CN106570529A - DE (differential evolution) algorithm-based gravity earth tide signal independent component analysis method - Google Patents
DE (differential evolution) algorithm-based gravity earth tide signal independent component analysis method Download PDFInfo
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Abstract
The present invention provides a DE (differential evolution) algorithm-based gravity earth tide signal independent component analysis method and belongs to the signal processing field. The method mainly comprises gravity earth tide signal three-dimensional orthogonal decomposition model-based analysis, gravity earth tide signal preprocessing, DE algorithm parameter setting, objective function optimization and gravity earth tide signal independent component analysis. According to the DE (differential evolution) algorithm-based gravity earth tide signal independent component analysis method of the invention, the three-dimensional orthogonal decomposition model of gravity earth tide signals is built; orthogonal decomposition of the harmonic component of the gravity earth tide signals is realized in the aspect of space, so that an extracted harmonic component frequency can reflect spatially independent geophysical information; and the DE algorithm is introduced into a traditional ICA algorithm, so that the defects of low convergence rate and local contraction of the ICA algorithm can be effectively avoided. The DE (differential evolution) algorithm-based gravity earth tide signal independent component analysis method is a novel method which can effectively perform orthogonal analysis on earth tide signals.
Description
Technical field
The present invention relates to a kind of optimized algorithm, more particularly to it is a kind of based on DE (differential evolution, difference
Evolve) independent component analysis method of the GRAVITY EARTH TIDE signal of algorithm, belong to field of signal processing.
Background technology
Under the tidal attraction effect of the celestial bodies such as the sun, the moon, ground club produces is stained with elastic deformation phenomenon, reflects this existing
The Observable geophysical signal of elephant is GRAVITY EARTH TIDE signal.GRAVITY EARTH TIDE signal reflects the day body tide such as the sun, moon
The mechanical periodicity of nighttide gravitation, if the tidal attraction component of each celestial body can be therefrom separately separated out, discloses the superposition between a component
Relation, by can be more deep understanding celestial body between action of gravity rule.
Containing abundant tide harmonic component in GRAVITY EARTH TIDE signal, according to the harmonic function exhibition of British Du Sen
Open, 386 harmonic waves that amplitude is constant can be resolved into, these tide harmonic components can be divided into according to length harmonic period
Long period wave system, day wave system, 3 kinds of harmonic series of semidiurnal wave system.Containing abundant geophysics physical message in these harmonic components,
Therefore the harmonic component in analysis GRAVITY EARTH TIDE signal is significant to studying GRAVITY EARTH TIDE.
Analysis work to earth tide for many years mainly carries out frequency analyses (harmonic analyses), current International Geophysical tide
The standard tidal analysis method that center (ICET) is recommended has Venedikov harmonic analyses method and ETERNA harmonic analyses methods.
Although this kind of method can carry out global analysises to GRAVITY EARTH TIDE signal, can not be by weight when partial analysis is carried out to signal
The relation of the harmonic component in power earth tide signal is comprehensively disclosed to be come, and the harmonic component extracted is produced with GRAVITY EARTH TIDE
Mechanism can not be corresponded.
DE (differential evolution, differential evolution) is a kind of algorithm based on Swarm Evolution, with memory
In individual optimal solution and population the characteristics of information sharing, i.e., realize asking optimization by the cooperation and competition in population between individuality
The solution of topic, its essence is a kind of greedy genetic algorithm with the excellent thought of guarantor based on real coding.But with traditional heredity
Algorithm is compared, and it is not only remained based on the global search strategy of population, is grasped using real coding, the simple variation based on difference
Make and man-to-man competition surviving policy, and reduce the complexity of genetic manipulation.
The content of the invention
The technical problem to be solved in the present invention is based on the Orthogonal Decomposition model of GRAVITY EARTH TIDE signal.By harmonic component
Generation mechanism, there is provided a kind of method of the GRAVITY EARTH TIDE signal independent component analysis based on DE algorithms, according to observation weight
Self-contained information in power earth tide signal, is optimized by what DE was calculated to the mixed matrix of most important solution in ICA algorithm, right
The harmonic component of GRAVITY EARTH TIDE signal realizes Orthogonal Decomposition from the angle in space, and the frequencies of harmonic components of extraction reflects spatially
Separate geophysical information.
The technical solution used in the present invention is：
1) the three-dimensional orthogonal decomposition model of GRAVITY EARTH TIDE signal is analyzed, such as Fig. 1, for tellurian certain observation station A,
Consider that it is subject in the presence of earth rotation, the Sun and the Moon power to lead tide, if its earth tide for causing is F, F can be decomposed into two
Individual orthogonal signal：Ground tilt tide signal FhWith GRAVITY EARTH TIDE signal Fg.Herein with regard to GRAVITY EARTH TIDE signal FgCarry out point
Analysis, Fg2 orthogonal vectors can be decomposed into：One component of signal F parallel to equatorial plane1, one parallel to earth rotation
Component of signal F of axle2。F1Again can be with Orthogonal Decomposition as 2 component of signals F11And F12(in the same plane), such gravity solid
Tidewater number is just three-dimensional orthogonal vector by Orthogonal Decomposition, as shown in Figure 1.According to three-dimensional orthogonal vector decomposition model, wherein F1With
Equatorial plane is parallel, not only related to earth rotation, and it is relevant to revolve around the sun with the earth, therefore major embodiment gravity solid
The day ripple F of tidewater number11, semidiurnal wave F12Harmonic componentss.F2Parallel with earth's axis, unrelated with earth rotation, its component embodies
The compositions such as year ripple, half a year ripple are mainly in GRAVITY EARTH TIDE signal, without day ripple, semidiurnal wave composition.So three-dimensional orthogonal divides
Harmonic component correspondence different in GRAVITY EARTH TIDE signal can just decomposed the three-dimensional corresponding with each harmonic wave just by solution model
In handing over vector.
2) random time section, same to longitude, the m roads GRAVITY EARTH TIDE signal S={ s in different latitude place are chosen1(t),s2
(t),...,sm(t) } as input.
3) to the m roads GRAVITY EARTH TIDE Signal Pretreatment in step 2：Observation signal is carried out using Eigenvalues Decomposition method
Albefaction and average value processing is removed, obtain whitening matrix W1, whitened signal
4) using DE algorithm optimization separation matrix W2。
4.1 arrange parameter：The population scale Np of initialization particle is population number in DE algorithms, at the same be also it is independent into
Demand solution solution mixes the number of the mixed matrix of solution in point parser；The dimension of the i.e. required problem of dimension D；Zoom factor F, affects to base
This vectorial level of disruption；Maximum iteration time Gm；Crossing-over rate CR, determines that how many members may be changed in population；Initially
Change algebraically G.
4.2 one random population X of initialization.
The 4.3 variation vector V for looking for noveltyi(g+1), iterative cycles are proceeded by, makes i=1:Np, according to formula Vi(g+1)=
xr1(g)+F·(xr2(g)-xr3(g)), wherein r1≠r2≠r3, two individuality x in random selection populationr2(g) and xr3(g), calculate
Weight (F (the x of difference vectorr2(g)-xr3(g))) and basis vector xr1G () is added and obtains new variation vector Vi(g+1)。
4.4 orthogonal matrixes X (c) looked for novelty, according to formula
jrandFor [1, D]
Interior randomly selected integer, D for problem dimension, CR ∈ (0, be 1) crossing-over rate, to new variation vector Vi(g+1) two are carried out
Item formula is intersected, and by random selection, makes at least one component of trial vector by the vector contribution that makes a variation, and obtains trial vector ui,j
(g+1), and to it enter the transposition of row matrix, obtain new orthogonal matrix X (c).
4.5 according to object function Fitness=max { { E { z4}-3(E{z2})2And orthogonal matrix X (c), (Z for asking for
Kurtosis value F, wherein：Kurt is kurtosis, and kurtosis is the fourth order cumulant of stochastic variable, and kurtosis value is bigger, and its non-Gaussian system is bigger,
It can obtain the maximum independent signal source of separating property as object function) the adaptive value Fitness of particle is obtained, as
Per the kurtosis value of signal all the way.
4.6 according to formula(i.e. using " greediness " selection strategy,
According to object vector xi(g+1) with trial vector ui(g+1) be follow-on object vector adaptive value f (xi(g)) and f (ui(g
+ 1)) selecting optimum individual) optimizing is carried out to adaptive value, if Fitnessnew ＜ Fitnessold (i), terminate circulation, it is right
Particle enters the transposition of row matrix, draws separation matrix W2, otherwise return to step 4.1.
5) according to formulaObtain output signalG is global matrix/sytem matrix.IfThen reach
Arrived separation (or) recover source signal target.
6) each harmonic signal components of GRAVITY EARTH TIDE signal are extracted, spectrum analyses is done, by result of spectrum analysis
Contrasted with theoretical value.
The invention has the advantages that：By DE algorithms in combination with traditional ICA algorithm, by the variation in DE algorithms, intersection,
The renewal of preference pattern applies to initial value sensitivity of the solution that mixed matrix is solved in ICA algorithm to improve traditional ICA algorithm and asks
Topic, is optimized to traditional ICA algorithm.Algorithm after improvement effectively extracts three independences from GRAVITY EARTH TIDE signal
Component, respectively：The long period wave system component that the reflection moon, the sun are produced relative to changes in the earths orbital geometry, and the reflection earth is certainly
The day wave system component for changing the line of production raw, and the semidiurnal wave system component that reflection earth rotation is produced, also, the independence decomposited from these
Concrete harmonic componentss are extracted in component.Effectively the change of the spheres such as these independent elements and the earth, the moon, the sun is produced
Raw gravitation tidal effect sets up corresponding relation.Can be used to contrast the difference of theoretical value and actual measured value, can be effectively and smart
The accurate abnormal accumulation information for obtaining information of earthquake or earthquake.
Description of the drawings
Fig. 1 is the algorithm flow chart of the present invention；
Fig. 2 is the GRAVITY EARTH TIDE signal three-dimensional orthogonal decomposition model of the present invention；
Fig. 3 is binomial crossover operation figure；
Fig. 4 is the GRAVITY EARTH TIDE signal waveforms in present example；
Fig. 5 is the independent harmonic component figure extracted with inventive algorithm in present example；
Fig. 6 is the frequency spectrum of the independent element signal for extracting in present example.
Specific embodiment
With reference to concrete accompanying drawing and example, the invention will be further described.
Embodiment 1：Independent Component Analysis Algorithm based on DE algorithms proposed by the present invention, as shown in figure 1, including following step
Suddenly：
1) GRAVITY EARTH TIDE signal in orthogonal model is analyzed, such as in Fig. 2 figures, for tellurian certain observation station A,
Consider that it is subject in the presence of earth rotation, the Sun and the Moon power to lead tide, if its earth tide for causing is F, F can be decomposed into two
Individual orthogonal signal：Ground tilt tide signal FhWith GRAVITY EARTH TIDE signal Fg.Herein with regard to GRAVITY EARTH TIDE signal FgCarry out point
Analysis, Fg2 orthogonal vectors can be decomposed into：One component of signal F parallel to equatorial plane1, one parallel to earth rotation
Component of signal F of axle2, F1Again can be with Orthogonal Decomposition as 2 component of signals F11And F12, such GRAVITY EARTH TIDE signal is just orthogonal
It is decomposed into three-dimensional orthogonal vector.
2) according to GRAVITY EARTH TIDE three-dimensional orthogonal model, act on tellurian GRAVITY EARTH TIDE signal by earth rotation,
The sun, the power to lead tide effect of the moon cause, and the GRAVITY EARTH TIDE signal isolated component isolated is 3, is arrived in January, 2010
In this period in June, 2010, in same longitude, three sampled points of different latitude, sampled point 1 (130 ° of E, 40 ° of N), sampled point 2
(130 ° of E, 50 ° of N), sampled point 3 (130 ° of E, 60 ° of N), chooses three road signal x1, x2, x3, corresponding GRAVITY EARTH TIDE signal waveform
As shown in Figure 4.
3) to observation signal pretreatment：Treating process signal using methods such as Eigenvalues Decompositions carries out albefaction and goes at average
Reason, obtains whitening matrix W1, whitened signal
4) using DE algorithm optimization separation matrix W2；
Solution procedure is as follows：
4.1 arrange parameter：The population scale Np of initialization particle, i.e. population number in DE algorithms, while being also independent
Demand solution solution mixes the number of the mixed matrix of solution in component analyses algorithm.Dimension D, i.e., the dimension of required problem, zoom factor F (affects
Level of disruption to basis vector), maximum iteration time Gm, crossing-over rate CR (determines that how many members may be changed in population
Become), algebraically G is initialized, as shown in table 1；
The parameter setting of table 1
4.2 one random population X of initialization；
4.3 proceed by iterative cycles, make i=1:Np, according to formula
Vi(g+1)=xr1(g)+F×(xr2(g)-xr3(g)), r1≠r2≠r3, F is zoom factor, in random selection population
Two individuality xr2(g) and xr3(g), calculate the weight (F × (x of difference vectorr2(g)-xr3(g))) and basis vector xr1G () is added
Obtain new variation vector Vi(g+1),
4.4 according to formula
For [1, D]
Interior randomly selected integer, D for problem dimension CR ∈ (0, be 1) crossing-over rate, as shown in Figure 3.
Binomial intersection is carried out to new variation vector, by random selection, make at least one component of trial vector by
Variation vector contribution, obtains trial vector ui,j(g+1), and to it enter the transposition of row matrix, obtain a new orthogonal matrix X
(c)；
4.5 according to object function Fitness=max { { E { z4}-3(E{z2})2And orthogonal matrix X (c), (ask for Z's
Kurtosis value F, kurtosis is the fourth order cumulant of stochastic variable, and kurtosis value is bigger, and its non-Gaussian system is bigger, its as object function,
The maximum independent signal source of separating property can be obtained.) the adaptive value Fitness of particle is obtained, as per the high and steep of signal all the way
Angle value.
4.6 according to formula(i.e. using " greediness " selection strategy,
According to object vector xi(g) and trial vector ui(g+1) the adaptive value f (x for beingi(g)) and f (ui(g+1) it is) optimum individual to select
Body.) optimizing is carried out to adaptive value, if Fitnessnew ＜ Fitnessold (i), terminate circulation, row matrix is entered to particle
Transposition, draws separation matrix W2, otherwise return to step Step 4.1.；
5) according to formulaObtain isolated componentG is global matrix/sytem matrix.IfThen reach
Arrived separation (or) recover the target of source signal, export the isolated component isolated as shown in Figure 5.
6) each harmonic signal components of GRAVITY EARTH TIDE signal are extracted, spectrum analyses are done, its spectrogram such as Fig. 6 institutes
Show, result of spectrum analysis is contrasted with theoretical value.
Wherein theoretic frequency value is calculated from Du Sen formula, as shown in table 2.Described frequency values unit is hertz
(Hz), e represents 10 power side in table 1.
The frequency spectrum of the independent element signal that table 2 is extracted and the contrast of theoretical value frequency spectrum
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.Not only the relation of harmonic component in GRAVITY EARTH TIDE signal is disclosed and is come and is believed with GRAVITY EARTH TIDE
Number Orthogonal Decomposition model it is corresponding.With reference to Fig. 1, the day ripple of GRAVITY EARTH TIDE signal is embodied in F11Direction, semidiurnal wave are embodied in
F12Direction.The compositions such as Nian Bo, half a year ripple are embodied in F2Direction, it can be seen that F11、F12、F2It is mutually orthogonal.With reference to table 2, respectively
Spectrum information contained by component is consistent with theoretical value, illustrates that the method is a kind of effective, and GRAVITY EARTH TIDE signal is carried out
The new method of quadrature analysis.
Above in conjunction with accompanying drawing to the present invention specific embodiment be explained in detail, but the present invention be not limited to it is above-mentioned
Embodiment, in the ken that those of ordinary skill in the art possess, can be with before without departing from present inventive concept
Put that various changes can be made.
Claims (2)
1. a kind of independent component analysis method of the GRAVITY EARTH TIDE signal based on DE algorithms, it is characterised in that：Including following steps
Suddenly：
1) the three-dimensional orthogonal decomposition model of GRAVITY EARTH TIDE is set up；
2) random time section, same to longitude, the m roads GRAVITY EARTH TIDE signal S={ s in different latitude place are chosen1(t),s2
(t),...,sm(t) } as input；
3) to the m roads GRAVITY EARTH TIDE Signal Pretreatment in step 2：Albefaction is carried out to observation signal using Eigenvalues Decomposition method
With remove average value processing, obtain whitening matrix W1, whitened signal
4) using DE algorithm optimization separation matrix W2；
4.1 arrange parameter：The population scale Np of initialization particle is the population number in DE algorithms, while being also independent element point
Demand solution solution mixes the number of the mixed matrix of solution in analysis algorithm；The dimension of the i.e. required problem of dimension D；Zoom factor F, affect to substantially to
The level of disruption of amount；Maximum iteration time Gm；Crossing-over rate CR, determines that how many members may be changed in population；Initialization generation
Number G；
4.2 one random population X of initialization；
The 4.3 variation vector V for looking for noveltyi(g+1), iterative cycles are proceeded by, makes i=1:Np, according to formula Vi(g+1)=xr1(g)
+F·(xr2(g)-xr3(g)), wherein r1≠r2≠r3, two individuality x in random selection populationr2(g) and xr3(g), calculate difference to
Weight (F (the x of amountr2(g)-xr3(g))) and basis vector xr1G () is added and obtains new variation vector Vi(g+1)；
4.4 orthogonal matrixes X (c) looked for novelty, according to formula
J=1,2 ..., D, jrandFor in [1, D]
Randomly selected integer, D for problem dimension, CR ∈ (0, be 1) crossing-over rate, to new variation vector Vi(g+1) binomial is carried out
Formula is intersected, and by random selection, makes at least one component of trial vector by the vector contribution that makes a variation, and obtains trial vector ui,j(g+
1), and to it enter the transposition of row matrix, obtain new orthogonal matrix X (c)；
4.5 according to object function Fitness=max { { E { z4}-3(E{z2})2And orthogonal matrix X (c), obtain the suitable of particle
Should value Fitness, the as kurtosis value per signal all the way.
4.6 according to formulaOptimizing is carried out to adaptive value, if
Fitnessnew ＜ Fitnessold (i), then terminate circulation, and the transposition of row matrix is entered to particle, draws separation matrix W2, otherwise
Return to step 4.1；
5) according to formulaG is global matrix/sytem matrix, obtains output signal
6) each harmonic signal components of GRAVITY EARTH TIDE signal are extracted, spectrum analyses are done, by result of spectrum analysis and reason
Contrasted by value.
2. the independent component analysis method of the GRAVITY EARTH TIDE signal of DE algorithms according to claim 1, it is characterised in that：
The detailed process that the three-dimensional orthogonal decomposition model of GRAVITY EARTH TIDE is set up in step 1 is：
For tellurian certain observation station A, in the presence of considering that it is subject to earth rotation, the Sun and the Moon power to lead tide, if its
The earth tide for causing is F, and F can be decomposed into two orthogonal signals：Ground tilt tide signal FhWith GRAVITY EARTH TIDE signal
Fg；Fg2 orthogonal vectors can be decomposed into：One component of signal F parallel to equatorial plane1, one parallel to earth rotation
Component of signal F of axle2；F1Can be again 2 component of signals F in the same plane with Orthogonal Decomposition11And F12。
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