A method for separating wind wave and swell based on variational mode decomposition

Abstract

The application provides a wind wave and swell separation method based on variational mode decomposition, and relates to the technical field of sea wave separation, and comprises the following steps: obtaining wave height displacement-time history data of a wave surface of the sea by a wave buoy; obtaining a segmentation frequency of wind waves and swell waves by using a two-dimensional spectrum method; performing mode decomposition on the wave height displacement-time history data and obtaining a center frequency of each constituent wave; dividing the constituent waves according to the segmentation frequency as a criterion to obtain wave surface curves of wind waves and swell waves. The application can obtain wave surface displacement of wind waves and swell waves in sea waves by using data of a single point buoy, solves the problem that a traditional method can only obtain a spectrum form of wind waves and swell waves and cannot obtain a wave surface displacement curve, and provides convenience for engineering application and scientific research.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of sea wave separation, in particular, especially relates to a method for separating wind wave and swell wave based on variational mode decomposition. BACKGROUND

[0002] The sea waves appearing in the ocean are usually mixed waves composed of wind waves and swell waves, the wind waves are the waves generated by local wind and always under the action of wind, and the swell waves are the waves left on the sea surface after the local wind decreases or turns or the waves transmitted from other sea areas. In terms of appearance characteristics, the wind waves are characterized by: the leeward side is steeper than the windward side, the two sides are asymmetric, the period is smaller, and the wave crest line is shorter; the swell waves are characterized by: the wave surface is flat, the two sides are symmetrical, the period is larger, the wave crest line is longer, and the regularity is more obvious.

[0003] The existing method for separating wind waves and swell waves adopts a two-dimensional spectrum method. The two-dimensional spectrum method determines the relationship between the wave direction spectrum and the wind speed vector according to the characteristics that wind and ocean surface interact to generate energy and then transmit to generate waves. When separating wind waves and swell waves, the four elements of wave direction, wind direction, wave speed and wind speed are considered, which can effectively distinguish the wind wave and swell wave components in the waves. Since the separation result obtained by the two-dimensional spectrum method is more stable and reliable, it is usually recognized as the standard value for separating wind waves and swell waves.

[0004] However, the existing separation method separates on the basis of the sea wave spectrum, and the obtained result is also in the form of spectrum and the statistical characteristics of the waves, and continuous wave height displacement data cannot be obtained. In actual engineering applications, especially in the research of wave evolution prediction, wave making in a pool, the action of waves on marine structures such as ships, etc., continuous wave height displacement data is needed, so the existing method has certain limitations in actual engineering applications. SUMMARY

[0005] Therefore, the purpose of the present application is to provide a method for separating wind waves and swell waves based on variational mode decomposition, so as to solve the technical problem that the existing method can only divide wind waves and swell waves but cannot obtain wind wave and swell wave displacement data.

[0006] The technical means adopted by the present application are as follows:

[0007] A method for separating wind waves and swell waves based on variational mode decomposition, comprising:

[0008] Obtaining continuous wave height displacement-time history data of the ocean wave surface by wave buoy;

[0009] Obtaining the separation frequency of wind waves and swell waves by using a two-dimensional spectrum method;

[0010] Performing mode decomposition on the wave height displacement-time history data and obtaining the center frequency of each constituent wave;

[0011] The waves are divided into wind waves and swell waves according to the dividing frequency.

[0012] Further, the dividing frequency of the wind waves and the swell waves is obtained by using a two-dimensional spectrum method, including the following steps:

[0013] The two-dimensional sea wave spectrum is smoothed, and a two-dimensional discrete convolution operation is performed on adjacent spectrum peaks by weighted averaging, and the formula is as follows:

[0014]

[0015] wherein S(i,j) is the original spectrum; is the spectrum after the two-dimensional discrete convolution operation; i and j are element numbers; is convolution; κ is the convolution dimension;

[0016] The dividing frequency of the wind waves and the swell waves is obtained by using the smoothed two-dimensional sea wave spectrum, and the formula is as follows:

[0017]

[0018] wherein f s is the dividing frequency; θ is the wave direction; U 10 is the wind speed at a height of 10 m; θ wind is the wind direction; and T is a threshold value.

[0019] Further, the wave height displacement-time history data is subjected to modal decomposition, and the center frequency of each component wave is obtained, including the following steps:

[0020] A variational modal decomposition algorithm is used to decompose the original input signal into a sum of a plurality of intrinsic modal functions, and the decomposition process is as follows:

[0021]

[0022]

[0023] wherein {u K}={u1,...,u K} represents K components obtained by decomposition; {ω K}={ω1,...,ω K} represents the center frequency in each component, δ(t) is the input signal, t is time, and j represents the jth component.

[0024] Further, the determination method of the wind waves and the swell waves is as follows:

[0025] The center frequency of the constituent wave is determined by taking the frequency division of wind wave and swell as the division standard; when the center frequency of the constituent wave is less than the division frequency, the constituent wave is swell; and when the center frequency of the constituent wave is greater than the division frequency, the constituent wave is wind wave.

[0026] Compared with the prior art, the present application has the following advantages:

[0027] The present application solves the problem that the traditional method can only obtain the spectrum of wind wave and swell but cannot obtain the wave surface displacement curve, and provides convenience for engineering application and scientific research. BRIEF DESCRIPTION OF DRAWINGS

[0028] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0029] Figure 1 The present application is a method flowchart.

[0030] Figure 2 The present application is a two-dimensional measured sea wave spectrum diagram.

[0031] Figure 3 The present application is a sea wave spectrum diagram after two-dimensional convolution transformation.

[0032] Figure 4 The present application is a wind wave and swell division frequency result diagram of sea wave spectrum.

[0033] Figure 5 The present application is a wind direction division result diagram based on frequency.

[0034] Figure 6 The present application is a sea wave wave height displacement-time sequence diagram.

[0035] Figure 7 The present application is the first-6 parts of 12 decomposition results of wave height displacement by variational mode decomposition.

[0036] Figure 8 The present application is the seventh-12 parts of 12 decomposition results of wave height displacement by variational mode decomposition.

[0037] Figure 9 The present application is a separated swell component wave surface diagram.

[0038] Figure 10 The present application is a separated wind wave component wave surface diagram.

[0039] Figure 11 The amplitude spectrum of the original sea wave of the present application.

[0040] Figure 12 The amplitude spectrum of the separated swell component of the present application.

[0041] Figure 13 The amplitude spectrum of the separated wind wave component of the present application. DETAILED DESCRIPTION

[0042] In order to make the person skilled in the art better understand the present application, the technical solutions in the embodiments of the present application will be described clearly and completely below in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by the person skilled in the art without creative labor should belong to the protection scope of the present application.

[0043] It should be noted that the terms "first", "second" and the like in the specification and claims of the present application and the above-described drawings are used to distinguish similar objects, and do not necessarily indicate a specific order or a chronological sequence. It should be understood that the data thus used can be interchanged under appropriate circumstances, so that the embodiments of the present application described herein can be implemented in an order other than that illustrated or described herein. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but can include other steps or units not clearly listed or inherent to the process, method, product or device.

[0044] The present application provides a method for separating wind wave and swell wave based on variational mode decomposition, as shown in Figure 1 The method comprises the following steps:

[0045] Step one, obtaining the segmentation frequency f from the two-dimensional spectrum of sea wave s

[0046] The two-dimensional spectrum method first smoothes the two-dimensional sea wave spectrum when dividing wind and swell waves. The two-dimensional discrete convolution operation needs to be performed on the adjacent spectrum peak by weighted averaging. The method is as follows:

[0047]

[0048] In the formula, S(i,j) is the original spectrum, is the spectrum after two-dimensional discrete convolution operation, both of which have i x j elements; the symbol represents convolution. When the convolution dimension κ takes the 3x3 constant matrix shown in formula (2):

[0049]

[0050] The identification criterion of wind wave can be determined according to formula (3) on the basis of the smoothed two-dimensional spectrum:

[0051]

[0052] In the formula, f s is the frequency division; θ is the wave direction; U 10 represents the wind speed at the height of 10 m; θ wind represents the wind direction; and T is the threshold value, which is usually 1.0-1.9.

[0053] The two-dimensional spectrum of sea wave is shown in Figure 2 , the smoothed result is shown in Figure 3 , the frequency division result is shown in Figure 4 , and the division of wind wave and swell wave is shown in Figure 5 .

[0054] Step 2, mode decomposition is performed on the measured wave height-time history data, and the center frequency of each constituent wave is obtained.

[0055] The VMD algorithm decomposes the original input signal into the sum of a plurality of intrinsic mode functions, which decomposes the input signal into discrete data of sub-band signals, and has certain sparse properties in the decomposition process. The wave height displacement signal used in the example in the present text is shown in Figure 6 . The signal is decomposed into modal components u k with a plurality of center frequencies ω k , and the decomposition process is:

[0056]

[0057]

[0058] In formula (3-2), {u K}={u1,...,u K} represents the K components obtained by decomposition;

[0059] {ω K}={ω1,...,ω K} represents the center frequency in each component.

[0060] The modal decomposition algorithm is as follows:

[0061] 1) initialization

[0062] 2) use the loop n=n+1, k=1:k

[0063] When ω ≥ 0, update parameters alternately and ω k :

[0064]

[0065]

[0066] Using the dual ascent method: ω ≥ 0

[0067]

[0068] The condition that the convergence satisfies is:

[0069]

[0070] In the examples in this paper, the 12 components obtained by decomposition are as shown in Figure 7-8 .

[0071] For any intrinsic modal function u(t), its Hilbert transform y(t) is:

[0072]

[0073] According to this definition, u(t) and y(t) in equation (3-7) form a conjugate complex pair, so the analytic signal z(t) can be obtained:

[0074] z(t) = x(t) + iu(t) = a(t)e iθ(t) (3-8)

[0075] In equation (3-8), the amplitude a(t) and angle θ(t) of the intrinsic modal function are expressed as:

[0076]

[0077]

[0078] Through Hilbert transform, the instantaneous frequency is defined as:

[0079]

[0080] In summary, by performing Hilbert transform on these IMF components, the Hilbert time-frequency spectrum of the signal x(t) can be finally obtained, denoted as:

[0081]

[0082] Equation (3-10) omits the residual amount, Re represents taking the real part, and this equation reflects the distribution of the instantaneous amplitude in the time-frequency plane.

[0083] Step three, the segmented frequency f s For the division standard, the modal with the center frequency f s is the swell, and the modal with the center frequency f s is the wind wave, and they are superimposed respectively.

[0084] According to the IMF definition:

[0085] u k (t) = A k (t) cos (φ k (t)) (3-12)

[0086] In the formula, A k (t) is the amplitude envelope of u k (t), and A k (t) ≥ 0; φ k (t) is the instantaneous phase of u k (t), and Compared with the instantaneous phase , the amplitude envelope A k (t) and the instantaneous angular frequency change more slowly.

[0087] The amplitude envelope A k (t) and the instantaneous angular frequency ω k (t) have been obtained by HHT, and then the wave surface can be expressed as:

[0088]

[0089] Finally, the wave surface displacement time history data of the wind wave and the swell are obtained respectively as shown in Table 1, wherein the obtained swell result is shown in Figure 9 , and the wind wave result is shown in Figure 10 . For the wave height displacement signal in Figure 6 , the Fourier spectrum is shown in Figure 11 ; Figure 12 the spectrum of the obtained swell is Figure 13 , and the spectrum of the obtained wind wave is . It can be seen that compared with the measured wave signal, the frequency amplitude distribution in the corresponding part is in good agreement.

[0090]

[0091]

[0092] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions recorded in the above embodiments can be modified, or some or all of the technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for separating wind waves and swell waves based on variational mode decomposition, characterized in that, The method comprises the following steps: Obtaining wave height displacement-time history data of ocean wave surface continuity by wave buoy; Obtaining the segmentation frequency of wind wave and swell wave by using two-dimensional spectrum method; Carrying out modal decomposition on the wave height displacement-time history data and obtaining the center frequency of each constituent wave; Dividing the constituent wave according to the segmentation frequency to obtain the wave surface curve of wind wave and swell wave; Obtaining the segmentation frequency of wind wave and swell wave by using two-dimensional spectrum method comprises the following steps: Carrying out smoothing processing on the two-dimensional sea wave spectrum, and carrying out two-dimensional discrete convolution operation on the adjacent spectrum peak by average weighting, and the formula is as follows: wherein, is the original spectrum; is the spectrum after two-dimensional discrete convolution operation; i and j is the number of elements; is the convolution; is the convolution dimension; Obtaining the segmentation frequency of wind wave through the two-dimensional sea wave spectrum after smoothing processing, and the formula is as follows: wherein, is the splitting frequency; is the wave direction; is the wind speed at 10 m height; is the wind direction; is the threshold value; Carrying out modal decomposition on the wave height displacement-time history data and obtaining the center frequency of each constituent wave comprises the following steps: Adopting the variational modal decomposition algorithm to decompose the wave height-time measured by the buoy into the sum of multiple intrinsic modal functions as the original input signal, and the decomposition process is as follows: wherein: denotes the K components resulting from the decomposition; denotes the center frequency in each component, is the input signal, is time, denotes the first component. 2.The method of separating wind waves from swell waves based on variational mode decomposition according to claim 1, wherein, The determination method of wind wave and swell wave is as follows: Determining the center frequency of the constituent wave according to the segmentation frequency of wind wave and swell wave as the division standard, when the center frequency of the constituent wave is less than the segmentation frequency, the constituent wave is swell wave, and when the center frequency of the constituent wave is greater than the segmentation frequency, the constituent wave is wind wave.

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