CN112906632A - Automatic extraction method of highly adaptive time delay target signal - Google Patents

Automatic extraction method of highly adaptive time delay target signal Download PDF

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CN112906632A
CN112906632A CN202110288519.4A CN202110288519A CN112906632A CN 112906632 A CN112906632 A CN 112906632A CN 202110288519 A CN202110288519 A CN 202110288519A CN 112906632 A CN112906632 A CN 112906632A
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葛双超
周世达
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North University of China
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Abstract

The invention discloses a highly self-adaptive time delay target signal automatic extraction method, which designs a general atom, does not need to construct a huge redundant dictionary in advance when carrying out sparse decomposition, sets atom characteristic parameters as bat individual position vectors, constructs flexible atoms by utilizing an improved bat algorithm to carry out optimal position search, and further realizes standardized optimal matching atom search; using sparse decomposition dual-threshold iteration stopping criterion, wherein residual ℓ -2 norm threshold is determined by background noise intensity without target signal sequencen s ℓ -2 norm adaptive determination; the iteration time threshold is set by a user according to real-time requirements. The application of the double criteria can ensure the signal extraction precision, improve the iteration speed and effectively avoid over decomposition. The method does not depend on complex prior knowledge and subsequent manual judgment and screening, can effectively extract the target signal and simultaneously reserve other components of the signal to the maximum extent, and is completely automaticA method for extracting non-stationary time delay signals is provided.

Description

Automatic extraction method of highly adaptive time delay target signal
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a method for automatically identifying and extracting a time delay target signal in background noise.
Background
Extraction of non-stationary time delay target signals is an important research content of modern signal processing, and has important application in the fields of vibration signal detection, earthquake monitoring, biomedical signal detection and the like.
The existing signal extraction method mainly comprises the following steps: wavelet decomposition, hilbert-yellow transform, Variational Modal Decomposition (VMD), and signal sparse decomposition algorithms, among others.
Wavelet decomposition is an important means of processing a time-delayed signal, but requires selection of appropriate wavelet basis functions and decomposition level numbers, which may otherwise result in an extracted signal that is not a target signal. The Hilbert-Huang transform has a good effect of extracting linear steady-state signals, but most natural signals are difficult to satisfy the premise, especially the extraction of time delay signals aliasing in noise, and the application effect of the Hilbert-Huang transform is not ideal. The variational modal decomposition has a good processing effect on non-stationary and non-linear signals under a certain condition, but local jump information is punished excessively in the processing process, and a boundary effect and an aliasing phenomenon of local features in a global range exist, so that the variational modal decomposition is not suitable for time delay local feature signal extraction. In addition, the VMD algorithm requires that the number of modes K is predefined, and it is necessary to manually determine whether each decomposed mode belongs to the target signal, so that the flexibility is insufficient. The sparse decomposition algorithm represents the signal in a self-adaptive manner as a linear combination of a plurality of atoms, can describe the local characteristics of the signal in detail, and is an effective non-stationary time delay signal extraction method. However, the traditional signal sparse decomposition algorithm needs to perform matching pursuit in a previously constructed redundant dictionary to determine the optimal matching atom, and the algorithm efficiency is not high enough.
Disclosure of Invention
The invention aims to improve the flexibility and the adaptivity of the identification and the extraction of a time delay target signal, and provides a time delay signal adaptive identification and extraction method based on a bat algorithm optimization sparse decomposition algorithm. The method and the device have the advantages that the dependence on complex prior information in the extraction process of the non-stationary target signal is eliminated, the flexibility of signal identification and extraction is improved, and the detection and extraction of the fully-automatic non-stationary time delay target signal are realized.
The invention is realized by adopting the following technical scheme:
a highly self-adaptive time delay target signal automatic extraction method comprises general atomic design, a target data segment automatic positioning detection algorithm, a real-time characteristic base atom sparse decomposition method, signal extraction based on improved bat algorithm optimization sparse decomposition and the like.
Firstly, designing a general atomic g atom, wherein the expression of the g atom is as follows:
Figure BDA0002981441300000021
wherein t is sampling time; t is t0For the moment of atom bilateral boundary, τ1And τ2Respectively, bilateral effective oscillation time; d1And d2Respectively, bilateral attenuation factors; f is the atomic signal frequency, phi is the atomic signal phase; ε is a bilateral scale factor.
The constructed g atoms have strong universality, can be matched with most typical signals through parameter adjustment, and almost cover main signal types in electromagnetic observation data.
The method comprises the following specific steps:
(1) and positioning the target data segment by using a target data segment automatic positioning detection algorithm, and then selecting a target-free signal data segment.
(2) Setting sparse decomposition double-threshold criterion: a residual i-2 norm threshold σ and a maximum iteration number threshold N. Sigma is determined by the intensity of background noise, i.e. the sequence n without target signalsThe l-2 norm of (d):
Figure BDA0002981441300000031
n is set by the user according to real-time requirements, typically to 30.
(3) Initializing, wherein the iteration number n is 1, and the number k of selected atoms is 0; current residual xinX; current optimum fitness Fitn best＝1E6。
(4) Determining an initialization time parameter tau according to an automatic positioning detection algorithm of the target data segment1，τ2And t0Extracting a target sample Ei＝x(t0-τ1:t0+τ2)。
(5) To EiHilbert transformation to obtain more accurate target parameter information
R(t)＝Ei(t)*h(t) (2)
Wherein: h (t) is the Hill transform factor. The following complex analytic signals are constructed:
z(t)＝x(t)+iR(t)＝A(t)eiφ(t) (3)
wherein A (t) is a function of amplitude
Figure BDA0002981441300000032
The bilateral scaling factor epsilon is determined by the logarithmic ratio of the amplitude maxima and the two adjacent sub-maxima.
Phi (t) is the phase function:
Figure BDA0002981441300000033
Eiis given by:
Figure BDA0002981441300000034
using the time-frequency information of the sample as the reference parameter para of the general atom0＝[ fφ d1 d2 t0 τ1 τ2 ε]Characteristic base atoms are obtained, the length of the atoms being the same as the original signal length.
(6) Initializing a bat population by using the time-frequency parameters determined in the step (4) and the step (5);
Figure BDA0002981441300000041
wherein
Figure BDA0002981441300000042
Denotes the initial position of the j-th bat of the nth generation, lambdajIs a random number, satisfies lambdaj∈(-1,1)；
(7) Finding the optimal bat position after nth sparse decomposition iteration by using an improved bat algorithm
Figure BDA0002981441300000043
Best matching atoms
Figure BDA0002981441300000044
And updating the fitness:
Figure BDA0002981441300000045
wherein N isiteFor the maximum iteration number of the improved bat algorithm, NpopThe number of bats;
Figure BDA0002981441300000046
for real-time flexible atoms, by real-time positioning of bat individuals
Figure BDA0002981441300000047
Obtained as a characteristic parameter by substituting the formula (1), i.e.
Figure BDA0002981441300000048
Normalized coefficient
Figure BDA0002981441300000049
Guarantee xinThe effective signal in (a) has the same energy as its sparse decomposition result,
Figure BDA00029814413000000410
Figure BDA00029814413000000411
is composed of
Figure BDA00029814413000000412
The corresponding decomposition coefficients.
(8) And determining
Figure BDA00029814413000000413
Whether or not:
if so: then k equals k +1 and the normalized best matching atom is calculated
Figure BDA00029814413000000414
Optimum atomic number
Figure BDA00029814413000000415
Updating residual errors
Figure BDA00029814413000000416
If not, the method comprises the following steps: xin+1＝ξn，
Figure BDA00029814413000000417
(9) Let n equal n +1, judge
Figure BDA00029814413000000418
Or n<And (3) whether N is true, if not, repeating the steps (1) to (9), and if at least one of N is true, executing the step (10).
(10) Obtaining a sparse decomposition optimal matching dictionary
Figure BDA00029814413000000419
Sparsely decomposing the step components
Figure BDA00029814413000000420
And extracting a target signal estimate
Figure BDA00029814413000000421
Firstly, determining the starting time and the duration time of a characteristic time delay signal by using an automatic positioning detection algorithm of a target data segment, and extracting the target data segment as a characteristic sample by using initial positioning; the target data segment automatic positioning detection algorithm is characterized in that a target signal is determined by searching an effective envelope window of a cross-correlation function of data to be processed and a standard sine atom by utilizing short-time Fourier transform and a related detection technologyThe time information obtained can determine the time domain parameters of the universal atoms, and intercept the target sample Ei. Thirdly, processing the characteristic sample by using Hilbert transform to obtain a target signal time-frequency parameter which is used as a characteristic base of the sparse decomposition dictionary, and constructing a general atom by taking the characteristic base as a center; the real-time flexible atom sparse decomposition method is to perform optimization solution in a characteristic parameter redundancy range by taking an atom parameter as a characteristic value, so as to avoid constructing a huge redundant dictionary. Finally, converting the matching tracking problem in the signal sparse decomposition process into an optimization problem by using an optimized bat algorithm, and adjusting the universal atoms in real time in a redundancy range according to the characteristic parameters to carry out sparse decomposition optimization; the improved bat algorithm is based on the classic bat algorithm, the signal residual error l-2 norm is used as a fitness function for optimizing, the influence of the update direction and speed of the optimal solution of a group on an optimization result is considered in the optimizing process, and the searching speed and precision of the algorithm are improved.
The improved bat algorithm optimized sparse decomposition algorithm is characterized in that the improved bat algorithm is utilized to convert a signal sparse decomposition matching tracking problem into an optimization problem, a general atomic characteristic parameter is used as a bat individual position parameter, a real-time atom is constructed by utilizing the position parameter and the fitness is calculated, the bat position is continuously optimized through iterative optimization to further realize the optimization of the general atomic parameter, a modern standardized optimal matching atom and a signal residual error can be obtained after the optimization of one generation of bats is completed, and the target signal extraction is realized through iterative optimization.
According to the method for automatically extracting the highly-adaptive time delay target signal, the sparse decomposition matching tracking problem is converted into the optimization problem by using the swarm intelligence algorithm, and then the time delay target signal is extracted by using the sparse decomposition algorithm. It is characterized in that:
1. the invention designs the universal atom which can be matched with various typical time delay signals, develops the time-frequency domain characteristic parameter initialization algorithm and improves the automation degree of non-stationary time delay signal identification.
2. The method optimizes the classic bat algorithm, increases the group optimizing direction factor, and improves the convergence speed and precision of the algorithm.
3. According to the method, the problem of matching and tracking of the traditional signal sparse decomposition redundant dictionary is converted into the problem of flexible atomic parameter optimization by using a group intelligent algorithm, so that a huge redundant dictionary is avoided being constructed, and the efficiency of signal sparse decomposition is greatly improved.
4. In the signal sparse decomposition process, the signal residual error l-2 norm is used as a fitness function, the atom time-frequency characteristic parameter is used as an optimization target, the dependence of the existing signal extraction method on various complex prior knowledge, preconditions and later manual intervention is eliminated, and other components of the signal can be furthest reserved while the target signal is extracted.
5. The invention provides a sparse decomposition dual-threshold criterion, a key threshold (a residual error l-2 norm threshold) is adaptively determined by an algorithm according to the background noise intensity, an iteration number threshold N is set by a user according to the real-time requirement, and the application of the dual-threshold criterion can ensure the signal extraction precision, improve the iteration speed and effectively avoid excessive decomposition.
The method is reasonable in design, is a fully-automatic time delay signal detection and extraction method, and has the advantages of high adaptivity, high efficiency, high precision and the like.
Drawings
Fig. 1 shows a time-domain waveform of the different parameters g atom.
Fig. 2 shows an automatic target data segment location detection algorithm.
Fig. 3 shows an example of automatic location detection of a target data segment.
Fig. 4 shows a flow chart of a highly adaptive delay target signal automatic extraction method.
Fig. 5 shows the non-stationary delay signal extraction results of different methods.
Figure 6 shows different approaches to non-stationary delay signal extraction error.
Detailed Description
The following provides a detailed description of specific embodiments of the present invention.
Height self-adaptationThe automatic extraction method of the time delay target signal is characterized in that a signal sparse decomposition method is utilized to extract a non-stable time delay signal, and the problem of sparse decomposition, matching and tracking of the signal is converted into an optimization problem through an improved bat algorithm. The method mainly comprises the following steps: first, the generic atoms of the design can be matched to most typical signals by parameter tuning. Secondly, the improved bat algorithm introduces a group optimizing direction factor, the group optimizing direction factor is a vector and normalization result formed by overlapping the speed of the current bat individual and the speeds of n bats nearby, the speed factor is updated in the group optimizing direction, and the bat individual can be effectively guided to jump out of a local optimal solution. Then, optimizing sparse decomposition based on the improved bat algorithm, without constructing a redundant dictionary in advance, adopting real-time flexible atoms, searching for optimal matching atoms by taking a residual error l-2 norm as a fitness function, calculating the optimal matching atoms and updating the residual error. Finally, a sparse decomposition double-threshold criterion is provided, namely a residual error l-2 norm threshold and an iteration number threshold N, so that the circulation is ended in advance after the residual error l-2 norm threshold is reached in the signal sparse decomposition process, excessive decomposition is avoided, and the decomposition efficiency is improved; and when the iteration times are more than N, ending the iteration, and avoiding the low efficiency caused by infinite loop of the algorithm. After iteration is stopped, the original signal is used for subtracting the final residual error to obtain the target signal estimator
Figure BDA0002981441300000073
Meanwhile, the optimal matching dictionary for signal sparse decomposition is composed of optimal matching atoms obtained by each iteration.
First, a general atomic g atom is designed, and most typical signals can be matched through parameter adjustment. The universal atom is subjected to standardization processing, so that the original signal and the sparsely decomposed signal have the same energy, and the universal atom characteristic parameter vector comprises effective signal start-stop time, attenuation factors, frequency, phase and damping ratio: para ═ f φ d1 d2 t0 τ1 τ2ε]。
Figure BDA0002981441300000081
Wherein t is sampling time; t is t0For the moment of atom bilateral boundary, τ1And τ2Respectively, bilateral effective oscillation time; d1And d2Respectively, bilateral attenuation factors, usually d1＝d2(ii) a f is the atomic signal frequency, phi is the atomic signal phase; ε is a bilateral scaling factor, typically 1.
As shown in FIG. 1, the time domain waveform of atomic g with different parameters is used as the damping factor d1＝d2When 0, epsilon is 1, g atoms degenerate into a standard sine wave (r); when ε is 1, τ1＝τ2Not equal to 0, the damping factor is increased, the high-frequency g atoms are shown as bilateral oscillation attenuation signals and are matched with the characteristics of a sharp impulse discharge signal ((r)), and the low-frequency g atoms are shown as triangle-like waves (sixth); when tau is2When the number is 0, g atoms show unilateral excited oscillation characteristics (c- (r)); when tau is10, g atoms show unilateral damped oscillation characteristic (c); when the bilateral scale factor is 0<ε<1, and when the atomic frequency is sufficiently low, g atoms represent a charge-discharge-like triangular wave (v).
Secondly, the invention adopts an automatic target data segment positioning detection algorithm based on a relevant detection technology. The correlation detection technology is a strong periodic signal extraction method, and the technology separates target signals by utilizing the irrelevance between signals and noise and signals with different components.
As shown in FIG. 2, the present invention utilizes the cross-correlation function envelope and the peak gradient as the characteristic values to perform the automatic segmentation extraction of the target signal.
Let the original sample sequence x (t) consist of two parts, x (t) xn(t)+s0(t) wherein xn(t) is a nonlinear, non-stationary signal; s0(t) is a target signal in the x sequence, and the expression is shown as 8
Figure BDA0002981441300000091
Wherein A isi、fi、ΦiAre respectively target signalsAmplitude, frequency and phase of the main frequency component, ti1～ti2Satisfying t for a target frequency signal occurrence periodi1<ti2<T, T is the total sampling time.
Firstly, preliminarily determining an estimated value of a key parameter of a signal to be extracted in original observation data x through short-time Fourier transform
Figure BDA0002981441300000092
Then constructing standard sine atoms
Figure BDA0002981441300000093
Determination of a target signal s using correlation detection techniques0iAt the time instant that occurs in the x sequence. x (t),
Figure BDA0002981441300000094
The cross-correlation function between the two signals is:
Figure BDA0002981441300000095
wherein x isnNon-stationary components of the original signal, and
Figure BDA0002981441300000096
not related;
Figure BDA0002981441300000097
is prepared by reacting with
Figure BDA0002981441300000098
The less correlated signal component. The first term of equation (9) is therefore approximately 0, i.e.:
Figure BDA0002981441300000099
as shown in the formula (10), the original sequence x (t) is related to the standard sinusoidal signal
Figure BDA00029814413000000910
The cross-correlation function envelope period is [ -t [ ]1-1 t2+1]。
For digital signals, equation (10) becomes:
Figure BDA00029814413000000911
wherein L is1And L2The start and end positions of the target signal are respectively, and N is the length N ═ f of the original data sequences*T，fsFor the sampling rate, K is the length of the standard sinusoidal signal K ═ fs。
In practical application, because the first term in the formula (9) is not absolutely 0, the maximum peak gradient is used as a characteristic parameter, and the gradient Delta is enveloped by the cross-correlation functionp：
Δp(i)＝Penv(i)-Penv(i-1) (12)
Wherein, Penv(i) Represents the value of the envelope of the cross-correlation function at the coordinate point i, when i is L1Where the maximum peak gradient of the cross-correlation function occurs.
And extracting the envelope curve of the cross-correlation function by using a soft threshold, wherein the ideal envelope range of the cross-correlation function is given by the following formula:
Figure BDA0002981441300000101
wherein the content of the first and second substances,
Figure BDA0002981441300000102
and
Figure BDA0002981441300000103
for enveloping the effective window soft threshold, λ, from top to bottomp,λnE (0,1), related to the signal-to-noise ratio; [ lp1lp2]And [ ln1 ln2]Respectively upper and lower effective envelope window boundaries. The target signal data segment range is given by:
Figure BDA0002981441300000104
wherein n isshiftIn order to be a factor of the offset,
Figure BDA0002981441300000105
represents rounding down, [ l1l2]For the active envelope window boundary, max () denotes taking the maximum value and min () denotes taking the minimum value. Lambda is a time parameter redundancy factor and satisfies lambda epsilon [ 1.011.2]And ensuring that the determined time parameter can completely cover the target signal segment. Extracting a target data segment Ei＝x(L1:L2) By using EiMaximum extreme point AmaxAnd its two side symmetric minor extreme points
Figure BDA0002981441300000106
Ratio judgment EiTime-domain oscillation characteristic of (2):
Figure BDA0002981441300000107
the single-side attenuation oscillation is carried out,
Figure BDA0002981441300000108
the single side is excited to oscillate,
Figure BDA0002981441300000109
bilateral oscillation. From the above information, the time parameter is determined using equation (15):
Eithe characteristic of single-side oscillation attenuation is as follows:
Figure BDA0002981441300000111
Eisingle-side stimulated oscillation characteristic:
Figure BDA0002981441300000112
Eithe two-sided oscillation characteristic is as follows:
Figure BDA0002981441300000113
as shown in fig. 3, in the example of automatic positioning detection of a target data segment, the upper graph is a positioning result, and the lower graph is an original signal time domain waveform. The upper and lower effective envelopes are shown as "at" and "at" scatter points in the figure, and "O" marks the time-localized position.
Thirdly, the improved bat algorithm flow adopted by the invention is as follows:
(1) initializing bat populations, wherein the bat number is NpopMaximum number of iterations NiteWhen the current iteration number m is equal to 0, searching a space dimension q, and initializing a pulse frequency f0＝{ f i 01,2, q } and a maximum value f of pulse frequencymaxAnd minimum value fminSound wave loudness
Figure BDA0002981441300000114
And maximum pulse transmission frequency
Figure BDA0002981441300000115
Randomly generating a bat group initial position according to the following formula
Figure BDA0002981441300000116
Figure BDA0002981441300000117
Wherein: lambda [ alpha ]jTo satisfy the random number of the Gaussian observation matrix, Pmax＝1.2*para0，Pmin＝0.8*para0。
(2) According to bat group position
Figure BDA0002981441300000118
Creating NpopFlexible atom formationn. For residual signal xinCalculating the bat individual fitness according to formula (16):
Figure BDA0002981441300000119
wherein the content of the first and second substances,
Figure BDA00029814413000001110
in order to be a function of the normalization,
Figure BDA00029814413000001111
determining and storing the optimal bat individual position of the current group according to the formula (17)
Figure BDA00029814413000001112
And optimal fitness.
Figure BDA0002981441300000121
(3) Let j be 1, i.e.,
Figure BDA0002981441300000122
(4) speed of updating bat individual
Figure BDA0002981441300000123
And position
Figure BDA0002981441300000124
The bat individual moving direction and speed have certain relevance to the global optimal solution. Thus introducing a population-optimizing direction factor. The bat individual direction update factor is as follows:
Figure BDA0002981441300000125
in order to avoid
Figure BDA0002981441300000126
Guiding the bat individual to move to the local optimal solution, and comparing the speed of the current bat individual with the nearby nrThe optimal directions of bat are added:
Figure BDA0002981441300000127
wherein, | | | represents the euclidean distance, and R is the group velocity factor threshold.
Normalizing the vector sum to obtain a normalized population optimizing direction factor:
Figure BDA0002981441300000128
by using
Figure BDA0002981441300000129
The bat group is guided to rapidly move to the direction of the global optimal solution, and the updating formula of the speed and the pulse emission frequency is as follows:
Figure BDA00029814413000001210
wherein r is1Is a random number, satisfies r1∈[0,1]；fiIs the search pulse frequency of the ith bat;
Figure BDA00029814413000001211
respectively representing the speed of the jth bat when the iteration times are m and m + 1; μ is a weighting factor.
(5) Generating a random number r for each bat2j∈[0,1]Updated bat position according to equation (21):
Figure BDA0002981441300000131
wherein λ isrjIs a random number satisfying lambdarj(-0.3 0.3)，
Figure BDA0002981441300000132
Is the mean value of the sound wave loudness of the m-th generation bat swarm,
Figure BDA0002981441300000133
respectively representing the position of the jth bat at the iteration times of m and m +1, and calculatingDegree of adaptability
Figure BDA0002981441300000134
(6) And determining
Figure BDA0002981441300000135
If yes, updating the optimization result
Figure BDA0002981441300000136
(7) Judging whether the algorithm meets the iteration termination condition
Figure BDA0002981441300000137
If not, executing the step (8); if m is m +1, k is k +1, and jump to step (11) after updating the residual error according to the following formula
Figure BDA0002981441300000138
Wherein
Figure BDA0002981441300000139
Is the normalized optimal atom for which the atomic number is normalized,
Figure BDA00029814413000001310
are the corresponding sparse decomposition coefficients.
(8) For each bat, a random number r is generated3jAnd updating the bat position by formula (23)
Figure BDA00029814413000001311
(9) Updating the loudness of the bats individual sound wave and the pulse emission frequency by a formula (24):
Figure BDA00029814413000001312
wherein the content of the first and second substances,
Figure BDA00029814413000001313
representing the pulse emission frequency of the jth bat when the iteration number is m + 1;
Figure BDA00029814413000001314
respectively representing the loudness of the sound wave of the jth bat when the iteration times are m and m-1; lambda is the attenuation coefficient of the pulse emission frequency, and belongs to (0, 1); gamma is the pulse emission frequency enhancement coefficient>0; when m → ∞ is reached,
Figure BDA0002981441300000141
(10) and judging whether the algorithm meets an iteration termination condition m or not by making m equal to m +1<NiteIf not, repeating the step (3-10); and (4) if the condition is met, executing the step (11).
(11) And stopping the bat algorithm iteration, and outputting:
Figure BDA0002981441300000142
designing a general atom, setting atom characteristic parameters as bat individual position vectors without constructing a huge redundant dictionary in advance when sparse decomposition is carried out, and constructing flexible atoms by utilizing an improved bat algorithm to carry out optimal position search so as to realize optimal atom search; adopting sparse decomposition double-threshold iteration stopping criterion, wherein the threshold of residual error l-2 norm is determined by background noise intensity, namely the threshold does not contain target signal sequence nsThe l-2 norm of (1) is determined adaptively; the iteration number threshold value N is set by a user according to real-time requirements. The application of the double criteria can ensure the signal extraction precision, improve the iteration speed and effectively avoid over decomposition.
The specific implementation flow is shown in fig. 4, and is as follows:
(1) and positioning the target data segment by using a target data segment automatic positioning detection algorithm, and then selecting a target-free signal data segment.
(2) Setting sparse decomposition double-threshold criterion: residual l-2 norm threshold σAnd a maximum iteration number threshold N. Sigma is determined by the intensity of background noise, i.e. the sequence n without target signalsThe l-2 norm of (d):
Figure BDA0002981441300000143
n is set by the user according to real-time requirements, typically to 30.
(3) Initializing, wherein the iteration number n is 1, and the number k of selected atoms is 0; current residual xinX; current optimum fitness Fitn best＝1E6。
(4) Determining an initialization time parameter tau according to an automatic positioning detection algorithm of the target data segment1，τ2And t0Extracting a target sample Ei＝x(t0-τ1:t0+τ2)。
(5) To EiHilbert transformation to obtain more accurate target parameter information
R(t)＝Ei(t)*h(t) (2)
Wherein: h (t) is the Hill transform factor. The following complex analytic signals are constructed:
z(t)＝x(t)+iR(t)＝A(t)eiφ(t) (3)
wherein A (t) is a function of amplitude
Figure BDA0002981441300000151
The bilateral scaling factor epsilon is determined by the logarithmic ratio of the amplitude maxima and the two adjacent sub-maxima.
Phi (t) is the phase function:
Figure BDA0002981441300000152
Eiis given by:
Figure BDA0002981441300000153
using the time-frequency information of the sample as the reference parameter para of the general atom0＝[f φ d1 d2 t0 τ1 τ2 ε]Characteristic base atoms are obtained, the length of the atoms being the same as the original signal length.
(6) Initializing a bat population by using the time-frequency parameters determined in the step (4) and the step (5);
Figure BDA0002981441300000154
wherein
Figure BDA0002981441300000155
Denotes the initial position of the j-th bat of the nth generation, lambdajIs a random number, satisfies lambdaj∈(-1,1)。
(7) Finding the optimal bat position after nth sparse decomposition iteration by using an improved bat algorithm
Figure BDA0002981441300000156
Best matching atoms
Figure BDA0002981441300000157
And updating the fitness:
Figure BDA0002981441300000161
wherein N isiteFor the maximum iteration number of the improved bat algorithm, NpopThe number of bats;
Figure BDA0002981441300000162
for real-time flexible atoms, by real-time positioning of bat individuals
Figure BDA0002981441300000163
Obtained as a characteristic parameter by substituting the formula (1), i.e.
Figure BDA0002981441300000164
Normalized coefficient
Figure BDA0002981441300000165
Guarantee xinThe effective signal in (a) has the same energy as its sparse decomposition result,
Figure BDA0002981441300000166
Figure BDA0002981441300000167
is composed of
Figure BDA0002981441300000168
The corresponding decomposition coefficients.
(8) And determining
Figure BDA0002981441300000169
Whether or not:
if so: then k equals k +1 and the normalized best matching atom is calculated
Figure BDA00029814413000001610
Optimum atomic number
Figure BDA00029814413000001611
Updating residual errors
Figure BDA00029814413000001612
If not, the method comprises the following steps: xin+1＝ξn，
Figure BDA00029814413000001613
(9) Let n equal n +1, judge
Figure BDA00029814413000001614
Or n<And (3) whether N is true, if not, repeating the steps (1) to (9), and if at least one of N is true, executing the step (10).
(10) Obtaining a sparse decomposition optimal matching dictionary
Figure BDA00029814413000001615
Sparsely decomposing the step components
Figure BDA00029814413000001616
And extracting a target signal estimate
Figure BDA00029814413000001617
Fifthly, to verify the reliability of the algorithm, the method is characterized by comprising the following steps of background noise nsAnd a time delay target signal s consisting of g atoms with two different parameters constructs a non-stationary original signal x:
x＝s+ns＝ns+150·g(c,0.3,10,10,13,2,π*1.1,1)+100·g(c,1,2,1,3,5,π/2,1)。
respectively utilizing wavelet analysis, VMD algorithm, sparse decomposition algorithm based on particle swarm algorithm and the method of the invention to identify and extract the time delay target signal s contained in the signal x. Wherein, the wavelet decomposition adopts an expert experience method to preferably select sym3 wavelet as a mother wavelet, and the decomposition layer number is 3 layers; the number of intrinsic modes of the VMD algorithm is set to be 4, and the first two modes are taken as extraction targets; the particle swarm algorithm and the bat algorithm adopt the same initial parameters of the population scale, the maximum iteration times, the stop threshold value and the like.
As shown in fig. 5 and 6, in the non-stationary delay signal extraction result and the extraction error map of different methods, both wavelet decomposition and VMD delay signal extraction cause global aliasing of local features, and the signal sparse decomposition method (PSO-SD) based on the particle swarm algorithm causes a large deviation between the extracted signal and the target signal due to the fact that the extracted signal falls into a local optimal solution, so that the method (IBA-SD) of the present invention has an ideal non-stationary delay signal extraction effect compared with other methods.
The result shows that the method does not depend on complex prior knowledge and subsequent manual judgment and screening, can effectively extract the target signal and simultaneously reserve other components of the signal to the maximum extent, is a fully-automatic non-stationary time delay signal extraction method, and has the advantages of high adaptivity, high convergence, high precision and the like.
Finally, it should be noted that the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the detailed description is made with reference to the embodiments of the present invention, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which shall be covered by the claims of the present invention.

Claims (5)

1. A highly adaptive time delay target signal automatic extraction method is characterized in that: the method comprises the following steps:
firstly, designing a general atomic g atom, wherein the expression of the g atom is as follows:
Figure FDA0002981441290000011
wherein t is sampling time; t is t0For the moment of atom bilateral boundary, τ1And τ2Respectively, bilateral effective oscillation time; d1And d2Respectively, bilateral attenuation factors; f is the atomic signal frequency, phi is the atomic signal phase; epsilon is a bilateral scale factor;
the method comprises the following specific steps:
(1) positioning the target data segment by using a target data segment automatic positioning detection algorithm, and then selecting a target-free signal data segment;
(2) setting sparse decomposition double-threshold criterion: a residual error l-2 norm threshold value sigma and a maximum iteration number threshold value N; sigma is determined by the intensity of background noise, i.e. the sequence n without target signalsThe l-2 norm of (d):
Figure FDA0002981441290000012
n is set by a user according to real-time requirements and is typically set to be 30;
(3) initializing, wherein the iteration number n is 1, and the number k of selected atoms is 0; current residual xinX; current optimum fitness Fitn best＝1E6；
(4) Determining an initialization time parameter tau according to an automatic positioning detection algorithm of the target data segment1，τ2And t0Extracting a target sample Ei＝x(t0-τ1:t0+τ2)；
(5) To EiHilbert transformation to obtain more accurate target parameter information
R(t)＝Ei(t)*h(t) (2)
Wherein: h (t) is the Hill transform factor. The following complex analytic signals are constructed:
z(t)＝x(t)+iR(t)＝A(t)eiφ(t) (3)
wherein A (t) is a function of amplitude
Figure FDA0002981441290000021
The bilateral scaling factor epsilon is determined by the logarithmic ratio of the amplitude maxima and the two adjacent sub-maxima.
Phi (t) is the phase function:
Figure FDA0002981441290000022
Eiis given by:
Figure FDA0002981441290000023
using the time-frequency information of the sample as the reference parameter para of the general atom0＝[f φ d1 d2 t0 τ1 τ2 ε]Obtaining characteristic base atoms, wherein the length of the atoms is the same as that of the original signals;
(6) initializing a bat population by using the time-frequency parameters determined in the step (4) and the step (5);
Figure FDA0002981441290000024
wherein
Figure FDA0002981441290000025
Denotes the initial position of the j-th bat of the nth generation, lambdajIs a random number, satisfies lambdaj∈(-1,1)；
(7) Finding the optimal bat position after nth sparse decomposition iteration by using an improved bat algorithm
Figure FDA0002981441290000026
Best matching atoms
Figure FDA0002981441290000027
And updating the fitness:
Figure FDA0002981441290000028
wherein N isiteFor the maximum iteration number of the improved bat algorithm, NpopThe number of bats;
Figure FDA0002981441290000029
for real-time flexible atoms, by real-time positioning of bat individuals
Figure FDA00029814412900000210
Obtained as a characteristic parameter by substituting the formula (1), i.e.
Figure FDA00029814412900000211
Normalized coefficient
Figure FDA00029814412900000212
Guarantee xinThe effective signal in (a) has the same energy as its sparse decomposition result,
Figure FDA0002981441290000031
Figure FDA0002981441290000032
is composed of
Figure FDA0002981441290000033
The corresponding decomposition coefficient;
(8) and determining
Figure FDA0002981441290000034
Whether or not:
if so: then k equals k +1 and the normalized best matching atom is calculated
Figure FDA0002981441290000035
Optimum atomic number
Figure FDA0002981441290000036
Updating residual errors
Figure FDA0002981441290000037
If not, the method comprises the following steps: xin+1＝ξn，
Figure FDA0002981441290000038
(9) Let n equal n +1, judge
Figure FDA0002981441290000039
Or n<N is true, if not, repeating the steps (1) to (9), and if at least one of the N is true, executing the step (10);
(10) obtaining a sparse decomposition optimal matching dictionary
Figure FDA00029814412900000310
Sparsely decomposing the step components
Figure FDA00029814412900000311
And extracting a target signal estimate
Figure FDA00029814412900000312
2. The method according to claim 1, wherein the method comprises: in the step (3), the target data segment automatic positioning detection algorithm is as follows:
let the original sample sequence x (t) consist of two parts, x (t) xn(t)+s0(t) wherein xn(t) is a nonlinear, non-stationary signal; s0(t) is a target signal in the x sequence, and the expression is shown as 8
Figure FDA00029814412900000313
Wherein A isi、fi、ΦiAmplitude, frequency and phase, t, respectively, of the main frequency component of the target signali1～ti2Satisfying t for a target frequency signal occurrence periodi1<ti2<T, T is total sampling time;
firstly, preliminarily determining an estimated value of a key parameter of a signal to be extracted in original observation data x through short-time Fourier transform
Figure FDA00029814412900000314
Then constructing standard sine atoms
Figure FDA0002981441290000041
Determination of a target signal s using correlation detection techniques0iThe time instants occurring in the x sequence; x (t),
Figure FDA0002981441290000042
The cross-correlation function between the two signals is:
Figure FDA0002981441290000043
wherein x isnIs original toNon-stationary components in the start signal, and
Figure FDA0002981441290000044
not related;
Figure FDA0002981441290000045
is prepared by reacting with
Figure FDA0002981441290000046
A signal component with weak correlation; the first term of equation (9) is therefore approximately 0, i.e.:
Figure FDA0002981441290000047
as shown in the formula (10), the original sequence x (t) is related to the standard sinusoidal signal
Figure FDA0002981441290000048
The cross-correlation function envelope period is [ -t [ ]1-1 t2+1]；
For digital signals, equation (10) becomes:
Figure FDA0002981441290000049
wherein L is1And L2The start and end positions of the target signal are respectively, and N is the length N ═ f of the original data sequences*T，fsFor the sampling rate, K is the length of the standard sinusoidal signal K ═ fs；
In practical application, because the first term in the formula (9) is not absolutely 0, the maximum peak gradient is used as a characteristic parameter, and the gradient Delta is enveloped by the cross-correlation functionp：
Δp(i)＝Penv(i)-Penv(i-1) (12)
Wherein, Penv(i) Represents the value of the envelope of the cross-correlation function at the coordinate point i, when i is L1Where cross correlation function occursA maximum peak gradient;
and extracting the envelope curve of the cross-correlation function by using a soft threshold, wherein the ideal envelope range of the cross-correlation function is given by the following formula:
Figure FDA0002981441290000051
wherein the content of the first and second substances,
Figure FDA0002981441290000052
and
Figure FDA0002981441290000053
for enveloping the effective window soft threshold, λ, from top to bottomp,λnE (0,1), related to the signal-to-noise ratio; [ lp1 lp2]And [ ln1 ln2]Upper and lower effective envelope window boundaries, respectively; the target signal data segment range is given by:
Figure FDA0002981441290000054
wherein n isshiftIn order to be a factor of the offset,
Figure FDA0002981441290000055
represents rounding down, [ l1l2]For the effective envelope window boundary, max () represents taking the maximum value, min () represents taking the minimum value; lambda is a time parameter redundancy factor and satisfies lambda epsilon [ 1.011.2]Ensuring that the determined time parameter can completely cover the target signal segment; extracting a target data segment Ei＝x(L1:L2) By using EiMaximum extreme point AmaxAnd its two side symmetric minor extreme points
Figure FDA0002981441290000056
Ratio judgment EiTime-domain oscillation characteristic of (2):
Figure FDA0002981441290000057
the single-side attenuation oscillation is carried out,
Figure FDA0002981441290000058
the single side is excited to oscillate,
Figure FDA0002981441290000059
bilateral oscillation; from the above information, the time parameter is determined using equation (15):
Eithe characteristic of single-side oscillation attenuation is as follows:
Figure FDA00029814412900000510
Eisingle-side stimulated oscillation characteristic:
Figure FDA00029814412900000511
Eithe two-sided oscillation characteristic is as follows:
Figure FDA00029814412900000512
3. the method according to claim 1, wherein the method comprises: in the step (6), the improved bat algorithm is as follows:
(1) initializing bat populations, wherein the bat number is NpopMaximum number of iterations NiteWhen the current iteration number m is equal to 0, searching a space dimension q, and initializing a pulse frequency f0＝{fi 01,2, q } and a maximum value f of pulse frequencymaxAnd minimum value fminSound wave loudness
Figure FDA0002981441290000061
And maximum pulse transmission frequency
Figure FDA0002981441290000062
Generation of the bat randomlyInitial position of bats group
Figure FDA0002981441290000063
Wherein: lambda [ alpha ]jTo satisfy the random number of the Gaussian observation matrix, Pmax＝1.2*para0，Pmin＝0.8*para0；
(2) According to bat group position
Figure FDA0002981441290000064
Creating NpopFlexible atom formationn(ii) a For residual signal xinCalculating the bat individual fitness according to formula (16):
Figure FDA0002981441290000065
wherein the content of the first and second substances,
Figure FDA0002981441290000066
in order to be a function of the normalization,
Figure FDA0002981441290000067
determining and storing the optimal bat individual position of the current group according to the formula (17)
Figure FDA0002981441290000068
And the optimal fitness;
Figure FDA0002981441290000069
(3) let j be 1, i.e.,
Figure FDA00029814412900000610
(4) speed of updating bat individual
Figure FDA00029814412900000611
And position
Figure FDA00029814412900000612
The moving direction and speed of the bat individual have certain relevance with the global optimal solution, so a group optimizing direction factor is introduced; the bat individual direction update factor is as follows:
Figure FDA00029814412900000613
in order to avoid
Figure FDA00029814412900000614
Guiding the bat individual to move to the local optimal solution, and comparing the speed of the current bat individual with the nearby nrThe optimal directions of bat are added:
Figure FDA0002981441290000071
wherein, | | | represents the euclidean distance, and R is the group velocity factor threshold;
normalizing the vector sum to obtain a normalized population optimizing direction factor:
Figure FDA0002981441290000072
by using
Figure FDA0002981441290000073
The bat group is guided to rapidly move to the direction of the global optimal solution, and the updating formula of the speed and the pulse emission frequency is as follows:
Figure FDA0002981441290000074
wherein r is1Is a random number, satisfies r1∈[0,1]；fiIs the search pulse of the ith batThe impulse frequency;
Figure FDA0002981441290000075
respectively representing the speed of the jth bat when the iteration times are m and m + 1; mu is a weight factor;
(5) generating a random number r for each bat2j∈[0,1]Updated bat position according to equation (21):
Figure FDA0002981441290000076
wherein λ isrjIs a random number satisfying lambdarj(-0.3 0.3)，
Figure FDA0002981441290000077
Is the mean value of the sound wave loudness of the m-th generation bat swarm,
Figure FDA0002981441290000078
respectively representing the position of the jth bat when the iteration times are m and m +1, and calculating the fitness
Figure FDA0002981441290000079
(6) And determining
Figure FDA00029814412900000710
If yes, updating the optimization result
Figure FDA00029814412900000711
(7) Judging whether the algorithm meets the iteration termination condition
Figure FDA00029814412900000712
If not, executing the step (8); if m is m +1, k is k +1, and jump to step (11) after updating the residual error according to the following formula
Figure FDA0002981441290000081
Wherein
Figure FDA0002981441290000082
Is to standardize the best-matching atoms,
Figure FDA0002981441290000083
is the corresponding optimum atomic coefficient;
(8) for each bat, a random number r is generated3jAnd updating the bat position by formula (23)
Figure FDA0002981441290000084
(9) Updating the loudness of the bats individual sound wave and the pulse emission frequency by a formula (24):
Figure FDA0002981441290000085
wherein the content of the first and second substances,
Figure FDA0002981441290000086
representing the pulse emission frequency of the jth bat when the iteration number is m + 1;
Figure FDA0002981441290000087
respectively representing the loudness of the sound wave of the jth bat when the iteration times are m and m-1; lambda is the attenuation coefficient of the pulse emission frequency, and belongs to (0, 1); gamma is the pulse emission frequency enhancement coefficient>0; when m → ∞ is reached,
Figure FDA0002981441290000088
(10) and judging whether the algorithm meets an iteration termination condition m or not by making m equal to m +1<NiteIf not, repeat the first step(3-10); if yes, executing the step (11);
(11) and stopping the bat algorithm iteration, and outputting:
Figure FDA0002981441290000089
4. the method according to claim 3, wherein the method comprises: the real-time flexible atom is a bat individual real-time position vector
Figure FDA0002981441290000091
Constructing a universal atom in real time as a universal atom characteristic parameter vector; finding the optimal solution of the bat position by using the residual error l-2 norm as a fitness function to further obtain a standardized optimal matching atom gk bestThe method is characterized in that real-time flexible atoms which are obtained by one-time iteration optimization and enable residual error l-2 norm to be minimum are obtained after standardization processing; the optimal atomic coefficients are obtained from the projection of the corresponding residual signals on the normalized optimally matched atoms, i.e.
Figure FDA0002981441290000092
5. The method of claim 4, wherein the method further comprises: the sparse decomposition double-threshold criterion is that the residual error l-2 norm threshold sigma is determined by the background noise intensity, namely the target signal sequence n is not containedsThe l-2 norm of (d):
Figure FDA0002981441290000093
the iteration number threshold value N is set by a user according to the real-time requirement, and is typically set to be 30; the target signal estimator
Figure FDA0002981441290000094
From the original signal and the last iteration residualξnAnd (3) calculating:
Figure FDA0002981441290000095
the signal sparse decomposition optimal matching dictionary is a dictionary formed by all optimized normalized optimal matching atoms when iteration stops
Figure FDA0002981441290000096
All components of the sparse decomposition are obtained by calculating normalized optimal matching atoms and optimal atom coefficients:
Figure FDA0002981441290000097
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