CN114578417A - Pulse type earthquake motion fitting method based on wavelet adjustment - Google Patents
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Abstract
The invention provides a pulse type earthquake motion fitting method based on a wavelet adjustment method, which comprises the following steps: fitting a pulse type earthquake motion wavelet function; substituting the field condition information to obtain a target acceleration response spectrum; obtaining the mother wave to calculate the acceleration response spectrum; adjusting the mother wave by adopting wavelet transformation based on the target acceleration response spectrum to obtain wavelets; acquiring a father wave by adopting an equivalent pulse velocity model; respectively solving wavelet coefficients of the wavelet and the parent wave; adjusting the wavelet coefficient of the wavelet to obtain an adjusted wavelet coefficient; and reconstructing the adjusted wavelet coefficient to obtain the near fault pulse seismic oscillation which is more in line with the actual situation.
Description
Technical Field
The invention provides an impulse type earthquake motion fitting method based on a wavelet adjustment method, and belongs to the field of impulse type earthquake motion fitting.
Background
The pulse type earthquake motion generated at the present stage is earthquake motion synthesized based on Fourier transform, and the earthquake motion can realize non-stationarity in a time domain through uniform modulation on amplitude in the time domain, but cannot realize non-stationarity in a frequency domain. The uniform modulation is realized by multiplying an envelope function by an acceleration time course, and the method cannot simulate the seismic motion containing velocity pulses. The time course of seismic oscillation is a time-frequency non-stationary random process with abrupt change characteristics. The seismic motion synthesis method based on Fourier transform cannot ensure that the synthesized seismic motion is time-frequency non-stationary. In order to be able to simulate the non-stationary nature of the time-frequency behavior of seismic oscillations, new signal processing tools must be sought. Therefore, the invention provides a pulse type seismic oscillation fitting method based on a wavelet adjustment method.
With the continuous development of national economic and technological levels, more and more large-sized buildings are built as lifelines in the near fault area and even across the fault in recent years. The natural vibration period of such a building (structure) is often larger than that of a general building (structure), and is easily affected by low-frequency excitation. The impulse seismic motion is a seismic motion containing a large amount of low-frequency components, and therefore, it is necessary to consider the influence of the impulse seismic motion on the structure. So far, the seismic record of the near fault pulse type seismic motion is insufficient, and for the area lacking the seismic record, no measured seismic record can be used as seismic motion input when the seismic design of a large building is carried out. But the artificial earth vibration can generate a series of earthquake motion meeting the condition of the proposed site in a short time, which can effectively make up for the deficiency. Therefore, it is necessary to study a method of fitting a near-fault pulse type seismic oscillation. The artificial synthetic seismic motion can not only obtain seismic waves meeting various site conditions, but also promote the development of structural seismic design to a certain extent. Therefore, it is very important to research a method capable of synthesizing earthquake motion which is as consistent as possible with the actual situation.
The method comprises the following steps of Wangyuan navigation, near fault area division and near fault velocity pulse type earthquake motion simulation [ D ]. southwest transportation university 2015:
(1) determining a target reaction spectrum S (T);
the target acceleration response spectrum was determined according to 5.2.1 in road engineering seismic Specification (JTG B02-2013), and is of the form shown below:
in the formula: t isg-a characteristic period of the reaction spectrum;
t-structure natural vibration period;
s (T) -target response spectrum;
Smax-reaction spectrum maximum.
(2) Calculating a target power spectrum S (omega);
according to the relation between the reaction spectrum and the power spectrum conversion which is proposed currently, the form is shown as the following formula.
Acceleration response spectrum from target
In the formula: sa T(xi, ω) -target acceleration response spectrum;
s (ω) -power spectrum;
ξ -damping ratio;
omega-structural natural frequency of vibration;
t-structure natural vibration period;
gamma-probability of surging.
(3) Calculating a Fourier amplitude spectrum A (omega);
the mathematical relationship between the power spectrum and the Fourier amplitude spectrum is shown in the formula.
In the formula: a (omega) -Fourier amplitude spectrum
(4) Calculating a phase spectrum;
generating a phase spectrum uniformly distributed over-2 pi to 2 pi
(5) Obtaining a steady acceleration time course by IFFT;
the earthquake motion X is simulated by adopting a trigonometric series model shown as the following formulaa。
Xa＝g(t)·xa(t)
In the formula:
-a phase angle;
ωk-the circular frequency;
A(ωk) -an amplitude spectrum;
n-number of frequency separation points in the frequency domain of the target response spectrum;
g (t) -an intensity envelope function;
xa(t) -smooth acceleration time course;
Xaacceleration time course
Calculating to obtain the time course of steady acceleration by using fast Fourier inverse transformation
(6) Multiplying by an envelope function to generate a non-stationary acceleration time interval;
to convert a stationary acceleration time course into a non-stationary acceleration time course, the generated stationary acceleration time course is non-uniformly modulated by multiplying by an intensity envelope function. The mathematical expression of the envelope function is shown as
Wherein: t is1-the start time of the plateau;
T2-end time of the plateau;
c-rate of change of decay phase.
(7) Fitting and iterating with a target acceleration response spectrum to obtain an acceleration time course;
in order to match the response spectrum of the non-stationary acceleration time course with the target acceleration response spectrum, iterative calculation needs to be performed on the non-stationary acceleration time course, so that the generated response spectrum of the non-stationary acceleration time course approaches the target spectrum.
The specific iterative calculation steps are as follows:
a. calculating the ratio of the target acceleration response spectrum to the non-stationary acceleration time course;
b. performing fast Fourier transform calculation on the non-stationary acceleration time course to obtain a phase spectrum and a Fourier amplitude spectrum, and multiplying the ratio calculated in the step a by the Fourier amplitude spectrum;
c. combining the adjusted Fourier amplitude spectrum with the phase spectrum, and calculating to obtain a stable acceleration time interval through fast Fourier inverse transformation;
d. multiplying by an intensity envelope function to calculate a non-stationary acceleration time course;
e. calculating the average relative error Em between the response spectrum of the non-stationary acceleration time course and the target acceleration response spectrum, judging whether the average relative error Em is less than 5%, if the average relative error Em is less than 5%, stopping iterative calculation, and otherwise returning to the step a.
After n times of iterative computation, the average relative error between the reaction spectrum of the non-stationary acceleration time course and the target acceleration reaction spectrum is less than 5 percent, and the iterative computation is stopped. Finally obtaining a calculated acceleration reaction spectrum curve and a target acceleration reaction spectrum curve
(8) Fourier transform is carried out on the acceleration time course finally generated in the step (7) to obtain a Fourier spectrum, and the frequency is smaller than frIs set to 0
(9) Combining the Fourier amplitude spectrum finally generated in the step (8) with the phase spectrum generated in the step (4), and calculating and generating a high-frequency acceleration time interval through inverse fast Fourier transform
(10) Simulating a low-frequency speed pulse time course by adopting an equivalent speed pulse model:
where ω (t) is an envelope function and is calculated by the following equation (3-9).
Wherein:
Vp-peak value of pulse
fpFrequency, 1/Tp，TpIs a pulse period
t1-the moment of occurrence of the peak of the cosine function
Self-oscillation period of T-structure
Gamma-decay rate
t0-time of occurrence of peak of envelope function
The low-frequency speed pulse time interval is derived to obtain a low-frequency acceleration time interval
(11) High and low frequency components are superposed to generate near fault pulse type earthquake motion
And (4) superposing the high-frequency acceleration time interval obtained in the step (9) and the low-frequency pulse acceleration time interval obtained in the step (10) to generate the near-fault pulse type seismic oscillation.
The literature [ wangynavigation, 2015] method for synthesizing seismic oscillation has the following disadvantages:
(1) the impulse type earthquake motion generated by the harmonic method based on Fourier transform cannot reflect the frequency domain non-stationarity of the earthquake motion. In the simulation of the high-frequency components, fourier transform methods are used in the generation of the acceleration time intervals, which are only suitable for processing stationary signals. However, the seismic waves are generally non-stationary signals, and the frequency of the seismic waves changes along with the time change, so that the frequency domain non-stationarity of the seismic motion cannot be reflected by the Fourier transform, and therefore the pulse type seismic motion generated by the harmonic wave method based on the Fourier transform cannot completely meet the seismic motion of the actual situation.
(2) The single equivalent velocity pulse model is used for simulating the low-frequency component of the artificial near fault pulse type earthquake motion, and the influence of different fault fracture mechanisms is not considered. A great deal of research shows that different fault fracture mechanisms can generate different types of impulse type earthquake motion, so that the low-frequency components of the artificial near fault impulse type earthquake motion simulated by using a single equivalent velocity impulse model are not comprehensive enough, and the earthquake motion generated by using the single equivalent velocity impulse model cannot completely meet the earthquake motion of the actual situation.
Disclosure of Invention
The invention provides a pulse type seismic motion fitting method based on a wavelet adjustment method, and the pulse type seismic motion time course obtained by fitting by the method can be more reasonably matched with the actual near fault seismic motion characteristic.
Step S1: fitting near fault seismic motion wavelet basis functions
Step S1.1: determining a scale vector S from equation (1)j
In the formula:
Sj-scale vector
n0Controlling the scale vector SjParameters of the range
m-scale vector SjNumber of points
Step S1.2: obtaining wavelet basis functions according to equation (2)
In the formula:
Zeta-wavelet basis function attenuation coefficient
Omega-wavelet basis function frequency coefficient
pi-time vector
tkWavelet basis function time parameter
Step S2: according to the impulse type earthquake motion wavelet basis function obtained in the step S1
Substituting the field condition information to obtain a target acceleration response spectrum Sa(Tj)]Target spectra
Step S3: calculating acceleration response spectrum (S) of original seismic oscillation, namely mother wave MWa(Tj)]Calculating the spectrum
Step S4: obtaining an adjustment coefficient gamma according to the formula (3)
In the formula: gamma-adjustment factor
[Sa(Tj)]Target spectraTarget acceleration response spectrum
[Sa(Tj)]Calculating the spectrumCalculating an acceleration response spectrum
Step S5: obtaining a target acceleration response spectrum [ S ] according to the formula (4)a(Tj)]Target spectraAnd calculating acceleration response spectrum Sa(Tj)]Calculating the spectrumError E ofrror。
In the formula:
Errorerror of target acceleration response spectrum from calculated acceleration response spectrum
m-scale vector SjNumber of points
[Sa(Tj)]Target spectrumTarget acceleration reactionStress spectrum
[Sa(Tj)]Calculating the spectrumCalculating an acceleration response spectrum
Step S6: obtaining wavelet coefficients C (s, p) according to equation (5)
In the formula:
C(sj,pi) -wavelet coefficients
Delta t-time interval of seismic oscillation acceleration time course
tkWavelet basis function time parameter
Sj-scale vector
piTime vector f (t)k) Primary seismic oscillation
m-scale vector SjNumber of points
M-number of data points of original seismic oscillation
Step S7: obtaining detail function D (s, t) in wavelet transform according to equation (6)
In the formula:
D(sj,tk) -detail function
Δp-wavelet function time interval
Step S8: obtaining a wavelet SW according to equation (7)
In the formula:
SW-wavelet
Step S9: the average relative error E between the calculated acceleration response spectrum and the target acceleration response spectrum is obtained in step S5rrorAnd judges whether it is less than 5%. If the average relative error is greater than 5%, returning to step S4; and if the average relative error is less than or equal to 5%, outputting the wavelets SW of the pulse seismic motion time course.
Step S10: the pulse period T is obtained according to the formula (8)pThe peak value V of the pulse is obtained from the formula (9)pThe peak time t of the pulse is obtained from the equation (10)1,V
ln(Tp)＝-6.45+1.11MwFormula (8)
ln(Vp)＝3.680+0.065Mw+0.025ln (R) formula (9)
ln(tl,v)＝1.35Mw-6.88 formula (10)
Wherein: t isp-pulse period
Vp-peak value of pulse
t1,V-pulse peak time
Distance of R-fault
MwMoment-magnitude
Step S11: speed time course v for simulating sliding impulse type near fault impulse type earthquake to provide near fault impulse type earthquakegAAs shown in equation (11).
Method for simulating forward directivity effect to provide time course v of near fault pulse type seismic velocitygBAs shown in equation (12).
νgB(t)＝Vpsin(ωpt) 0≤t≤TpFormula (12)
Wherein:
νgAsimulation sliding impulse type near fault impulse type seismic velocity time course
νgBSimulation of forward directional effect near fault pulse type seismic velocity time course
Vp-peak value of pulse
TpPulse period
ωpPulse frequency of fromp＝2π/TpDetermining
Step S12: velocity time course v obtained in step S11gADerivation is carried out to obtain acceleration time course alphagAAs shown in formula (13). Velocity time course v obtained in step S11gAIntegral calculation to obtain displacement time interval dgA. As shown in equation (14).
In the formula: t ispDetermined by dividing the maximum of equations (11) and (14), i.e.:
velocity time interval v obtained in step S11gBDerivation is carried out to obtain acceleration time course alphagBAs shown in formula (15). Velocity time course v obtained in step S11gBIntegral calculation to obtain displacement time interval dgBAs shown in formula (16).
αgB(t)＝ωpVpcos(ωpt),0≤t≤TpFormula (15)
In the formula:
αgAsimulation sliding impulse type near fault impulse type earthquake acceleration time course
dgASimulation sliding impulse type near fault impulse type earthquake displacement time course
Alpha gB-simulated forward directional effect near fault pulse type seismic acceleration time course
dgBSimulation forward directivity effect near fault pulse type seismic displacement time course
Vp-peak value of pulse
Tp-pulse period
ωpPulse frequency of fromp＝2π/TpDetermining
TpDetermined by dividing the maximum of equations (12) and (16), i.e.:
step S13: father wave FW for obtaining pulse type earthquake motion time range
Step S14: calculating the pulse period Tp
ln(Tp)＝-6.45+1.11MwFormula (17)
In the formula: t isp-pulse period
Step S15: determining the number of layers n of a wavelet decomposition
In the formula: f. ofpPulse frequency
number of layers for n-wavelet transform decomposition
foriginalFrequency band range of the signal
Delta t-time interval of seismic dynamic acceleration time interval
Step S16: decomposing the parent wave into n layers by multi-scale discrete wavelet transform as shown in formula (18)
In the formula: FW-father wave
FWcD1，…，FWcDn-each frequency band corresponding to the detail component of the parent wave after wavelet decomposition
FWcAnFrequency band corresponding to approximate component of parent wave after wavelet decomposition
n-number of layers of wavelet decomposition
Step S17: the parent wave wavelet coefficient LW is determined by step S16cAn
LWcAn＝FWcAn
In the formula:
LWcAn-wavelet coefficient of parent wave
Step S18: decomposing the wavelet into n layers by multi-scale discrete wavelet transform as shown in formula (18)
In the formula: SW-wavelet
SWcD1，…，SWcDn-each frequency band corresponding to a detail component of a wavelet decomposition
SWcAn-bands corresponding to approximate components of wavelets after wavelet decomposition
n-number of layers of wavelet decomposition
Step S19: wavelet coefficients HW of wavelets are determined by step S18cAn
HWcAn＝SWcAn
In the formula:
SWcAnwavelet coefficients of wavelets
Step S20: solving wavelet adjustment coefficient beta according to equation (20)coef
βcoef＝FWcAn/SWcAnFormula (20)
In the formula: beta is acoefWavelet adjustment coefficient
Step S21: obtaining the adjusted wavelet coefficient SW 'according to the formula (21)'cAn
SW′cAn＝βcoef·SWcAnFormula (21)
In the formula: SW'cAn-adjusted wavelet coefficients
Step S22: the adjusted wavelet coefficient SW 'is obtained according to the formula (21)'cAnReplacing wavelet coefficients SW after wavelet SW decompositioncAnPerforming wavelet change reconstruction to obtain the near fault pulse type seismic oscillation AW
AW-near fault pulse type seismic motion.
(1) The impulse type earthquake motion generated based on the wavelet transformation can reflect the frequency domain non-stationarity of the earthquake motion. The wavelet transformation can acquire frequency by constructing wavelet basis functions with different characteristics to realize non-stationary signal processing, so that the frequency domain non-stationarity of earthquake motion is reflected, and the pulse earthquake motion generated based on the wavelet method is more suitable for the earthquake motion of actual conditions.
(2) The invention provides an impulse type earthquake motion fitting method based on a wavelet adjustment method for the first time. The study on the seismic dynamic acceleration time-history curve generated based on the wavelet adjustment method finds that the original time domain characteristics of the mother wave in the time domain are reserved after the mother wave is adjusted through discrete wavelet transformation. In the frequency domain, the spectral characteristics of impulsive seismic motion combine the characteristics of parent and parent waves. Therefore, the characteristics of the pulse type earthquake motion based on the wavelet adjustment method and the actual near fault earthquake motion are more consistent.
(3) The invention provides an optimal number of decomposition layers in the generation of a near fault impulse type earthquake. There is a correlation between the number of decomposition layers and the pulse period. The invention passes through the sum pulse period TpHarmonic magnitude MwThe statistical analysis shows that the pulse period and the magnitude have strong correlation, and the invention is just about the pulse period TpHarmonic vibration level MwThe statistical rule obtained by least square fitting is more reasonable and closer to the real pulse period value. Therefore, it isAccording to the invention, more accurate wavelet coefficients are obtained by determining the optimal decomposition layer number, and seismic oscillation more in line with actual conditions can be generated.
(4) The invention uses different equivalent velocity pulse models to generate the father wave of the near fault pulse type earthquake motion, and considers the influence of different fault fracture mechanisms. It has been found through extensive research that different fault-breaking mechanisms produce different types of impulse-type seismic motion. Therefore, the earthquake motion generated by using different equivalent velocity pulse models can better accord with the earthquake motion of the earthquake of the actual situation.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a time course curve of the acceleration of the parent wave.
FIG. 3 is a graph of parent wave acceleration time course.
Fig. 4 is a graph of a near fault pulse type acceleration time course.
Detailed Description
Seismic motion fitting parameters:
(1) example parameters are as follows: the engineering field category is II type field; the earthquakes are grouped into a third group (Tg ═ 0.45 s); the seismic fortification intensity is 7 degrees; the moment-vibration level is 6.5; the structural damping ratio is 0.05; the 50-year overrun probability is 10% (recurrence period 475 years), and the corresponding design basic earthquake motion peak acceleration is 0.15 g; the class A highway bridge E1 is used for seismic action and is in the form of near fault pulse seismic motion.
The mother wave is an El Mayor-Cucapah _ Mexico wave. The specific information is shown in table 1, and the time course curve of the acceleration of the parent wave is shown in fig. 1.
TABLE 1
The father wave is determined by an equivalent velocity pulse model, and the values of model parameters are as follows: t20 s, Vp＝60cm/s、t0＝5s、t15.6s, γ is 3; the acceleration time course curve of the parent wave is shown in figure 2.
(2) And (3) fitting: taking the approximate fault pulse type seismic oscillation of an equivalent velocity pulse model of a synthetic sliding impact effect as an example;
the results obtained by the calculations performed in the above steps S1 to S18 are shown in FIG. 3.
Wherein, fig. 2 is a time course curve of the acceleration of the mother wave.
Fig. 3 is a parent wave acceleration time course curve.
Fig. 4 is a graph of a near fault pulse type acceleration time course.
(1) The invention provides a near fault seismic motion fitting method based on a wavelet adjustment method, and the method can better inherit the time domain and frequency domain characteristics of parent waves and parent waves of the fitted seismic motion and is more consistent with the characteristics of the actual near fault seismic motion (steps S1-S22).
(2) The invention provides the method for generating the optimal decomposition layer number in the near fault impulse type earthquake, which can calculate more accurate wavelet coefficient and generate earthquake motion more conforming to the actual situation (step S15).
(3) The invention adjusts the seismic oscillation based on the target response spectrum and applies the continuous wavelet transform method, can realize the fitting of the target response spectrum, and can better reserve the time-frequency characteristic of the in-situ vibration (step S9).
Claims (1)
1. A pulse type seismic oscillation fitting method based on a wavelet adjustment method is characterized by comprising the following steps:
step S1: fitting near fault seismic motion wavelet basis functions
Step S1.1: determining a scale vector S from equation (1)j
In the formula:
Sj-scale vector
n0Controlling the scale vector SjParameters of the range
m-scale vector SjNumber of points
Step S1.2: obtaining wavelet basis functions according to equation (2)
In the formula:
Zeta-wavelet basis function attenuation coefficient
Omega-wavelet basis function frequency coefficient
pi-time vector
tkWavelet basis function time parameter
Step S2: according to the impulse type seismic motion wavelet basis function obtained in the step S1
Substituting the field condition information to obtain a target acceleration response spectrum Sa(Tj)]Target spectra
Step S3: calculating acceleration response spectrum (S) of original seismic oscillation, namely mother wave MWa(Tj)]Calculating the spectrum
Step S4: an adjustment coefficient gamma is obtained from the equation (3)
In the formula: gamma-adjustment factor
[Sa(Tj)]Target spectraTarget acceleration response spectrum
[Sa(Tj)]Calculating the spectrum-calculating a sumVelocity response spectrum
Step S5: obtaining a target acceleration response spectrum [ S ] according to the formula (4)a(Tj)]Target spectraAnd calculating acceleration response spectrum Sa(Tj)]Calculating the spectrumError E ofrror；
In the formula:
Errorerror of target acceleration response spectrum from calculated acceleration response spectrum
m-scale vector SjNumber of points
[Sa(Tj)]Target spectraTarget acceleration response spectrum
[Sa(Tj)]Calculating the spectrumCalculating an acceleration response spectrum
Step S6: obtaining wavelet coefficients C (s, p) according to equation (5)
In the formula:
C(sj,pi) -wavelet coefficients
Delta t-time interval of seismic oscillation acceleration time course
tkWavelet basis function time parameter
Sj-scale vector
pi-time vector
f(tk) Primary seismic oscillation
m-scale vector SjNumber of points
M-number of data points of original seismic oscillation
Step S7: obtaining detail function D (s, t) in wavelet transform according to equation (6)
In the formula:
D(sj,tk) -detail function
Δp-wavelet function time interval
Step S8: obtaining a wavelet SW according to equation (7)
In the formula:
SW-wavelet
Step S9: the average relative error E between the calculated acceleration response spectrum and the target acceleration response spectrum is obtained in step S5rrorAnd judging whether the content is less than 5%; if the average relative error is greater than 5%, returning to step S4; if the average relative error is less than or equal to 5%, outputting wavelets SW of the pulse type earthquake motion time course;
step S10: the pulse period T is obtained according to the formula (8)pThe peak value V of the pulse is obtained from the formula (9)pThe peak time t of the pulse is obtained from the equation (10)1,V
ln(Tp)＝-6.45+1.11MwFormula (8)
ln(Vp)＝3.680+0.065Mw+0.025ln (R) formula (9)
ln(tl,v)＝1.35Mw-6.88 formula (10)
Wherein: t isp-pulse period
Vp-peak value of pulse
t1,V-pulse peak time
Distance of R-fault
MwMoment-magnitude
Step S11: analog slide-impact type near fault pulse type earthquake extraction near faultVelocity time course v of pulse type earthquakegAAs shown in formula (11);
method for simulating forward directivity effect to provide time course v of near fault pulse type seismic velocitygBAs shown in formula (12);
νgB(t)＝Vpsin(ωpt)0≤t≤Tpformula (12)
Wherein:
νgAsimulation sliding impulse type near fault impulse type seismic velocity time course
νgBSimulation of forward directional effect near fault pulse type seismic velocity time course
Vp-peak value of pulse
Tp-pulse period
ωpPulse frequency of fromp＝2π/TpDetermining
Step S12: velocity time course v obtained in step S11gADerivation is carried out to obtain acceleration time course alphagAAs shown in formula (13); velocity time course v obtained in step S11gAIntegral calculation to obtain displacement time interval dgA(ii) a As shown in formula (14);
in the formula: t ispDetermined by dividing the maximum of equations (11) and (14), i.e.:
velocity time course v obtained in step S11gBDerivation is carried out to obtain acceleration time course alphagBAs shown in formula (15); velocity time course v obtained in step S11gBIntegral calculation to obtain displacement time interval dgBAs shown in formula (16);
αgB(t)＝ωpVpcos(ωpt),0≤t≤Tpformula (15)
In the formula:
αgAsimulation sliding impulse type near fault impulse type earthquake acceleration time course
dgASimulation sliding impulse type near fault impulse type earthquake displacement time course
αgBSimulation of forward directional effect near fault impulse type seismic acceleration time course
dgBSimulation of forward directional effect near fault pulse type seismic displacement time course
Vp-peak value of pulse
Tp-pulse period
ωpPulse frequency, from ωp＝2π/TpDetermining
TpDetermined by dividing the maximum of equations (12) and (16), i.e.:
step S13: obtaining parent wave FW of pulse type earthquake motion time
Step S14: calculating the pulse period Tp
ln(Tp)＝-6.45+1.11MwFormula (17)
In the formula: t isp-pulse period
Step S15: determining the number of layers n of a wavelet decomposition
In the formula: f. ofpPulse frequency
number of layers for n-wavelet transform decomposition
foriginalFrequency band range of the signal
Delta t-time interval of seismic oscillation acceleration time course
Step S16: decomposing the parent wave into n layers by multi-scale discrete wavelet transform as shown in formula (18)
In the formula: FW-father wave
FWcD1，…，FWcDn-each frequency band corresponding to the detail component of the parent wave after wavelet decomposition
FWcAnFrequency band corresponding to approximate component of parent wave after wavelet decomposition
n-number of layers of wavelet decomposition
Step S17: the parent wave wavelet coefficient LW is determined by step S16cAn
LWcAn＝FWcAn
In the formula:
LWcAn-wavelet coefficient of parent wave
Step S18: decomposing the wavelet into n layers by multi-scale discrete wavelet transform as shown in formula (18)
In the formula: SW-wavelet
SWcD1，…，SWcDn-each frequency band corresponding to a detail component of a wavelet decomposition
SWcAn-bands corresponding to approximate components of wavelets after wavelet decomposition
n-number of layers of wavelet decomposition
Step S19: wavelet coefficients HW of wavelets are determined by step S18cAn
HWcAn＝SWcAn
In the formula:
SWcAnwavelet coefficients of wavelets
Step S20: solving wavelet adjustment coefficient beta according to equation (20)coef
βcoef＝FWcAn/SWcAnFormula (20)
In the formula: beta is acoefWavelet adjustment coefficient
Step S21: obtaining the adjusted wavelet coefficient SW 'according to the formula (21)'cAn
SW′cAn＝βcoef·SWcAnFormula (21)
In the formula: SW'cAn-adjusted wavelet coefficients
Step S22: the adjusted wavelet coefficient SW 'is obtained according to the formula (21)'cAnReplacing wavelet coefficients SW after wavelet SW decompositioncAnPerforming wavelet change reconstruction to obtain the near fault pulse type seismic oscillation AW
AW-near fault pulse type seismic motion.
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