CN107679456B - Ocean platform vibration response noise elimination method based on extreme value-residue decomposition - Google Patents

Ocean platform vibration response noise elimination method based on extreme value-residue decomposition Download PDF

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CN107679456B
CN107679456B CN201710795081.2A CN201710795081A CN107679456B CN 107679456 B CN107679456 B CN 107679456B CN 201710795081 A CN201710795081 A CN 201710795081A CN 107679456 B CN107679456 B CN 107679456B
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刘福顺
卢洪超
金磊
陈杰峰
刘程程
齐聪山
崔高杰
高树健
汪沐阳
周星宇
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Ocean University of China
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Abstract

The invention relates to an extreme value-residue decomposition-based ocean platform vibration response denoising method which comprises the steps of data segmentation, sense component selection, extreme value-residue low-order state space solving, denoising signal reconstruction and the like. The method directly processes the response signal, decomposes the measured data into real components and noise components, and selects the extreme value and the residual number of the real components through the frequency spectrum signal without system information and kernel function; for longer data segments, segmentation processing is carried out by using a sliding window, a frequency window is created, and sense components of each segment of intercepted data are selected according to an amplitude-frequency diagram, so that the calculation efficiency is higher; the method is suitable for denoising of most structural response data in engineering and signal denoising of high background noise data, and has a wide engineering application range and application prospects.

Description

Ocean platform vibration response noise elimination method based on extreme value-residue decomposition
Technical Field
The invention relates to the field of response signal denoising, in particular to an extreme value-residue decomposition-based ocean platform vibration response denoising method, which aims at denoising signals of actually measured data of structures such as offshore wind power, ocean platforms and the like under the action of complex ocean environment loads such as wind, wave, current and the like.
Background
When the marine structure is tested, the response signal often contains a large amount of environmental noise, and the noise has a large influence on the subsequent processing of the response signal. The traditional signal denoising methods include a low-rank approximation algorithm based on Singular Value Decomposition (SVD), a wavelet denoising method, Kalman filtering and other methods, and the methods have a good denoising effect on low-energy noise, but have certain limitations in use.
The low-rank approximation algorithm based on Singular Value Decomposition (SVD) is to perform SVD on a Hankel matrix formed by response data, a smaller singular value corresponds to a noise component and is set to be zero so as to achieve the purpose of noise elimination, and the low-rank approximation algorithm has an ideal noise elimination effect on signals with smaller signal-to-noise ratio; however, when the noise energy is larger, the singular value corresponding to the noise component may be larger than the singular value corresponding to the structure inherent component, thereby showing the noise cancellation limitation; in addition, when the response data is large, the dimension of the Hankel matrix is large, a large amount of computer resources are consumed for SVD, the operation efficiency is low when the number of data points is large, and even the calculation cannot be completed. The wavelet denoising method is to apply wavelet decomposition to a Frequency Response Function (FRF) in a frequency domain to denoise, and is applied to a 2-degree-of-freedom quality-spring-damping system, thereby effectively eliminating Gaussian white noise added in a signal, but the wavelet denoising algorithm has larger dependence on the selection of a wavelet kernel function, and the selection of a proper wavelet kernel function is difficult and is limited in practical application; the kalman filtering method needs to know system information, which is often unavailable; researchers do a lot of work on signal denoising, but the current signal denoising methods have more or less certain limitations.
Disclosure of Invention
The invention aims to solve the technical problems that aiming at the defects that traditional noise elimination methods such as SVD decomposition and wavelet decomposition methods are low in calculation efficiency and difficult in wavelet kernel function selection, the ocean platform vibration response noise elimination method based on extreme value-residue decomposition is provided, response signals are directly processed without system information and kernel functions, a longer data segment is processed in a segmentation mode through a sliding window, the method has higher calculation efficiency, and a quick and effective signal noise elimination method can be provided for ocean structure test signals.
The invention is realized by adopting the following technical scheme: an extreme value-residue decomposition-based ocean platform vibration response noise elimination method comprises the following steps:
step S1, data segmentation: for response data yn(n-1, 2, …) to obtain
Figure GDA0003065923190000011
Wherein the content of the first and second substances,
Figure GDA0003065923190000012
for equal length data segments intercepted from the original response data, n0Is the length of equal length data; the original response data is processed in a segmented mode, so that the problem that when the noise-eliminating signal data is large, the calculation efficiency is low and even calculation cannot be performed is solved;
step S2, sense component selection: fourier analysis is carried out on the intercepted data segment, a frequency window is created, sense components with larger energy in the data segment are selected according to an amplitude-frequency diagram, and the sense components are contained in the frequency window;
step S3, solving the extreme value-residue low-order state space: carrying out Prony decomposition on the intercepted data segment, and solving an extreme value and a residual number by using a low-order state space method;
s4, reconstructing a noise-eliminating signal;
and (4) repeatedly executing the step (S2) to the step (S4), and sequentially processing each data segment intercepted in the step (S1), so that the noise in the whole segment of signal is effectively eliminated, and the purpose of eliminating the noise is achieved.
Further, the selecting of the sense component in the step S2 specifically includes the following steps:
step S21, discrete fourier transform of the segmented signal: fourier transform is respectively carried out on each section of signal to obtain
Figure GDA0003065923190000021
Step S22,Drawing an amplitude-frequency graph: according to the sampling frequency fsObtaining frequency of amplitude-frequency diagram
Figure GDA0003065923190000022
Drawing a relational graph of (l) to (l) Y (l), namely an amplitude-frequency graph;
step S23, using the corresponding frequency f at the peak of the amplitude-frequency diagrampFor the center frequency, a frequency window width h is set, and a frequency window range for obtaining the sense component is
Figure GDA0003065923190000023
Further, in step S3, the solution method for the extremum-residue low-order state space is specifically as follows:
step S31, discrete response signal Prony decomposition:
Figure GDA0003065923190000024
where p is the order of decomposition, Δ t is the sampling interval, λm＝-αm+iωmIn order to be an extreme value,
Figure GDA0003065923190000025
is the corresponding residue, αmAs damping coefficient, ωmIs the angular frequency, AmIs the amplitude, θmIs the phase;
step S32, constructing a Hankel matrix: a Hankel matrix is defined according to the structural response signals:
Figure GDA0003065923190000026
where ξ and η represent the number of rows and columns of H (k);
step S33, solving the extremum-residue low-price state space: using Singular Value Decomposition (SVD) technique to obtain an implementation matrix estimate of the system
Figure GDA0003065923190000027
To pair
Figure GDA0003065923190000028
Performing eigenvalue analysis with z as the eigenvaluemM is 1,2, …, p, and an extremum λ is obtainedm＝ln(zm) At, finally finding the corresponding residue gammamThen the corresponding arrays λ and γ are:
λ＝[λreal,1 λreal,2 … λreal,m λnoise,1 λnoise,2 … λnoise,l]；
γ＝[γreal,1 γreal,2 … γreal,m γnoise,1 γnoise,2 … γnoise,l]；
in the formula ofreal,iAnd gammareal,iI is 1,2, …, m represents the extreme value of the real component and the corresponding residue;
Figure GDA0003065923190000031
j 01,2, … … l represents the extremum of the noise and the corresponding residue.
Further, in step S4, the noise-canceling signal reconstruction specifically includes:
step S41, obtaining the extreme value and the residue according to the step S33, and the frequency window range according to the step S23, and according to the relationship between the extreme value and the frequency
Figure GDA0003065923190000032
Converting the extreme value obtained in the step S33 into a frequency, obtaining an extreme value and a corresponding residue within the frequency window range:
λreal＝[λreal,1 λreal,2 … λreal,m]；
γreal＝[γreal,1 γreal,2 … γreal,m]；
step S43, reconstructing the denoised signal
Figure GDA0003065923190000033
In the formula yrealTo be a denoised signal.
Compared with the prior art, the invention has the advantages and positive effects that:
1) the ocean platform vibration response noise elimination method based on extreme value-residue decomposition, provided by the invention, is used for carrying out equal-length segmentation processing on response signals, creating a frequency window, and carrying out sense component selection on each section of intercepted data according to an amplitude-frequency diagram, so that the problem that the traditional method is low in calculation efficiency and even cannot calculate when the noise elimination signal data is large is solved, meanwhile, the calculation precision can be improved, and the method is suitable for noise elimination of most structural response data in engineering;
2) the method directly processes the response signal, decomposes the measured data into real components and noise components, and selects the extreme value and the residual number of the real components through the frequency spectrum signal without system information and kernel function; the inherent information of the structure is represented by using an extreme value-residue method, so that signal reconstruction is facilitated, and the inherent information of the structure is not changed even if a real signal is polluted by noise; the method can also be used for signal denoising of high background noise data, and has a wide engineering application range and an application prospect.
Drawings
FIG. 1 is a flow chart of a denoising method according to an embodiment of the present invention;
FIG. 2 is a diagram of a numerical model of an ocean platform;
FIG. 3 is a schematic diagram of the time course and the frequency spectrum of a noise signal with a signal-to-noise ratio of 20dB and no noise according to an embodiment of the present invention;
fig. 4 is a schematic diagram showing the comparison of the time course and frequency spectrum of a signal after noise cancellation by using the method of the embodiment of the invention and a signal without noise.
Detailed Description
In order to make the above objects, features and advantages of the present invention more clearly understood, the present invention will be further described with reference to the accompanying drawings and examples. It should be noted that the embodiments and features of the embodiments of the present application may be combined with each other without conflict.
The embodiment provides an extreme value-residue decomposition-based ocean platform vibration response noise cancellation method, which specifically includes, with reference to fig. 1: step S1, data segmentation; step S2, selecting sense components; step S3, solving the extremum-residue low order state space, and step S4, reconstructing the noise cancellation signal, specifically:
1) the processing procedure of the data section of step S1 is as follows:
for the raw response data yn(n is 1,2, …), if the data volume is large, it will result in low computation efficiency, in order to solve this problem, this embodiment will segment the signal through the sliding window to obtain
Figure GDA0003065923190000041
In the formula
Figure GDA0003065923190000042
For equal length data segments intercepted from the original data, n0The window length is expressed by a parameter for the length of the equal-length data, the length can be defined by a user, the calculation efficiency can be effectively improved, and the noise elimination of the whole response data can be completed by respectively eliminating the noise of each data segment.
2) The specific process of selecting the sense component in step S2 is as follows:
(1) and performing discrete Fourier transform on the intercepted data segment:
Figure GDA0003065923190000043
Figure GDA0003065923190000044
the intercepted ith section of data;
(2) drawing an amplitude-frequency graph:
according to the sampling frequency fsThe frequency of the amplitude-frequency diagram is obtained,
Figure GDA0003065923190000045
drawing a relational graph of (l) to (l) Y (l), namely an amplitude-frequency graph;
(3) at the corresponding frequency f at the peakpSetting the width of a frequency window as h for the central frequency, and obtaining the frequency window range of the sense component as
Figure GDA0003065923190000046
The frequency window is determined according to the amplitude-frequency diagram, the spectrum at the peak is a narrow spectrum,the width of the window can be set smaller; if the spectrum is wide, the window width is set to be large, and the frequency window needs to contain the component with large energy.
The step selects the signal component with stronger energy according to the frequency spectrum, and is convenient to find out the extreme value and the residue of the sense component through the corresponding relation that the module of the extreme value is the angular frequency.
3) The specific process of solving the extreme value-residue low-order state space in the step S3 is as follows:
(1) prony decomposition is carried out on the intercepted data segment, the extreme value and the residue are solved by applying a low-order state space method, the Prony decomposition is carried out on the discrete response signal,
Figure GDA0003065923190000047
where p is the order of decomposition, Δ t is the sampling interval, λm＝-αm+iωmIn order to be an extreme value,
Figure GDA0003065923190000048
is a corresponding residue, and αmAs damping coefficient, ωmIs the angular frequency, AmIs the amplitude, θmIs the phase;
(2) defining a Hankel matrix from the structural response signals
Figure GDA0003065923190000051
Where ξ and η represent the number of rows and columns of H (k);
(3) solving an extremum-residue low-price state space:
using Singular Value Decomposition (SVD) technique to obtain an implementation matrix estimate of the system
Figure GDA0003065923190000052
Figure GDA0003065923190000053
Figure GDA0003065923190000054
Figure GDA0003065923190000055
To pair
Figure GDA0003065923190000056
Performing eigenvalue analysis with z as the eigenvaluemM is 1,2, …, p, and an extremum λ is obtainedm＝ln(zm) At, finally finding the corresponding residue gammam：
λ＝[λreal,1 λreal,2 … λreal,m λnoise,1 λnoise,2 … λnoise,l]
γ＝[γreal,1 γreal,2 … γreal,m γnoise,1 γnoise,2 … γnoise,l]
Lambda is an array formed by all extreme values of Prony decomposition, gamma is an array formed by corresponding reserved numbers, wherein lambda isreal,iAnd gammareal,iI is 1,2, …, m represents the extreme value of the real component and the corresponding residue;
Figure GDA0003065923190000057
and expressing the extreme value and the corresponding residue of the noise, decomposing the actually measured data into a real component and a noise component, and respectively representing the components of the actually measured data by using the extreme value and the residue.
4) The specific process of reconstructing the noise-canceling signal in step S4 is as follows:
(1) obtaining an extreme value and a reserve number in a frequency window range: according to the relationship between the extreme value and the frequency of
Figure GDA0003065923190000058
Converting the extreme value obtained in the step S3 into frequency to obtain an extreme value and a corresponding reserve number in a frequency window range:
λreal＝[λreal,1 λreal,2 … λreal,m]；
γreal＝[γreal,1 γreal,2 … γreal,m]；
(2) the signal after the noise cancellation is reconstructed and,
Figure GDA0003065923190000059
in the formula yrealTo be a denoised signal. The method comprises the steps of selecting an extreme value and a residue of a real component through a frequency spectrum signal, and representing the actually measured data component by using the extreme value and the residue to facilitate signal reconstruction in noise elimination.
And repeating the processing processes from the step S2 to the step S4, and sequentially processing each data segment intercepted in the step S1, thereby efficiently eliminating the noise in the whole segment of signals and achieving the purpose of noise elimination.
And (3) experimental verification:
the method is characterized in that a certain ocean platform is taken as a prototype, model simplification is carried out, a numerical model shown in figure 2 is established, the platform structure comprises 20 nodes and 48 units, the bottom 4 nodes are fixed, the other 16 nodes are provided, each node has 6 directional degrees of freedom (namely x, y and z translation, and rotation around x, y and z, and each degree of freedom has a response signal), and the total number of degrees of freedom is 96. Geometric parameters are as follows: the total height of the model is 30m, the bottom length is 16.22m, the width is 13.22m, the height of each layer is about 8.5m, and the elastic modulus is 2.1 multiplied by 1011Pa, density 7.8X 103kg/m3The cross section of the upright post is 0.050064m2Inertia moment of 0.022075m4The cross section area of the cross brace diagonal brace is 0.19905m2Inertia moment of 0.0031218m4。
And (4) comparing the results:
1) applying pulse excitation to the x direction of the ocean platform numerical model node 1 to obtain response data of the node in the x direction, adding white noise with the signal-to-noise ratio of 20dB to the response data, and simulating the noise of actually measured data. Before and after the addition of noise, its time and frequency spectrum pair is as shown in fig. 3. It can be seen from the time-course diagram that after the noise is added, a small amount of 'glitch' appears in the signal, and the noise component in the spectrogram is more obvious.
2) By using the invention, the frequency window ranges of the system six-order components are selected as (6.8, 7.2), (8.8, 9.2), (10.8, 11.2), (18.2, 18.7), (20.1, 20.5) and (23, 23.5), the extreme value and the residue of the frequency window range are substituted into the step S42, and the reconstruction is carried out to obtain the signal after noise elimination. The comparison of the time interval and the frequency spectrum of the signal after noise cancellation with the pair of the signal without noise shown in fig. 4 shows that the invention can effectively cancel the noise in the impulse response signal.
The above description is only a preferred embodiment of the present invention, and not intended to limit the present invention in other forms, and any person skilled in the art may apply the above modifications or changes to the equivalent embodiments with equivalent changes, without departing from the technical spirit of the present invention, and any simple modification, equivalent change and change made to the above embodiments according to the technical spirit of the present invention still belong to the protection scope of the technical spirit of the present invention.

Claims (2)

1. An ocean platform vibration response noise elimination method based on extreme value-residue number decomposition is characterized by comprising the following steps:
step S1, data segmentation: for response data yn(n-1, 2, …) to obtain
Figure FDA0003065923180000011
Wherein the content of the first and second substances,
Figure FDA0003065923180000012
for equal length data segments intercepted from the original response data, n0Is the length of equal length data;
step S2, sense component selection: fourier analysis is carried out on the intercepted data segment, a frequency window is created, sense components with larger energy in the data segment are selected according to an amplitude-frequency diagram, and the sense components are contained in the frequency window;
step S21, discrete fourier transform of the segmented signal: fourier transform is respectively carried out on each intercepted signal section to obtain
Figure FDA0003065923180000013
Step S22, drawing an amplitude-frequency graph: according to the sampling frequency fsObtaining frequency of amplitude-frequency diagram
Figure FDA0003065923180000014
Drawing a relational graph of (l) to (l) Y (l), namely an amplitude-frequency graph;
step S23, using the corresponding frequency f at the peak of the amplitude-frequency diagrampFor the center frequency, a frequency window width h is set, and a frequency window range for obtaining the sense component is
Figure FDA0003065923180000015
Step S3, solving the extreme value-residue low order state space, namely, carrying out Prony decomposition on the intercepted data segment, solving the extreme value and the residue, decomposing the actually measured data into real components and noise components according to the step S2, and representing the real components and the noise components by using the extreme value and the residue;
step S31, discrete response signal Prony decomposition:
Figure FDA0003065923180000016
Figure FDA0003065923180000017
where p is the order of decomposition, Δ t is the sampling interval, λm＝-αm+iωmIn order to be an extreme value,
Figure FDA0003065923180000018
is the corresponding residue, αmAs damping coefficient, ωmIs the angular frequency, AmIs the amplitude, θmIs the phase;
step S32, constructing a Hankel matrix: a Hankel matrix is defined according to the structural response signal;
Figure FDA0003065923180000019
where ξ and η represent the number of rows and columns of H (k);
step S33, solving the extremum-residue: using singular valuesDecomposition technique to obtain an implementation matrix estimate of the system
Figure FDA00030659231800000110
To pair
Figure FDA00030659231800000111
Performing eigenvalue analysis with z as the eigenvaluemM is 1,2, …, p, and an extremum λ is obtainedm＝ln(zm) T and corresponding residue gammam；
λ＝[λreal,1 λreal,2 … λreal,m λnoise,1 λnoise,2 … λnoise,l]；
γ＝[γreal,1 γreal,2 … γreal,m γnoise,1 γnoise,2 … γnoise,l]；
Lambda is an array formed by all extreme values decomposed by Prony, gamma is an array formed by corresponding reserved numbers, and lambda isreal,iAnd gammareal,iI is 1,2, …, m represents the extreme value of the real component and the corresponding residue;
Figure FDA0003065923180000021
representing the extreme value of the noise and the corresponding residue;
and step S4, reconstructing the noise-eliminated signal.
2. The extremum-residue decomposition based ocean platform vibrational response noise canceling method of claim 1, wherein: in step S4, the noise cancellation signal reconstruction specifically includes:
step S41, obtaining the extreme value and the residue according to step S33, and the frequency window range of the sense component in step S23 according to the relationship between the extreme value and the frequency
Figure FDA0003065923180000022
Converting the extreme value obtained in the step S33 into a frequency, obtaining an extreme value and a corresponding residue within the frequency window range:
λreal＝[λreal,1 λreal,2 … λreal,m]；
γreal＝[γreal,1 γreal,2 … γreal,m]；
step S42, reconstructing the denoised signal
Figure FDA0003065923180000023
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