CN106468787A - GRAVITY EARTH TIDE signal independence harmonic component extraction method based on PBIL - Google Patents
GRAVITY EARTH TIDE signal independence harmonic component extraction method based on PBIL Download PDFInfo
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Abstract
The present invention provides one kind to belong to field of signal processing based on PBIL (Population Based Incremental Learning, based on colony's incremental learning) algorithm to GRAVITY EARTH TIDE signal independence harmonic component extraction method.The method of the present invention mainly includes analysis based on GRAVITY EARTH TIDE signal in orthogonal decomposition model, the pretreatment of GRAVITY EARTH TIDE signal, the parameter setting of PBIL algorithm, the foundation of optimization object function, GRAVITY EARTH TIDE signal independent component analysis harmonic are extracted.This algorithm introduces PBIL algorithm, the precocity that effectively prevent traditional independent composition analysis algorithm and the phenomenon being absorbed in local convergence in traditional independent element analysis algorithm, improves separating effect and more preferable implementation.
Description
Technical field：
The present invention relates to a kind of optimized algorithm, more particularly, to one kind are divided to GRAVITY EARTH TIDE signal independence harmonic wave based on PBIL
Amount extraction algorithm, belongs to field of signal processing.
Background technology：
Under the tidal attraction of the celestial bodies such as the sun, the moon acts on, ground club produces is stained with elastic deformation, and earth surface is taken up an official post
The gravity of any also can generating period change therewith, reflects that the Observable geophysical signal of this phenomenon is GRAVITY EARTH TIDE
Signal.To the analysis of GRAVITY EARTH TIDE signal in geodesy, have in the correlation geoscience such as geophysics and seismology
Have a wide range of applications.
The tidal generating that the celestial bodies such as the sun, the moon produce at the earth's surface changes with the relative position of their tracks and becomes
Change, the tidal generating producing in any point is launched according to the harmonic function of Du Sen, can resolve into 386 that amplitude is constant humorous
Ripple.These tidal waves both can be divided into long-period wave, day ripple, semidiurnal wave and ripple on the 1/3rd by its cycle, also can be by generation
Mechanism is divided into a day ripple (semidiurnal wave) system, the moon ripple (first quarter moon ripple) system, year the composition such as ripple (half a year ripple) system.
At present, traditional analysis method to GRAVITY EARTH TIDE signal it is impossible to from GRAVITY EARTH TIDE signal generator reason
Clearly explain the relation of each harmonic component and different celestial body gravitation tidal effects in GRAVITY EARTH TIDE signal.Meanwhile, tradition
Independent composition analysis algorithm higher to the numerical requirements initially dissolving mixed matrix, and bound term fixes, the no spy such as learning rate
Point, it is impossible to adapt to the environment of change, reaches optimum convergence effect, is easily trapped into local optimum, does not reach preferable separating effect.
Content of the invention：
The technical problem to be solved in the present invention is by analyzing GRAVITY EARTH TIDE signal in orthogonal decomposition model, being divided by harmonic wave
The generation mechanism of amount, provides a kind of GRAVITY EARTH TIDE signal independence harmonic component extraction method based on PBIL algorithm, root
According to self-contained information in the GRAVITY EARTH TIDE signal of observation, by PBIL to solution most important in independent composition analysis algorithm
Mixed matrix is optimized, and gravity observation of Earth tide signal is carried out with independent component analysis harmonic extraction.
The technical solution used in the present invention is：A kind of GRAVITY EARTH TIDE signal independence harmonic component extraction side based on PBIL
Method, the step of methods described is as follows：
Step 1. analyzes the Orthogonal Decomposition model of GRAVITY EARTH TIDE signal；
Step 2. obtains the GRAVITY EARTH TIDE signal observation at observation station：By the analysis of model, choose arbitrarily certain
Time period, with the m road pending gravity observation of Earth tide signal of longitude different latitude：X=[x1(t),x2(t),…,xm(t)]；
Step 3. is to observation signal pretreatment：Treat process signal using Eigenvalues Decomposition method and carry out albefaction and nodularization
Process, obtain the signal after albefaction and nodularization
The initialization of the mixed matrix of Step 4. solution：During independent component extraction,Y represents that independent element divides
The independent element obtaining after analysis algorithm process, W is the mixed matrix of solution, and according to the priori of pending signal, to solution, mixed matrix enters
Row is uniformly distributed at random and initializes：B=[b1:D,b2:D,…,bm:D]T, i=1,2 ... m,
Wherein, the quantity of pending signal is m, and dimension is D, the quantity of the maximum independent element obtaining after separating
Step 5. algorithm optimization solves the mixed matrix process of solution：
Step 5.1. makesObtain initial independent harmonic component, Z is obtained with its second order away from E { Z2And quadravalence
Away from E { Z4, substitute into formula F={ kurt (Z)=E { Z4}-3(E{Z2})2The Z kurtosis value F that asks for, wherein：Kurt is kurtosis, high and steep
Degree is the fourth order cumulant of stochastic variable, and f is the kurtosis value of each road signal in Z, arranges to obtain F=according to descending order
(f1,f2,…,fM), obtain adaptation value information and the position subscript information comprising particle in F；
Step 5.2. selects the position subscript of K=k × M particle from adaptive value F according to its order, according to obtain
Position subscript selects to obtain from BI=1,2 ... N, wherein l are the l time number of iterations, and k is to select
Rate k ∈ (0,1)；
Step 5.3. is by BbestSubstitute into Hebbian formulaCarry out the probability vector of colony
Renewal, wherein BoldThe solution referring to not carry out selection mixes matrix particle, poldRepresent the particle distribution vector before not being updated, learn
Practise speed α, α ∈ (0,1)；When being calculated first time, pold=p0=0.5, Bold=B；
Step 5.4. works asWhen, particle is circulated calculating, return to step Step 5.1；Otherwise tie
Shu Xunhuan, obtains optimal solution and mixes matrix B；
Step 6. makes W=B, according to independent component extractionIndependent harmonic component after being processed；
Step 7. carries out spectrum analyses and obtains its frequency values f to independent harmonic component YObservation, by fObservationWith theoretical value carry out
Contrast, obtains its independent harmonic component classification.
Described step Step 1, the analysis to GRAVITY EARTH TIDE signal in orthogonal model is specially：
A is tellurian a certain observation station, the sun power to lead tide power that it is subject to and lunar gravitation main decomposition be tilt
Earth tide signal FhWith GRAVITY EARTH TIDE signal Fg, to GRAVITY EARTH TIDE signal FgCarry out Orthogonal Decomposition, one parallel to the earth certainly
Component of signal F of rotating shaft1, component of signal F parallel to equatorial plane2, F2Parallel with equatorial plane, this component of signal is only
Affected by earth rotation, independent element harmonic component, this day ripple and the semidiurnal wave mainly causing containing earth rotation, F1And the earth
The axis of rotation is parallel, F1Component of signal on direction is not affected by earth rotation, and the direction contains to be made by the moon and sun power to lead tide
With the independent harmonic componentss producing, i.e. long-period wave.
The invention has the beneficial effects as follows:PBIL algorithm is divided the method for counting carefully to combine with traditional independent element by the present invention, leads to
Cross the learning rate in PBIL algorithm, the renewal of probabilistic model applies to the solution solving mixed matrix in independent composition analysis algorithm,
To improve the initial value tender subject of traditional independent composition analysis algorithm, traditional independent composition analysis algorithm is optimized.
Algorithm after improvement extracts three isolated components effectively from GRAVITY EARTH TIDE signal, respectively：The reflection moon, sun phase
The long period wave system component that changes in the earths orbital geometry is produced, and the day wave system component that reflection earth rotation produces, and reflection
The semidiurnal wave system component that earth rotation produces, and, extract concrete harmonic componentss from the isolated component that these decomposite.Have
These independent elements are set up corresponding closing with the gravitation tidal effect that the change of the spheres such as the earth, the moon, the sun produces by effect ground
System.
Brief description
Fig. 1 is the GRAVITY EARTH TIDE signal in orthogonal decomposition model figure of the present invention；
Fig. 2 is the algorithm flow chart of the present invention；
Fig. 3 is the GRAVITY EARTH TIDE signal waveforms of the present invention；
Fig. 4 is the independent harmonic component figure being extracted with inventive algorithm；
Fig. 5 is the spectrogram of the independent element signal extracting in present example.
Specific embodiment
With reference to concrete drawings and Examples, the invention will be further described.
Embodiment 1：Referring to Fig. 1-Fig. 5, a kind of GRAVITY EARTH TIDE signal independence harmonic component extraction method based on PBIL,
The step of methods described is as follows：
Step 1. analyzes the Orthogonal Decomposition model of GRAVITY EARTH TIDE signal；
Step 2. obtains the GRAVITY EARTH TIDE signal observation at observation station：By the analysis of model, choose arbitrarily certain
Time period, with the m road pending gravity observation of Earth tide signal of longitude different latitude：X=[x1(t),x2(t),…,xm(t)]；
Step 3. is to observation signal pretreatment：Treat process signal using Eigenvalues Decomposition method and carry out albefaction and nodularization
Process, obtain the signal after albefaction and nodularization
The initialization of the mixed matrix of Step 4. solution：During independent component extraction,Y represents that independent element divides
The independent element obtaining after analysis algorithm process, W is the mixed matrix of solution, and according to the priori of pending signal, to solution, mixed matrix enters
Row is uniformly distributed at random and initializes：B=[b1:D,b2:D,…,bm:D]T, i=1,2 ... m
Wherein, the quantity of pending signal is m, by the quantity of the maximum independent element obtaining after separatingDescribed dimension
Spending D is：In PBIL algorithm, the dimension of each particle should become certain mathematical relationship with maximum independent element quantity.Plant in PBIL algorithm
Group's particle carries out transposition and just can get MSolution mix matrix, size M of described population is：In PBIL algorithm
Population number, is also the number that in independent composition analysis algorithm, demand solution solution mixes the mixed matrix of solution simultaneously；
Step 5. algorithm optimization solves the mixed matrix process of solution：
Step 5.1. makesObtain initial independent harmonic component, Z is obtained with its second order away from E { Z2And quadravalence
Away from E { Z4, substitute into formula F={ kurt (Z)=E { Z4}-3(E{Z2})2The Z kurtosis value F that asks for, wherein：Kurt is kurtosis, high and steep
Degree is the fourth order cumulant of stochastic variable, and kurtosis value is bigger, and its non-Gaussian system is bigger, and it can be divided as object function
From the independent signal source that performance is maximum, f is the kurtosis value of each road signal, arranges F=(f according to descending order1,f2,…,
fM), obtain adaptation value information and the position subscript information comprising particle in F；
Step 5.2. selects the position subscript of K=k × M particle from adaptive value F according to its order, according to obtain
Position subscript selects to obtain from BI=1,2 ... N, wherein l are the l time number of iterations, described choosing
Rate of selecting is k：The adaptive value of the particle being calculated by object function, the therefrom percentage ratio of selection advantage colony, k ∈ (0,1)；
Step 5.3. is by BbestSubstitute into Hebbian formulaCarry out the probability vector of colony
Renewal, wherein BoldThe solution referring to not carry out selection mixes matrix particle, poldRepresent the particle distribution vector before not being updated, institute
The learning rate stated is α, the learning rate to advantage particle convergence of population in PBIL algorithm, α ∈ (0,1), described probability
Vectorial p0For：The probability of colony, belongs to and is uniformly distributed, p0=0.5, when being calculated first time, pold=p0=0.5,
Bold=B；
Step 5.4. works asWhen, particle is circulated calculating, return to step Step 5.1；Otherwise tie
Shu Xunhuan, obtains optimal solution and mixes matrix B；
Step 6. makes W=B, according to independent component extractionIndependent harmonic component after being processed, the present invention
The independent harmonic component that algorithm extracts is as shown in Figure 4；
Step 7. carries out spectrum analyses and obtains its frequency values f to independent harmonic component YObservation, by fObservationWith theoretical value carry out
Contrast, as shown in table 2, obtains its independent harmonic component classification, frequency spectrum such as Fig. 5 institute of the independent element signal that the present invention extracts
Show.
Wherein theoretic frequency value calculates, as shown in table 1 from Du Sen formula.Described frequency values unit is hertz
(Hz), in Tables 1 and 2, e represents 10 power side.
GRAVITY EARTH TIDE signal can be successfully separated out following harmonic wave state by this algorithm：Semidiurnal wave signal, day ripple letter
Number, long-period wave signal.And, the component of signal isolated also complies with GRAVITY EARTH TIDE signal in orthogonal decomposition model, can be certainly
The each harmonic component of dynamic correspondence.
Table 1 GRAVITY EARTH TIDE each Harmonic Theory frequency values
The frequency values of the independent harmonic component of table 2 and the contrast of theoretical value frequency values
Described step Step 1, the analysis to GRAVITY EARTH TIDE signal in orthogonal model is specially：
As shown in figure 1, A is tellurian a certain observation station, the sun power to lead tide power that it is subject to and lunar gravitation mainly divide
Solve as ground tilt tide signal FhWith GRAVITY EARTH TIDE signal Fg, to GRAVITY EARTH TIDE signal FgCarry out Orthogonal Decomposition, put down for one
Row is in component of signal F of earth's axis1, component of signal F parallel to equatorial plane2, F2Parallel with equatorial plane, should
Component of signal is only affected by earth rotation, the independent element harmonic component mainly causing containing earth rotation, this day ripple and half day
Ripple, F1Parallel with earth's axis, F1Component of signal on direction is not affected by earth rotation, and the direction contains by the moon and too
The independent harmonic componentss that positive power to lead tide effect produces, i.e. long-period wave.GRAVITY EARTH TIDE signal waveform such as Fig. 3 institute of the present invention
Show.
PBIL algorithm is the evolution algorithm based on probabilistic model for the class, and this algorithm combines competition learning and evolutionary computation two
The knowledge in individual field, the generation to instruct offspring for the knowledge learning probability being obtained by competition learning, then use probability to
Amount, to constrain each individual value, to solve optimization problem.
Present invention may also apply to having the separation problem of the mixed signals such as priori, including：Earth tide is believed
Number harmonic component extraction etc., it may also be used for the difference of contrast theoretical value and actual measured value, can effectively and accurately obtain
The abnormal accumulation information of information of earthquake or earthquake.
Above in association with accompanying drawing, the specific embodiment of the present invention is explained in detail, but the present invention be not limited to above-mentioned
Embodiment, in the ken that those of ordinary skill in the art possess, can also be before without departing from present inventive concept
Put that various changes can be made.
Claims (2)
1. a kind of GRAVITY EARTH TIDE signal independence harmonic component extraction method based on PBIL it is characterised in that：Methods described
Step is as follows：
Step 1. analyzes the Orthogonal Decomposition model of GRAVITY EARTH TIDE signal；
Step 2. obtains the GRAVITY EARTH TIDE signal observation at observation station：By the analysis of model, choose any certain time
Section, with the m road pending gravity observation of Earth tide signal of longitude different latitude：X=[x1(t),x2(t),…,xm(t)]；
Step 3. is to observation signal pretreatment：Treat process signal using Eigenvalues Decomposition method and carry out albefaction and spheroidising,
Obtain the signal after albefaction and nodularization
The initialization of the mixed matrix of Step 4. solution：During independent component extraction,Y represents that independent component analysis are calculated
Method process after the independent element that obtains, W is the mixed matrix of solution, according to the priori of pending signal, to solution mixed matrix carry out with
Machine is uniformly distributed and initializes：B=[b1:D,b2:D,…,bm:D]T, i=1,2 ... m,
Wherein, the quantity of pending signal is m, and dimension is D, the quantity of the maximum independent element obtaining after separating
Step 5. algorithm optimization solves the mixed matrix process of solution：
Step 5.1. makesObtain initial independent harmonic component, Z is obtained with its second order away from E { Z2And quadravalence away from E
{Z4, substitute into formula F={ kurt (Z)=E { Z4}-3(E{Z2})2The Z kurtosis value F that asks for, wherein：Kurt is kurtosis, kurtosis
It is the fourth order cumulant of stochastic variable, f is the kurtosis value of each road signal in Z, arranges to obtain F=(f according to descending order1,
f2,…,fM), obtain adaptation value information and the position subscript information comprising particle in F；
Step 5.2. selects the position subscript of K=k × M particle from adaptive value F according to its order, according to the position obtaining
Subscript selects to obtain from BI=1,2 ... N, wherein l are the l time number of iterations, and k is selection rate k ∈
(0,1)；
Step 5.3. is by BbestSubstitute into Hebbian formulaCarry out the probability vector of colony more
Newly, wherein BoldThe solution referring to not carry out selection mixes matrix particle, poldRepresent the particle distribution vector before not being updated, study speed
Rate α, α ∈ (0,1)；When being calculated first time, pold=p0=0.5, Bold=B；
Step 5.4. works asWhen, particle is circulated calculating, return to step Step 5.1；Otherwise terminate to follow
Ring, obtains optimal solution and mixes matrix B；
Step 6. makes W=B, according to independent component extractionIndependent harmonic component after being processed；
Step 7. carries out spectrum analyses and obtains its frequency values f to independent harmonic component YObservation, by fObservationWith theoretical value carry out right
Ratio obtains its independent harmonic component classification.
2. the GRAVITY EARTH TIDE signal independence harmonic component extraction method based on PBIL according to claim 1, its feature
It is：Described step Step 1, the analysis to GRAVITY EARTH TIDE signal in orthogonal model is specially：
A is tellurian a certain observation station, the sun power to lead tide power that it is subject to and lunar gravitation main decomposition be tilt solid
Tidewater FhWith GRAVITY EARTH TIDE signal Fg, to GRAVITY EARTH TIDE signal FgCarry out Orthogonal Decomposition, one parallel to earth's axis
Component of signal F1, component of signal F parallel to equatorial plane2, F2Parallel with equatorial plane, this component of signal is only subject to ground
The impact of revolutions, independent element harmonic component, this day ripple and the semidiurnal wave mainly causing containing earth rotation, F1And earth rotation
Axle is parallel, F1Component of signal on direction is not affected by earth rotation, and the direction contains is produced by the moon and the effect of sun power to lead tide
Raw independent harmonic componentss, i.e. long-period wave.
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| CN109375279A (en) * | 2018-10-16 | 2019-02-22 | 淮海工学院 | A kind of static weight observation data gravity tide correction extracting method |
| CN112834821A (en) * | 2020-12-31 | 2021-05-25 | 国网上海市电力公司 | Multi-harmonic source harmonic responsibility quantification method for multi-direct-current feed-in full cable power supply area |
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| CN109375279A (en) * | 2018-10-16 | 2019-02-22 | 淮海工学院 | A kind of static weight observation data gravity tide correction extracting method |
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