CN112711737A - Marine structure weak nonlinear signal decomposition method - Google Patents
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Abstract
The invention relates to a weak nonlinear signal decomposition method for a marine structure, which comprises the following steps: determining the original dynamic response of the marine structure to be tested, performing FFT (fast Fourier transform) on the original dynamic response, and performing equidistant sliding segmentation on the full-frequency-band frequency spectrum; carrying out IFFT transformation on each divided sub-frequency band in sequence to obtain an original dynamic response sub-signal corresponding to each sub-frequency band; decomposing and reconstructing the original dynamic response sub-signals corresponding to the sub-bands based on the Prony sequence; comparing the relative residual error between the original dynamic response sub-signal corresponding to each sub-frequency band and the reconstructed dynamic response sub-signal, and judging the decomposition precision of the original dynamic response sub-signal corresponding to each sub-frequency band; and reconstructing the full-band dynamic response signal and judging the integral decomposition precision of the full-band original dynamic response signal. The method can efficiently realize high-precision decomposition of the nonlinear signals of the marine structure, and provides a foundation for modal parameter identification, time-frequency analysis, noise elimination and other applications of the nonlinear signals.
Description
Technical Field
The invention belongs to the technical field of power design of marine structures, and particularly relates to a weak nonlinear signal decomposition method for a marine structure.
Background
To ensure safe operation of offshore wind power structures during their service life, structural designs have evolved from a simple strength design phase to a reliability design phase. The dynamic design process of the structure is not simple structure dynamic characteristic calculation any more, but is gradually developed into a dynamic response analysis process of the whole structure. The actual marine structure is in a complex marine environment, the complexity of an actual measurement signal is determined, and therefore the actual measurement signal generally has the characteristics of nonlinearity, non-stationarity and the like, high-precision and high-efficiency decomposition of the marine structure nonlinear signal is difficult to achieve by adopting the traditional methods such as fast Fourier transform, wavelet transform, empirical mode decomposition and the like, a more accurate signal decomposition model and a high-efficiency model optimization algorithm are constructed, and the method is a key for improving the characterization of the decomposition method on the nonlinear and non-stationary signals.
The fast Fourier transform can quickly transform the signal from time domain to frequency domain, and the inverse Fourier transform can be used to quickly extract the signal component in the target frequency interval. However, due to linear and periodic assumptions, the direct application of fourier transform to decompose signals may encounter spectrum leakage or spectrum aliasing in the analysis process, and secondly, the number of sine waves formed after fourier transform is not constant, so that real structural information cannot be embodied. The wavelet analysis overcomes the problem of single resolution of Fourier transform, has the characteristic of multi-resolution, has the capability of representing local information of signals in both time domain and frequency domain, and can dynamically adjust both time window and frequency window according to the specific form of the signals. Because of these features, wavelet analysis can detect transient components in a signal and exhibit its frequency components. However, the biggest challenge of performing time-frequency analysis on signals by using wavelet transform lies in the selection of mother wavelet functions, and the effects obtained by selecting different mother wavelets for time-frequency analysis on the same signal are often very different; meanwhile, similar to the fourier transform, the wavelet transform requires that the signal within the wavelet window must be approximately stationary. The empirical wavelet transform is provided on the basis of empirical mode decomposition and wavelet transform, the frequency spectrum is divided in a self-adaptive manner by searching maximum and minimum value points in the Fourier frequency spectrum of the signal, and a wavelet basis function is automatically selected to construct a wavelet filter bank, so that amplitude modulation-frequency modulation single-component signals with tight support characteristics can be extracted from the multi-component signals. However, the method and the frequency band division result of the improved method based on the method are easily interfered by frequency spectrum leakage and noise pollution, and the problem that each order mode of the signal cannot be accurately separated exists.
Empirical mode decomposition decomposes signals one by one from high to low based on frequency, but due to the influence of the complex environment where the actual marine structure is located, the problems of mode mixing and end effect are usually generated, the decomposition effect is poor, and even the decomposition failure problem can occur. Although the problem of mode aliasing and the like is overcome by the variation empirical mode decomposition provided on the basis of the empirical mode decomposition, certain required parameters are difficult to determine in advance, and the application of the variation empirical mode decomposition to the actual marine structure engineering is limited to a certain extent.
Disclosure of Invention
Compared with the traditional one-time decomposition method, the invention can efficiently realize the high-precision decomposition of the marine structure nonlinear signal, and provides a basis for modal parameter identification, time-frequency analysis, noise elimination and other applications of the nonlinear signal.
In order to achieve the above object, the present invention provides a method for decomposing weak nonlinear signals of marine structures, comprising:
arranging an acceleration sensor at the key monitoring point position of the marine structure to be detected to monitor acceleration information and determine the original dynamic response of the marine structure to be detected;
performing FFT (fast Fourier transform) on an original dynamic response signal of the marine structure to be detected, and performing equidistant sliding segmentation on a full-band frequency spectrum of the obtained original dynamic response signal;
carrying out IFFT transformation on each divided sub-frequency band in sequence to obtain an original dynamic response sub-signal corresponding to each sub-frequency band;
decomposing the original dynamic response sub-signals corresponding to the sub-bands based on the Prony sequence to obtain characteristic information contained in the original dynamic response sub-signals corresponding to the sub-bands, and reconstructing the dynamic response sub-signals corresponding to the sub-bands based on the characteristic information;
comparing the relative residual error between the original dynamic response sub-signal corresponding to each sub-frequency band and the corresponding reconstructed dynamic response sub-signal, and judging the decomposition precision of the original dynamic response sub-signal corresponding to each sub-frequency band;
and superposing the reconstructed dynamic response sub-signals corresponding to the sub-frequency bands, reconstructing a full-band dynamic response signal, comparing the relative residual error of the full-band original dynamic response signal and the full-band reconstructed dynamic response signal, and judging the integral decomposition precision of the full-band original dynamic response signal.
Preferably, the determined original dynamic response of the marine structure to be tested is a non-linear continuous signal expressed as:
in the formula, ρn、θn、ωn、ξnIs amplitude, phase, frequency and damping coefficient, NyRepresenting the number of components in the nonlinear signal;
dispersing and FFT transforming the continuous original dynamic response signal y (t) to obtain a signal full-band frequency spectrum:
where y (t) represents the discrete raw dynamic response signal,
the obtained full-band frequency spectrum of the original dynamic response signal is divided at equal intervals in a sliding way, and each sub-band is expressed as fn-1，fn]N is 1, 2, …, N; wherein N ═ Fs/2Δf，f0＝0，fN＝Fs/2，FsThe sampling frequency and Δ f are widths of the divided sub-bands.
Preferably, the divided sub-bands are sequentially IFFT-transformed to obtain original dynamic response sub-signals corresponding to the sub-bands:
y(kn)＝IFFT(FFT(y(n))|f(n-1，n))，n＝1，2，...，N
in the formula (f)(n-1，n)Is a frequency fn-1，fn]The "|" is a truncation operation, i.e. truncating the frequency band f from the frequency domain(n-1，n)。
Preferably, the original power response sub-signals corresponding to each sub-band are subjected to complex exponential decomposition based on the pluronic sequence, that is:
in the formula, y (k)n) The original dynamic response sub-signal representing the nth sub-band,
the sampling interval is Deltat, kn＝0，1，...，Np-1，NpThe number of points of the sampling signal;
obtaining the characteristic information lambda contained in the original dynamic response sub-signal corresponding to each sub-frequency bandn、γnAnd respectively reconstructing the sub-band dynamic response sub-signals based on the characteristic information.
Preferably, the resolution precision of the original dynamic response sub-signal corresponding to each sub-band is judged by using the relative residual:
in the formula, max is the maximum value, | | is the absolute value,
representing the original dynamic response sub-signal corresponding to the nth sub-band,
representing the reconstructed dynamic response sub-signal corresponding to the nth sub-band,
the relative residual error between the original dynamic response sub-signal corresponding to the nth sub-band and the corresponding reconstructed dynamic response sub-signal is obtained.
Preferably, the full-band dynamic response signal is reconstructed by superimposing the reconstructed dynamic response sub-signals corresponding to the respective sub-bands:
preferably, the overall decomposition precision of the full-band original dynamic response signal is determined by comparing the relative residual error between the full-band original dynamic response signal and the full-band reconstructed dynamic response signal:
in the formula, YorRepresenting the full-band original dynamic response signal, YreRepresenting a full band reconstructed dynamic response signal.
Compared with the prior art, the invention has the advantages and positive effects that:
the invention provides a marine structure weak nonlinear signal decomposition method aiming at the decomposition problem of marine structure dynamic response, can efficiently realize high-precision decomposition of marine structure nonlinear signals compared with the traditional one-time decomposition method, and provides a foundation for modal parameter identification, time-frequency analysis, noise elimination and other applications of marine structure dynamic response signals.
(1) According to the invention, the original dynamic response signal frequency spectrum of the nonlinear marine structure to be tested is subjected to equidistant sliding segmentation, so that signal components with significant differences in amplitude and frequency are separated from a frequency domain, and the nonlinearity and the non-stationarity of the signal are weakened to a certain extent.
(2) The divided sub-bands are subjected to IFFT conversion in sequence, the obtained original dynamic response sub-signals corresponding to the sub-bands are subjected to Poynie decomposition, the characteristic information contained in the original dynamic response sub-signals corresponding to the sub-bands can be accurately and efficiently extracted, corresponding signals can be reconstructed based on the information, and the reconstructed dynamic response sub-signals corresponding to the sub-bands are compared with the original dynamic response sub-signals corresponding to the sub-bands, so that the decomposition precision of a single frequency band is ensured.
(3) Meanwhile, by controlling the decomposition precision of each sub-band corresponding to the original dynamic response sub-signal, the characteristic information contained in the full-band complete signal can be accurately obtained, the full-band dynamic response signal can be completely reconstructed based on the information, the integral decomposition precision is ensured, and the error problem caused by one-time decomposition in the traditional method is avoided; meanwhile, by utilizing FFT and IFFT transformation, the decomposition efficiency and the decomposition precision are greatly improved, and a foundation is provided for application of modal parameter identification, time-frequency analysis, noise elimination and the like of nonlinear signals.
Drawings
FIG. 1 is an overall flow chart of the weak nonlinear signal decomposition method of the marine structure according to the present invention;
FIG. 2 is a schematic diagram of sensor installation and signal selection for a wind power plant at sea;
FIG. 3 is a schematic diagram of a selected measured signal and its spectrum sliding segmentation;
FIG. 4 is a plot of Poroni decomposition and spectra of the dynamic response sub-signals corresponding to the first 4 sub-bands;
fig. 5 shows the complete nonlinear signal obtained by reconstruction.
Detailed Description
The following further describes embodiments of the present invention with reference to the accompanying drawings.
The embodiment of the invention provides a marine structure weak nonlinear signal decomposition method, as shown in fig. 1, comprising the following steps:
(1) and arranging an acceleration sensor at the key monitoring point position of the marine structure to be detected to monitor acceleration information and determine the original dynamic response of the marine structure to be detected. Because the complex environment of the marine structure in the actual engineering determines the complexity of the measured signal, the monitored original dynamic response signal generally has the characteristics of nonlinearity, non-stationarity and the like, namely the determined original dynamic response of the marine structure to be measured is a nonlinear continuous signal, and can be regarded as being composed of a series of components, which are expressed as:
in the formula, ρn、θn、ωn、ξnIs amplitude, phase, frequency and damping coefficient, NyRepresenting the number of components in the non-linear signal.
(2) Dispersing and FFT (fast Fourier transform) the continuous original dynamic response signals y (t) to obtain the full-band frequency spectrum of the original dynamic response signals:
where y (t) represents the discrete raw dynamic response signal,
the obtained full-band frequency spectrum of the original dynamic response signal is divided at equal intervals in a sliding way, and each sub-band is expressed as fn-1，fn]N is 1, 2, …, N; wherein N ═ Fs/2Δf，f0＝0，fN＝Fs/2，FsThe sampling frequency and Δ f are widths of the divided sub-bands.
Because the complexity of the actual marine structure is determined by the complex environment, and the actual measurement signal generally has the characteristics of nonlinearity, non-stationarity and the like, the invention separates the signal components with obvious differences in amplitude and frequency from the frequency domain by performing equidistant sliding segmentation on the frequency spectrum of the nonlinear signal, weakens the nonlinearity and the non-stationarity of the signal to a certain extent, and can obviously improve the subsequent decomposition precision of the Prony method.
(3) Carrying out IFFT transformation on each divided sub-band in sequence to obtain an original dynamic response sub-signal corresponding to each sub-band:
y(kn)＝IFFT(FFT(y(n))|f(n-1，n))，n＝1，2，...，N
in the formula (f)(n-1，n)Is a frequency fn-1，fn]The "|" is a truncation operation, i.e. truncating the frequency band f from the frequency domain(n-1，n)。
(4) Performing complex exponential decomposition on the original power response sub-signals corresponding to the sub-bands based on the Prony sequence, namely:
in the formula, y (k)n) The original dynamic response sub-signal representing the nth sub-band,
the sampling interval is Deltat, knx0，1，...，Np-1，NpThe number of points of the sampled signal.
Obtaining the characteristic information lambda contained in the original dynamic response sub-signal corresponding to each sub-frequency bandn、γn，λn、γnThe dynamic response sub-signals corresponding to the sub-bands can be respectively reconstructed based on the characteristic information, and the accuracy of decomposition can be judged by comparing the reconstructed dynamic response sub-signals with the original dynamic response sub-signals.
(5) When the pronoun method is used for decomposition, different orders are used to affect the reconstruction accuracy, so in this embodiment, the relative residual is used to represent the decomposition accuracy, and the decomposition accuracy of the original dynamic response sub-signal corresponding to each sub-band is determined by comparing the relative residual between the original dynamic response sub-signal corresponding to each sub-band and the corresponding reconstructed dynamic response sub-signal:
in the formula, max is the maximum value, | | is the absolute valueFor the value of the one or more parameters,
representing the original dynamic response sub-signal corresponding to the nth sub-band,
representing the reconstructed dynamic response sub-signal corresponding to the nth sub-band,
the relative residual error between the original dynamic response sub-signal corresponding to the nth sub-band and the corresponding reconstructed dynamic response sub-signal is obtained.
In this embodiment, the divided sub-bands are sequentially subjected to IFFT, and the obtained original power response sub-signals corresponding to the sub-bands are subjected to pluronic decomposition, so that feature information included in the original power response sub-signals corresponding to the sub-bands can be accurately and efficiently extracted, and the reconstructed power response sub-signals corresponding to the sub-bands can be compared with the original power response sub-signals corresponding to the sub-bands based on corresponding signals reconstructed based on the information, thereby ensuring the decomposition accuracy of a single frequency band.
(6) Superposing the reconstructed dynamic response sub-signals corresponding to the sub-frequency bands to reconstruct a full-frequency-band dynamic response signal:
then comparing the relative residual error of the full-band original dynamic response signal and the full-band reconstructed dynamic response signal, and judging the overall decomposition precision of the full-band original dynamic response signal:
in the formula, YorRepresenting the full-band original dynamic response signal, YreRepresenting a full band reconstructed dynamic response signal.
Meanwhile, if the calculation accuracy does not meet the requirement and the frequency bandwidth needs to be reduced, the steps (2) - (7) are continuously repeated.
In the embodiment, by controlling the decomposition precision of each sub-band corresponding to the original dynamic response sub-signal, the characteristic information contained in the full-band complete signal can be accurately obtained, the full-band dynamic response signal can be completely reconstructed based on the information, the overall decomposition precision is ensured, and the error problem caused by one-time decomposition in the conventional method is avoided; meanwhile, by utilizing FFT and IFFT transformation, the decomposition efficiency is greatly improved, and a foundation is provided for application of modal parameter identification, time-frequency analysis, noise elimination and the like of nonlinear signals.
In summary, the invention provides a marine structure weak nonlinear signal decomposition method aiming at the decomposition problem of marine structure dynamic response, compared with the traditional one-time decomposition method, the method can efficiently realize high-precision decomposition of marine structure nonlinear signals, and provides a foundation for modal parameter identification, time-frequency analysis, noise elimination and other applications of marine structure dynamic response signals. Namely: according to the invention, the original dynamic response signal frequency spectrum of the nonlinear marine structure to be tested is subjected to equidistant sliding segmentation, so that signal components with significant differences in amplitude and frequency are separated from a frequency domain, and the nonlinearity and the non-stationarity of the signal are weakened to a certain extent. Then, the divided sub-bands are subjected to IFFT conversion in sequence, the obtained original dynamic response sub-signals corresponding to the sub-bands are subjected to Poynie decomposition, the characteristic information contained in the original dynamic response sub-signals corresponding to the sub-bands can be accurately and efficiently extracted, corresponding signals can be reconstructed based on the information, and the reconstructed dynamic response sub-signals corresponding to the sub-bands are compared with the original dynamic response sub-signals corresponding to the sub-bands, so that the decomposition precision of a single frequency band is ensured. Meanwhile, by controlling the decomposition precision of each sub-band corresponding to the original dynamic response sub-signal, the characteristic information contained in the full-band complete signal can be accurately obtained, the full-band dynamic response signal can be completely reconstructed based on the information, the integral decomposition precision is ensured, and the error problem caused by one-time decomposition in the traditional method is avoided; meanwhile, by utilizing FFT and IFFT transformation, the decomposition efficiency is greatly improved, and a foundation is provided for application of modal parameter identification, time-frequency analysis, noise elimination and the like of nonlinear signals.
The marine structure weak nonlinear signal decomposition method is verified by a specific example, which specifically comprises the following steps:
taking a single-pile wind driven generator in a certain offshore wind farm running state as an example, as shown in fig. 2, decomposing and reconstructing an actually measured nonlinear signal of a structural vibration response of the single-pile wind driven generator, setting a sampling frequency to be 200Hz, selecting an acceleration sensor installed at the top of a fan to obtain an original dynamic response of the structure, wherein data of the sensor in the x direction is shown in fig. 2; selecting data of 1000-1030 seconds for decomposition, wherein the corresponding acceleration time domain graph is shown in fig. 3 (a); fig. 3(b) is a frequency spectrum diagram of the selected signal, and as shown in the figure, the frequency spectrum is sequentially subjected to equidistant sliding division, and the frequency bandwidth after division is as the width of a rectangular frame in the figure, it should be noted that, for convenience of representation, the frequency bandwidth in the figure is much larger than the frequency bandwidth in the actual decomposition.
Fig. 4 is a puloni decomposition and spectrogram of sub-signals corresponding to the first 4 sub-bands, where the solid line is the original dynamic response sub-signal corresponding to each sub-band, and the dotted line is the reconstructed dynamic response sub-signal corresponding to the original dynamic response sub-signal corresponding to each sub-band, which can be seen that the corresponding signal of each sub-band can be accurately decomposed and reconstructed, and since each sub-band contains few frequency components, the order taken during decomposition is lower than that taken during one-time decomposition, which can significantly increase the decomposition speed; at the same time, by setting
The decomposition precision is ensured.
Then, the sub-signals correspondingly reconstructed by each sub-band are superposed to obtain a full-band reconstruction signal, and as a result, as shown in fig. 5, by comparing the residual error between the original dynamic response signal and the reconstructed dynamic response signal, it can be seen that the method of the present invention realizes high-precision decomposition of the actually measured nonlinear signal, and provides a basis for modal parameter identification, time-frequency analysis, noise elimination, etc. of the nonlinear 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 (7)
1. A marine structure weak nonlinear signal decomposition method is characterized by comprising the following steps:
arranging an acceleration sensor at the key monitoring point position of the marine structure to be detected to monitor acceleration information and determine the original dynamic response of the marine structure to be detected;
performing FFT (fast Fourier transform) on an original dynamic response signal of the marine structure to be detected, and performing equidistant sliding segmentation on a full-band frequency spectrum of the obtained original dynamic response signal;
carrying out IFFT transformation on each divided sub-frequency band in sequence to obtain an original dynamic response sub-signal corresponding to each sub-frequency band;
decomposing the original dynamic response sub-signals corresponding to the sub-bands based on the Prony sequence to obtain characteristic information contained in the original dynamic response sub-signals corresponding to the sub-bands, and reconstructing the dynamic response sub-signals corresponding to the sub-bands based on the characteristic information;
comparing the relative residual error between the original dynamic response sub-signal corresponding to each sub-frequency band and the corresponding reconstructed dynamic response sub-signal, and judging the decomposition precision of the original dynamic response sub-signal corresponding to each sub-frequency band;
and superposing the reconstructed dynamic response sub-signals corresponding to the sub-frequency bands, reconstructing a full-band dynamic response signal, comparing the relative residual error of the full-band original dynamic response signal and the full-band reconstructed dynamic response signal, and judging the integral decomposition precision of the full-band original dynamic response signal.
2. The marine structure weak nonlinear signal decomposition method according to claim 1, characterized in that:
the determined original dynamic response of the marine structure to be measured is a nonlinear continuous signal expressed as:
in the formula, ρn、θn、ωn、ξnIs amplitude, phase, frequency and damping coefficient, NyRepresenting the number of components in the nonlinear signal;
dispersing and FFT transforming the continuous original dynamic response signal y (t) to obtain a signal full-band frequency spectrum:
where y (t) represents the discrete raw dynamic response signal,
the obtained full-band frequency spectrum of the original dynamic response signal is divided at equal intervals in a sliding way, and each sub-band is expressed as fn-1，fn]N is 1, 2, …, N; wherein N ═ Fs/2Δf，f0＝0，fN＝Fs/2，FsThe sampling frequency and Δ f are widths of the divided sub-bands.
3. The marine structure weak nonlinear signal decomposition method according to claim 2, characterized in that the divided sub-bands are subjected to IFFT transformation in sequence to obtain original dynamic response sub-signals corresponding to the sub-bands:
y(kn)＝IFFT(FFT(y(n))|f(n-1，n))，n＝1，2，...，N
in the formula (f)(n-1，n)Is a frequency fn-1，fn]The "|" is a truncation operation, i.e. truncating the frequency band f from the frequency domain(n-1，n)。
4. The method as claimed in claim 3, wherein the original dynamic response sub-signals corresponding to each sub-band are complex-exponential decomposed based on Prony's sequence, that is:
in the formula, y (k)n) The original dynamic response sub-signal representing the nth sub-band,
the sampling interval is Deltat, kn＝0，1，...，Np-1，NpThe number of points of the sampling signal;
obtaining the characteristic information lambda contained in the original dynamic response sub-signal corresponding to each sub-frequency bandn、γnAnd respectively reconstructing the sub-band dynamic response sub-signals based on the characteristic information.
5. The marine structure weak nonlinear signal decomposition method according to claim 4, wherein the decomposition precision of the original dynamic response sub-signal corresponding to each sub-band is judged by using relative residuals:
in the formula, max is the maximum value, | | is the absolute value,
representing the original dynamic response sub-signal corresponding to the nth sub-band,
representing the reconstructed dynamic response sub-signal corresponding to the nth sub-band,
the relative residual error between the original dynamic response sub-signal corresponding to the nth sub-band and the corresponding reconstructed dynamic response sub-signal is obtained.
6. The marine structure weak nonlinear signal decomposition method according to claim 5, wherein the reconstructed dynamic response sub-signals corresponding to the respective sub-bands are superimposed to reconstruct a full-band dynamic response signal:
7. the marine structure weak nonlinear signal decomposition method according to claim 6, wherein a relative residual between the full-band original dynamic response signal and the full-band reconstructed dynamic response signal is compared to determine an overall decomposition accuracy of the full-band original dynamic response signal:
in the formula, YorRepresenting the full-band original dynamic response signal, YreRepresenting a full band reconstructed dynamic response signal.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108875706A (en) * | 2018-07-18 | 2018-11-23 | 中国海洋大学 | The ocean structure Time-Frequency Analysis Method collected based on sliding average and energy |
| CN110991395A (en) * | 2019-12-17 | 2020-04-10 | 中国海洋大学 | Maritime work structure actual measurement signal maximum energy iteration extraction method |
| US20200284687A1 (en) * | 2019-02-19 | 2020-09-10 | Dalian University Of Technology | A method for automatically detecting free vibration response of high-speed railway bridge for modal identification |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN108875706A (en) * | 2018-07-18 | 2018-11-23 | 中国海洋大学 | The ocean structure Time-Frequency Analysis Method collected based on sliding average and energy |
| US20200284687A1 (en) * | 2019-02-19 | 2020-09-10 | Dalian University Of Technology | A method for automatically detecting free vibration response of high-speed railway bridge for modal identification |
| CN110991395A (en) * | 2019-12-17 | 2020-04-10 | 中国海洋大学 | Maritime work structure actual measurement signal maximum energy iteration extraction method |
Non-Patent Citations (1)
| Title |
|---|
| 罗金平，喻旭明，陈杰峰，刘福顺: "一种海上浮式风电基础频域动力响应分析新技术", 《振动工程学报》 * |
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