CN109884694A - A kind of high-speed rail focus seismic signal time-frequency analysis method based on extruding adding window Fourier transformation - Google Patents
A kind of high-speed rail focus seismic signal time-frequency analysis method based on extruding adding window Fourier transformation Download PDFInfo
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Abstract
The present invention discloses a kind of based on the high-speed rail focus seismic signal time-frequency analysis method for squeezing adding window Fourier transformation, comprising: 01: carrying out average value processing to the high-speed rail focus seismic signal of acquisition；02: Fourier transformation being carried out to high-speed rail focus seismic signal, obtains the energy Spectral structure of signal；03: adaptively determining interpolation multiple using the energy Spectral structure of signal；04: interpolation is carried out to by step 01 treated high-speed rail focus seismic signal according to interpolation multiple；05: adding window Fourier transformation being carried out to the seismic signal after interpolation using window function；06: calculate signal adding window Fourier Transform Coefficients phase about time difference and obtain extrusion position, then signal adding window Fourier Transform Coefficients are accumulated to extrusion position；07: obtaining final time frequency analysis result and modulus value obtains final time-frequency distributions.The result that this method obtains can more subtly reflect that the time-frequency characteristics of high-speed rail focus seismic signal and spectrum component change with time.
Description
Technical field
It is the invention belongs to exploration geophysics field, in particular to a kind of based on the high-speed rail shake for squeezing adding window Fourier transformation
Focus earthquake signal Time-Frequency Analysis Method.
Background technique
Ended for the end of the year 2017, China's high-speed rail revenue kilometres account for the 66% of world's high-speed rail total amount up to 2.5 ten thousand kilometers.Have daily
Thousands of times high-speed rail train high-speed cruisings are on the high-speed rail route of widely dispersed.The high-speed rail train high speed of so huge quantity
It operates on high-speed rail route, can not only cause the vibration of high-speed rail train and roadbed, and can will vibrate with various types of earthquakes
Wave blazes abroad.Embedding detector can receive ground caused by high-speed rail train operation in the range of tens meters of high-speed rail route two sides
Seismic wave, i.e. high-speed rail focus seismic signal.The signal that wave detector receives is analyzed, the fortune of high-speed rail train may be not only analyzed
Row state, and be expected to that the underground structure near high-speed rail route is imaged.However, in face of this completely new high-speed rail focus
Data are shaken, the variation which kind of spectrum analysis means to detect spectrum component using is extremely crucial.It is this for analyzing at present
High-speed rail operation causes seismic signal means to be extremely limited, and mainly includes:
The prior art 1: discrete Fourier transform
Such method carries out Fast Fourier Transform (FFT) or discrete Fourier transform to the digital signal that wave detector receives,
It can get the amplitude spectrum of signal.
The characteristics of prior art 1:
Advantage: simple and easy, calculation amount is small and not by interference from human factor.
Disadvantage: 1, can only analyze frequency content, can not analyze the starting and end time of various frequency contents；2, Wu Fafen
Various frequency contents are analysed to change with time rule.
The prior art 2: Short Time Fourier Transform
Such method utilizes window function to intercept a segment signal at every point of time, then carries out in Fu to the signal after interception
Leaf changes to obtain local frequency content.
The characteristics of prior art 2:
Advantage: realize that relatively simple, calculation amount is small and not by interference from human factor.
Disadvantage: frequency resolution is poor, is limited to the constraint of uncertainty principle.
The prior art 3: continuous wavelet transform
Morther wavelet is carried out flexible and translation and forms a series of small wave systems by such method, then by small wave system and signal with this
It does inner product and obtains a series of Continuous Wavelet Transform Coefficients.
The characteristics of prior art 3:
Advantage: relatively simple, calculation amount is smaller.
Disadvantage: 1, frequency resolution is poor, is limited to the constraint of uncertainty principle；2, the selection of morther wavelet is more tired
It is difficult；3, it is formed by m- scale domain when result is, and scale needs conversion that can just become frequency.
Summary of the invention
The purpose of the present invention is to provide a kind of based on the high-speed rail focus seismic signal time-frequency for squeezing adding window Fourier transformation
Analysis method, to solve the above technical problems.The present invention can analyze the frequency content of high-speed rail focus seismic signal at any time
Variation, and the time-frequency distributions of high-speed rail focus seismic signal are obtained using adding window Fourier transformation is squeezed, it is transported for subsequent judgement train
Row state provides data.
To achieve the goals above, the present invention adopts the following technical scheme:
A kind of high-speed rail focus seismic signal time-frequency analysis method based on extruding adding window Fourier transformation, including following step
It is rapid:
Step 01: average value processing is carried out to the high-speed rail focus seismic signal of acquisition；
Step 02: the high-speed rail focus seismic signal after carrying out average value processing to step 01 carries out Fourier transformation to obtain
The energy Spectral structure of signal；
Step 03: adaptively determining interpolation multiple using the energy Spectral structure of signal；
Step 04: according to interpolation multiple to by step 1 obtain go mean value high-speed rail focus seismic signal carry out interpolation with
Obtain the seismic signal of more high sampling rate；
Step 05: adding window Fourier transformation being carried out to the seismic signal after interpolation using window function；
Step 06: calculate signal adding window Fourier Transform Coefficients phase about time difference and obtain extrusion position, so
Signal adding window Fourier Transform Coefficients are accumulated to extrusion position afterwards；
Step 07: obtaining final time frequency analysis result and modulus value obtains final time-frequency distributions.
Further, step 01 specifically includes:
One-dimensional seismic signal is indicated with s [m], shares M sampled point, and time sampling interval is Δ t, and m indicates that signal exists
The index of time orientation；Mean value is gone in the following way:
Further, step 02 specifically includes:
Discrete Fourier transform is carried out to signal s [m] and obtains S [k] are as follows:
Wherein, M indicates the sampling number of one-dimensional signal, and Δ f is the frequency domain sampling interval, andK indicates frequency
Rate index, range is from 0 to M-1；The energy spectrum EF [k] along frequency domain of the one-dimensional signal is obtained by S [k Δ f] are as follows:
Further, step 03 specifically includes:
The ENERGY E of the one-dimensional signal is calculated in frequency domain:
Then the energy accumulation function ACCU_EF [q] of EF [k] is calculated
Upper frequency limit index Q is found according to following criterion in energy accumulation function ACCU_EF [q]:
Wherein λ is threshold value, and value is greater than or equal to 0.999；Then interpolation multiple R is determined according to the following formula:
WhereinIt is rounded in expression.
Further, step 04 specifically includes:
A new sequence SS [k] is constructed, RM point is shared, as follows with the relationship of S [k]:
Then inversefouriertransform is done to the new sequence SS [k], the new time series ss [m] after resampling can be obtained:
Wherein real { } expression takes real.
Further, step 05 specifically includes:
The window function of selection is g [m], does adding window Fourier transformation to seismic signal ss [m] after interpolation and obtains result WFT
[m, k] are as follows:
Wherein l is temporary time index, and m is time index, and k is Frequency Index.Final extruding transformation knot is assumed simultaneously
Fruit is
Assume that final extruding transformation results are SWFT [m, k] simultaneously, and its whole is initialized as 0.
Further, step 06 specifically includes:
WFT_phs [m, k] indicates the phase of adding window Fourier Transform Coefficients WFT [m, k], and phase WFT_phs [m, k] is along m
It is available that index calculates difference:
Wherein
Wherein img () indicates to take the imaginary part of plural number, and real () expression takes real, and abs () expression takes the modulus of complex number
Value.Corresponding extrusion position k is obtained in the following way to dif [m, k]1:
Wherein round () indicates to be rounded floating number；The accumulation of corresponding adding window Fourier Transform Coefficients WFT [m, k] is arrived
New position:
SWFT[m,k1]=SWFT [m, k1]+WFT[m,k]。
Further, step 07 specifically includes:
The time-frequency distributions for obtaining high-speed rail focus seismic signal to extruding transformation results SWFT [m, k] calculating modulus value are as follows:
SWFT_E [m, k]=abs (SWFT [m, k]).
Further, the time-frequency distributions obtained according to step 07 detect the motion state of high-speed rail train.
Compared with the existing technology, the invention has the following advantages: the present invention is the ground caused for high-speed rail operation
A kind of Time-Frequency Analysis Method of signal is shaken, the frequency content for being mainly used for portraying high-speed rail focus seismic signal changes with time,
For a kind of quick data processing method；The present invention carries out the average value processing that zero-suppresses to high-speed rail focus seismic signal first, then to letter
Number carry out spectrum analysis determine signal interpolation multiple and interpolation to improve difference accuracy, finally to the adding window Fourier transformation of signal
Coefficient carries out extrusion operation in a frequency direction to obtain high-precision time-frequency distributions.It is compared to conventional time-frequency distributions, this hair
The high-precision time-frequency distributions of bright acquisition can accurately portray high-speed rail focus seismic signal frequency component and change with time, and can use
In the operating status (at the uniform velocity or acceleration) of detection high-speed rail train.
Attached drawing table explanation
Fig. 1 is flow chart of the present invention；
Fig. 2 is one of high-speed rail focus seismic signal that single detector receives when train 1 passes through；
Fig. 3 is the high-speed rail source signal after taking mean value；
Fig. 4 is the amplitude spectrum of high-speed rail source signal after mean value；
Fig. 5 is the energy spectrum of high-speed rail source signal after mean value；
Fig. 6 is energy accumulation function；
Fig. 7 is one of high-speed rail source signal after interpolation；
Fig. 8 is single detector receives when the train 1 obtained using adding window Fourier transformation is passed through high-speed rail focus
Shake the time-frequency distributions of signal.
Fig. 9 is the high-speed rail shake received using single detector when the train 1 that adding window Fourier transformation obtains passes through is squeezed
The time-frequency distributions of focus earthquake signal.
Figure 10 is the high-speed rail shake received using single detector when the train 2 that adding window Fourier transformation obtains passes through is squeezed
The time-frequency distributions of focus earthquake signal.
Specific embodiment
With reference to the accompanying drawing and the present invention will be further described in detail.
The present invention is a kind of Time-Frequency Analysis Method of caused seismic signal when passing through for high-speed rail.The present invention is first to adopting
The seismic signal collected carries out Fourier transformation to obtain the energy spectrum of signal, and the interpolation times of signal is then determined using energy spectrum
Number simultaneously carries out interpolation to signal, then calculates the adding window Fourier transformation of signal after interpolation, utilizes signal adding window Fourier transformation
Phase spectrum difference determine the extrusion position of frequency content, finally corresponding coefficient is accumulated to extrusion position obtain it is high-precision
Time-frequency spectrum provides a high-precision time-frequency spectrum to analyze each period frequency content.
Refering to Figure 1, the present invention provides a kind of high-speed rail focus seismic signal based on extruding adding window Fourier transformation
Time-Frequency Analysis Method, comprising the following steps:
Step 01: average value processing is carried out to the high-speed rail focus seismic signal of acquisition；
Step 02: the high-speed rail focus seismic signal after carrying out average value processing to step 01 carries out Fourier transformation, obtains
The energy Spectral structure of signal；
Step 03: adaptively determining interpolation multiple using the energy Spectral structure of signal；
Step 04: according to interpolation multiple to by step 1 obtain go mean value high-speed rail focus seismic signal carry out interpolation with
Obtain the seismic signal of more high sampling rate；
Step 05: adding window Fourier transformation being carried out to the seismic signal after interpolation using window function；
Step 06: calculate signal adding window Fourier Transform Coefficients phase about time difference and obtain extrusion position, so
Signal adding window Fourier Transform Coefficients are accumulated to extrusion position afterwards；
Step 07: obtaining final time frequency analysis result and modulus value obtains final time-frequency distributions.
Step 01: average value processing is carried out to the high-speed rail focus seismic signal of acquisition, is specifically included:
One-dimensional seismic signal is indicated with s [m], shares M sampled point, and time sampling interval is Δ t, and m indicates that signal exists
The index of time orientation.Mean value is gone in the following way:
High-speed rail focus seismic signal after removing average value processing in step 02 carries out Fourier transformation to obtain the energy of signal
Spectral structure specifically includes:
Discrete Fourier transform is carried out to signal s [m] and obtains S [k] are as follows:
Wherein, M indicates the sampling number of one-dimensional signal, and Δ f is the frequency domain sampling interval, andK is indicated
Frequency Index, range is from 0 to M-1.The energy spectrum EF [k] along frequency domain of the one-dimensional signal is obtained by S [k Δ f] are as follows:
Interpolation multiple is adaptively determined using the energy Spectral structure of signal in step 03, is specifically included:
The ENERGY E of the one-dimensional signal is calculated in frequency domain:
Then the energy accumulation function ACCU_EF [q] of EF [k] is calculated
Upper frequency limit index Q is found according to following criterion in energy accumulation function ACCU_EF [q]:
Wherein λ is threshold value, and value is generally chosen for the value greater than 0.999.Then interpolation multiple is determined according to the following formula
R:
WhereinIt is rounded in expression.
In step 04 according to interpolation multiple to by step 1 obtain go mean value high-speed rail focus seismic signal carry out interpolation with
The seismic signal for obtaining more high sampling rate, specifically includes:
A new sequence SS [k] is constructed, RM point is shared, as follows with the relationship of S [k]:
Then inversefouriertransform is done to the new sequence SS [k], the new time series ss [m] after obtaining resampling:
Wherein real { } expression takes real.
Window function carries out adding window Fourier transformation to the seismic signal after interpolation in step 05, specifically includes:
If the window function chosen is g [m], adding window Fourier transformation is done to seismic signal ss [m] after interpolation and obtains result
WFT [m, k] are as follows:
Wherein l is temporary time index, and m is time index, and k is Frequency Index.Final extruding transformation knot is assumed simultaneously
Fruit is SWFT [m, k], and SWFT [m, k] is all initialized as 0.
In step 06 calculate signal adding window Fourier Transform Coefficients phase about time difference and obtain extrusion position, so
Signal adding window Fourier Transform Coefficients are accumulated to extrusion position afterwards, are specifically included:
WFT_phs [m, k] indicates adding window Fourier Transform Coefficients phase, and WFT_phs [m, k] calculates difference along m index and obtains
It arrives:
Wherein phs_img_dif [m, k] and phs_real_dif [m, k] are as follows:
Wherein img () indicates to take the imaginary part of plural number, and real () expression takes real, and abs () expression takes the modulus of complex number
Value.Corresponding extruding frequency location k is obtained in the following way to dif [m, k]1:
Wherein round () indicates to be rounded floating number.The accumulation of corresponding adding window Fourier Transform Coefficients WFT [m, k] is arrived
New position [m, k1]:
SWFT[m,k1]=SWFT [m, k1]+WFT[m,k]
Final time frequency analysis result is obtained in step 07 and modulus value obtains final time-frequency distributions, specific as follows:
The time-frequency distributions for obtaining high-speed rail focus seismic signal to extruding transformation results SWFT [m, k] calculating modulus value are as follows:
SWFT_E [m, k]=abs (SWFT [m, k])
For the signal received by the single low-frequency detector away from high-speed rail route 30m when high-speed rail is passed through.Fig. 2 is train
Vibration signal caused by high-speed rail focus received by 1 single detector when passing through, sampling interval 5ms share 3001
Sampled point.Fig. 3 is after mean value as a result, Fig. 4 is corresponding amplitude spectrum, and Fig. 5 is corresponding energy spectrum, and Fig. 6 is energy accumulation
Function.Being taken as λ is 0.999, and it is 1147 that energy spectrum as shown in Figure 6, which obtains Q, it is hereby achieved that interpolation multiple R is 14 times.Fig. 7
For the signal after 14 times of interpolation, and Fig. 8 is the high-speed rail focus earthquake obtained when train 1 passes through using conventional adding window Fourier transformation
The time-frequency distributions of signal, and Fig. 9 is the high-speed rail focus seismic signal obtained when train 1 passes through using adding window Fourier transformation is squeezed
Time-frequency distributions, the frequency of each discrete spectrum remains unchanged at any time, illustrate train by when wave detector in driving at a constant speed shape
State.It is each discrete based on the high-speed rail focus seismic signal time-frequency distributions for squeezing adding window Fourier transformation when Figure 10 passes through for train
The frequency of spectrum becomes larger increase with time, illustrates train by being in state of giving it the gun when wave detector.
Finally, it should be noted that the above example is to the purpose of the present invention, technical solution and beneficial effect provide into
The verifying of one step, this only belongs to specific implementation example of the invention, is not intended to limit the scope of protection of the present invention, in the present invention
Spirit and principle within, any modification made, improve or equivalent replacement etc. (such as change window function, replacement interpolation scheme,
Replace difference method etc.), it should all be within the scope of the present invention.
Claims (8)
1. a kind of based on the high-speed rail focus seismic signal time-frequency analysis method for squeezing adding window Fourier transformation, which is characterized in that packet
Include following steps:
Step 01: average value processing is carried out to the high-speed rail focus seismic signal of acquisition；
Step 02: the high-speed rail focus seismic signal after carrying out average value processing to step 01 carries out Fourier transformation to obtain signal
Energy Spectral structure；
Step 03: adaptively determining interpolation multiple using the energy Spectral structure of signal；
Step 04: the high-speed rail focus seismic signal after removing average value processing to what is obtained by step 01 according to interpolation multiple carries out slotting
Value is to obtain the seismic signal of more high sampling rate；
Step 05: adding window Fourier transformation being carried out to the seismic signal after interpolation using window function；
Step 06: calculate signal adding window Fourier Transform Coefficients phase about time difference and obtain extrusion position, then will
Signal adding window Fourier Transform Coefficients are accumulated to extrusion position；
Step 07: obtaining final time frequency analysis result and modulus value obtains final time-frequency distributions.
2. a kind of based on the high-speed rail focus seismic signal time-frequency analysis side for squeezing adding window Fourier transformation as described in claim 1
Method, which is characterized in that step 01 specifically includes:
One-dimensional seismic signal is indicated with s [m], shares M sampled point, and time sampling interval is Δ t, and m indicates signal in the time
The index in direction；Mean value is gone in the following way:
3. a kind of based on the high-speed rail focus seismic signal time-frequency analysis side for squeezing adding window Fourier transformation as described in claim 1
Method, which is characterized in that step 02 specifically includes:
Discrete Fourier transform is carried out to signal s [m] and obtains S [k] are as follows:
Wherein, M indicates the sampling number of one-dimensional signal, and Δ f is the frequency domain sampling interval, andK refers to for frequency
Mark, range is from 0 to M-1；The energy spectrum EF [k] along frequency domain of the one-dimensional signal is obtained by S [k Δ f] are as follows:
4. a kind of based on the high-speed rail focus seismic signal time-frequency analysis side for squeezing adding window Fourier transformation as described in claim 1
Method, which is characterized in that step 03 specifically includes:
The ENERGY E of the one-dimensional signal is calculated in frequency domain:
Then the energy accumulation function ACCU_EF [q] of EF [k] is calculated
Upper frequency limit index Q is found according to following criterion in energy accumulation function ACCU_EF [q]:
Wherein λ is threshold value, and value is greater than or equal to 0.999；Then interpolation multiple R is determined according to the following formula:
WhereinIt is rounded in expression.
5. a kind of based on the high-speed rail focus seismic signal time-frequency analysis side for squeezing adding window Fourier transformation as described in claim 1
Method, which is characterized in that step 04 specifically includes:
A new sequence SS [k] is constructed, RM point is shared, as follows with the relationship of S [k]:
Then inversefouriertransform is done to the new sequence SS [k], the new time series ss [m] after resampling can be obtained:
Wherein real { } expression takes real.
6. a kind of based on the high-speed rail focus seismic signal time-frequency analysis side for squeezing adding window Fourier transformation as described in claim 1
Method, which is characterized in that step 05 specifically includes:
The window function of selection is g [m], does adding window Fourier transformation to seismic signal ss [m] after interpolation and obtains result WFT [m, k]
Are as follows:
Wherein l indicates temporary time index, and m is time index, and k is Frequency Index, while assuming final extruding time-frequency conversion knot
Fruit is SWFT [m, k], and SWFT [m, k] is all initialized as 0.
7. a kind of based on the high-speed rail focus seismic signal time-frequency analysis side for squeezing adding window Fourier transformation as described in claim 1
Method, which is characterized in that step 06 specifically includes:
Calculating difference along m index to the phase WFT_phs [m, k] of WFT [m, k] can be obtained:
Wherein
Wherein img () indicates to take the imaginary part of plural number, and real () expression takes real, and abs () expression takes plural modulus value；It is right
Dif [m, k] obtains corresponding extrusion position k in the following way1:
Wherein round () indicates to be rounded floating number；The accumulation of corresponding adding window Fourier Transform Coefficients WFT [m, k] is arrived newly
Position:
SWFT[m,k1]=SWFT [m, k1]+WFT[m,k]。
8. a kind of based on the high-speed rail focus seismic signal time-frequency analysis side for squeezing adding window Fourier transformation as described in claim 1
Method, which is characterized in that step 07 specifically includes:
The time-frequency distributions for obtaining high-speed rail focus seismic signal to extruding transformation results SWFT [m, k] calculating modulus value are as follows:
SWFT_E [m, k]=abs (SWFT [m, k]).
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| CN116451347A (en) * | 2023-04-07 | 2023-07-18 | 长安大学 | Seismic wave numerical simulation method and device for high-speed rail mobile seismic source |
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| CN110806534A (en) * | 2019-12-04 | 2020-02-18 | 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 |
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| CN116451347A (en) * | 2023-04-07 | 2023-07-18 | 长安大学 | Seismic wave numerical simulation method and device for high-speed rail mobile seismic source |
| 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 |
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