 to determine the critical frequency. .

[0033] The AD test is based on the goodness-of-fit test logic, and it tests the complex form of the M×N-dimensional samples obtained by expanding S4 using a nonparametric bootstrapping algorithm. The modulus value, i.e. the actual amplitude of the signal, is used to test whether its distribution conforms to the preset statistical distribution characteristics. The critical frequency, i.e. the frequency node where the distribution characteristics change significantly, is determined by quantifying the deviation between the sample modulus value and the theoretical distribution. The amplitude information of the expanded sample can be transformed into a quantifiable critical frequency index, providing key basic data for the subsequent construction of critical frequency clusters and standard deviation calculation. Compared with traditional distribution testing methods, the AD test is more sensitive to the data at the tail of the sample and can accurately capture the abrupt change points of the amplitude distribution of the electromagnetic field signal of the electrically large metal cavity, ensuring the accuracy and stability of the critical frequency. This provides reliable core parameter support for the subsequent screening of the optimal frequency stirring bandwidth with the smallest standard deviation, ensuring the scientific nature and accuracy of the frequency stirring bandwidth determination.

[0034] S6. Standard Deviation Calculation and Bandwidth Selection: Based on the equivalent mechanical stirring position number M set in S4 and the preset number of self-sampling times m, repeat the small sample expansion operation in S4 and the critical frequency determination process in S5 m times to obtain the standard deviation and bandwidth selection. For each of the candidate stirring bandwidths corresponding to a critical frequency cluster, calculate the standard deviation of each critical frequency cluster. The candidate stirring bandwidth with the smallest standard deviation was selected as the frequency stirring bandwidth of the electrically powered metal cavity. ; In S6, the number of self-sampling times m is a preset number based on the nonparametric bootstrapping algorithm, resulting in m sets of critical frequencies, and thus the critical frequency cluster is obtained. The standard deviation of the critical frequency cluster was calculated. .

[0035] It also includes a processing progress judgment step, that is, judging by... and The size, if This indicates that all alternative mixing bandwidths have been processed; if Then execute S4 until the condition is met. .

[0036] Specifically, the technical principles of this invention are described in [reference needed]. Figure 3 As shown, based on the transmitting antenna 203 and receiving antenna The test with 204 yielded the real part of 1×N samples. and the virtual part Then, a nonparametric bootstrapping algorithm (301) is performed, using the nonparametric bootstrapping algorithm to extract the real parts of the 1×N small samples. and the virtual part Each sample is self-sampled into M×N samples; then, the modulus of the M×N samples is subjected to an A / D test 302 to obtain the critical frequencies; then, the above nonparametric bootstrapping process 301 is repeated to obtain the critical frequency cluster 303, and the standard deviation 304 of the critical frequency cluster 303 is calculated; finally, the minimum standard deviation is addressed 305, and the minimum standard deviation is selected. One alternative mixing bandwidth , , ..., The stirring bandwidth corresponding to the value with the smaller standard deviation is used as the stirring bandwidth BW306 for frequency stirring.

[0037] In summary, this invention solves the problems in the evaluation of electromagnetic field distribution in electrically powered metal cavities, such as aircraft cabins. Traditional full-wave simulation is computationally intensive, time-consuming, and limited by hardware resources. Mechanical stirring or source stirring schemes are difficult to adapt to special cavity structures. In frequency stirring technology, the stirring bandwidth depends on experience, requires a large number of test samples, and is prone to underestimating the peak electromagnetic field due to excessive bandwidth or increasing uncertainty due to insufficient bandwidth. This invention achieves the goal of scientifically and accurately selecting the optimal frequency stirring bandwidth without complex hardware or a large number of samples.

[0038] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for determining the frequency stirring bandwidth of an electrically large metal cavity based on a small sample size, characterized in that: Includes the following steps: S1. Configure the test system and determine the test parameters: Set the transmitting antenna... and receiving antenna The antenna is placed inside the metal cavity of the open university, while the vector network analyzer is placed outside the cavity. The antenna maintains a preset distance from the ground and the metal wall, avoiding line-of-sight transmission. The transmitting antenna... Receiving antenna Connect the two ports of the vector network analyzer using coaxial cables and determine the test frequency band. Frequency step interval ; S2. Calibration and Data Acquisition: Based on the test system configured in S1 and the determined test frequency band. Frequency step interval Calibrate the vector network analyzer and measure the transmitting antenna. With receiving antenna Transmission coefficient between , corresponding to each frequency point Separate the real and imaginary parts, and store them as 1×N dimensional real parts respectively. and the virtual part ; S3. Determine the alternative stirring bandwidth: based on the electrically large metal cavity volume obtained in S1. and the speed of light The constant value, combined with the frequency within the test band Calculations yielded One alternative stirring bandwidth that satisfies the frequency point number relationship , , ..., ; S4. Small sample size expansion: Select one of the bandwidth values ​​from S3. Based on the 1×N dimensional real part collected and stored by S2 and the virtual part For small samples, a nonparametric bootstrapping algorithm is used to self-sample them into M×N dimensional samples to construct an equivalent mechanical stirrer, where M is the number of equivalent mechanical stirring positions and N is the number of frequency points in the test band. The expanded real and imaginary parts are then sorted and formed into modulus values. S5. Determination of critical frequency: Perform Anderson-Darling AD test on the modulus of the expanded sample in S4 to determine the critical frequency; S6. Standard Deviation Calculation and Bandwidth Selection: Based on the equivalent mechanical stirring position number M set in S4 and the preset number of self-sampling times m, repeat the small sample expansion operation in S4 and the critical frequency determination process in S5 m times to obtain the standard deviation and bandwidth selection. For each of the candidate stirring bandwidths corresponding to a critical frequency cluster, calculate the standard deviation of each critical frequency cluster. The candidate stirring bandwidth with the smallest standard deviation was selected as the frequency stirring bandwidth of the electrically powered metal cavity. .

2. The method for determining the frequency stirring bandwidth of an electrically large metal cavity based on a small sample size, as described in claim 1, is characterized in that: In S1, the antenna is at least 1m away from the ground and any metal wall.

3. The method for determining the frequency stirring bandwidth of an electrically large metal cavity based on a small sample size, as described in claim 1, is characterized in that: In S3, the candidate stirring bandwidth is determined by the following formula: ； in, It is the speed of light, and ; The volume of the electrically large cavity; For frequency.

4. The method for determining the frequency stirring bandwidth of an electrically large metal cavity based on a small sample size, as described in claim 3, is characterized in that: In S3, any alternative bandwidth All must satisfy the following relation: ； in, For the first Number of frequency points within the available mixing bandwidth.

5. The method for determining the frequency stirring bandwidth of an electrically large metal cavity based on a small sample size, as described in claim 4, is characterized in that: In S4, the number of frequency points N in the test frequency band and the test frequency band Frequency step interval The matching relationship is: 。 6. The method for determining the frequency stirring bandwidth of an electrically large metal cavity based on a small sample size, as described in claim 5, is characterized in that: In S4, the expanded real and imaginary parts are reorganized into real parts respectively. and the virtual part Specifically: ； ； The resulting modulus is: ; The modulus was tested using the AD method of S5 to determine the critical frequency. .

7. The method for determining the frequency stirring bandwidth of an electrically large metal cavity based on a small sample size, as described in claim 6, is characterized in that: In S6, the number of self-sampling times m is a preset number based on the nonparametric bootstrapping algorithm, resulting in m sets of critical frequencies, and thus the critical frequency cluster is obtained. The standard deviation of the critical frequency cluster was calculated. .

8. The method for determining the frequency stirring bandwidth of an electrically large metal cavity based on a small sample size, as described in claim 7, is characterized in that: It also includes a processing progress judgment step, that is, judging by... and The size, if This indicates that all alternative mixing bandwidths have been processed; if Then execute S4 until the condition is met. .

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