Unstable wave directional spectrum estimation method

Abstract

The invention relates to an unsteady-state sea wave direction spectrum estimation method. The method comprises the steps of S1, signal decomposition; s2, direction distribution calculation; s3, adaptively adjusting the time domain analysis step length; s4, performing nonparametric kernel estimation on the transient wavelet distribution probability; and S5, direction spectrum time domain adaptive reconstruction is carried out. In the time domain analysis process of wavelet analysis, a two-dimensional plug-in non-uniform bandwidth algorithm is adopted to determine a data-adaptive two-dimensional non-uniform and non-parametric kernel function, the probability of different wavelets in a wave number-direction space is analyzed, the lateral propagation sea wave energy in the non-main wave direction is estimated, and the wave energy in the non-main wave direction is obtained. Therefore, the precision and the anti-noise capability of the direction spectrum estimation method are improved. In the time domain analysis process of wavelet analysis, a sea wave signal fluctuation intensity detection algorithm based on the frequency-direction-wave number three-dimensional change rate of wave energy distribution is introduced, the time duration of sea wave signal sections is divided according to the fluctuation intensity, the time domain precision is adjusted, the calculation efficiency is improved, and meanwhile, the sea wave signals which rapidly change in the time domain are accurately captured. Measurement is avoided.

Description

Technical Field

[0001] The present invention belongs to the technical field of ocean wave observation data processing, and in particular relates to a method for estimating a non-steady-state ocean wave directional spectrum. Background Art

[0002] The marine and coastal engineering industries rely on observing ocean waves and estimating their characteristic values. Because ocean waves are three-dimensional, their energy doesn't propagate in a fixed direction. Therefore, in addition to wave height and periodicity, engineering applications also require estimating the directional distribution of wave energy, known as the directional spectrum.

[0003] Estimating the wave directional spectrum involves two steps: the first is data measurement, which involves measuring basic wave information such as water surface elevation, water surface slope, and water flow velocity through buoys, wave height meter arrays, or current meters; the second is directional spectrum estimation, which involves processing basic wave information through some algorithms to obtain the directional spectrum.

[0004] Currently, there are several existing methods for estimating directional spectra based on Fourier transforms. The Bayesian directional method and iterative maximum likelihood method are considered the most advanced methods in this branch. The Bayesian directional method, proposed by Hashimoto, incorporates a Bayesian regression analysis model as the core of directional spectrum analysis and utilizes machine learning algorithms for self-iteration and self-evaluation to ultimately determine the optimal directional spectrum estimate. However, the Bayesian directional method assumes a linear dispersion relationship between wave number and frequency, making it unsuitable for nonlinear wave fields.

[0005] The iterative maximum likelihood method, proposed by Davis, provides an independent wavenumber spectrum. However, its reliance on spatial Fourier transforms limits its wavenumber resolution capabilities. The limited number of sensor points makes the iterative maximum likelihood method highly sensitive to array arrangement. Irrational array arrangement can limit the resolution frequency band, significantly reducing the reliability of the results and making it difficult to compensate for this with other methods or high-precision acquisition equipment. More importantly, the Bayesian directional method and iterative maximum likelihood method are based on Fourier transforms and can only process steady-state signals, making them unsuitable for unsteady wave fields.

[0006] In the existing art, there is an analysis method (WDM) that uses wavelets as a signal basis. It is currently the only spectral estimation method capable of analyzing non-steady-state wave fields. By using the spatial position of the measurement point and the phase difference of the wave signal between different locations, it can estimate the time evolution of the wave number, spectral density, and wave direction. However, the existing method assumes that there is only a single wavelet in space and time. During the calculation process, only the characteristic information of the wavelet with the most significant wave energy is retained, and other wavelets with relatively lower energy are ignored. Therefore, this method seriously underestimates the degree of wave directional diffusion in practical applications. In addition, the wave number resolution capability of the existing method is affected by the layout of the field sensor array. It is very sensitive to noise in the measurement data, prone to singular solutions, and has low reliability of the analysis results.

[0007] References:

[0008] Donelan, MA, et al. (1996). "Nonstationary Analysis of the DirectionalProperties of Propagating Waves." Journal of PhysicalOceanography 26(9):1901-1914.

[0009] Davis,REand LARegier(1977)."Methods for estimating directionalwave spectra from multi-element arrays."

[0010] Hashimoto, N. and K. Kobune (1988). "Estimation of Directional Spectrumthrough a Bayesian Approach." CoastalEngineeringinJapan 31(2):183-198. Summary of the Invention

[0011] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a method for estimating the directional spectrum of unsteady ocean waves, so as to solve the problems of poor accuracy and low reliability of the directional estimation results encountered in the directional spectrum estimation of unsteady ocean waves.

[0012] The present invention solves the technical problem by the following technical solutions:

[0013] A method for estimating the directional spectrum of unsteady ocean waves, characterized in that the method comprises the following steps:

[0014] S1. Signal decomposition: Wavelet transform is used to decompose the wave signal to obtain the time-frequency localization characteristics of different frequency components, including the time domain evolution information of amplitude and phase;

[0015] S2. Direction distribution calculation: At each time and frequency scale, the coefficient matrix of the wavelet transform is used to calculate the possible direction distribution and extract the energy value of each direction;

[0016] S3. Adaptive adjustment of time domain analysis step size: The time domain analysis time period is divided according to the changing characteristics of the wave signal. If the wave signal fluctuation is relatively stable within a certain time period and is lower than the dynamic threshold, all wave information within the preset larger time step is used as a single sample for subsequent probability analysis. If the wave direction changes drastically within a certain time period, the time step is shortened according to the degree of fluctuation, and the wave information of the short period is used as the subsequent estimation sample.

[0017] S4. Non-parametric kernel estimation of transient wavelet distribution probability: Based on the wavenumber-direction distribution calculation results of each time-domain sample, a two-dimensional bandwidth optimization algorithm is used to iteratively determine the optimal wavenumber bandwidth and optimal direction bandwidth of the current sample set, and a two-dimensional non-uniform kernel function is constructed for the current time-domain sample. Subsequently, a non-parametric estimation method is used to perform statistical distribution modeling on the wavenumber-direction distribution results of each time-domain sample using the two-dimensional non-uniform kernel function, generating a "wavenumber-direction" probability map of the wavelet in the array of each sample, effectively retaining the existence probability of lateral low-energy wavelets;

[0018] S5. Time-domain adaptive reconstruction of directional spectrum: The calculation results of all time-domain samples are integrated, and the total wave energy value is obtained by referring to the collection results of the field signal. The wave energy units are allocated according to the continuous wavelet probability distribution to meet the conservation of total energy. The estimation results of adjacent time-domain samples are dynamically overlapped according to the control of the wave fluctuation degree to maintain the smooth transition of wave information in the time-domain evolution, and the "wave number-direction" time-domain distribution of each frequency is obtained, that is, the "wave number-direction-frequency-time" four-dimensional estimation result of wave energy.

[0019] The advantages and beneficial effects of the present invention are:

[0020] 1. The present invention has a wide range of applications: it uses a wavelet transform algorithm to decompose wave signals and is applicable to both steady-state and non-steady-state waves; and it does not presuppose a wave dispersion relation and is applicable to linear, weakly nonlinear, and strongly nonlinear waves.

[0021] 2. The present invention has high directional resolution accuracy: a non-parametric kernel estimation algorithm based on transient wavelet distribution probability is proposed, which retains the wave information of lateral propagation, improves the directional resolution capability, and solves the problem of underestimating diffusion intensity.

[0022] 3. The results of the present invention are highly reliable: a probability estimation algorithm on a time scale is introduced to solve the problem of contamination of the estimation results by noise or outlier data at individual moments, making the estimation results smooth, continuous and highly reliable on a time scale.

[0023] 4. The algorithm of the present invention is highly efficient: the time step of the algorithm analysis is automatically adjusted according to the degree of wave fluctuation, which can improve the efficiency of the algorithm while retaining high-precision high-frequency transient information of the waves.

[0024] 5. The estimation results of the present invention are rich in information: compared with the wave energy distribution information in frequency and direction provided by the existing technical solutions, the present invention can provide four-dimensional distribution information of wave energy in frequency, wave number, direction and time dimensions. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 This is a diagram showing the arrangement of a nine-point sensor array according to the present invention;

[0026] Figure 2 This is a graph showing the results of the data-adaptive nonparametric kernel estimation of the continuous wave number distribution of the present invention;

[0027] Figure 3 This is a schematic diagram of the dynamic overlapping segments of adjacent time-domain data of the present invention;

[0028] Figure 4 This is a comparison diagram of the global and local wave direction time domain evolution effects of the new wavelet method of the present invention and the traditional wavelet method;

[0029] Figure 5 This is a comparison diagram of the global frequency time domain evolution effects of the new wavelet method of the present invention and the traditional wavelet method;

[0030] Figure 6 This is a comparison diagram of the global wavenumber time domain evolution effect between the new wavelet method of the present invention and the traditional wavelet method;

[0031] Figure 7 This is a comparison diagram of the "wave number-direction" wave spectrum effects of the new wavelet method of the present invention and the traditional wavelet method;

[0032] Figure 8 This is a comparison chart of the "frequency-wavenumber" wave spectrum effects of the new wavelet method of the present invention and the traditional wavelet method;

[0033] Figure 9 Comparison of (a) directional diffusion effect and (b) directional diffusion reconstruction error of each frequency between the new wavelet method of the present invention and the traditional wavelet method. DETAILED DESCRIPTION

[0034] The present invention will be further described in detail below through specific examples. The following examples are only illustrative and not restrictive, and the scope of protection of the present invention cannot be limited thereto.

[0035] In order to demonstrate the performance superiority of the technical solution of the present invention, multiple groups of three-dimensional wave fields were simulated by a numerical wave tank, and the difference in directional spectrum estimation accuracy between the existing wavelet analysis method and the method proposed in the present invention was compared.

[0036] Steady-state wave example

[0037] Calculation parameters: characteristic wave height H s =3m, characteristic wave period T p = 15s, vertical wave incidence with diffusion angles of 20° on the left and right, flat seabed, still water depth of 22m, and a total time length of 5000s.

[0038] S1. Confirm the sensor measurement point array and signal sampling parameters. In this example, the sensor measurement points are arranged in a regular grid of nine measurement points commonly used in the industry. The array design plan is as follows: Figure 1 As shown, the sensor collects the real-time wavefront signal at the location, with a sampling frequency of 2 Hz and a total sampling time of T = 5000 s, and obtains the final nine-point spatial coordinate set, namely [x n ,y n ], nine-segment wavefront sequence, namely η n .

[0039] S2. Confirm the wavelet transform parameters and algorithm. The Morlet wavelet is selected as the basic unit form of the wavelet, and its calculation expression is shown in formula (1):

[0040]

[0041] Among them, the dimensionless frequency ω0 is set to 6. According to the convolution theorem, the actual calculation of wavelet changes can use fast Fourier transform to improve the calculation efficiency. The expression is shown in formula (2), and the wavelet coefficient matrix W is obtained n (s).

[0042]

[0043] S3. Analysis of the time-frequency information of the wavefront signal. The wavefront sequence collected at each measuring point is transformed using the wavelet transform to obtain the energy evolution information of the signal in the time-frequency domain, specifically: the phase time-domain change φ(f0,t0) and energy time-domain change E(f0,t0) of each frequency band. The above wave information is obtained through the wavelet transform coefficient W n (s) is obtained, and the amplitude and phase calculation formulas are shown in formula (3).

[0044]

[0045] S4. Calculate the time domain evolution of the wave number vector. According to the linear transformation relationship between the signal travel distance and its own phase, for any two pairs of measuring points (xa ,x b ), (x c ,x d ), the conversion relationship between the phase difference and the spatial position can constitute the analytical equation of the current wave number vector, as shown in formula (4). Therefore, to solve all possible measurement point pairs of the array, the solution results of all wave number vectors at each moment can be traversed. For any time t = t0, all possible wave number vectors constitute the set

[0046] φ mn (t) = k x (t)X mn +k y (t)Y mn (4)

[0047] The traditional wavelet method calculation process ends at this moment. By calculating the mean and variance of the wave number vector results at each time step, the single main wave number vector k at the current moment is obtained. main The traditional wavelet results of the current example will be displayed and compared after the subsequent signal wavelet method calculation is completed.

[0048] S5. Evaluate the stability of the wave. According to the above operation steps, the time domain evolution of the wave number vector, the time domain evolution of the phase, and the time domain evolution of the energy of each frequency band of the current wave condition have been obtained; the wave non-steady state evaluation parameter β t Determined as the temporal and spatial evolution gradient of wave number Temporal and spatial evolution gradient of wave height The function of the change in two-dimensional wave characteristics, as shown in formula (5), is used to determine whether there is short-term interference or other wave processes involved in the wave movement; according to this evaluation parameter, the time domain wave number vector samples are dynamically divided, that is, short time domain samples are used in strong non-steady state to improve the wave dynamic analysis response speed, and long time domain samples are used in steady state to improve the anti-noise performance of the wave analysis effect;

[0049]

[0050] The evaluation parameter of the wave steady state is one of the core innovations of this patent. By performing time domain calculation on the steady state of the wave, the stability of the wave movement in each period in the entire wave signal can be grasped. For the period when the wave changes dramatically, the division of the time domain samples can be dynamically reduced to improve the analytical response speed. For the period when the wave is stable, the time domain samples and overlapping segments are appropriately enlarged to improve the stability of the analysis and the ability to resist noise. The traditional wavelet method does not take into account the existence of noise and the subsequent consideration of improving the stability of the time domain samples. This makes the traditional method prone to singular solutions and energy mutation phenomena that do not conform to the actual physical characteristics during actual application.

[0051] S6. Nonparametric kernel estimation of each time-domain wavenumber sample. Based on the discontinuous calculation results of the wavenumber vector samples in terms of value and direction, a nonparametric kernel estimation algorithm is used to optimally restore the spatial distribution of the wavenumbers. The two-dimensional kernel estimation algorithm uses a recursive algorithm based on a linear diffusion process. The recursive formula and the optimized bandwidth calculation formula are shown in Equations (6) and (7), respectively.

[0052]

[0053] According to the above formula, the optimal numerical bandwidth and the optimal angular bandwidth adapted to the current wave number set are calculated respectively. Substituting them into the kernel estimation formula (8), the data adaptive plane two-dimensional non-uniform kernel function of each wave number node can be obtained;

[0054]

[0055] The kernel function is used to calculate grid by grid in the space of the current discrete wavenumber sample to obtain the spatially continuous wavenumber distribution. The assumption that "the total occurrence probability of the wavenumber vector is unity" is introduced to normalize the wavenumber distribution. The normalized result is defined as the "wavenumber spatial distribution probability" of the current time domain sample, denoted by P k , the kernel function estimation effect is as follows Figure 2 shown.

[0056] Figure 2 (a) shows the actual discrete wave number vector distribution calculated from the original signal. Figure 2 (b) shows the continuous wavenumber distribution space after non-parametric kernel estimation, where the numerical value represents the distribution probability of the wavenumber, and the wavenumber distribution is normalized by taking the total distribution probability as 1. This link is one of the core innovations of this patent, using a continuous "probability distribution" instead of "actual discrete wavenumber results". Compared with the single-point analytical solution of the traditional wavelet method, this link realizes the spatiotemporal coexistence of multiple wavelets through non-parametric kernel estimation, and can restore the energy of the wavenumber components that are not solved due to low probability of existence;

[0057] The traditional wavelet method assumes that "only a single wavelet form exists in the space-time where the array is located", so the discrete wavenumber results are averaged to determine the main wavenumber vector, so only a single wavenumber result is obtained in the end. This calculation idea ultimately leads to the low-energy wavenumbers being continuously discarded and offset in the calculation; the new wavelet method in this patent introduces a probability distribution function to estimate the most likely wavenumber probability distribution that causes the current discrete wavenumber distribution, assigns values ​​to the possibility of the existence of all wavenumbers, and thus effectively retains the energy of non-dominant wavenumbers, fundamentally solving the analytical shortcoming of the traditional wavelet method of underestimating directional diffusion.

[0058] S7, wave number space energy distribution. For a certain instantaneous result, after obtaining the continuous wave number space distribution probability P kThen, the instantaneous wave energy information obtained in S3 is distributed to the entire wave number space according to the wave number existence probability value, and the calculation is shown in formula (9), thereby obtaining the instantaneous wave number energy distribution of energy conservation;

[0059]

[0060] Therefore, by summarizing all the above processes, the above calculation process is repeated for any time and any frequency wavenumber space to obtain continuous "time-frequency-wavenumber-direction" four-dimensional data.

[0061] S8. Reconstruct the time domain directional spectrum based on the dynamic overlapping segment. The dynamic overlapping length Dt(t0) is used when splicing the estimation results of two adjacent time periods, such as Figure 3 As shown, the adjustment of the length is based on the non-steady-state evaluation result calculated in S5. During the period of strong non-steady-state, the overlapping length is shortened to respond to the current rapid wave changes. On the contrary, during the steady-state wave period, the overlapping length is appropriately lengthened to smooth the time domain changes of the wave.

[0062] S9. Selective information extraction of multi-dimensional directional spectra; according to the above process, the energy distribution of the continuous "time-frequency-wavenumber-direction" four-dimensional information of wave information has been completed. In practical applications, any two dimensions of the four dimensions can be selectively integrated, and finally six wave spectrum forms are obtained: "frequency-time" energy evolution, "wavenumber-time" energy evolution, "direction-time" energy evolution, "frequency-direction" wave spectrum, "frequency-wavenumber" wave spectrum, and "wavenumber-direction" wave spectrum; the above six wave spectra of the new wavelet method are compared with the corresponding wave spectra of the traditional wavelet method as shown in the figure below.

[0063] Figure 4 The results of the "direction-time" energy evolution calculation of the two wavelet methods are shown. From the macroscopic wave direction evolution, i.e. (a) and (c), the new wavelet method gives a continuous wave distribution for the wave direction at each time node. Therefore, compared with the traditional method, its estimation results are smoother and meet the characteristics of continuous energy distribution of the displayed waves. Since the traditional wavelet method calculates separately at each time, its macroscopic energy evolution is discontinuous, and a large number of sudden wave angle changes occur; through local details, i.e. (b) and (d), the new wavelet method effectively reduces the influence of abnormal solutions brought by noise, showing a significantly improved noise-reliable performance, while the estimation results of the traditional wavelet method are unstable and accompanied by difficult-to-explain wave direction "burrs". Such noise interference reduces the practical application reliability of the traditional method.

[0064] Figure 5The "frequency-time" energy evolution calculation results of the two wavelet methods are displayed. The figure shows that the frequency evolution effects of the two methods are basically the same, reflecting that although the new wavelet method adds dynamic overlapping segments and wavenumber probability distribution processing to the algorithm to improve the algorithm's anti-noise performance and solution stability, the algorithm does not compromise the time domain analysis effect of the wavelet method. The new wavelet method still maintains the same time domain analysis response speed as the traditional wavelet method, and its internal overlapping processing does not affect its non-steady-state analysis performance in the frequency space.

[0065] Figure 6 The "wavenumber-time" evolution calculation results of two wavelet methods are shown in the figure. The new wavelet method introduces the analytical concept of "distribution probability" in the wavenumber space, and gives a complete wavenumber distribution in the wavelet wavenumber space at each time node. Therefore, in the macroscopic wavenumber time domain evolution results, as shown in (a), the wavenumber analysis results are more continuous and smooth, which is more consistent with the evolution characteristics of the field waves. The traditional wavelet method only has a single wavenumber result for each time node and discards the non-dominant wave components. Therefore, the energy of the intuitive wavenumber evolution image is too concentrated, which makes its calculation results susceptible to noise and singular solutions, resulting in unreasonable calculation results such as discrete, discontinuous and jumping wavenumber evolution. The "wavenumber-time" evolution wave spectrum shows that the optimization of the wavenumber estimation of the new wavelet method exists in each design wavenumber calculation process, which improves the detection performance of the new wavelet method for other potential non-dominant wavenumber components in space from the source.

[0066] Figure 7 The results of the "wavenumber-direction" wave spectrum estimation of two wavelet methods are presented in this paper. The new wavelet method significantly improves the energy continuity of the wavenumber space distribution, effectively restores the energy of the non-dominant wavelet wave components, and ultimately provides an energy-continuous wavenumber distribution consistent with the test wave characteristics. The traditional method only calculates the dominant wavenumber, so the energy decreases rapidly outside the dominant wavenumber space. This is an analytical shortcoming caused by the traditional wavelet method constantly discarding non-dominant wavelet characteristics in the calculation. From this wave spectrum comparison, it can be confirmed that the new wavelet method has a significant performance improvement in wavenumber energy restoration, which makes the new wavelet method more tolerant to singular solutions and noise, making it more suitable for complex on-site wave observation operations.

[0067] Figure 8The "frequency-wavenumber" wave spectrum estimation effects of the two methods are demonstrated in the figure. The new wavelet method has a significantly improved wave detail capture effect compared with the traditional method. At the same time, even in the high-frequency signal, there is still significant wave energy retained and it still meets the preset wave linear dispersion relationship. This shows that the new wavelet method does not blindly use energy smoothing to reconstruct non-dominant wave components in the process of wave detail reconstruction. On the contrary, the high-frequency signal in Figure (a) is consistent with the dispersion equation curve, which confirms that the non-parametric kernel estimation algorithm in the algorithm is an effective data adaptive estimation choice for wave information reconstruction. The traditional wavelet method has a large amount of energy loss, and its high-frequency reconstructed waves begin to deviate from the dispersion curve. This shows that the traditional method is seriously interfered by potential noise at this time, and the wave energy reconstruction information at this time is contaminated by singular solutions and noise. The wave spectrum comparison further confirms the good stability of the new wavelet method and the effective reconstruction performance of wave information. The new wavelet method can restore wave energy while ensuring that the restored wave components are consistent with the actual wave characteristics rather than blindly smoothing.

[0068] Figure 9 The directional diffusion reconstruction effects of the two wavelet methods are demonstrated in (a). The directional diffusion function of the main peak position is shown. The new wavelet method has a significantly improved directional diffusion restoration effect compared with the traditional method. This is because it essentially restores the non-dominant wave energy on both sides, thereby improving the wavelet method's reconstruction effect on wave details. The traditional method, due to its "single wavelet" assumption, only retains the dominant wave number, and therefore seriously underestimates the directional diffusion. In the case of strong diffusion, it still gives a narrow diffusion result. As can be seen from (b), the new wavelet method not only improves the directional diffusion estimation accuracy of the main peak, but this performance improvement is a common feature of the entire frequency band. The new wavelet method doubles the analytical accuracy in the entire analytical frequency band, confirming the good performance of the method.

[0069] Although the embodiments and drawings of the present invention are disclosed for illustrative purposes, those skilled in the art will understand that various substitutions, changes and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A method for estimating the directional spectrum of unsteady ocean waves, characterized by: The steps of the method are: S1. Signal decomposition: Wavelet transform is used to decompose the wave signal to obtain the time-frequency localization characteristics of different frequency components, including the time domain evolution information of amplitude and phase; S2. Direction distribution calculation: At each time and frequency scale, the coefficient matrix of the wavelet transform is used to calculate the possible direction distribution and extract the energy value of each direction; S3. Adaptive adjustment of time domain analysis step size: The time domain analysis time period is divided according to the changing characteristics of the wave signal. If the wave signal fluctuation is relatively stable within a certain time period and is lower than the dynamic threshold, all wave information within the preset larger time step is used as a single sample for subsequent probability analysis. If the wave direction changes drastically within a certain time period, the time step is shortened according to the degree of fluctuation, and the wave information of the short period is used as the subsequent estimation sample. S4. Nonparametric kernel estimation of transient wavelet distribution probability: Based on the wavenumber-direction distribution calculation results of each time-domain sample, a two-dimensional bandwidth optimization algorithm is used to iteratively determine the optimal wavenumber bandwidth and optimal direction bandwidth for the current sample set. A two-dimensional non-uniform kernel function is then constructed for the current time-domain sample. Subsequently, a nonparametric estimation method is used to perform statistical distribution modeling on the wavenumber-direction distribution results of each time-domain sample using the two-dimensional non-uniform kernel function. This generates a "wavenumber-direction" probability map for the wavelet in the array of each sample, effectively retaining the probability of the existence of lateral low-energy wavelets. S5. Time-domain adaptive reconstruction of directional spectrum: The calculation results of all time-domain samples are integrated, and the total wave energy value is obtained by referring to the collection results of the field signal. The wave energy units are allocated according to the continuous wavelet probability distribution to meet the conservation of total energy. The estimation results of adjacent time-domain samples are dynamically overlapped according to the wave fluctuation degree to maintain the smooth transition of wave information in the time-domain evolution, and the "wave number-direction" time-domain distribution of each frequency is obtained, that is, the "wave number-direction-frequency-time" four-dimensional estimation result of wave energy.

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