Method and apparatus for analyzing wave direction angle

Abstract

The application relates to a wave direction angle analysis method and device, belonging to the field of wave test simulation. The specific process comprises the following steps: 1) generating a wave height data array of a target area; 2) performing forward and backward smoothing on the wave height data array of the target area to obtain a doubled data array; 3) calculating a covariance matrix of the doubled data array; 4) calculating an optimized covariance matrix by using a spatial smoothing method; 5) calculating all eigenvalues and eigenvectors of the optimized covariance matrix; 6) arranging the eigenvalues according to the size, distinguishing a signal subspace / noise subspace, and constructing a noise matrix; 7) performing translation and reciprocal weighting processing on the eigenvalues of the noise subspace to obtain a weighted noise matrix; 8) utilizing the orthogonal relationship between a wave guide vector and the weighted noise matrix to construct a spectral function; and 9) calculating the spectral function corresponding to all angles, and the angle corresponding to the peak value of the spectral function is the oblique wave direction estimation angle. The method can quickly and accurately calculate the wave field direction angle in real time.

Description

Technical Field

[0001] This invention relates to a method and apparatus for analyzing wave direction angles, belonging to the field of wave test simulation. Background Technology

[0002] With the development of coastal engineering in recent years, the direction of incident waves is often unknown in many practical engineering projects and pool experiments. Especially in pool experiments, the propagation direction of generated waves does not strictly follow the specified direction, and the wave propagation direction needs to be corrected multiple times to meet the target direction required by the experiment. Therefore, determining the wave direction angle within the wave field is a very important hydrodynamic analysis method.

[0003] There are two main existing methods for wave direction angle analysis: one uses a three-point wave height meter for wave measurement and an iterative solution method to establish an analysis method for determining the incident angle of oblique waves, but this method can only be used to analyze regular waves in a single direction. The other method calculates the representative direction using a representative frequency, which can analyze the direction angle of oblique waves (irregular), but still can only analyze the angle of a single oblique wave. Calculating the direction angle when oblique waves from multiple directions are superimposed has always been a challenge.

[0004] This invention proposes a method for analyzing the direction angle of oblique waves. By using wave height meter array data at measuring points, the direction angle of single / multiple directional regular / irregular waves can be calculated in real time, providing richer technical means for hydrodynamic analysis of wave fields. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method for analyzing wave direction angles, which can quickly and accurately calculate wave field direction angles in real time.

[0006] This invention provides a method for analyzing wave direction angles, comprising the following steps, such as... Figure 2 As shown:

[0007] S1. Generate a wave height data array for the target area;

[0008] S2. Smooth the wave height data array of the target area forward and backward to obtain a doubled data array;

[0009] S3. Calculate the covariance matrix of the doubled data array;

[0010] S4. Calculate the optimized covariance matrix using the spatial smoothing method;

[0011] S5. Calculate all eigenvalues ​​and eigenvectors of the optimized covariance matrix;

[0012] S6. Arrange the subspaces according to the size of the eigenvalues, distinguish between the signal subspace and the noise subspace, and construct the noise matrix;

[0013] S7. The eigenvalues ​​of the noise subspace are shifted and weighted by inverse to obtain the weighted noise matrix;

[0014] S8. Construct the spectral function using the orthogonality between the wave steering vector and the weighted noise matrix;

[0015] S9. Calculate the spectral function corresponding to all angles. The angle corresponding to the peak value of the spectral function is the estimated angle of the oblique wave direction.

[0016] Furthermore, in S1, let the wave be an oblique wave, with M oblique waves at the far point, and the angle of the m-th oblique wave be... The strength is There are N wave height meters, and the data signal collected by the nth wave height meter is: The distance between two adjacent wave height meters is d, such as Figure 1 As shown.

[0017] The signal delay between two adjacent wave height meters caused by the m-th oblique wave is expressed as:

[0018] (1)

[0019] in, This represents the amplitude of the m-th oblique wave. Represents the imaginary unit. This represents the angular frequency of the m-th oblique wave. Indicates time, This represents the wave velocity of the m-th oblique wave. This represents the wavelength of the m-th oblique wave;

[0020] The signal collected by each wave height meter is:

[0021] (2)

[0022] Rewritten in matrix form, the wave height data array for the target area is obtained:

[0023] (3)

[0024] (4)

[0025] Where P represents the data signal collected by the wave height meter. Length, Let N be the Nth randomly generated Gaussian white noise, with a mean of 0 and a variance of . ; The guiding matrix, where each wave guiding vector... Describe oblique waves from The amount of phase delay between wave height meters caused by directional incidence. This represents the amplitude matrix, which describes the amplitude of different oblique waves. This is a Gaussian white noise matrix. This is the data signal matrix collected by the wave height meter.

[0026] Furthermore, in S2, for Perform forward and backward smoothing (i.e., time flipping, with the forward data becoming the original data) to obtain the backward data matrix:

[0027] (5)

[0028] Where J is the commutative matrix (1s on the secondary diagonal and 0s elsewhere). and Together they form a doubled data array.

[0029] Furthermore, in S3, The covariance matrix is:

[0030] (6)

[0031] in, They are The abbreviated form; Represents the conjugate transpose of a matrix. Represents the mean of the matrix. Represents the identity matrix;

[0032] In practice, estimation is performed using a finite number of samples K. The covariance matrix is:

[0033] (7)

[0034] The covariance matrix of the backward data matrix is:

[0035] (8)

[0036] in, yes The abbreviated form;

[0037] Then, and The average value is used as the covariance matrix of the doubled data array:

[0038] (9)

[0039] Furthermore, in S4, for two coherent oblique waves, i.e., two oblique waves with the same or multiple angular frequencies, the covariance matrix will be... Rank deficiency (e.g., two coherent oblique waves reduce the rank from 2 to 1). An improved method is to divide an array of N wave height meters into Z overlapping subarrays of size Q, where Z = N - Q + 1.

[0040] For example, the original array is [1,2,3,4,5,6]. The resulting subarrays (Q=4) are: [1,2,3,4], [2,3,4,5], [3,4,5,6]. Then, the covariance matrix of each overlapping subarray is averaged to obtain the optimized covariance matrix:

[0041] (10)

[0042] in It is the first The covariance matrix of overlapping submatrices. This processing allows for spatial smoothing, and the rank of the covariance matrix can be recovered through piecewise processing, satisfying:

[0043] (11)

[0044] in, Let C denote the rank of the matrix, and let C denote the number of incoherent oblique waves (i.e., the circular frequencies are not the same and are not multiples of each other).

[0045] Furthermore, in S6, It is a Hermitian self-conjugate matrix, which can be proven. Given p positive real eigenvalues ​​and mutually orthogonal eigenvectors, The eigenvalues ​​are sorted by size, with the largest q eigenvalues ​​being the first q. and the corresponding feature vector Reflecting the characteristics of the signal subspace, the remaining eigenvalues and the corresponding feature vector It reflects the characteristics of the noise subspace.

[0046] based on Using eigenvectors from the noisy subspace, construct the noise matrix:

[0047] (12)

[0048] Furthermore, in S7, the eigenvalues ​​of the noise subspace... Perform translation and reciprocal weighting:

[0049] (13)

[0050] In the formula This is the minimum value, used to prevent numerical instability; it is set to 10. -16 ~10 -10 . Represents eigenvalues The smallest one.

[0051] Construct the weighted noise matrix:

[0052] (14)

[0053] in, Represents a diagonal matrix;

[0054] This processing can weaken the influence of residual wave signal components in the noise subspace and enhance the ability to distinguish adjacent wave signals.

[0055] Furthermore, in S8, the weighted noise matrix and the wave steering vector They have an orthogonal relationship.

[0056] (15)

[0057] Therefore, for any angle Orthogonality is measured by calculating the spectral function:

[0058] (16)

[0059] when When the direction is the true signal direction, the denominator approaches zero. A sharp peak appears when When the direction is not the signal direction, the denominator is a non-zero value. The amplitude is low.

[0060] A wave direction angle analysis device includes: at least one processor, and a memory communicatively connected to the at least one processor;

[0061] The memory stores instructions that can be executed by the processor, which are then executed by the at least one processor to cause the at least one processor to perform the wave direction angle analysis method described above.

[0062] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0063] (1) Existing methods for analyzing the oblique wave direction angle require a large amount of signal data and have large errors. This invention utilizes the orthogonality between the signal space and the noise space to quickly and accurately analyze the oblique wave direction angle using extremely short time data, thus realizing real-time measurement of the oblique wave direction angle.

[0064] (2) Existing methods for analyzing the direction angle of oblique waves can only identify a single direction angle. When the wave field is composed of oblique waves in multiple directions, the existing methods will fail. However, the present invention can be applied to the real-time measurement of the direction angle of multiple oblique waves superimposed, and can analyze the direction angle of multiple oblique waves in the wave field at one time.

[0065] (3) In addition, the application scenario is extended from regular waves to irregular waves for the first time. When applied to irregular waves, the main frequency component in the received signal is filtered out by filtering, and then the filtered signal is processed in the same way as regular waves. In this way, the direction angle of single / multi-directional oblique waves (irregular) can be quickly and accurately determined.

[0066] This invention provides a method for analyzing the direction angle of oblique waves, which can analyze the direction angle of single / multiple oblique waves (regular / irregular) in real time. This invention expands the existing method system for wave field direction angle identification and innovatively proposes a multi-dimensional hydrodynamic analysis technique, providing a more complete technical means for wave field hydrodynamic analysis. Attached Figure Description

[0067] Figure 1 Schematic diagram of the model.

[0068] Figure 2 Calculation flowchart.

[0069] Figure 3 A schematic diagram of the simulation results of a single oblique wave (regular) (40°), where (a) the spatial spectrum distribution at 1s, and (b) the angle change diagram corresponding to the spatial spectrum extreme values ​​within 30s.

[0070] Figure 4 A schematic diagram of the simulation results of a single oblique wave (regular) (-40°), where (a) the spatial spectrum distribution at 1s, and (b) the angle change diagram corresponding to the spatial spectrum extreme values ​​within 30s.

[0071] Figure 5 Spatial spectrum distribution of two oblique waves (same frequency rule) at 1 second (-30° and 45°).

[0072] Figure 6 Angular variation of spatial spectrum extrema (-30° and 45°) of two oblique waves (same frequency rule) within 30s.

[0073] Figure 7 Spatial spectrum distribution of two oblique waves (same frequency rule) at 1 second (30° and 45°).

[0074] Figure 8 Angular variation diagrams of spatial spectrum extrema corresponding to two oblique waves (same frequency rule) within 30s (30° and 45°).

[0075] Figure 9 A schematic diagram of the simulation results of a single oblique wave (irregular) (20°), where (a) is the spatial spectrum distribution at 80s, and (b) is the angle change diagram corresponding to the spatial spectrum extreme values ​​within 80s.

[0076] Figure 10 A schematic diagram of the simulation results of a single oblique wave (irregular) (60°), where (a) is the spatial spectrum distribution at 80s, and (b) is the angle change diagram corresponding to the spatial spectrum extreme values ​​within 80s.

[0077] Figure 11 Spatial spectrum distribution of two oblique waves (irregular at the same frequency) at 20s (10° and 60°).

[0078] Figure 12 Angular variation diagrams of spatial spectrum extrema corresponding to 10° and 60° within 80s for two oblique waves (irregular at the same frequency).

[0079] Figure 13 Spatial spectrum distribution of two oblique waves (irregular at the same frequency) at 20s (-10° and 10°).

[0080] Figure 14 Angular variation diagram of spatial spectrum extreme values ​​(-10° and 10°) of two oblique waves (irregular at the same frequency) within 80s. Detailed Implementation

[0081] Example 1:

[0082] (1) Simulation verification of a single oblique wave (regular);

[0083] First, a single oblique wave (regular) with an angle of ±40° is constructed. A simulated wave train with a period of 2 seconds and a wave height of 0.06 m is generated. The wave height meter data is generated with a time step of 0.01 seconds, for a total of 30 seconds of data. For each calculation of the angle corresponding to the current time, the data from the previous second is used for analysis. The curves of the spatial spectrum function as a function of angle at time 1 second under each condition are shown below. Figure 3 (a) and Figure 4 As shown in (a) above, the curves showing the change in the angle of the spectral peak position under various operating conditions throughout the simulation process are as follows: Figure 3 (b) and Figure 4 As shown in (b) of the diagram.

[0084] As can be seen from the figure, the spatial spectrum curve obtained by the method of the present invention has a sharp and obvious peak, while other positions are highly stable. The angle corresponding to the peak is completely consistent with the angle of the constructed signal. The angle calculated for a continuous time within 30 seconds is also completely consistent with the angle of the constructed signal.

[0085] Example 2:

[0086] (2) Simulation verification of two oblique waves (same frequency rule);

[0087] Two oblique wave (same frequency rule) signals are then constructed. Oblique wave 1: period 1s, angle -30°, wave height 0.04m; Oblique wave 2: period 1s, angle 45°, wave height 0.06m. The wave height meter data is generated with a time step of 0.01s, for a total of 30s of data. The data from the previous 1s is used for analysis when calculating the angle corresponding to the current time. The spatial spectrum function calculated at time 1s under various operating conditions as a function of angle is shown below. Figure 5 As shown in the figure. The curves showing the change of the spectral peak position and corresponding angle over time under various operating conditions during the entire simulation process are as follows. Figure 6 As shown.

[0088] As can be seen from the figure, the angle corresponding to the maximum value of the spatial spectral function at 1s corresponds very well to the oblique wave directions of the two structures. The two angles calculated over a continuous time period of 30s also perfectly match the oblique wave angles of the two structures. Further adjustments were made to the angles of the two oblique waves at 30° and 45°. Figure 7 and Figure 8 Simulation results are presented. The figures show that even for two closely adjacent directional angles, this method can accurately determine the oblique wave angle.

[0089] Example 3:

[0090] (3) Simulation verification of a single oblique wave (irregular);

[0091] A single oblique wave (irregular) with angles of 20° and 60° was constructed. The simulated wave train had a peak period of 1.0 s and a wave height of 0.04 m. The wave height meter data was generated at a time step of 0.01 s, for a total of 80 s of data. For each calculation of the angle corresponding to the current time, data from all previous time points were analyzed. The spatial spectral function as a function of angle at time 80 s for each condition is shown below. Figure 9 (a) and Figure 10 As shown in (a) below, the curves showing the change in the angle of the spectral peak position under various operating conditions throughout the simulation process are as follows: Figure 9 (b) and Figure 10 As shown in (b) of the diagram.

[0092] As can be seen from the figure, for the discrimination of a single oblique wave (irregular) direction angle, the error increases with the increase of the angle, but it still fluctuates within a small range. The method provided by this invention can control the error between the discriminated angle and the actual angle within ±5°, which can meet the accuracy requirements of most practical applications.

[0093] Example 4:

[0094] (4) Simulation verification of two oblique waves (irregular);

[0095] Two oblique wave (irregular) signals with the same frequency are constructed. Oblique wave 1: period 1s, angle 10°, wave height 0.04m; Oblique wave 2: period 1s, angle 60°, wave height 0.04m. The time step for generating wave height meter data is 0.01s, generating a total of 80s of data. Data from all previous times is used for analysis when calculating the angle corresponding to the current time. The curves of the spatial spectrum function as a function of angle at time 80s under various operating conditions are as follows. Figure 11 As shown below, the curves depicting the change in the angle of the spectral peak position under various operating conditions throughout the simulation process are as follows: Figure 12 As shown.

[0096] As can be seen from the figure, for the discrimination of two oblique (irregular) wave direction angles, the error between the discrimination angle and the actual angle increases with the increase of the angle. Accurate discrimination is possible for small angles, and the accuracy requirements are also met for large angles.

[0097] The angles of the two oblique waves were further adjusted to 10° and -10°. Figure 13 and Figure 14 Simulation results are presented. The figures show that even for two closely adjacent directional angles, this method can accurately determine the oblique wave angle.

Claims

1. A method for analyzing wave direction angles, characterized in that, The steps are as follows: S1. Generate a wave height data array for the target area; S2. Smooth the wave height data array of the target area forward and backward to obtain a doubled data array; S3. Calculate the covariance matrix of the doubled data array; S4. Calculate the optimized covariance matrix using the spatial smoothing method; S5. Calculate all eigenvalues ​​and eigenvectors of the optimized covariance matrix; S6. Arrange the subspaces according to the size of the eigenvalues, distinguish between the signal subspace and the noise subspace, and construct the noise matrix; S7. The eigenvalues ​​of the noise subspace are shifted and weighted by inverse to obtain the weighted noise matrix; S8. Construct the spectral function using the orthogonality between the wave steering vector and the weighted noise matrix; S9. Calculate the spectral function corresponding to all angles. The angle corresponding to the peak value of the spectral function is the estimated angle of the oblique wave direction.

2. The wave direction angle analysis method according to claim 1, characterized in that, In S1, let the waves be oblique waves, and there are M oblique waves at the far point. The angle of the m-th oblique wave is... The strength is There are N wave height meters, and the data signal collected by the nth wave height meter is: The distance between two adjacent wave height meters is d; The signal delay between two adjacent wave height meters caused by the m-th oblique wave is expressed as: (1) in, This represents the amplitude of the m-th oblique wave. Represents the imaginary unit. This represents the angular frequency of the m-th oblique wave. Indicates time, This represents the wave velocity of the m-th oblique wave. This represents the wavelength of the m-th oblique wave; The signal collected by each wave height meter is: (2) Rewritten in matrix form, the wave height data array for the target area is obtained: (3) (4) Where P represents the data signal collected by the wave height meter. Length, Let N be the Nth randomly generated Gaussian white noise, with a mean of 0 and a variance of . ; The guiding matrix, where each wave guiding vector... Describe oblique waves from The amount of phase delay between wave height meters caused by directional incidence; This represents the amplitude matrix, describing the amplitude of different oblique waves; The matrix is ​​Gaussian white noise. This is the data signal matrix collected by the wave height meter.

3. The wave direction angle analysis method according to claim 2, characterized in that, In S2, for After smoothing both the front and back sides, we obtain the backward data matrix: (5) Where J is the commutation matrix. and Together they form a doubled data array.

4. The wave direction angle analysis method according to claim 3, characterized in that, In S3, The covariance matrix is: (6) in, They are The abbreviated form; Represents the conjugate transpose of a matrix. Represents the mean of the matrix. Represents the identity matrix; In practice, estimation is performed using a finite number of samples K. The covariance matrix is: (7) The covariance matrix of the backward data matrix is: (8) in, yes The abbreviated form; Then, and The average value is used as the covariance matrix of the doubled data array: (9)。 5. The wave direction angle analysis method according to claim 4, characterized in that, In S4, for two coherent oblique waves, i.e., two oblique waves with the same or multiple angular frequencies, the covariance matrix will be... The rank is deficient; the improved method is to divide an array of N wave height meters into Z overlapping subarrays of size Q, where Z = N - Q + 1. Then, the covariance matrix of each overlapping submatrix is ​​averaged to obtain the optimized covariance matrix: (10) in It is the first The covariance matrix of overlapping submatrices; this processing enables spatial smoothing. The rank of the covariance matrix is ​​recovered through piecewise processing, satisfying: (11) in, Let C represent the rank of the matrix, and let C represent the number of incoherent oblique waves.

6. The wave direction angle analysis method according to claim 5, characterized in that, In S6, It is a Hermitian self-conjugate matrix, which can be proven. Given p positive real eigenvalues ​​and mutually orthogonal eigenvectors, The eigenvalues ​​are sorted by size, with the top q eigenvalues ​​having the largest values. and the corresponding feature vector Reflecting the characteristics of the signal subspace, the remaining eigenvalues and the corresponding feature vector This reflects the characteristics of the noise subspace; based on Using eigenvectors from the noisy subspace, construct the noise matrix: (12)。 7. The wave direction angle analysis method according to claim 6, characterized in that, In S7, the eigenvalues ​​of the noise subspace Perform translation and reciprocal weighting: (13) In the formula This is the minimum value, used to prevent numerical instability; it is set to 10. -16 ~10 -10 ; Represents eigenvalues The smallest one; Construct the weighted noise matrix: (14) in, This represents a diagonal matrix.

8. The wave direction angle analysis method according to claim 7, characterized in that, In S8, the weighted noise matrix and the wave steering vector They are orthogonal; (15) Therefore, for any angle Orthogonality is measured by calculating the spectral function: (16) when When the direction is the true signal direction, the denominator approaches zero. A sharp peak appears when When the direction is not the signal direction, the denominator is a non-zero value. The amplitude is low.

9. A wave direction angle analysis device, characterized in that, include: At least one processor, and a memory communicatively connected to said at least one processor; The memory stores instructions executable by the processor, which are executed by the at least one processor to cause the at least one processor to perform a wave direction angle analysis method according to any one of claims 1-8.

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