CN107480391A - Nearly tomography Nonstationary MDP analogy method based on data-driven - Google Patents
Nearly tomography Nonstationary MDP analogy method based on data-driven Download PDFInfo
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Abstract
Nearly tomography Nonstationary MDP analogy method provided by the invention based on data-driven, a series of superposition of simple component signals is decomposed into first with SWT nearly tomography Nonstationary MDP records, secondly Hilbert conversion is carried out to every single order simple component signal, by introducing stochastic variable and realizing the simulation to Nonstationary MDP sample using signal reconstruction technology.Redundant wavelet basic function is used using this method, make what expression of the primary signal on redundancy basic function can regard that signal represents on a series of basic functions as to be averaged, wavelet coefficient and scale coefficient and primary signal are isometric, it ensure that translation invariance, the oscillation effect in dyadic wavelet transform can not only be suppressed well, and the disturbance of part wavelet coefficient will not bring the serious distortion of signal, so as to reduce dependence of the quality reconstruction of signal to single wavelet coefficient, so there is preferable advantage in terms of carrying out seismic wave decomposition and reconstruction using SWT, it ensure that the precision of sample simulation.
Description
Technical field
The present invention relates to earthquake synthesis technical field, more particularly to a kind of nearly tomography based on data-driven is non-flat quietly
Shake analogy method.
Background technology
By the earth shock of seimic wave propagation, commonly referred to as earthquake motion, Chi-chi earthquake have some be substantially distinguished from,
The characteristics of Far-field earthquake moves, Chi-chi earthquake includes radio-frequency component and low-frequency pulse composition, because pulse repetition has amplitude
The characteristics of short when greatly, holding, therefore serious destruction can be caused to engineering structure.However, Chi-chi earthquake actual observation record quantity
It is very limited, so proposing that for the efficient analogy method of Chi-chi earthquake be urgent problem to be solved.
At present, domestic and foreign scholars are superimposed compared with the stochastic model frequently with reflection radio-frequency component and simple parsing impulse function
Analogy method, wherein, using a variety of equivalent pulse type function models carry out impulse speed displacement time-histories analogy method, due to
Equivalent pulse mould shapes are single, are not particularly suited for some actual measurement pulse recordings with special shape, and radio-frequency component
Then need to be obtained according to the Power Spectrum Model of earthquake motion.
On the other hand, earthquake motion is a kind of nonstationary random process, and most seismic motion records reflect by force
Degree is dual non-stationary with frequency, and the seismic motion record of nearly fault region is no exception, and the stochastic simulation of steady earthquake motion is
Based on earthquake power spectrum, earthquake motion time history sample is readily available by the trigonometrical number addition method, however with steady earthquake motion
Compare, the time-varying power spectrum model of description earthquake motion non-stationary characteristic does not have blanket analytical expression.In summary, closely
The effective analogy method of tomography Nonstationary MDP still suffers from very big difficulty.
At present, non-stationary signal decomposition and reconstruction technology is often used to simulating seismic motion sample, that is, utilizes signal decomposition side
Original seismic data is converted to multilayer arrowband " subsequence " by method, and obtains nearly tomography using signal reconstruction technology on this basis
Ground motion simulation formula.Wherein, being suitable for the decomposition method of Nonstationary MDP includes discrete wavelet transformation, wavelet packet point
Solution, empirical mode decomposition, overall experience mode decomposition etc..Empirical mode decomposition, overall experience mode decomposition method be not complete
Fundamentals of Mathematics, be largely dependent upon the experience of user；Wavelet decomposition, WAVELET PACKET DECOMPOSITION method do not have translation invariant
Property, then it can cause the loss of reconfiguration information, the disturbance of part wavelet coefficient can also bring the serious distortion of signal, with actual signal
Differ larger, reconstruct analog result is not accurate enough.
The content of the invention
The technical problems to be solved by the invention are the deficiency of the analogy method for existing Nonstationary MDP, there is provided
A kind of nearly tomography Nonstationary MDP analogy method based on data-driven, in order to realize foregoing invention purpose, the present invention provides
Following technical scheme：
A kind of nearly tomography Nonstationary MDP analogy method based on data-driven, comprises the following steps：
(1) original nearly tomography Nonstationary MDP record is decomposed into the superposition of several simple component signals by SWT；
(2) simple component signal described in every single order is converted using Hilbert respectively to obtain its instantaneous amplitude and instantaneous phase,
And instantaneous frequency is tried to achieve according to the instantaneous phase；
(3) it is modeled, is completed near disconnected using the instantaneous frequency of equally distributed starting phase angle and Gaussian Profile
The stochastic simulation of layer Nonstationary MDP sample.
This method is any it is assumed that completely from actual measurement seismic motion record data in itself without introducing in advance, passes through first
Original seismic motion record is decomposed into multilayer arrowband " subsequence " by SWT, and secondly each arrowband " subsequence " is carried out successively
Hilbert is converted and then is obtained its instantaneous amplitude and instantaneous frequency, by the instantaneous amplitude that two above step obtains with it is instantaneous
Frequency can provide basis for the simulation of Nonstationary MDP sample, finally obtain Chi-chi earthquake using signal reconstruction technology
Formula is simulated, SWT can be considered a kind of special wavelet-decomposing method, and it uses redundant wavelet basic function, makes original record superfluous
What the expression on complementary basis function can regard that signal represents on a series of basic functions as is averaged, wavelet coefficient and scale coefficient with it is former
Beginning, it is isometric to record, and ensure that translation invariance, can not only suppress the oscillation effect in dyadic wavelet transform, and portion well
The disturbance of wavelet coefficient is divided not bring the serious distortion of signal, so as to reduce the quality reconstruction of signal to single wavelet coefficient
Dependence, so there is preferable advantage in terms of carrying out seismic wave decomposition and reconstruction using SWT, so as to improve sample simulation
Precision.
Further, in step (1), SWT is in the form of two divided-frequency by the original nearly tomography Nonstationary MDP record
Point solution's expression is：
Wherein, Dj(t) it is jth layer details coefficients, represents radio-frequency component；M is whole points
The number of plies of solution；AM(t) it is approximation component, represents low-frequency component.
Further, in step (2), Hilbert transition structures are passed through for any simple component signal c (t)
Go out its complex analytic signal form z (t),
Z (t)=c (t)+iH [c (t)]=a (t) eiφ(t), wherein, a (t) and φ (t) represents the width changed over time respectively
Value and phase；H () operator representation Hilbert is converted,Wherein, s becomes for integration
Amount；P represents Cauchy's principal value；
Further, instantaneous amplitude isInstantaneous phase is φ (t)=tan-1{H[c
(t)]/c (t) }, instantaneous frequency is
Further, it is to the stochastic simulation formula of the nearly tomography Nonstationary MDP sample：
Wherein,To submit to the jth order component of Gaussian Profile
Instantaneous frequency, i.e.,φjFor jth rank [0,2 π] equally distributed random initial phase angle.
Further, in addition to step (4), the step (4) are non-using the optimum theory algorithm adjustment nearly tomography
Steady earthquake motion sample, it is set to be matched with goal response spectrum.
Further, step (4) comprises the following steps：
(4-1) passes through formulaAdjustment simple component described in per single order
The amplitude and frequency of signal, wherein, x1,x2,…,xnFor the regulation coefficient of earthquake motion amplitude components；xn+1,xn+2,...,x2nFor ground
The regulation coefficient of vibration frequency component；X={ x1,x2,…,x2n}TFor regulation coefficient vector；M is the number of plies all decomposed；AM(t) it is approximation component；
(4-2) establishes Multi-variables optimum design theoretical model, and its formula is：
Minimize:Constraints is：xj＞ 0, j=1,
2 ..., 2n, wherein, S [y (x, t), Tp] for analog sample in specified T eigenperiodpWhen reaction spectrum, ST(Tp) it is the cycle
For TpWhen goal response spectrum；P is the number of response spectrum period discrete point；V is the object function established；
(4-3) solves the minimization problem of the object function V using Nonlinear Quasi Newton's algorithm, you can realizes simulation sample
This matching composed with goal response.
Compared with prior art, beneficial effects of the present invention：The present invention uses redundant wavelet basic function using SWT, makes original
What expression of the beginning signal on redundancy basic function can regard that signal represents on a series of basic functions as is averaged, wavelet coefficient and chi
It is isometric with primary signal to spend coefficient, ensure that translation invariance, can not only suppress the vibration in dyadic wavelet transform well
Effect, and the disturbance of part wavelet coefficient will not bring the serious distortion of signal, so as to reduce the quality reconstruction pair of signal
The dependence of single wavelet coefficient, so there is preferable advantage in terms of carrying out seismic wave decomposition and reconstruction using SWT, and it can guarantee that
The precision of sample simulation, in the prior art, the matching difficult to realize with goal response spectrum of the artificial ripple with nearly fault feature, because
This is on the basis of above-mentioned analogy method, in order to further such that sample and the target simulating to obtain by original Chi-chi earthquake
Response spectrum matches, and adjusts the amplitude of each simple component and frequency size by introducing multiple variables, then sets up optimum theory
Model is simultaneously solved using Nonlinear Quasi Newton method algorithm iteration, you can realizes the matched compatible with goal response spectrum.The present invention
Not only the technical advantage in terms of decomposition and reconstruction can significantly improve the precision of sample simulation, and the optimization mould established to method
Type is easier to realize and required with the earthquake resistant engineering that match of goal response spectrum, and be advantageous to raising engineering structure antidetonation time-domain analysis can
By degree, the inventive method could be applicable in, the stochastic simulation of the general earthquake motion in far field, there is universal applicability.
Brief description of the drawings
Fig. 1 is the flow chart of the nearly tomography Nonstationary MDP analogy method matched in the present invention with response spectrum.
Fig. 2 a, Fig. 2 b and Fig. 2 c are respectively three groups of actual measurement Chi-chi earthquake sample records used in embodiment 1.
Fig. 3 a are the details coefficients of Fig. 2 a in embodiment 1.
Fig. 3 b are the approximation component of Fig. 2 a in embodiment 1.
Fig. 4 is instantaneous frequency distribution and its Gauss Distribution Fitting of the order component of earthquake motion sample 1 first in embodiment 1.
Fig. 5 is the comparison diagram with goal response spectrum before being adjusted in embodiment 1.
When Fig. 6 a are the non-stationary of earthquake motion sample 1 in embodiment 1-frequency feature.
Fig. 6 b be embodiment 1 in by earthquake motion sample 1 simulate generation sample non-stationary when-frequency feature.
Fig. 7 is the comparison diagram with goal response spectrum after being adjusted in embodiment 1.
Fig. 8 a, Fig. 8 b and Fig. 8 c are respectively the three groups of analog samples matched in embodiment 1 with goal response spectrum.
Embodiment
With reference to embodiment and embodiment, the present invention is described in further detail.But this should not be understood
Following embodiment is only limitted to for the scope of the above-mentioned theme of the present invention, it is all that this is belonged to based on the technology that present invention is realized
The scope of invention.
Embodiment 1
A kind of nearly tomography Nonstationary MDP analogy method based on data-driven, such as Fig. 1, comprises the following steps：
(1) original nearly tomography Nonstationary MDP record is decomposed into the superposition of several simple component signals by SWT；
(2) simple component signal described in every single order is converted using Hilbert respectively to obtain its instantaneous amplitude and instantaneous phase,
And instantaneous frequency is tried to achieve according to the instantaneous phase；
(3) it is modeled, is completed near disconnected using the instantaneous frequency of equally distributed starting phase angle and Gaussian Profile
The stochastic simulation of layer Nonstationary MDP sample；
(4) using the optimum theory algorithm adjustment nearly tomography Nonstationary MDP sample, itself and goal response spectrum are made
Match somebody with somebody.
For convenience of explanation, we by taking the Chi-chi earthquake sample of actual measurement as an example, Fig. 2 a, Fig. 2 b and Fig. 2 c show reality
Three groups of samples of Chi-chi earthquake of survey, sample frequency fs=100Hz, a length of T=30s during sampling, to above-mentioned original near disconnected
Layer Nonstationary MDP record sample carries out SWT decomposition, and expression formula is：
Wherein, Dj(t) it is jth layer details coefficients, represents radio-frequency component；M is whole points
The number of plies of solution；AM(t) it is approximation component, represents low-frequency component, because approximation component highest frequency is according to fs/2j+1It is determined that j is
Decomposition order, when Decomposition order is taken as 8, the highest frequency of approximation component is only 0.19Hz, it is possible to for preferably representing
The trend term of original seismic motion record.
By taking sample 1 as an example, 8 layers of details coefficients and approximation component are distinguished as shown in Figure 3 a and Figure 3 b shows, then using Hilbert
Transition structure goes out its complex analytic signal form z (t), z (t)=c (t)+iH [c (t)]=a (t) eiφ(t), wherein, a (t) and φ
(t) amplitude and phase changed over time is represented respectively；H () operator representation Hilbert is converted,Wherein, s is integration variable；P represents Cauchy's principal value；Instantaneous amplitude isInstantaneous phase is φ (t)=tan-1{ H [c (t)]/c (t) }, instantaneous frequency is
Then it is modeled using the instantaneous frequency of equally distributed starting phase angle and Gaussian Profile,Wherein,For the instantaneous frequency of jth order component, it is to obey Gauss
The stochastic variable of distribution, i.e.,φjFor jth rank [0,2 π] equally distributed random initial phase angle, such as scheme
Shown in 4.
The analog result of the above-mentioned nearly tomography Nonstationary MDP sample based on data-driven, such as Fig. 5, it is observed that
When original non-stationary sample and analog sample have a consistent non-stationary-frequency feature, such as Fig. 6 a and Fig. 6 b.Show this analogy method
Reliable results.
But according to Fig. 5 can be seen that by the obtained response spectrum curve of above-mentioned SWT+Hilbert conversion analog samples often with
There is certain deviation in goal response spectrum, by simulating formula：
Adjust each simple component signal amplitude and
Frequency, wherein, x1,x2,...,xnFor the regulation coefficient of earthquake motion amplitude components；xn+1,xn+2,...,x2nFor earthquake dynamic frequency point
The regulation coefficient of amount；X={ x1,x2,...,x2n}TFor regulation coefficient vector；M is the number of plies all decomposed； AM(t) it is approximation component.
Multi-variables optimum design theoretical model is established by constructing 2n regulation coefficient, its formula is：
Minimize:Constraints is：xj＞ 0, j=1,
2 ..., 2n, wherein, S [y (x, t), Tp] for analog sample in specified T eigenperiodpWhen reaction spectrum, ST(Tp) it is the cycle
For TpWhen goal response spectrum；P is the number of response spectrum period discrete point；V is the object function established；Using Nonlinear Quasi
Newton's algorithm solves the minimization problem of the object function V, you can realizes analog sample and the matching of goal response spectrum, such as schemes
7, it is final to obtain the three groups of analog samples matched with goal response spectrum, such as Fig. 8 a, Fig. 8 b and Fig. 8 c.
Claims (7)
1. a kind of nearly tomography Nonstationary MDP analogy method based on data-driven, it is characterised in that comprise the following steps：
(1) original nearly tomography Nonstationary MDP record is decomposed into the superposition of several simple component signals by SWT；
(2) simple component signal described in every single order is converted using Hilbert respectively to obtain its instantaneous amplitude and instantaneous phase, and root
Instantaneous frequency is tried to achieve according to the instantaneous phase；
(3) it is modeled, is completed non-to nearly tomography using the instantaneous frequency of equally distributed starting phase angle and Gaussian Profile
The stochastic simulation of steady earthquake motion sample.
2. the nearly tomography Nonstationary MDP analogy method based on data-driven as claimed in claim 1, it is characterised in that
In step (1), the original nearly tomography Nonstationary MDP record is divided the solution's expression to be by SWT in the form of two divided-frequency：Wherein, Dj(t) it is jth layer details coefficients, represents radio-frequency component；M is the number of plies all decomposed；
AM(t) it is approximation component, represents low-frequency component.
3. the nearly tomography Nonstationary MDP analogy method based on data-driven as claimed in claim 2, it is characterised in that
In step (2), its complex analytic signal form z is gone out by Hilbert transition structures for any simple component signal c (t)
(t), z (t)=c (t)+iH [c (t)]=a (t) eiφ(t), wherein, a (t) and φ (t) represent respectively the amplitude that changes over time with
Phase；H () operator representation Hilbert is converted,Wherein, s is integration variable；P
Represent Cauchy's principal value；
4. the nearly tomography Nonstationary MDP analogy method based on data-driven as claimed in claim 3, it is characterised in that wink
When amplitude beInstantaneous phase is φ (t)=tan-1{ H [c (t)]/c (t) }, instantaneous frequency is
5. the nearly tomography Nonstationary MDP analogy method based on data-driven as claimed in claim 4, it is characterised in that right
The stochastic simulation formula of the nearly tomography Nonstationary MDP sample is：
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Wherein,To submit to the instantaneous frequency of the jth order component of Gaussian Profile；φjIt is equally distributed for jth rank [0,2 π]
Random initial phase angle.
6. the nearly tomography Nonstationary MDP analogy method based on data-driven as described in claim 1-5 is any, its feature
It is, in addition to step (4), the step (4) are using the optimum theory algorithm adjustment nearly tomography Nonstationary MDP sample
This, makes it be matched with goal response spectrum.
7. the nearly tomography Nonstationary MDP analogy method based on data-driven as claimed in claim 6, it is characterised in that step
Suddenly (4) comprise the following steps：
(4-1) passes through formulaAdjustment simple component letter described in per single order
Number amplitude and frequency, wherein, x1,x2,...,xnFor the regulation coefficient of earthquake motion amplitude components；xn+1,xn+2,...,x2nFor ground
The regulation coefficient of vibration frequency component；X={ x1,x2,...,x2n}TFor regulation coefficient vector；M is the number of plies all decomposed；AM(t) it is approximation component；
(4-2) establishes Multi-variables optimum design theoretical model, and its formula is：
Minimize:Constraints is：xj＞ 0, j=1,2 ...,
2n, wherein, S [y (x, t), Tp] for analog sample in specified T eigenperiodpWhen reaction spectrum, ST(Tp) be the cycle be TpWhen
Goal response spectrum；P is the number of response spectrum period discrete point；V is the object function established；
(4-3) solves the minimization problem of the object function V using Nonlinear Quasi Newton's algorithm, you can realize analog sample with
The matching of goal response spectrum.
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| CN108256236A (en) * | 2018-01-19 | 2018-07-06 | 哈尔滨工业大学 | Nearly tomography seismic design spectra modification method based on Chinese earthquake resistant code |
| CN110069836A (en) * | 2019-04-03 | 2019-07-30 | 河海大学 | A kind of height frequency range is alternately and target composes matched improvement influence matrix method |
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| CN110244355B (en) * | 2019-07-25 | 2021-06-08 | 西南交通大学 | Pulse earthquake motion simulation method based on earthquake source fault model |
| CN112285770A (en) * | 2020-10-28 | 2021-01-29 | 重庆大学 | Seismic wave phase spectrum disturbance method based on real number wavelet transformation |
| CN114117827A (en) * | 2022-01-24 | 2022-03-01 | 四川省公路规划勘察设计研究院有限公司 | Random simulation and parameter sensitivity analysis method for Yanglian fault model |
| CN114117827B (en) * | 2022-01-24 | 2022-04-15 | 四川省公路规划勘察设计研究院有限公司 | Random simulation and parameter sensitivity analysis method for Yanglian fault model |
| CN114966835A (en) * | 2022-04-24 | 2022-08-30 | 福州大学 | Near-fault seismic motion fitting method based on improved time domain superposition method |
| CN115437303A (en) * | 2022-11-08 | 2022-12-06 | 壹控智创科技有限公司 | Wisdom safety power consumption monitoring and control system |
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