Feature mode tracking method based on feature vector correlation

Abstract

The invention relates to a characteristic mode tracking method based on characteristic vector correlation, which belongs to the technical field of antennas and comprises a pre-processing part and a post-processing part. The pre-processing filtering method is used for different radiation structures, and only a mode which has a remarkable influence on the antenna performance is reserved; the post-processing sequentially solves the problem of mode exchange and the problem of mode degeneration. In the stage of solving the mode exchange problem, tracking curve intersections are recognized, variance criteria are executed to judge whether the intersections have the mode exchange problem or not, and then feature vector correlation is utilized for rematching; in the stage of solving the mode degeneracy problem, firstly, a degeneracy phenomenon mode pair is recognized, an energy criterion is executed for judgment, then, the degeneracy mode pair is corrected, finally, a tracking curve is optimized, and the purpose of smoothing the tracking curve is achieved. Compared with a traditional method, the mode number is reduced in the pre-processing stage, the subsequent calculation time is saved, the mode tracking error problem is classified and processed in the post-processing stage, and the accuracy of the tracking result is guaranteed.

Description

Technical Field

[0001] The invention belongs to the technical field of antennas and relates to a characteristic mode tracking method based on characteristic vector correlation. Background Art

[0002] Antennas are important devices for mobile communications, and the rapid development of the communications field has increased the requirements for their performance. Traditional antenna design methods are not only time-consuming and laborious, but in some cases they cannot even meet performance indicators. Different from traditional antenna design methods, the characteristic mode theory is based on the method of moments, has the advantages of both numerical and analytical methods, and is widely used in the analysis of electromagnetic radiation and scattering problems. Characteristic mode analysis obtains the impedance matrix of the antenna to be tested through the method of moments, and establishes a generalized eigenvalue equation based on the impedance matrix to obtain the characteristic mode and eigenvector. For each sampling frequency point, there is a corresponding eigenvalue, and each eigenvalue has its corresponding mode. It is necessary to associate the eigenvalues ​​in these discrete frequency points through the correlation between each mode point, and connect the eigenvalues ​​belonging to the same characteristic mode at each frequency point in series with a smooth curve to form a complete mode curve. Accurate characteristic mode tracking is the prerequisite for subsequent characteristic mode analysis of the antenna structure, which is of great significance for the accurate design of the antenna structure.

[0003] When performing characteristic mode tracking, there are two common types of mode tracking errors. The first is the mode exchange problem, which is mainly caused by fuzzy correlation. It usually occurs when the mode at the current frequency point is highly correlated with two or more modes at subsequent frequencies, or when the correlation with all subsequent modes is insufficient, and an erroneous crossing phenomenon occurs between the mode curves. The nature of mode exchange is related to the sampling frequency spacing and the solution accuracy. The second is the mode degeneracy problem. When the eigenvalues ​​of two or more different modes at a certain frequency are close to each other, they may become physically difficult to distinguish, resulting in mode curves that should actually cross each other, but do not cross during mode tracking. At the same time, when the target structure is complex or the mesh is fine, it will lead to a significant increase in the amount of calculation and serious tracking time consumption.

[0004] In order to deal with these problems, domestic and foreign scholars have proposed three types of characteristic mode tracking algorithms. The first type is based on the far-field correlation method, which uses the characteristics of the characteristic mode radiation far field being relatively stable and mutually orthogonal in the far field to track the mode. For example, the literature "Miers Z, Lau B K. Wideband characteristic mode tracking utilizing far-field patterns [J]. IEEE Antennas and Wireless Propagation Letters, 2015, 14: 1658-1661." proposed a characteristic mode tracking method for complex structures through far-field analysis. For a given frequency, the far-field radiation patterns of the electric field and magnetic field are mutually orthogonal. Using the orthogonal characteristics, each mode has no correlation with other modes and has good stability. The far-field correlation method can solve the problems of mode exchange and mode degeneration very well, but this method needs to calculate the far-field characteristics of the antenna before mode tracking, which makes the calculation complicated. The second method is based on the characteristic current correlation method, which uses the orthogonality of the characteristic vector to perform pattern matching, such as the literature "Raines BD, Rojas R G. Wideband characteristic mode tracking [J]. IEEE Transactions on Antennas and Propagation, 2021, 60 (7): 3537-3541." Based on this method, two arbitration methods are proposed to solve the correlation ambiguity problem. One is to use the frequency adaptive tracking method. When the correlation of the fuzzy characteristic vector is small, the frequency interval is reduced and the correlation is recalculated; the other is to compare the correlation coefficients. When the frequency interval is small, the mode pair with a large correlation coefficient is selected for matching. Although this method is more accurate, reducing the frequency interval will increase the amount of calculation, and the mode degeneracy problem cannot be well solved. The third type of method is based on the bounded linear eigenvector correlation method, which performs pattern matching by calculating the eigenvector correlation. This method is the simplest, such as the document "Yang Z, Su D, Li Y, et al. An improved method for tracking of characteristic modes [C]. 2016 IEEE International Conference on Computational Electromagnetics (ICCEM), Guangzhou, China: IEEE, 2016: 103-105." Based on this method, the existing tracking algorithm is improved by using eigenvalue estimation and reducing the correlation threshold.This eigenvalue estimation method is used to eliminate eigenvalues ​​and corresponding eigenvectors whose eigenvalues ​​are much larger than 10 times the estimated value, and to limit the number of modes that need to be correlated to reduce the computational complexity. However, the correlation between adjacent frequency points of all modes within the estimated value range still needs to be calculated, and the amount of calculation is still large. At the same time, lowering the threshold does not substantially solve the problems of mode exchange and mode degeneration. Summary of the invention

[0005] In view of this, the purpose of the present invention is to propose a characteristic mode pattern tracking method based on characteristic vector correlation, so as to solve the problems of mode exchange and mode degeneration as well as the problem of long tracking time existing in the existing characteristic mode pattern tracking.

[0006] The present invention is divided into two parts, pre-processing and post-processing. 1) In the pre-processing part, according to different radiation structures, the eigenvalues ​​at the same frequency are arranged in ascending order from small to large. The order of arrangement of the eigenvalues ​​is the mode order, and the eigenvalues ​​that have a significant impact on the antenna performance are screened out, and the eigenvalues ​​corresponding to the modes that are difficult to excite are filtered out, thereby shortening the subsequent calculation time. The number of eigenvalues ​​screened out changes according to the complexity of the antenna structure. According to the screened eigenvalues, the corresponding eigenvectors are found, and the eigenvectors are normalized to eliminate the influence of the eigenvector amplitude. The vector direction remains unchanged, thereby improving the accuracy and stability of the correlation calculation and simplifying the subsequent analysis and processing steps. 2) In the post-processing part, the mode exchange problem is first processed, and then the mode degeneration problem is solved. The stage of solving the mode exchange problem is divided into three steps: identifying the mode exchange problem, judging the identification mode exchange problem, and correcting the mode exchange problem. First, the frequency of the intersection of the eigenvalue curve is identified, and the variance criterion is used to determine whether the intersection is a mode exchange problem. Finally, for the mode pairs with mode exchange problems, the correlation calculated by the Pearson correlation coefficient is used to re-match. The stage of solving the mode degeneration problem: It is divided into four steps: identifying the mode degeneration problem, judging the mode degeneration problem, correcting the mode degeneration problem, and optimizing the mode tracking curve. First, the mode pairs that meet the mode degeneration phenomenon are screened out, and then the energy criterion is used to judge whether it is a mode degeneration problem. If the criterion conditions are met, the mode pairs are exchanged to correct the mode degeneration problem, and finally the optimization process is performed to obtain a smooth mode tracking curve. Compared with the traditional method, the present invention reduces the number of mode tracking in the pre-processing stage, and only performs correlation calculations on mode pairs with mode exchange problems, which greatly shortens the mode tracking and calculation time. In the subsequent processing, the mode exchange problem and the mode degeneration problem are classified and processed, and the normalized eigenvector is used to participate in the calculation to avoid the influence of the eigenvector amplitude, which well guarantees the accuracy of the tracking results and has good application value.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] 1. A characteristic mode tracking method based on characteristic vector correlation comprises the following steps:

[0009] Pre-processing stage: screening tracking patterns and normalizing feature vectors;

[0010] Step 1: Use electromagnetic simulation software to model and simulate the target structure, obtain the impedance matrix of the target structure surface, establish a generalized eigenvalue equation, and obtain the eigenvalue λ and eigenvector J of the target structure;

[0011] Step 2: Arrange the eigenvalues ​​at each sampling frequency in ascending order from small to large, and set the eigenvalue threshold λ according to the complexity of the antenna. max , filter out the values ​​less than the eigenvalue threshold λ max The eigenvalues ​​are used for processing in subsequent steps; the eigenvalues ​​at each sampling frequency point are marked in ascending order as the mode arrangement order;

[0012] Step 3: Find the corresponding eigenvector according to the selected eigenvalues; in order to eliminate the influence of the amplitude between vectors and make each eigenvector have the same weight in the calculation, the eigenvector is normalized to improve the accuracy and stability of the correlation calculation;

[0013] Post-processing stage: the stage of solving the mode exchange problem and the stage of solving the mode degeneration problem;

[0014] Solving the mode switching problem stage:

[0015] Step 4: There are three work processes to solve the mode exchange problem: identifying the mode exchange problem, judging the mode exchange problem, and correcting the mode exchange problem. The process of identifying the mode exchange problem is: traversing all sampling frequencies, identifying the intersections of the tracking curves, recording the mode pairs and sampling frequencies with intersections, and storing them in the mode intersection table; the process of judging the mode exchange problem is: executing the variance criterion on the mode pairs in the mode intersection table. If the criterion conditions are met, it is judged as a mode exchange problem and stored in the exchange problem table; the process of correcting the mode exchange problem is: in the exchange problem table, starting from the minimum sampling frequency, the Pearson correlation coefficients of adjacent frequency points of all modes are calculated, and the mode pairs with the largest correlation coefficients are re-matched;

[0016] Solving the problem of model degeneration stage:

[0017] Step 5: There are four work processes to solve the mode degeneration problem: identifying the mode degeneration problem, judging the mode degeneration problem, correcting the mode degeneration problem, and optimizing the mode tracking curve; the process of identifying the mode exchange problem is: traversing all sampling frequencies, identifying the mode that meets the mode degeneration phenomenon, recording the identified degenerate mode pairs and sampling frequencies, and storing them in the degenerate phenomenon table; the process of judging the mode exchange problem is: executing energy judgment on the mode pairs in the degenerate phenomenon table, if the judgment conditions are met, it is judged as a mode degeneration problem and stored in the degenerate problem table; the process of correcting the mode exchange problem is: in the degenerate problem table, the eigenvalues ​​and corresponding eigenvectors of the degenerate mode pairs are exchanged for correction processing; the process of optimizing the mode tracking curve is: smoothing the eigenvalue curve by estimating the eigenvalue method to obtain the final smooth mode tracking curve;

[0018] Furthermore, in step 1, modeling and simulation analysis are performed in electromagnetic simulation software to obtain the impedance matrix [Z] of the target structure. The impedance matrix [Z] can be expressed as:

[0019] [Z]=[R]+j[X] (1) Where [R] represents the real part of the impedance matrix, and [X] represents the imaginary part of the impedance matrix, which can be obtained by the following formula:

[0020]

[0021] Where [R] and [X] are both symmetric matrices, and [R] is a semi-positive definite matrix; [Z]* is the conjugate matrix of the impedance matrix [Z];

[0022] Then according to the generalized eigenvalue equation of characteristic mode theory:

[0023] [X] i [J] i =λ i [R] i [J] i (4)

[0024] i represents the sampling frequency point number, [R] i and [X] i is the sampling frequency f i The real and imaginary parts of the impedance matrix under [J] i and λ i is the sampling frequency f i The eigenvectors and eigenvalues ​​of i and [X] i The eigenvalue and corresponding eigenvector at each sampling frequency can be calculated.

[0025] Furthermore, in step 2, the eigenvalue λ at each sampling frequency point is iArrange in ascending order from small to large, identify the order of eigenvalues ​​at the initial sampling frequency as the mode order, and select the eigenvalue at the initial sampling frequency point where the absolute value |λ1| is less than the eigenvalue threshold λ max The mode is recorded as p, and λ max Set to 300; For complex target structures, usually more modes need to be tracked. A fixed threshold may result in insufficient number of modes to be tracked, leading to incorrect mode tracking. Although increasing the threshold can alleviate the above problems, it will increase unnecessary calculations. Considering various factors, a reserved value of q can be set. Then the total number of modes tracked at each frequency point is p+q. The value of q is related to the frequency point f i The total number of eigenvalues ​​is the frequency point f i The total number of patterns size(λ) in the target structure i ), usually q is set to size(λ i ) / 200; the subsequent frequency point eigenvalue patterns are arranged in ascending order to match the pattern at the initial sampling frequency.

[0026] Further, in step 3, the corresponding eigenvector is found according to the required eigenvalues ​​screened out;

[0027] In order to avoid the influence of the eigenvector amplitude on the correlation calculation and improve the accuracy and stability of the calculation, the eigenvector is normalized:

[0028]

[0029] Among them, the eigenvector [J m ] i At sampling frequency f i The eigenvector corresponding to the mode m, [J m ] i =(x1,x2,…x n ), x1,x2,…x n is the characteristic vector [J m ] i All elements in [J m ]' i is the normalized feature vector;

[0030] Furthermore, step 4 specifically includes three processes: identifying the mode exchange problem, judging the mode exchange problem, and correcting the mode exchange problem.

[0031] Step 4.1: Identify the mode exchange problem: traverse all sampling frequency points, calculate the difference of the eigenvalues ​​of any two modes at all adjacent frequency points, and find the mode pair whose difference between the current frequency point and the previous frequency point has the opposite sign or one of the difference values ​​is zero. The judgment criteria are as follows:

[0032]

[0033] is the sampling frequency f i The eigenvalue difference between mode m and mode n is calculated. If there is a mode pair whose eigenvalue difference satisfies (6) at adjacent frequency points, then there is an intersection point in the eigenvalue curve at that point. Record the mode pair m, n and sampling frequency point f where the intersection point exists. i , and store them in the pattern intersection table, with one row storing one intersection point;

[0034] Step 4.2: Determine the mode exchange problem: In the mode cross table, perform the variance criterion on each row;

[0035] First calculate the rate of change of the eigenvalue:

[0036]

[0037] is the frequency f i The eigenvalue and frequency f of mode j at i-1 The change rate between the eigenvalues ​​of mode k at the intersection table is calculated by calculating the eigenvalue change rate of mode pairs m and n in the mode cross table, and we can get

[0038] The variance of the obtained eigenvalue change rate is calculated, and the change rate The average value of Will Calculate the variance and get the following formula:

[0039]

[0040] The rate of change can be calculated The variance of var mm , similarly, we can calculate The variance of var nn , The variance of var mn , The variance of var nm ;

[0041] By calculating the variance of the rate of change of the eigenvalue curve, the larger the variance, the more dispersed the data is, and the mode exchange problem occurs. The variance of the rate of change of the curve is greater than the variance of the normal curve rate of change. The mode exchange error problem can be judged based on the variance of the curve rate of change; for the variance var mm , var mn , var nn With var nm Implement the variance criterion:

[0042]

[0043] If the mode pair in the mode cross table satisfies (9), it is determined to be a mode exchange error problem. The sampling frequency points and mode pairs with mode exchange problems are recorded and stored in the exchange problem table, with each row representing a mode exchange error problem.

[0044] Step 4.3: Correct the mode switching problem: Starting from the minimum frequency point where the mode switching problem occurs, calculate the frequency point f for all modes in the switching problem table one by one i Each mode and frequency f i+1 The Pearson correlation coefficient of all modes is calculated as follows:

[0045]

[0046] Cov([J m ] i ',[J n ] i ') represents the normalized eigenvector [J m ] i 'With [J n ] i 'The covariance, Var[J m ] i ' represents the normalized eigenvector variance [J m ] i 'The variance, r mn is the correlation coefficient between mode m and mode n;

[0047] The absolute value of the correlation coefficient will be the maximum value max|r mn |The modes m and n are matched together, at the frequency point f i+1 The matched mode does not participate in the frequency point f i The correlation calculation of the subsequent mode at the frequency point f i+1 The same mode is incorrectly matched to the frequency point f i Two or more modes at a time.

[0048] Furthermore, step 5 specifically includes four processes: identifying the pattern degeneration problem, judging the pattern degeneration problem, correcting the pattern degeneration problem, and optimizing the pattern tracking curve.

[0049] Step 5.1: Identify the pattern degeneration problem: The eigenvalue difference between the two patterns at the degenerate frequency point should be less than the eigenvalue difference between the two patterns at the previous and next frequency points. Traverse all sampling frequency points and identify the pattern that meets the pattern degeneration phenomenon. That is, perform the following judgment on all patterns at adjacent frequency points:

[0050]

[0051] If the difference of the eigenvalues ​​of the existing mode pairs at adjacent frequency points satisfies (11), it is preliminarily identified as a mode degeneration problem, and the sampling frequency points f where the preliminarily identified mode degeneration phenomenon exists are recorded. i and mode pairs j and k, and store them in the degenerate phenomenon table, one row stores a problem point;

[0052] Step 5.2: Determine the mode degeneration problem: In the degeneration phenomenon table, perform energy criterion on each row to determine whether a mode exchange problem occurs;

[0053] First, the calculation mode stores electrical energy, [X] e with [X] m The matrix forms representing the electric energy and magnetic energy storage operators, respectively, are related to the imaginary part of the impedance matrix [X] as follows:

[0054]

[0055] Where ω=2πf, ω is the angular frequency, f is the frequency, and further we can get:

[0056]

[0057] Mode to store electrical energy:

[0058]

[0059] For mode j at frequency f i The electrical energy stored at j ] i ' is the sampling frequency f i The eigenvector corresponding to mode j, [J j ] i ' T For [J j ] i ', the stored energy of mode k can be obtained in the same way

[0060] Mode coupling power:

[0061]

[0062] For mode j and mode k at frequency f i The coupled electric energy at

[0063] Energy criteria are implemented for mode storage energy and inter-mode coupling energy:

[0064]

[0065] If the mode pair in the degeneracy phenomenon table satisfies (16), it is determined to be a mode degeneracy problem. The sampling frequency points and mode pairs with mode degeneracy problems are recorded and stored in the degeneracy problem table. Each row is a mode degeneracy error problem.

[0066] Step 5.3: Correcting the mode degeneration problem: Correct each row in the degeneration problem table, and perform mode exchange processing on each mode pair starting from the sampling frequency point of the row to obtain a tracking result curve after correcting the mode degeneration problem. This curve may have a smoothness problem at the mode degeneration problem, which needs further optimization processing;

[0067] Step 5.4: Optimize the tracking curve of the model: Multiply both sides of the generalized eigenvalue equation (4) by [J] i T We can get (17), [J] i T for [J] i The transposed matrix of

[0068] [J] i T [X] i [J] i =λ i [J] i T [R] i [J] i (17) From this we can obtain:

[0069]

[0070] The eigenvectors of adjacent frequency points change very little. It is known that f i The imaginary and real parts of the impedance matrix at can be calculated according to f i-1 A certain mode eigenvector at f is estimated i Eigenvalues ​​in the same mode:

[0071]

[0072] For mode p according to f i-1 The eigenvector at f is estimated i The eigenvalue at the point where the mode degeneracy problem occurs i , according to the previous frequency f i-1 and the next frequency f i+1 The eigenvector of the estimated frequency point f i The eigenvalue at the point, taking the mean of the two values, we can get the frequency point f i The eigenvalues ​​used at the position are used to achieve the purpose of smoothing the curve. The smoothing process will not affect the accuracy of the result.

[0073] The beneficial effects of the present invention are as follows: the present invention proposes a characteristic mode tracking method based on the correlation of characteristic vectors. The core of the invention is to classify and solve two types of mode tracking error problems to obtain correct mode tracking. By screening out the required eigenvalues ​​in pre-processing, the number of eigenvalues ​​is related to the complexity of the antenna structure, which can reduce the number of mode tracking and shorten the tracking time. In the subsequent part, a three-step process of identifying the mode exchange problem, judging the mode exchange problem, and correcting the mode exchange problem is proposed for the mode exchange problem. A four-step process of identifying the mode degeneration problem, judging the mode degeneration problem, correcting the mode degeneration problem, and optimizing the mode tracking curve is proposed for the mode degeneration problem. It can solve the two common mode tracking error problems well, and the number of correlation coefficient calculations is also greatly reduced, shortening the calculation time, and finally smoothing the tracking curve. The invention can accurately track the mode while taking into account the problem of time-consuming calculation, and has good application value.

[0074] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0076] Figure 1 The overall process of pattern tracking;

[0077] Figure 2 Flowchart for solving mode switching problem for post-processing;

[0078] Figure 3 Flowchart for post-processing solution mode degeneration problem;

[0079] Figure 4 Two classic antenna structures, (a) is a rectangular patch antenna, and (b) is a fractal antenna;

[0080] Figure 5 The characteristic angle curve diagram obtained by tracing the rectangular patch using the traditional method;

[0081] Figure 6 Current distributions of mode 1 and mode 10 at 4.04 GHz, 4.2 GHz, 4.36 GHz, and 4.52 GHz;

[0082] Figure 7It is a characteristic angle curve diagram obtained after the rectangular patch is tracked by the method of the present invention;

[0083] Figure 8 This is the characteristic angle curve obtained by tracing the fractal antenna using the traditional method;

[0084] Fig. 9 It is a characteristic angle curve diagram obtained after the fractal antenna is tracked by the method of the present invention;

[0085] Fig.10 This is the current distribution of the fractal antenna near 2.49 GHz. DETAILED DESCRIPTION

[0086] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0087] It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and thus the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0088] In the following description, numerous details are discussed to provide a more thorough explanation of the embodiments of the present invention. However, it is obvious to those skilled in the art that the embodiments of the present invention can be implemented without these specific details. In other embodiments, well-known structures and devices are shown in the form of block diagrams rather than in detail to avoid making the embodiments of the present invention difficult to understand.

[0089] like Figure 1 As shown in FIG. 1 , the present invention proposes a method for tracking a characteristic mode based on the correlation of characteristic vectors. The core of the method is to classify and process the problem of pattern tracking errors. The present invention is divided into five steps in total, steps 1-3 belong to the pre-processing stage, and steps 4-5 belong to the post-processing stage. Figure 2 and Figure 3 As shown, the specific steps are as follows:

[0090] Step 1: Use electromagnetic simulation software to model and simulate the target structure, obtain the impedance matrix of the target structure surface, establish a generalized eigenvalue equation, and obtain the eigenvalue λ and eigenvector J of the target structure;

[0091] Step 2: Arrange the eigenvalues ​​at each sampling frequency in ascending order from small to large, and set the eigenvalue threshold λ according to the complexity of the antenna. max , filter out the values ​​less than the eigenvalue threshold λ max The eigenvalues ​​are used for processing in subsequent steps; the eigenvalues ​​at each sampling frequency point are marked in ascending order as the mode arrangement order;

[0092] Step 3: Find the corresponding eigenvector according to the selected eigenvalues; in order to eliminate the influence of the amplitude between vectors and make each eigenvector have the same weight in the calculation, the eigenvector is normalized to improve the accuracy and stability of the correlation calculation;

[0093] Step 4: Solve the mode exchange problem in three workflows: identify the mode exchange problem, judge the mode exchange problem, and correct the mode exchange problem;

[0094] The process of identifying the mode exchange problem is as follows: traverse all sampling frequencies, identify the intersections of the tracking curves, record the mode pairs and sampling frequencies with the intersections, and store them in the mode cross table; the process of judging the mode exchange problem is as follows: perform the variance criterion on the mode pairs in the mode cross table. If the criterion conditions are met, it is determined to be a mode exchange problem and stored in the exchange problem table; the process of correcting the mode exchange problem is as follows: in the exchange problem table, starting from the minimum sampling frequency, calculate the Pearson correlation coefficient of adjacent frequency points for all modes, and rematch the mode pairs with the largest correlation coefficient;

[0095] Step 5: There are four workflows to solve the pattern degeneration problem: identifying the pattern degeneration problem, judging the pattern degeneration problem, correcting the pattern degeneration problem, and optimizing the pattern degeneration problem;

[0096] The process of identifying the mode exchange problem is: traverse all sampling frequencies, identify the mode that meets the mode degeneration phenomenon, record the identified degenerate mode pairs and sampling frequencies, and store them in the degenerate phenomenon table; the process of judging the mode exchange problem is: perform energy judgment on the mode pairs in the degenerate phenomenon table. If the judgment conditions are met, it is judged as a mode degeneration problem and stored in the degenerate problem table; the process of correcting the mode exchange problem is: in the degenerate problem table, exchange the eigenvalues ​​and corresponding eigenvectors of the degenerate mode pairs for correction processing; the process of optimizing the mode tracking curve is: smooth the eigenvalue curve by estimating the eigenvalue method to obtain the final smooth mode tracking curve;

[0097] The characteristic mode tracking method based on characteristic vector correlation proposed in the present invention mainly solves the characteristic value and characteristic vector in step 1, and the specific contents are as follows:

[0098] Modeling and simulation analysis are performed in electromagnetic simulation software to obtain the impedance matrix [Z] of the target structure. The impedance matrix [Z] can be expressed as:

[0099] [Z] = [R] + j [X] (20) where [R] represents the real part of the impedance matrix and [X] represents the imaginary part of the impedance matrix, which can be obtained by the following formula:

[0100]

[0101] Where [R] and [X] are both symmetric matrices, and [R] is a semi-positive definite matrix; [Z]* is the conjugate matrix of the impedance matrix [Z];

[0102] Then according to the generalized eigenvalue equation of characteristic mode theory:

[0103] [X] i [J] i =λ i [R] i [J] i (twenty three)

[0104] i represents the sampling frequency point number, [R] i and [X] i is the sampling frequency f i The real and imaginary parts of the impedance matrix under [J] i and λ i is the sampling frequency f i The eigenvectors and eigenvalues ​​of i and [X] i The eigenvalue and corresponding eigenvector at each sampling frequency can be calculated. Taking the eigenvalue and eigenvector as an example, at the sampling frequency f i There will be n eigenvalues ​​and n eigenvectors of dimension n×1, where n is the total number of modes of the antenna being solved under the current segmentation accuracy.

[0105] The characteristic mode tracking method based on characteristic vector correlation proposed in the present invention, step 2 is mainly to screen the required characteristic values, and the specific contents are as follows:

[0106] The eigenvalue λ at each sampling frequency point i Arrange in ascending order from small to large, identify the order of eigenvalues ​​at the initial sampling frequency as the mode order, and select the eigenvalue at the initial sampling frequency point where the absolute value |λ1| is less than the eigenvalue threshold λ max The mode is recorded as p, and λ maxSet to 300; For complex target structures, usually more modes need to be tracked. A fixed threshold may result in insufficient number of modes to be tracked, leading to incorrect mode tracking. Although increasing the threshold can alleviate the above problems, it will increase unnecessary calculations. Considering various factors, a reserved value of q can be set. Then the total number of modes tracked at each frequency point is p+q. The value of q is related to the frequency point f i The total number of eigenvalues ​​is the frequency point f i The total number of patterns size(λ) in the target structure i ), usually q is set to size(λ i ) / 200; the subsequent frequency point eigenvalue patterns are arranged in ascending order and matched with the pattern at the initial sampling frequency, that is, at different sampling frequencies, the eigenvalues ​​in the same row have the same pattern, and the pattern matching is preliminarily completed.

[0107] The characteristic mode tracking method based on characteristic vector correlation proposed in the present invention, step 3 is mainly to screen the corresponding characteristic vector, and the specific contents are as follows:

[0108] By filtering out the required eigenvalues, the corresponding eigenvectors are found, that is, (p+q) columns of eigenvectors with a dimension of n×1 are obtained. Each column represents a eigenvector of a mode. At different sampling frequencies, the eigenvectors in the same column are of the same mode.

[0109] In order to avoid the influence of the eigenvector amplitude on the correlation calculation and improve the accuracy and stability of the calculation, the eigenvector is normalized:

[0110]

[0111] Among them, the eigenvector [J m ] i At sampling frequency f i The eigenvector corresponding to the mode m, [J m ] i =(x1,x2,…x n ), x1,x2,…x n is the characteristic vector [J m ] i All elements in [J m ]' i is the normalized feature vector;

[0112] The characteristic mode tracking method based on characteristic vector correlation proposed in the present invention, step 4 is mainly to solve the mode exchange problem, which specifically includes three processes: identifying the mode exchange problem, judging the mode exchange problem, and correcting the mode exchange problem:

[0113] Step 4.1: Identify the mode exchange problem: traverse all sampling frequency points, calculate the difference of the eigenvalues ​​of any two modes at all adjacent frequency points, and find the mode pair whose difference between the current frequency point and the previous frequency point has the opposite sign or one of the difference values ​​is zero. The judgment criteria are as follows:

[0114]

[0115] is the sampling frequency f i The eigenvalue difference between mode m and mode n is calculated. If there is a mode pair whose eigenvalue difference satisfies (25) at adjacent frequency points, then there is an intersection point in the eigenvalue curve at that point. Record the mode pair m, n and sampling frequency point f where the intersection point exists. i , and store them in the pattern intersection table, with one row storing one intersection point;

[0116] Step 4.2: Determine the mode exchange problem: In the mode cross table, perform the variance criterion on each row;

[0117] First calculate the rate of change of the eigenvalue:

[0118]

[0119] is the frequency f i The eigenvalue and frequency f of mode j at i-1 The change rate between the eigenvalues ​​of mode k at the intersection table is calculated by calculating the eigenvalue change rate of mode pairs m and n in the mode cross table, and we can get

[0120] The variance of the obtained eigenvalue change rate is calculated, and the change rate The average value of Will Calculate the variance and get the following formula:

[0121]

[0122] The rate of change can be calculated The variance of var mm , similarly, we can calculate The variance of var nn , The variance of var mn , The variance of var nm ;

[0123] By calculating the variance of the rate of change of the eigenvalue curve, the larger the variance, the more dispersed the data is, and the mode exchange problem occurs. The variance of the rate of change of the curve is greater than the variance of the normal curve rate of change. The mode exchange error problem can be judged based on the variance of the curve rate of change; for the variance var mm , var mn , var nn With var nm Implement the variance criterion:

[0124]

[0125] If the mode pair in the mode cross table satisfies (28), it is determined to be a mode exchange error problem. For normal crossover of characteristic mode curves, the curve change rate changes slowly, while for mode exchange error problems, the curve change rate changes suddenly at adjacent frequency points. Record the sampling frequency points and mode pairs with mode exchange problems and store them in the exchange problem table, with each row representing a mode exchange error problem.

[0126] Step 4.3: Correct the mode switching problem: Starting from the minimum frequency point where the mode switching problem occurs, calculate the frequency point f for all modes in the switching problem table one by one i Each mode and frequency f i+1 The Pearson correlation coefficient of all modes is calculated as follows:

[0127]

[0128] Cov([J m ] i ',[J n ] i ') represents the normalized eigenvector [J m ] i 'With [J n ] i 'The covariance, Var[J m ] i ' represents the normalized eigenvector variance [J m ] i 'The variance, r mn is the correlation coefficient between mode m and mode n, and the absolute value of the correlation coefficient | r mn |The value range is between 0 and 1. mn =0, it means that there is no linear correlation between the two variables. mn |=1, indicating that the two variables are completely correlated;

[0129] will have the maximum absolute value of the correlation coefficient max|r mn |The modes m and n are matched together, at the frequency point f i+1 The matched mode does not participate in the frequency point fi The correlation calculation of the subsequent mode at the frequency point f i+1 The same mode is incorrectly matched to the frequency point f i For two or more modes at a certain location, this method only calculates the correlation coefficient for the mode pairs with mode exchange problems, without calculating the correlation coefficient for all modes, which greatly reduces the amount of calculation.

[0130] The characteristic mode tracking method based on characteristic vector correlation proposed in the present invention, step 5 is mainly to solve the problem of mode degeneration, which specifically includes four processes of identifying the problem of mode degeneration, judging the problem of mode degeneration, correcting the problem of mode degeneration, and optimizing the mode tracking curve:

[0131] Step 5.1: Identify the pattern degeneration problem: The eigenvalue difference between the two patterns at the degenerate frequency point should be less than the eigenvalue difference between the two patterns at the previous and next frequency points. Traverse all sampling frequency points and identify the pattern that meets the pattern degeneration phenomenon. That is, perform the following judgment on all patterns at adjacent frequency points:

[0132]

[0133] If the difference of the eigenvalues ​​of the existing mode pairs at adjacent frequency points satisfies (30), it is preliminarily identified as a mode degeneration problem, and the sampling frequency points f where the mode degeneration phenomenon is preliminarily identified are recorded. i and mode pairs j and k, and store them in the degenerate phenomenon table, one row stores a problem point;

[0134] Step 5.2: Determine the mode degeneration problem: In the degeneration phenomenon table, perform energy criterion on each row to determine whether a mode exchange problem occurs;

[0135] First, the calculation mode stores electrical energy, [X] e with [X] m The matrix forms representing the electric energy and magnetic energy storage operators, respectively, are related to the imaginary part of the impedance matrix [X] as follows:

[0136]

[0137] Where ω=2πf, ω is the angular frequency, f is the frequency, and further we can get:

[0138]

[0139] Mode to store electrical energy:

[0140]

[0141] For mode j at frequency f i The electrical energy stored at j ]i ' is the sampling frequency f i The eigenvector corresponding to mode j, [J j ] i ' T For [J j ] i 'The transposed matrix, similarly, the stored electrical energy of mode k can be obtained

[0142] Mode coupling power:

[0143]

[0144] For mode j and mode k at frequency f i The coupled electric energy at

[0145] Energy criterion is performed on the mode storage energy and the inter-mode coupling energy, that is, the mode pair where the mode degeneration problem occurs. At the frequency point where the degeneration problem occurs, the mode energy diagram will have a cross phenomenon, and the inter-mode coupling energy will have a peak. The specific criterion is as follows:

[0146]

[0147] If the mode pair in the degeneracy phenomenon table satisfies (35), it is determined to be a mode degeneracy problem. The sampling frequency points and mode pairs with mode degeneracy problems are recorded and stored in the degeneracy problem table. Each row is a mode degeneracy error problem.

[0148] Step 5.3: Correcting the mode degeneration problem: Correct each row in the degeneration problem table, and perform mode exchange processing on each mode pair starting from the sampling frequency point of the row to obtain a tracking result curve after correcting the mode degeneration problem. This curve may have a smoothness problem at the mode degeneration problem, which needs further optimization processing;

[0149] Step 5.4: Optimize the model tracking curve: Multiply both sides of the generalized eigenvalue equation (23) by [J] i T We can get (36), [J] i T for [J] i The transposed matrix of :

[0150] [J] i T [X] i [J] i =λ i [J] i T [R] i [J] i (36) From this we can obtain:

[0151]

[0152] The eigenvectors of adjacent frequency points change very little. It is known that f i The imaginary and real parts of the impedance matrix at can be calculated according to f i-1 A certain mode eigenvector at f is estimated i Eigenvalues ​​in the same mode:

[0153]

[0154] For mode p according to f i-1 The eigenvector at f is estimated i The eigenvalue at the point where the mode degeneracy problem occurs i , according to the previous frequency f i-1 and the next frequency f i+1 The eigenvector of the estimated frequency point f i The eigenvalue at the point, taking the mean of the two values, we can get the frequency point f i The eigenvalues ​​used at the position are used to achieve the purpose of smoothing the curve. The smoothing process will not affect the accuracy of the result.

[0155] Example 1

[0156] Embodiment 1 is a rectangular patch antenna, and its structure is as follows Figure 4 As shown in (a), the size is 120mm×60mm, combined with Figure 1 The model was built using FEKO commercial software and then the solution was set to characteristic mode analysis. The operating frequency range of FEKO software was set to 1GHz-5GHz, the number of simulation frequency points was 26, the frequency interval was 160MHz, and the number of triangles was 654. Figure 1 , Figure 2 and Figure 3 , using FEKO commercial software to solve the characteristic mode and then export its impedance matrix to matlab, then calling matlab's built-in function eig to solve the characteristic impedance and its eigenvalues ​​and eigenvectors, and store them separately in frequency order. For Example 1, at any sampling frequency point, the number of eigenvalues ​​is 945, and the number of eigenvectors with a dimension of 945×1 is 945, which represents the total number of modes of the rectangular patch antenna at the current segmentation accuracy. In the entire sampling frequency band, there are 26 such eigenvalues ​​and eigenvectors, and 26 is the number of discrete sampling frequencies.

[0157] Set the eigenvalue threshold to 300, sort the original eigenvalue column vectors in ascending order, keep the corresponding relationship between each column of the matrix composed of eigenvectors and the eigenvalue column vector, and then perform the eigenvalue screening operation to screen out the eigenvalues ​​with an absolute value less than 300 at the initial frequency point, and find the first 6 eigenvalues ​​with an absolute value less than 300. Then the number of modes to be tracked is 16, that is, at each frequency point, the number of eigenvalues ​​to be tracked is 16×1, and the number of eigenvectors with a dimension of 945×1 is 16, that is, the eigenvectors can form a matrix with a dimension of 945×16, and the eigenvalue columns from the 1st to the 16th are identified as modes 1 to 16, and the matrix composed of eigenvectors from the 1st to the 16th columns are identified as modes 1 to 16. Normalize the eigenvectors to facilitate subsequent correlation calculations.

[0158] Identify the intersections in the initial eigenvalue curve graph, and judge the mode exchange problem. Find 103 mode pairs with mode exchange problems between different frequencies. Remove duplicates from the 103 mode pairs and merge them to obtain 16 modes with mode exchange problems. The first mode exchange problem occurs at the second sampling frequency. Pearson correlation coefficients are calculated for the 16 modes starting from the second frequency, and the mode pairs with the largest correlation coefficients are re-matched. Then, the 16 selected modes are identified for mode degeneration problem criteria, and 31 mode pairs are found to have mode degeneration between different frequencies. The 31 mode pairs are judged for mode degeneration. Finally, only one mode pair has mode degeneration problems. The mode pair with problems is exchanged and optimized.

[0159] To illustrate the performance and time advantages of this method, we compare it with the traditional bounded linear eigenvector correlation method. The traditional bounded linear eigenvector correlation method: sort the eigenvalues, take the first 40 eigenvalues ​​to calculate the Pearson correlation coefficient between all patterns of adjacent frequency points, and then track the pattern corresponding to the maximum correlation coefficient.

[0160] Under the same conditions, the characteristic angle curve obtained by traditional method is as follows: Figure 5 As shown in the figure, due to the relatively simple antenna structure, the linear correlation of the eigenvectors corresponding to the eigenvalues ​​of each mode is very obvious, so the mode tracking results of the two algorithms are mostly correct, but when tracking the frequency band of 4.2GHz-4.52GHz, there are still errors in mode 1 and mode 10. To further illustrate this tracking problem, Figure 6The current distribution diagrams drawn by the characteristic vectors of mode 1 and mode 10 at four adjacent frequency points of 4.04GHz, 4.20GHz, 4.36GHz, and 4.52GHz are given. The results show that at 4.04GHz to 4.20GHz, the current distribution changes of mode 1 and mode 4 are very small, and the modes can be tracked correctly. However, due to the mode degeneracy between 4.2-4.36GHz, the characteristic vectors of the two modes are confused, and the correlation coefficient cannot be used for correct tracking. When the tracking method proposed by the present invention is applied in this frequency band, the characteristic angle curve diagram obtained is as follows Figure 7 As shown, the error problem of the traditional feature vector correlation tracking method is successfully corrected at 4.36GHz. The time required for the traditional feature vector correlation tracking method and the tracking method proposed by the present invention is shown in Table 1:

[0161] Table 1

[0162]

[0163] It can be seen from Table 1 that, although the pattern tracking method proposed in the present invention increases some time cost compared to the traditional method, it can well solve the pattern tracking error problem, and the increased time is acceptable.

[0164] Embodiment 2 Embodiment 1 is a fractal antenna, and its structure is as follows Figure 4 As shown in (b), the size is 100mm×64mm, placed 10mm away from the infinite ground plane, combined with Figure 1 The model was built using FEKO commercial software and then the solution was set to characteristic mode analysis. The operating frequency range of FEKO software was set to 2.1GHz-2.7GHz, the number of simulation frequency points was 76, the frequency interval was 8MHz, and the number of triangles was 825. Figure 1 , Figure 2 and Figure 3 , using FEKO commercial software to solve the characteristic mode and then export its impedance matrix to matlab, then calling matlab's built-in function eig to solve the characteristic impedance and its eigenvalues ​​and eigenvectors, and store them separately in frequency order. For Example 2, at any sampling frequency point, the number of eigenvalues ​​is 825, and the number of eigenvectors with a dimension of 825×1 is 825, which represents the total number of modes of the rectangular patch antenna at the current segmentation accuracy. In the entire sampling frequency band, there are 76 such eigenvalues ​​and eigenvectors, and 76 is the number of discrete sampling frequencies.

[0165] Set the eigenvalue threshold to 300, sort the original eigenvalue column vectors in ascending order, keep the corresponding relationship between each column of the matrix composed of eigenvectors and the eigenvalue column vector, and then perform the eigenvalue screening operation to screen out the eigenvalues ​​with an absolute value less than 300 at the first frequency point, and find the first 9 eigenvalues ​​with an absolute value less than 300. Then the number of modes to be tracked is 18, that is, at each frequency point, the number of eigenvalues ​​to be tracked is 18×1, and the number of eigenvectors with a dimension of 825×1 is 18, that is, the eigenvectors can form a matrix with a dimension of 825×18, and the eigenvalues ​​from the 1st to the 18th are identified as modes 1 to 18, and the matrix composed of eigenvectors from the 1st to the 18th columns are identified as modes 1 to 18. Normalize the eigenvectors to facilitate subsequent correlation calculations.

[0166] Identify the intersections in the initial eigenvalue curve graph, and judge the mode exchange problem. Find 23 mode pairs with mode exchange problems between different frequencies. Remove duplicates from the 23 mode pairs and merge them. Get 15 modes with mode exchange problems. The first mode exchange problem occurs at the 16th sampling frequency. Pearson correlation coefficients are calculated for the 15 modes starting from the 16th frequency, and the mode pairs with the largest correlation coefficients are re-matched. Then, the 18 selected modes are identified for mode degeneration problem judgment. Find 47 mode pairs with mode degeneration between different frequencies. Mode degeneration judgment is performed on 31 mode pairs. Finally, only 3 pairs of modes have mode degeneration problems. The mode pairs with problems are exchanged and optimized.

[0167] To illustrate the performance and time advantages of this method, we compare it with the traditional bounded linear eigenvector correlation method. The traditional bounded linear eigenvector correlation method: sort the eigenvalues, take the first 40 eigenvalues ​​to calculate the Pearson correlation coefficient between all modes of adjacent frequency points, and then track the mode according to the eigenvalue corresponding to the maximum correlation coefficient.

[0168] Under the same conditions, the characteristic angle curve obtained by traditional method is as follows: Figure 8 As shown in the figure, due to the complex antenna structure, three errors appear in the tracking results, all of which are pattern degeneracy problems. However, using the tracking method proposed in the present invention, the tracking results are as follows Fig. 9 As shown, you can see that all tracking error issues have been resolved. Fig.10 The current distribution diagram drawn by the eigenvector near 2.49GHz is given. It can be seen that the corrected current distribution has continuity, indicating that the mode degeneration problem has been successfully corrected here. The time required for the traditional eigenvector correlation tracking method and the tracking method proposed in the present invention is shown in Table 2:

[0169] Table 2

[0170]

[0171] It can be seen from Table 2 that the tracking method proposed in the present invention takes into account both accuracy and efficiency, and can not only accurately correct the pattern tracking error problem, but also save time, which has obvious advantages.

[0172] In the above embodiments, the description's reference to "this embodiment" indicates that a particular feature, structure, or characteristic described in conjunction with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple occurrences of "this embodiment" do not necessarily all refer to the same embodiment.

[0173] In the above-described embodiments, although the invention has been described in conjunction with specific embodiments of the invention, many substitutions, modifications, and variations of these embodiments will be apparent to those of ordinary skill in the art based on the foregoing description. For example, other storage structures (e.g., dynamic RAM (DRAM)) may use the embodiments discussed. Embodiments of the invention are intended to encompass all such substitutions, modifications, and variations that fall within the broad scope of the appended claims.

[0174] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A method for tracking characteristic modes based on characteristic vector correlation, characterized in that: The steps include: Pre-processing stage: screening tracking patterns and normalizing feature vectors; Step 1: Use electromagnetic simulation software to model and simulate the target structure, obtain the impedance matrix of the target structure surface, establish a generalized eigenvalue equation, and obtain the eigenvalue λ and eigenvector J of the target structure; Step 2: Arrange the eigenvalues ​​at each sampling frequency in ascending order from small to large, and set the eigenvalue threshold λ according to the complexity of the antenna. max , filter out the values ​​less than the eigenvalue threshold λ max The eigenvalues ​​are used for processing in subsequent steps; the eigenvalues ​​at each sampling frequency point are marked in ascending order as the mode arrangement order; Step 3: Find the corresponding eigenvector according to the selected eigenvalues; in order to eliminate the influence of the amplitude between vectors and make each eigenvector have the same weight in the calculation, the eigenvector is normalized to improve the accuracy and stability of the correlation calculation; Post-processing stage: the stage of solving the mode exchange problem and the stage of solving the mode degeneration problem; Solving the mode switching problem stage: Step 4: Solve the mode exchange problem in three workflows: identify the mode exchange problem, judge the mode exchange problem, and correct the mode exchange problem; The process of identifying the mode exchange problem is as follows: traverse all sampling frequencies, identify the intersections of the tracking curves, record the mode pairs and sampling frequencies with intersections, and store them in the mode intersection table; The process of judging the mode exchange problem is as follows: the variance criterion is executed on the mode pairs in the mode cross table. If the criterion conditions are met, it is determined as a mode exchange problem and stored in the exchange problem table. The process of correcting the mode exchange problem is as follows: in the exchange problem table, starting from the minimum sampling frequency point, the Pearson correlation coefficient of adjacent frequency points of all modes is calculated, and the mode pair with the largest correlation coefficient is re-matched. Solving the problem of model degeneration stage: Step 5: There are four workflows to solve the pattern degeneration problem: identifying the pattern degeneration problem, judging the pattern degeneration problem, correcting the pattern degeneration problem, and optimizing the pattern tracking curve; The process of identifying the mode exchange problem is as follows: traverse all sampling frequencies, identify the modes that meet the mode degeneration phenomenon, record the identified degenerate mode pairs and sampling frequencies, and store them in the degeneracy phenomenon table; The process of judging the mode exchange problem is: perform energy judgment on the mode pairs in the degenerate phenomenon table. If the judgment conditions are met, it is judged as a mode degeneracy problem and stored in the degenerate problem table; the process of correcting the mode exchange problem is: in the degenerate problem table, exchange the eigenvalues ​​and corresponding eigenvectors of the degenerate mode pairs for correction processing; the process of optimizing the mode tracking curve is: smooth the eigenvalue curve through the estimated eigenvalue method to obtain the final smooth mode tracking curve.

2. The characteristic mode tracking method based on characteristic vector correlation according to claim 1 is characterized in that: In step 1, modeling and simulation analysis are performed in electromagnetic simulation software to obtain the impedance matrix [Z] of the target structure. The impedance matrix [Z] can be expressed as: [Z]=[R]+j[X] (1) Where [R] represents the real part of the impedance matrix, and [X] represents the imaginary part of the impedance matrix, which can be obtained by the following formula: Where [R] and [X] are both symmetric matrices, and [R] is a semi-positive definite matrix; [Z]* is the conjugate matrix of the impedance matrix [Z]; Then according to the generalized eigenvalue equation of characteristic mode theory: [X] i [J] i =λ i [R] i [J] i (4) i represents the sampling frequency number, [R] i and [X] i is the sampling frequency f i The real and imaginary parts of the impedance matrix under [J] i and λ i is the sampling frequency f i The eigenvectors and eigenvalues ​​of i and [X] i The eigenvalue and corresponding eigenvector at each sampling frequency can be calculated.

3. The characteristic mode tracking method based on characteristic vector correlation according to claim 1 is characterized in that: In step 2, the eigenvalue λ at each sampling frequency point is i Arrange in ascending order from small to large, identify the order of eigenvalues ​​at the initial sampling frequency as the mode order, and select the eigenvalue at the initial sampling frequency point where the absolute value |λ1| is less than the eigenvalue threshold λ max The mode is recorded as p, and λ max Set to 300; For complex target structures, usually more modes need to be tracked. A fixed threshold may result in insufficient number of modes to be tracked, leading to incorrect mode tracking. Although increasing the threshold can alleviate the above problems, it will increase unnecessary calculations. Considering various factors, a reserved value of q can be set. Then the total number of modes tracked at each frequency point is p+q. The value of q is related to the frequency point f i The total number of eigenvalues ​​is the frequency point f i The total number of patterns size(λ) in the target structure i ), usually q is set to size(λ i ) / 200; the subsequent frequency point eigenvalue patterns are arranged in ascending order to match the pattern at the initial sampling frequency.

4. The characteristic mode tracking method based on characteristic vector correlation according to claim 1 is characterized in that: In step 3, the corresponding eigenvector is found according to the required eigenvalues ​​screened out; In order to avoid the influence of the eigenvector amplitude on the correlation calculation and improve the accuracy and stability of the calculation, the eigenvector is normalized: Among them, the eigenvector [J m ] i At the sampling frequency f i The eigenvector corresponding to the mode m, [J m ] i =(x1,x2,…x n ), x1,x2,…x n is the characteristic vector [J m ] i All elements in [J m ]' i is the normalized feature vector.

5. The characteristic mode tracking method based on characteristic vector correlation according to claim 1 is characterized in that: Step 4 specifically includes three processes: identifying mode exchange problems, judging mode exchange problems, and correcting mode exchange problems; Step 4.1: Identify the mode exchange problem: traverse all sampling frequency points, calculate the difference of the eigenvalues ​​of any two modes at all adjacent frequency points, and find the mode pair whose difference between the current frequency point and the previous frequency point has the opposite sign or one of the difference values ​​is zero. The judgment criteria are as follows: is the sampling frequency f i The eigenvalue difference between mode m and mode n is calculated. If there is a mode pair whose eigenvalue difference satisfies (6) at adjacent frequency points, then there is an intersection point in the eigenvalue curve at that point. Record the mode pair m, n and sampling frequency point f where the intersection point exists. i , and store them in the pattern intersection table, with one row storing one intersection point; Step 4.2: Determine the mode exchange problem: In the mode cross table, perform the variance criterion on each row; First calculate the rate of change of the eigenvalue: is the frequency f i The eigenvalue and frequency of mode j at f i-1 The change rate between the eigenvalues ​​of mode k at the intersection table is calculated by calculating the eigenvalue change rate of mode pairs m and n in the mode cross table, and we can get The variance of the obtained eigenvalue change rate is calculated, and the change rate The average value of Will Calculate the variance and get the following formula: The rate of change can be calculated The variance of var mm , similarly, we can calculate The variance of var nn , The variance of var mn , The variance of var nm ; By calculating the variance of the rate of change of the eigenvalue curve, the larger the variance, the more dispersed the data is, and the mode exchange problem occurs. The variance of the rate of change of the curve is greater than the variance of the normal curve rate of change. The mode exchange error problem can be judged based on the variance of the curve rate of change; for the variance var mm , var mn , var nn With var nm Implement the variance criterion: If the mode pair in the mode cross table satisfies (9), it is determined to be a mode exchange error problem. The sampling frequency points and mode pairs with mode exchange problems are recorded and stored in the exchange problem table, with each row representing a mode exchange error problem. Step 4.3: Correct the mode switching problem: Starting from the minimum frequency point where the mode switching problem occurs, calculate the frequency point f for all modes in the switching problem table one by one i Each mode and frequency f i+1 The Pearson correlation coefficient of all modes is calculated as follows: Cov([J m ] i ',[J n ] i ') represents the normalized eigenvector [J m ] i 'With [J n ] i 'The covariance, Var[J m ] i ' represents the normalized eigenvector variance [J m ] i 'The variance, r mn is the correlation coefficient between mode m and mode n; will have the maximum absolute value of the correlation coefficient max|r mn |The modes m and n are matched together, at the frequency point f i+1 The matched mode does not participate in the frequency point f i The correlation calculation of the subsequent mode at the frequency point f i+1 The same mode is incorrectly matched to the frequency point f i Two or more modes at the same time.

6. The characteristic mode tracking method based on characteristic vector correlation according to claim 1 is characterized in that: Step 5 specifically includes four processes: identifying the pattern degeneration problem, judging the pattern degeneration problem, correcting the pattern degeneration problem, and optimizing the pattern tracking curve: Step 5.1: Identify the pattern degeneration problem: The eigenvalue difference between the two patterns at the degenerate frequency point should be less than the eigenvalue difference between the two patterns at the previous and next frequency points. Traverse all sampling frequency points and identify the pattern that meets the pattern degeneration phenomenon. That is, perform the following judgment on all patterns at adjacent frequency points: If the difference of the eigenvalues ​​of the existing mode pairs at adjacent frequency points satisfies (11), it is preliminarily identified as a mode degeneration problem, and the sampling frequency points f where the preliminarily identified mode degeneration phenomenon exists are recorded. i and mode pairs j and k, and store them in the degenerate phenomenon table, one row stores a problem point; Step 5.2: Determine the mode degeneration problem: In the degeneration phenomenon table, perform energy criterion on each row to determine whether a mode exchange problem occurs; First, the calculation mode stores electrical energy, [X] e with [X] m The matrix forms representing the electric energy and magnetic energy storage operators respectively are related to the imaginary part of the impedance matrix [X] as follows: [X] m -[X] e =[X] Where ω=2πf, ω is the angular frequency, f is the frequency, and further we can get: Mode to store electrical energy: For mode j at frequency f i The electrical energy stored at j ] i ' is the sampling frequency f i The eigenvector corresponding to mode j, [J j ] i ' T For [J j ] i 'The transposed matrix, similarly, the stored electrical energy of mode k can be obtained Mode coupling power: For mode j and mode k at frequency f i The coupled electric energy at Energy criteria are implemented for mode storage energy and inter-mode coupling energy: If the mode pair in the degeneracy phenomenon table satisfies (16), it is determined to be a mode degeneracy problem. The sampling frequency points and mode pairs with mode degeneracy problems are recorded and stored in the degeneracy problem table. Each row is a mode degeneracy error problem. Step 5.3: Correcting the mode degeneration problem: Correct each row in the degeneration problem table, and perform mode exchange processing on each mode pair starting from the sampling frequency point of the row to obtain a tracking result curve after correcting the mode degeneration problem. This curve may have a smoothness problem at the mode degeneration problem, which needs further optimization processing; Step 5.4: Optimize the tracking curve of the model: Multiply both sides of the generalized eigenvalue equation (4) by [J] i T We can get (17), [J] i T for [J] i The transposed matrix of From this we can get: The eigenvectors of adjacent frequency points change very little. It is known that f i The imaginary and real parts of the impedance matrix at f i-1 A certain mode eigenvector at f is estimated i Eigenvalues ​​in the same mode: For mode p according to f i-1 The eigenvector at f is estimated i The eigenvalue at the point where the mode degeneracy problem occurs i , according to the previous frequency f i-1 and the next frequency f i+1 The eigenvector of the estimated frequency point f i The eigenvalue at the point, taking the mean of the two values, we can get the frequency point f i The eigenvalues ​​used at the position are used to achieve the purpose of smoothing the curve. The smoothing process will not affect the accuracy of the result.

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