CN106468787A - GRAVITY EARTH TIDE signal independence harmonic component extraction method based on PBIL - Google Patents

Abstract

The invention provides a method for extracting independent harmonic components of gravity solid tide signals based on a PBIL (Population-Based Incremental Learning) algorithm, which belongs to the field of signal processing. The method of the present invention mainly includes the analysis based on the orthogonal decomposition model of the gravity solid tide signal, the preprocessing of the gravity solid tide signal, the parameter setting of the PBIL algorithm, the establishment of the optimization objective function, the independent component analysis and harmonic extraction of the gravity solid tide signal . This algorithm introduces the PBIL algorithm into the traditional independent component analysis algorithm, which effectively avoids the premature and local convergence of the traditional independent component analysis algorithm, and improves the separation effect and better implementability.

Description

Extraction Method of Independent Harmonic Components of Gravity Solid Tide Signal Based on PBIL

Technical field:

The invention relates to an optimization algorithm, in particular to an algorithm for extracting independent harmonic components of gravity solid tide signals based on PBIL, and belongs to the field of signal processing.

Background technique:

Under the tidal gravitational force of celestial bodies such as the sun and the moon, the earth will undergo elastic deformation, and the gravity at any point on the earth's surface will also change periodically. The observable geophysical signal reflecting this phenomenon is the gravitational solid tidal signal . The analysis of gravitational solid tide signals has a wide range of applications in related earth sciences such as geodesy, geophysics and seismology.

The tidal potential produced by celestial bodies such as the sun and the moon on the earth's surface changes with the relative position of their orbits. The tidal potential generated at any point can be expanded according to Dussen's harmonic function and can be decomposed into 386 harmonics with constant amplitudes. These tidal waves can be divided into long-period waves, diurnal waves, semi-diurnal waves and one-third diurnal waves according to their periods, and can also be divided into diurnal (half-diurnal) and lunar (half-moon) systems according to their generation mechanism. , annual wave (semi-annual wave) and other components.

At present, the traditional analysis methods for gravitational solid tidal signals cannot clearly explain the relationship between each harmonic component in the gravitational solid tidal signal and the gravitational tidal effect of different celestial bodies from the perspective of the generation mechanism of the gravitational solid tidal signal. At the same time, the traditional independent component analysis algorithm has high requirements on the numerical value of the initialization unmixing matrix, and the constraint items are fixed, and there is no learning rate, etc., which cannot adapt to the changing environment and achieve the optimal convergence effect, and it is easy to fall into the local optimum. to a better separation effect.

Invention content:

The technical problem to be solved in the present invention is to provide a method for extracting independent harmonic components of the gravity solid tide signal based on the PBIL algorithm by analyzing the orthogonal decomposition model of the gravity solid tide signal and through the generation mechanism of the harmonic component. The information contained in the solid tide signal itself is optimized by PBIL to the most important unmixing matrix in the independent component analysis algorithm, and the independent component analysis and harmonic extraction are performed on the gravity solid tide observation signal.

The technical scheme adopted in the present invention is: a method for extracting independent harmonic components of gravity solid tide signals based on PBIL, the steps of the method are as follows:

Step 1. Analyze the orthogonal decomposition model of gravity solid tide signal;

Step 2. Obtain the observed value of the gravitational solid tide signal at the observation point: through the analysis of the model, select any certain period of time, and the m-channel gravitational solid tide observation signal to be processed at the same longitude and different latitude: X=[x ₁ (t), _x2 (t),..., _xm (t)];

Step 3. Preprocessing the observed signal: use the eigenvalue decomposition method to whiten and spheroidize the signal to be processed, and obtain the whitened and spheroidized signal

Step 4. Initialization of the unmixing matrix: in the process of independent component extraction, Y represents the independent component obtained after processing by the independent component analysis algorithm, W is the unmixing matrix, according to the prior knowledge of the signal to be processed, the unmixing matrix is initialized with random uniform distribution: B=[b _1:D ,b _{2: D} ,...,b _m:D ] ^T ,i=1,2,...m,

Among them, the number of signals to be processed is m, the dimension is D, and the number of the largest independent components obtained after separation

Step 5. The algorithm optimizes the process of solving the unmixing matrix:

Step 5.1. Order Obtain the initial independent harmonic component, calculate its second-order distance E{Z ² } and fourth-order distance E{Z ⁴ } for Z, and substitute it into the formula F={kurt(Z)=E{Z ⁴ }-3(E {Z ² }) ² } Calculated Z kurtosis value F, where: kurt is kurtosis, kurtosis is the fourth-order cumulant of random variables, f is the kurtosis value of each signal in Z, according to the order from large to Arrange in small order F=(f ₁ ,f ₂ ,...,f _M ), get the fitness value information and position subscript information of particles contained in F;

Step 5.2. Select the position subscripts of K=k×M particles from the fitness value F according to their order, and select from B according to the obtained position subscripts i=1,2,...N, where l is the number of iterations of the lth time, k is the selectivity k∈(0,1);

Step 5.3. Substitute B ^best into the Hebbian formula Update the probability vector of the population, where B ^old refers to the unmixed matrix particles that have not been selected, p ^old represents the particle distribution vector before the update, and the learning rate α, α∈(0,1); When calculating, p ^old =p ₀ =0.5, B ^old =B;

Step 5.4. When , the particles perform cyclic calculation and return to Step 5.1; otherwise, end the cycle and obtain the optimal unmixing matrix B;

Step 6. Let W=B, extract according to independent components Get the processed independent harmonic components;

Step 7. Perform spectrum analysis on the independent harmonic component Y to obtain its frequency value f _observation , compare the f _observation with the theoretical value of , and obtain the classification of its independent harmonic component.

In the step Step 1, the analysis of the orthogonal model of the gravity solid tide signal is specifically as follows:

A is a certain observation point on the earth, the tidal force of the sun and the gravitational force of the moon are mainly decomposed into the ground tilt solid tide signal F _h and the gravity solid tide signal F _g , and the gravity solid tide signal F _g is decomposed orthogonally, A signal component F ₁ parallel to the earth's rotation axis, a signal component F ₂ parallel to the equatorial plane, F ₂ is parallel to the equatorial plane, this signal component is only affected by the earth's rotation, and mainly contains independent component harmonics caused by the earth's rotation Components, namely diurnal and semi-diurnal waves, F ₁ is parallel to the earth's rotation axis, and the signal component in the F ₁ direction is not affected by the earth's rotation, and this direction contains independent harmonic components produced by the tidal forces of the moon and the sun, that is, long-period Wave.

The beneficial effects of the present invention are: the present invention combines PBIL algorithm with traditional independent component subdivision algorithm, applies the update of learning rate in PBIL algorithm, probability model to the solving of unmixing matrix in independent component analysis algorithm, improves The initial value sensitivity problem of the traditional independent component analysis algorithm is optimized. The improved algorithm effectively extracts three independent components from the gravitational solid tide signal, which are: the long-period wave system component reflecting the orbital changes of the moon and the sun relative to the earth, and the diurnal wave system component reflecting the earth’s rotation. And reflect the semi-diurnal wave system components produced by the earth's rotation, and extract specific harmonic components from these decomposed independent components. Effectively establish a corresponding relationship between these independent components and the gravitational tidal effect produced by the orbital changes of the earth, the moon, the sun and other celestial bodies.

Description of drawings

Fig. 1 is the orthogonal decomposition model diagram of gravity solid tide signal of the present invention;

Fig. 2 is the algorithm flowchart of the present invention;

Fig. 3 is the waveform diagram of gravity solid tide signal of the present invention;

Fig. 4 is the independent harmonic component figure extracted with algorithm of the present invention;

Fig. 5 is a spectrum diagram of extracted independent component signals in the example of the present invention.

detailed description

The present invention will be further described below in conjunction with specific drawings and embodiments.

Embodiment 1: Referring to Fig. 1-Fig. 5, a kind of independent harmonic component extraction method of gravity solid tidal signal based on PBIL, the steps of described method are as follows:

Step 1. Analyze the orthogonal decomposition model of gravity solid tide signal;

Step 2. Obtain the observed value of the gravitational solid tide signal at the observation point: through the analysis of the model, select any certain period of time, and the m-channel gravitational solid tide observation signal to be processed at the same longitude and different latitude: X=[x ₁ (t), _x2 (t),..., _xm (t)];

Step 3. Preprocessing the observed signal: use the eigenvalue decomposition method to whiten and spheroidize the signal to be processed, and obtain the whitened and spheroidized signal

Step 4. Initialization of the unmixing matrix: in the process of independent component extraction, Y represents the independent component obtained after processing by the independent component analysis algorithm, W is the unmixing matrix, according to the prior knowledge of the signal to be processed, the unmixing matrix is initialized with random uniform distribution: B=[b _1:D ,b _{2: D} ,…,b _m:D ] ^T ,i=1,2,…m

Among them, the number of signals to be processed is m, and the number of the largest independent components that will be obtained after separation The dimension D is: the dimension of each particle in the PBIL algorithm should have a certain mathematical relationship with the maximum number of independent components. In the PBIL algorithm, the population particles can be transposed to obtain M The unmixing matrix, the size M of the population is: the number of populations in the PBIL algorithm, and also the number of unmixing unmixing matrices that need to be unmixed in the independent component analysis algorithm;

Step 5. The algorithm optimizes the process of solving the unmixing matrix:

Step 5.1. Order Obtain the initial independent harmonic component, calculate its second-order distance E{Z ² } and fourth-order distance E{Z ⁴ } for Z, and substitute it into the formula F={kurt(Z)=E{Z ⁴ }-3(E {Z ² }) ² } Calculated Z kurtosis value F, where: kurt is kurtosis, kurtosis is the fourth-order cumulant of random variables, the larger the kurtosis value, the greater its non-Gaussianity, and it is the target function, the independent signal source with the largest separation performance can be obtained, f is the kurtosis value of each signal, and F=(f ₁ ,f ₂ ,…,f _M ) is arranged in order from large to small, and the particles contained in F can be obtained Fitness value information and location subscript information;

Step 5.2. Select the position subscripts of K=k×M particles from the fitness value F according to their order, and select from B according to the obtained position subscripts i=1,2,...N, where l is the number of iterations of the lth time, the selectivity k: the fitness value of the particles calculated by the objective function, the percentage of the dominant group selected from it, k∈(0,1 );

Step 5.3. Substitute B ^best into the Hebbian formula Carry out the update of the probability vector of the population, wherein B ^old refers to the unmixed matrix particles that have not been selected, p ^old represents the particle distribution vector before the update, the learning rate is α, and the tendency of the population to the dominant particle in the PBIL algorithm The closest learning rate, α∈(0,1), the probability vector p ₀ is: the initial probability of the population, which belongs to a uniform distribution, p ₀ =0.5, when calculating for the first time, p ^old =p ₀ = 0.5, B ^old = B;

Step 5.4. When , the particles perform cyclic calculation and return to Step 5.1; otherwise, end the cycle and obtain the optimal unmixing matrix B;

Step 6. Let W=B, extract according to independent components After obtaining the processed independent harmonic component, the independent harmonic component extracted by the algorithm of the present invention is as shown in Figure 4;

Step 7. Carry out frequency spectrum analysis to independent harmonic component Y and obtain its frequency value f _observation , compare f _observation with theoretical value, as shown in table 2, obtain its independent harmonic component classification, the independent component that the present invention extracts The spectrum of the signal is shown in Figure 5.

The theoretical frequency value is calculated from Dussen's formula, as shown in Table 1. The unit of the frequency value is hertz (Hz), and e in Table 1 and Table 2 represents a power of 10.

This algorithm can successfully separate the gravity solid tide signal into the following harmonic states: semi-diurnal wave signal, diurnal wave signal, and long-period wave signal. Moreover, the separated signal components also conform to the orthogonal decomposition model of the gravity solid tide signal, and can automatically correspond to each harmonic component.

Table 1 Theoretical frequency values of each harmonic of gravity solid tide

Table 2 Comparison of frequency values of independent harmonic components and theoretical frequency values

In the step Step 1, the analysis of the orthogonal model of the gravity solid tide signal is specifically as follows:

As shown in Figure 1, A is a certain observation point on the earth, and the solar tidal force and lunar gravitational force it receives are mainly decomposed into the ground tilt solid tide signal F _h and the gravity solid tide signal F _g , and the gravitational solid tide signal F Orthogonal decomposition of _g , a signal component F ₁ parallel to the earth's rotation axis, a signal component F ₂ parallel to the equatorial plane, F ₂ is parallel to the equatorial plane, this signal component is only affected by the earth's rotation, mainly includes the earth's rotation The independent component harmonic component caused by , namely diurnal wave and semi-diurnal wave, F ₁ is parallel to the earth's rotation axis, and the signal component in the F ₁ direction is not affected by the earth's rotation, and this direction contains the independent harmonic generated by the moon and the sun's tidal force Wave components, that is, long-period waves. The gravitational solid tide signal waveform of the present invention is shown in FIG. 3 .

The PBIL algorithm is an evolutionary algorithm based on a probability model. This algorithm combines the knowledge of competitive learning and evolutionary computing. The knowledge obtained through competitive learning - learning probability to guide the generation of offspring, and then use the probability vector to constrain each Individual value, to solve the optimization problem.

The present invention can also be used for the separation of mixed signals with prior knowledge, including: harmonic component extraction of earth solid tide signals, etc. It can also be used to compare the difference between theoretical values and actual measured values, and can effectively and accurately obtain earthquake Precursor information or abnormal accumulation information of earthquakes.

The specific embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments. Variations.

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),…,x_m(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=[b_1:D,b_2:D,…,b_m: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,…,f_M), 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 B^bestSubstitute into Hebbian formulaCarry out the probability vector of colony more Newly, wherein B^oldThe solution referring to not carry out selection mixes matrix particle, p^oldRepresent the particle distribution vector before not being updated, study speed Rate α, α ∈ (0,1)；When being calculated first time, p^old=p₀=0.5, B^old=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 Y_Observation, by f_ObservationWith 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 F_hWith GRAVITY EARTH TIDE signal F_g, to GRAVITY EARTH TIDE signal F_gCarry 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.