CN109884694B - High-speed rail seismic source seismic signal time-frequency analysis method based on extrusion windowing Fourier transform - Google Patents
High-speed rail seismic source seismic signal time-frequency analysis method based on extrusion windowing Fourier transform Download PDFInfo
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Abstract
The invention discloses a high-speed rail seismic source seismic signal time-frequency analysis method based on extrusion windowing Fourier transform, which comprises the following steps of: 01: carrying out mean value removing processing on the acquired seismic signals of the high-speed rail seismic source; 02: carrying out Fourier transform on the seismic signals of the high-speed rail seismic source to obtain the energy spectrum distribution of the signals; 03: adaptively determining an interpolation multiple by using the energy spectrum distribution of the signal; 04: interpolating the seismic signals of the high-speed rail seismic source processed in the step 01 according to the interpolation multiple; 05: carrying out windowing Fourier transform on the seismic signals after interpolation by using a window function; 06: calculating the time difference of the phase of the signal windowed Fourier transform coefficient and obtaining the extrusion position, and then accumulating the signal windowed Fourier transform coefficient to the extrusion position; 07: and obtaining a final time frequency analysis result and solving a modulus value to obtain final time frequency distribution. The result obtained by the method can more finely reflect the time-frequency characteristics and the frequency spectrum component of the seismic signal of the high-speed rail seismic source along with the change of time.
Description
Technical Field
The invention belongs to the field of exploration geophysics, and particularly relates to a high-speed rail seismic source seismic signal time-frequency analysis method based on extrusion windowing Fourier transform.
Background
By the end of 2017, the business mileage of the high-speed rail in China reaches 2.5 kilometers, and the business mileage accounts for 66 percent of the total amount of the high-speed rail in the world. There are thousands of high-speed trains operating at high speed on a wide range of high-speed rail lines each day. Such a huge number of high-speed trains running on the high-speed railway not only cause vibration of the high-speed train and the roadbed, but also propagate the vibration as various types of seismic waves. The detectors embedded in the range of dozens of meters on two sides of the high-speed rail line can receive seismic waves caused by the running of the high-speed rail train, namely seismic signals of a seismic source of the high-speed rail. The signals received by the detector are analyzed, so that the running state of the high-speed rail train can be analyzed, and the imaging of the underground structure near the high-speed rail line is expected. However, in the face of the brand new high-speed rail seismic source seismic data, what kind of spectrum analysis means is adopted to detect the change of the spectrum components is extremely critical. At present, the means for analyzing the seismic signals caused by the operation of the high-speed rail is very limited, and mainly comprises:
prior art 1: discrete Fourier transform
The method carries out fast Fourier transform or discrete Fourier transform on the digital signal received by the detector, and can obtain the amplitude spectrum of the signal.
The characteristics of the prior art 1:
the advantages are that: the method is simple and easy to implement, small in calculation amount and free from interference of human factors.
The disadvantages are as follows: 1. only frequency components can be analyzed, and the starting time and the ending time of various frequency components cannot be analyzed; 2. the change law of various frequency components with time cannot be analyzed.
Prior art 2: short time Fourier transform
The method intercepts a section of signal by using a window function at each time point, and then performs Fourier transformation on the intercepted signal to obtain local frequency components.
The characteristics of the prior art 2:
the advantages are that: the method is simple to realize, small in calculation amount and free from interference of human factors.
The disadvantages are as follows: the frequency resolution is poor and is limited by the uncertainty principle.
Prior art 3: continuous wavelet transform
The method includes the steps that mother wavelets are subjected to expansion and translation to form a series of wavelet families, and then the wavelet families and signals are subjected to inner product to obtain a series of continuous wavelet transformation coefficients.
The characteristics of the prior art 3:
the advantages are that: is simpler and has less calculation amount.
The disadvantages are as follows: 1. the frequency resolution is poor and is limited by the constraint of an uncertainty principle; 2. the selection of mother wavelets is difficult; 3. the result is a time-scale domain, and the scale needs to be transformed to frequency.
Disclosure of Invention
The invention aims to provide a high-speed rail seismic source seismic signal time-frequency analysis method based on extrusion windowing Fourier transform, and the method is used for solving the technical problem. The method can analyze the change of the frequency components of the seismic signals of the high-speed rail seismic source along with time, and obtains the time-frequency distribution of the seismic signals of the high-speed rail seismic source by adopting the extrusion windowed Fourier transform, thereby providing data for the subsequent judgment of the train running state.
In order to achieve the purpose, the invention adopts the following technical scheme:
a high-speed rail seismic source seismic signal time-frequency analysis method based on extrusion windowing Fourier transform comprises the following steps:
step 01: carrying out mean value removing processing on the acquired seismic signals of the high-speed rail seismic source;
step 02: performing Fourier transform on the seismic signals of the high-speed rail seismic source subjected to the mean value removing processing in the step 01 to obtain energy spectrum distribution of the signals;
step 03: adaptively determining an interpolation multiple by using the energy spectrum distribution of the signal;
step 04: interpolating the high-speed rail seismic source seismic signals with the mean value removed, which are obtained in the step 1, according to the interpolation multiple to obtain seismic signals with a higher sampling rate;
step 05: carrying out windowing Fourier transform on the seismic signals after interpolation by using a window function;
step 06: calculating the time difference of the phase of the signal windowed Fourier transform coefficient and obtaining the extrusion position, and then accumulating the signal windowed Fourier transform coefficient to the extrusion position;
step 07: and obtaining a final time frequency analysis result and solving a modulus value to obtain final time frequency distribution.
Further, step 01 specifically includes:
using s [ M ] to represent one-dimensional seismic signals, wherein the total number of M sampling points is delta t, and M represents the index of the signals in the time direction; the mean value is removed by:
further, step 02 specifically includes:
performing discrete Fourier transform on the signal S [ m ] to obtain S [ k ] as:
wherein M represents the number of sampling points of the one-dimensional signal, and Δ f is the frequency domain sampling interval, an
k represents a frequency index ranging from 0 to M-1; from S [ k Δ f]Obtaining the energy spectrum EF [ k ] of the one-dimensional signal along the frequency domain]Comprises the following steps:
further, step 03 specifically includes:
the energy E of the one-dimensional signal is calculated in the frequency domain:
then, the energy accumulation function ACCU _ EF [ q ] of EF [ k ] is calculated
Finding the frequency upper limit index Q in the energy accumulation function ACCU _ EF [ Q ] according to the following criteria:
wherein lambda is a threshold value, and the value of lambda is greater than or equal to 0.999; the interpolation factor R is then determined according to the following formula:
wherein
Meaning rounding up.
Further, step 04 specifically includes:
a new sequence SS [ k ] is constructed, sharing RM points, which is related to S [ k ] as follows:
then, the new sequence SS [ k ] is processed with inverse Fourier transform, and a new time sequence SS [ m ] after resampling can be obtained:
where real { } denotes the real part of the complex number.
Further, step 05 specifically includes:
the selected window function is g [ m ], windowing Fourier transform is carried out on the seismic signal ss [ m ] after interpolation to obtain a result WFT [ m, k ], and the result WFT [ m, k ] is:
wherein l is a temporary time index, m is a time index, and k is a frequency index. While assuming the final crush transform results as
Also assume that the final crush transform result is SWFT [ m, k ], and all of them are initialized to 0.
Further, step 06 specifically includes:
WFT _ phs [ m, k ] represents the phase of windowed fourier transform coefficients WFT [ m, k ], and the phase WFT _ phs [ m, k ] calculates the difference along the m index to obtain:
wherein
Where img () denotes taking the imaginary part of the complex number, real () denotes taking the real part of the complex number, and abs () denotes taking the modulus of the complex number. For dif [ m, k ]]The corresponding pressing position k is obtained by1:
Where round () represents rounding the floating point number; the corresponding windowed fourier transform coefficients WFT [ m, k ] are accumulated to the new position:
SWFT[m,k1]＝SWFT[m,k1]+WFT[m,k]。
further, step 07 specifically includes:
and calculating the module value of the extrusion transformation result SWFT [ m, k ] to obtain the time-frequency distribution of the seismic signals of the high-speed rail seismic source as follows:
SWFT_E[m,k]＝abs(SWFT[m,k])。
further, the motion state of the high-speed train is detected according to the time-frequency distribution obtained in the step 07.
Compared with the prior art, the invention has the following beneficial effects: the invention relates to a time-frequency analysis method for seismic signals caused by high-speed rail operation, which is mainly used for depicting the change of frequency components of seismic signals of a high-speed rail seismic source along with time and is a rapid data processing method; the method comprises the steps of firstly carrying out zero mean value removing processing on seismic signals of a high-speed rail seismic source, then carrying out spectrum analysis on the signals to determine signal interpolation multiples and carrying out interpolation to improve difference precision, and finally carrying out extrusion operation on windowed Fourier transform coefficients of the signals in the frequency direction to obtain high-precision time-frequency distribution. Compared with the conventional time frequency distribution, the high-precision time frequency distribution obtained by the method can accurately depict the change of frequency components in seismic signals of the high-speed rail seismic source along with time, and can be used for detecting the running state (constant speed or acceleration) of a high-speed rail train.
Description of the figures
FIG. 1 is a flow chart of the present invention;
FIG. 2 shows a seismic signal of a high-speed rail source received by a single detector when the train 1 passes by;
FIG. 3 is a high-speed rail seismic source signal after averaging;
FIG. 4 is an amplitude spectrum of a seismic source signal for a high-speed rail after averaging;
FIG. 5 is an energy spectrum of a seismic source signal for a high-speed rail after averaging;
FIG. 6 is an energy accumulation function;
FIG. 7 is a high-speed rail seismic source signal after interpolation;
fig. 8 is a time-frequency distribution of a seismic signal of a high-speed rail source received by a single detector when the train 1 passes through, obtained by using windowed fourier transform.
Fig. 9 is a time-frequency distribution of seismic signals of a high-speed rail source received by a single detector when the train 1 passes through, which is obtained by using an extrusion windowed fourier transform.
Fig. 10 is a time-frequency distribution of a seismic signal of a high-speed rail source received by a single detector when the train 2 passes through, obtained by using an extruded windowed fourier transform.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention relates to a time-frequency analysis method for seismic signals caused by the passing of a high-speed rail. According to the method, firstly, Fourier transform is carried out on acquired seismic signals to obtain energy spectrums of the signals, then interpolation multiples of the signals are determined by the energy spectrums and interpolation is carried out on the signals, windowed Fourier transform of the interpolated signals is calculated, extrusion positions of frequency components are determined by phase spectrum difference of the windowed Fourier transform of the signals, finally, corresponding coefficients are accumulated to the extrusion positions to obtain high-precision time-frequency spectrograms, and the high-precision time-frequency spectrograms are provided for analyzing the frequency components in each time period.
Referring to fig. 1, the invention provides a high-speed rail seismic source seismic signal time-frequency analysis method based on extrusion windowing fourier transform, which includes the following steps:
step 01: carrying out mean value removing processing on the acquired seismic signals of the high-speed rail seismic source;
step 02: performing Fourier transform on the seismic signals of the high-speed rail seismic source subjected to the mean value removing processing in the step 01 to obtain the energy spectrum distribution of the signals;
step 03: adaptively determining an interpolation multiple by using the energy spectrum distribution of the signal;
step 04: interpolating the high-speed rail seismic source seismic signals with the mean value removed, which are obtained in the step 1, according to the interpolation multiple to obtain seismic signals with a higher sampling rate;
step 05: carrying out windowing Fourier transform on the seismic signals after interpolation by using a window function;
step 06: calculating the time difference of the phase of the signal windowed Fourier transform coefficient and obtaining the extrusion position, and then accumulating the signal windowed Fourier transform coefficient to the extrusion position;
step 07: and obtaining a final time frequency analysis result and solving a modulus value to obtain final time frequency distribution.
Step 01: the method comprises the following steps of carrying out mean value removing processing on the acquired seismic signals of the high-speed rail seismic source, and specifically comprises the following steps:
and s [ M ] is used for representing the one-dimensional seismic signal, M sampling points are totally arranged, the time sampling interval is delta t, and M represents the index of the signal in the time direction. The mean value is removed by:
the high-speed rail seismic source seismic signals subjected to the mean value removing processing in the step 02 are subjected to Fourier transform to obtain energy spectrum distribution of the signals, and the method specifically comprises the following steps:
performing discrete Fourier transform on the signal S [ m ] to obtain S [ k ] as:
where M represents the number of samples of a one-dimensional signal and Δ f is the number of samples in the frequency domainSeparate, and
k represents a frequency index ranging from 0 to M-1. From S [ k Δ f]Obtaining the energy spectrum EF [ k ] of the one-dimensional signal along the frequency domain]Comprises the following steps:
in step 03, the interpolation multiple is adaptively determined by using the energy spectrum distribution of the signal, and the method specifically includes:
the energy E of the one-dimensional signal is calculated in the frequency domain:
then, the energy accumulation function ACCU _ EF [ q ] of EF [ k ] is calculated
Finding the frequency upper limit index Q in the energy accumulation function ACCU _ EF [ Q ] according to the following criteria:
wherein λ is a threshold value, and the value is generally selected to be a value greater than 0.999. The interpolation factor R is then determined according to the following formula:
wherein
Meaning rounding up.
In step 04, interpolating the mean-removed high-speed rail seismic source seismic signal obtained in step 1 according to the interpolation multiple to obtain a seismic signal with a higher sampling rate, which specifically comprises:
a new sequence SS [ k ] is constructed, sharing RM points, which is related to S [ k ] as follows:
then, the new sequence SS [ k ] is subjected to inverse Fourier transform to obtain a resampled new time sequence SS [ m ]:
where real { } denotes the real part of the complex number.
In step 05, the windowing fourier transform of the interpolated seismic signal is performed by the window function, which specifically includes:
if the selected window function is g [ m ], performing windowed Fourier transform on the interpolated seismic signal ss [ m ] to obtain a result WFT [ m, k ] which is:
wherein l is a temporary time index, m is a time index, and k is a frequency index. Meanwhile, the final extrusion transformation result is assumed to be SWFT [ m, k ], and the SWFT [ m, k ] is all initialized to 0.
In step 06, calculating a time difference of the phase of the signal windowed fourier transform coefficient and obtaining an extrusion position, and then accumulating the signal windowed fourier transform coefficient to the extrusion position, specifically including:
WFT _ phs [ m, k ] represents the windowed Fourier transform coefficient phase, and WFT _ phs [ m, k ] calculates the difference along the m index to yield:
where phs _ img _ dif [ m, k ] and phs _ real _ dif [ m, k ] are as follows:
where img () denotes taking the imaginary part of the complex number, real () denotes taking the real part of the complex number, and abs () denotes taking the modulus of the complex number. For dif [ m, k ]]The corresponding extrusion frequency position k is obtained by1:
Where round () represents rounding a floating point number. Corresponding windowed Fourier transform coefficients WFT [ m, k ]]Accumulated to a new position m, k1]：
SWFT[m,k1]＝SWFT[m,k1]+WFT[m,k]
The final time-frequency analysis result is obtained in step 07 and the modulus value is calculated to obtain the final time-frequency distribution, which is as follows:
and calculating the module value of the extrusion transformation result SWFT [ m, k ] to obtain the time-frequency distribution of the seismic signals of the high-speed rail seismic source as follows:
SWFT_E[m,k]＝abs(SWFT[m,k])
take the signal received by a single low frequency detector 30m from the high-speed rail line when the high-speed rail passes by as an example. Fig. 2 shows a vibration signal caused by a high-speed rail seismic source received by a single detector when the train 1 passes by, and the sampling interval is 5ms, and 3001 sampling points are total. Fig. 3 shows the results after the averaging, fig. 4 shows the corresponding amplitude spectrum, fig. 5 shows the corresponding energy spectrum, and fig. 6 shows the energy accumulation function. When λ is 0.999, Q is 1147 from the energy spectrum shown in fig. 6, and thus the interpolation factor R is 14. Fig. 7 is a signal after 14 times of interpolation, fig. 8 is time-frequency distribution of seismic signals of a high-speed rail seismic source obtained by using conventional windowing fourier transform when the train 1 passes, and fig. 9 is time-frequency distribution of seismic signals of a high-speed rail seismic source obtained by using extrusion windowing fourier transform when the train 1 passes, and the frequency of each discrete spectrum is kept unchanged along with time, which indicates that the train is in a constant-speed driving state when passing through the detector. FIG. 10 is a time-frequency distribution of seismic signals of a high-speed rail seismic source based on extrusion windowed Fourier transform when a train passes through, and the frequency of each discrete spectrum is increased along with the increase of time, so that the train is in an acceleration driving state when passing through a detector.
Finally, it should be noted that the above-mentioned embodiments provide further verification for the purpose, technical solution and advantages of the present invention, which only belong to the specific embodiments of the present invention, and are not used to limit the protection scope of the present invention, and any modification, improvement or equivalent replacement (such as changing the window function, replacing the interpolation scheme, replacing the difference method, etc.) made within the spirit and principle of the present invention should be within the protection scope of the present invention.
Claims (8)
1. A high-speed rail seismic source seismic signal time-frequency analysis method based on extrusion windowing Fourier transform is characterized by comprising the following steps:
step 01: carrying out mean value removing processing on the acquired seismic signals of the high-speed rail seismic source;
step 02: performing Fourier transform on the seismic signals of the high-speed rail seismic source subjected to the mean value removing processing in the step 01 to obtain energy spectrum distribution of the signals;
step 03: adaptively determining an interpolation multiple by using the energy spectrum distribution of the signal;
step 04: interpolating the high-speed rail seismic source seismic signals subjected to the mean value removing processing obtained in the step 01 according to the interpolation multiple to obtain seismic signals with a higher sampling rate;
step 05: carrying out windowing Fourier transform on the seismic signals after interpolation by using a window function;
step 06: calculating the difference of the phase of the signal windowing Fourier transform coefficient with respect to time and obtaining an extrusion position, and then accumulating the signal windowing Fourier transform coefficient to the extrusion position;
step 07: and obtaining a final time frequency analysis result and solving a modulus value to obtain final time frequency distribution.
2. The high-speed rail seismic source seismic signal time-frequency analysis method based on the extrusion windowing Fourier transform as claimed in claim 1, wherein the step 01 specifically comprises:
using s [ M ] to represent one-dimensional seismic signals, wherein the total number of M sampling points is delta t, and M represents the index of the signals in the time direction; the mean value is removed by:
3. the high-speed rail seismic source seismic signal time-frequency analysis method based on the extrusion windowing Fourier transform as claimed in claim 2, wherein the step 02 specifically comprises:
performing discrete Fourier transform on the signal S [ m ] to obtain S [ k ] as:
wherein M represents the number of sampling points of the one-dimensional seismic signal, and Δ f is a frequency domain sampling interval, an
k is a frequency index ranging from 0 to M-1; from S [ k ]]Obtaining the energy spectrum EF [ k ] of the one-dimensional seismic signal along the frequency domain]Comprises the following steps:
4. the high-speed rail seismic source seismic signal time-frequency analysis method based on the extrusion windowing Fourier transform as claimed in claim 3, wherein the step 03 specifically comprises:
calculating the energy E of the one-dimensional seismic signal in the frequency domain:
then, an energy accumulation function ACCU _ EF [ q ] of EF [ k ] is calculated, where q is an index of the energy accumulation function,
finding the frequency upper limit index Q in the energy accumulation function ACCU _ EF [ Q ] according to the following criteria:
wherein lambda is a threshold value, and the value of lambda is greater than or equal to 0.999; the interpolation factor R is then determined according to the following formula:
wherein
Meaning rounding up.
5. The high-speed rail seismic source seismic signal time-frequency analysis method based on the extrusion windowed Fourier transform as claimed in claim 4, wherein the step 04 specifically comprises:
a new sequence SS [ k ] is constructed, sharing RM points, which is related to S [ k ] as follows:
then, the new sequence SS [ k ] is processed with inverse Fourier transform, and a new time sequence SS [ m ] after resampling can be obtained:
where real { } denotes the real part of the complex number.
6. The high-speed rail seismic source seismic signal time-frequency analysis method based on the extrusion windowing Fourier transform as claimed in claim 5, wherein the step 05 specifically comprises:
the selected window function is g [ m ], windowing Fourier transform is carried out on the seismic signal ss [ m ] after interpolation to obtain a result WFT [ m, k ], and the result WFT [ m, k ] is:
wherein l represents a temporary time index, k is a frequency index, and the final extrusion time-frequency transformation result is assumed to be SWFT [ m, k ], and the SWFT [ m, k ] is initialized to be 0.
7. The time-frequency analysis method for seismic signals of a high-speed rail seismic source based on the extrusion windowed Fourier transform as claimed in claim 6, wherein the step 06 specifically comprises:
computing the difference along the m index for phase WFT _ phs [ m, k ] of WFT [ m, k ] can result in:
wherein
Wherein img () represents the imaginary part of the complex number, real () represents the real part of the complex number, and abs () represents the modulus of the complex number; for dif [ m, k ]]The corresponding pressing position k is obtained by1:
Where round () represents rounding the floating point number; the corresponding windowed fourier transform coefficients WFT [ m, k ] are accumulated to the new position:
SWFT[m,k1]＝SWFT[m,k1]+WFT[m,k]。
8. the time-frequency analysis method for seismic signals of a high-speed rail seismic source based on the extrusion windowed Fourier transform as claimed in claim 7, wherein the step 07 specifically comprises:
and calculating the module value of the extrusion transformation result SWFT [ m, k ] to obtain the time-frequency distribution of the seismic signals of the high-speed rail seismic source as follows:
SWFT_E[m,k]＝abs(SWFT[m,k])。
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| CN110806534B (en) * | 2019-12-04 | 2021-08-17 | 绵阳市维博电子有限责任公司 | Railway 25Hz phase-sensitive track signal detection method and system based on channel multiplexing |
| CN111427091B (en) * | 2020-05-06 | 2023-05-02 | 芯元(浙江)科技有限公司 | Random noise suppression method for seismic exploration signals by extruding short-time Fourier transform |
| CN116451347B (en) * | 2023-04-07 | 2024-04-23 | 长安大学 | Seismic wave numerical simulation method and device for high-speed rail mobile seismic source |
| CN118656366A (en) * | 2024-08-20 | 2024-09-17 | 吉林省智广恒胜科技有限公司 | Railway mileage determination method and system based on Fourier analysis |
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