CN112560699A - Gear vibration information source underdetermined blind source separation method based on density and compressed sensing - Google Patents

Gear vibration information source underdetermined blind source separation method based on density and compressed sensing Download PDF

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CN112560699A
CN112560699A CN202011503046.7A CN202011503046A CN112560699A CN 112560699 A CN112560699 A CN 112560699A CN 202011503046 A CN202011503046 A CN 202011503046A CN 112560699 A CN112560699 A CN 112560699A
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陆建涛
李妙珍
李舜酩
程龙欢
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a gear vibration information source underdetermined blind source separation method based on density and compressed sensing, which comprises the following steps of firstly, carrying out noise reduction pretreatment on an acquired signal by adopting a wavelet noise reduction method; secondly, short-time Fourier transform is used for the mixed signals, and a convolution mixed model in a time domain is converted into a linear mixed model in each frequency band; then, a single source point extraction method based on sparse coding and a vibration source number identification method based on a density peak value clustering method are used for realizing effective estimation of a mixed matrix; restoring the source signal by a compressed sensing method to obtain a separated signal; and finally, carrying out order and amplitude correction on the separated signals of each frequency band, and then converting the separated signals from a frequency domain into a time domain. The method estimates the number of the vibration sources by a density peak value clustering method, enhances the robustness to noise, reduces the probability of generating false peak values, further reduces the estimation error of the number of the vibration sources, and can effectively complete the separation work of mixed signals.

Description

Gear vibration information source underdetermined blind source separation method based on density and compressed sensing
Technical Field
The invention belongs to the field of signal processing and blind source separation, and particularly relates to a gear vibration information source underdetermined blind source separation method based on density and compressed sensing.
Background
In engineering applications, vibration signals generated by various parts in the working process are generally required to judge the working state and health condition of the parts. For example, some specific periodic vibration signals generated by rotating components such as gears in the working process can reflect the working state and health condition of the system, but such effective signals can be mixed with other components and environmental noise during acquisition, so that characteristic signals are submerged, and effective judgment is difficult to obtain by directly adopting multi-source mixed signals for analysis and processing. Therefore, research on the hybrid vibration signal blind source separation method is receiving attention.
The blind source separation is a modern signal processing method for effectively estimating a source signal only from an observation signal acquired by a sensor under the condition that prior knowledge of the source signal and a transmission channel is unknown or less, and has good application prospects in the aspects of state monitoring, fault diagnosis, vibration reduction, noise reduction and the like of mechanical equipment. Underdetermined blind source separation refers to a signal processing method for estimating source signals when the number of sensors is less than the number of vibration source signals. Compared with positive definite blind source separation, underdetermined blind source separation increases the difficulty of signal separation, and meaningful estimation components are difficult to obtain only through the independence of signals. At present, signals are estimated by utilizing sparsity of the signals, most classically, sparse component analysis is carried out, and the sparse component analysis mainly comprises two parts, namely mixing matrix estimation and source recovery. Among them, the estimation of the number of vibration sources is one of the difficulties in the underdetermined blind source separation problem. Some learners adopt a potential function method to estimate the number of the sources, but the potential function method is sensitive to division intervals and not strong in robustness to noise, and false peaks are easily generated, so that errors are generated in estimation of the number of the source signals, and further, errors are generated in separation of the source signals. Therefore, it is meaningful to research how to effectively estimate the number of source signals under the underdetermined condition, and blind source separation under the underdetermined condition can be more effectively carried out.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the defects in the blind source separation method, the invention provides a gear vibration source underdetermined blind source separation method based on density and compressed sensing, which is used for estimating the number of vibration sources by a density peak value clustering method to enhance the robustness to noise and reduce the probability of generating false peak values, thereby reducing the estimation error of the number of vibration sources and the estimation error of a mixed matrix and a source signal.
The technical scheme is as follows: the invention relates to a gear vibration information source underdetermined blind source separation method based on density and compressed sensing, which comprises the following steps of:
(1) carrying out denoising pretreatment on the acquired signal by adopting a wavelet denoising method;
(2) short-time Fourier transform is used for the mixed signals, and a linear convolution mixed model in a time domain is converted into a linear instantaneous mixed model in each frequency band;
(3) the single source point extraction method based on sparse coding and the vibration source number identification method based on the density peak value clustering method realize effective estimation of a mixed matrix;
(4) restoring the source signal by a compressed sensing method to obtain a separated signal:
(5) and (4) carrying out order and amplitude correction on the separated signals of each frequency band acquired in the step (4), and then converting the separated signals from a frequency domain into a time domain.
Further, the step (2) is realized as follows:
the linear convolution mixture model is:
Figure BDA0002844046290000021
where x (t) represents an m-dimensional discrete-time signal received at time t, and x (t) ([ x ])1(t),x2(t),···,xm(t)]T(ii) a s (t) represents an n-dimensional discrete time signal emitted at time t, and s (t) is s1(t),s2(t),···,sn(t)]T；HpAn mxn-dimensional hybrid coefficient matrix representing a time delay of p; v (t) represents the noise signal at time t; denotes the convolution operator;
transform equation (5) to the z-domain:
x(z)＝H(z)s(z)+v(z) (6)
where H (z) is an m × n order matrix:
Figure BDA0002844046290000022
wherein h isji(p) represents filter coefficients of the hybrid filter from the ith source to the jth observation, i being 1 to n, and j being 1 to m;
converting the denoised mixture signal x (t) from the time domain to the frequency domain using a short-time fourier transform, approximating a linear convolution mixture model as a linear instantaneous mixture model at each frequency:
x(t,f)＝H(f)s(t,f) (8)
wherein h (f) ═ h1(f),h2(f),···,hN(f)]Is a frequency domain filter.
Further, the step (3) is realized as follows:
all time-frequency vectors are combined to form a matrix U (t, f) ═ x1(t,f),···,xK(t,f)]Then xi(t, f) x can be divided by U (t, f)iVectors other than (t, f) are encoded, i.e.:
xi(t,f)＝U(f)c,s.t.ci＝0 (9)
the problem of identifying a single source point translates to0Norm optimization problem:
min||c||0,s.t.xi(t,f)＝U(f)c,ci＝0 (10)
when c is sufficiently sparse, it is converted to l1Norm optimization problem, and in turn translates into:
Figure BDA0002844046290000031
after the single source point is obtained, clustering the single source point to obtain the estimation of the mixed matrix, wherein the information expressed by each clustering center is the estimation of one column vector of the mixed matrix, namely:
Figure BDA0002844046290000032
wherein, yi(i ═ 1,2, ·, K) denotes the extracted single source points, and the number of classes is the number of source signals.
Further, the step (4) is realized as follows:
the compressed sensing mathematical model is as follows:
y(y1,y2,···,yn)T＝Ux＝UVs＝Ws (16)
wherein y represents a compressed signal with a length of m, m is less than n, a sensing matrix W (m × n) is UV, and a compression reconstruction process is an inverse process of obtaining a compressed sensing;
two mixed signals of length t can be converted into y ═ (y)11,y12,···,y1t,y21,y22,···,y2t)T；
Using estimation matrices
Figure BDA0002844046290000033
To construct a sensing matrix W, and using the identity matrix E, the sensing matrix W (mt × nt) is obtained by compressing the sensing model when the signal y (mt × 1) is mixediTo expand the estimation matrix
Figure BDA0002844046290000034
Of (2), i.e.
Figure BDA0002844046290000035
The specific conversion is as follows:
Figure BDA0002844046290000041
wherein the reconstructed signal x ═ (x)11,x12,···,x1t,···,xn1,xn1,···,xnt)TDimension is (nt × 1);
smoothing l0Norm is defined as
Figure BDA0002844046290000042
Wherein:
Figure BDA0002844046290000043
the smaller the smoothing parameter σ, the closer F(s) is to l0Norm, the initial sigma value is large, the sigma value is gradually reduced along with the iteration process, and the source signal is estimated by adopting the following formula:
Figure BDA0002844046290000044
s←s-HT(HHT)(Hs-x) (21)
alternately updating equation (20) and equation (21) results in an estimate of the source signal under-determined conditions.
Has the advantages that: compared with the prior art, the invention has the beneficial effects that: the method has the advantages that the convolution mixed gear vibration signal can be separated, and compared with a method for separating an instantaneous mixed signal, the method is closer to the actual situation; density peak value clustering method to cut-off distance dcThe selection of the method has robustness, the method is only sensitive to the relative size of the point, the cluster can be identified no matter the shape of the cluster and the dimension of the embedding space, and the method has the advantages of few parameters, high efficiency, easiness in implementation and the like.
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FIG. 1 is a flow chart of the network of the present invention;
FIG. 2 is a distribution diagram of data points for density peak clustering;
fig. 3 is a data point decision diagram for density peak clustering.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings:
as shown in fig. 1, the invention provides a gear vibration information source underdetermined blind source separation method based on density and compressed sensing, which specifically comprises the following steps:
step 1: and carrying out denoising pretreatment on the acquired signal by adopting a wavelet denoising method.
If the function φ (t) satisfies the condition:
Figure BDA0002844046290000045
phi (t) is called the mother function of a wavelet or the basic wavelet, wherein,
Figure BDA0002844046290000051
for the fourier transform of phi (t), the wavelet function is obtained by scaling and shifting the basic wavelet function, and is expressed as:
Figure BDA0002844046290000052
in the formula, a and b represent a scaling parameter and a translation parameter of wavelet transform, respectively.
For any signal f (t), the wavelet transform pair is:
Figure BDA0002844046290000053
Figure BDA0002844046290000054
where denotes the conjugate, ω f (a, b) denotes the wavelet transform of the signal f (t), and equation (4) denotes the signal reconstruction.
Step 2: and (3) using short-time Fourier transform to the mixed signal, and converting a linear convolution mixed model in a time domain into a linear instantaneous mixed model in each frequency band. The specific process is as follows:
the linear convolution blending process can be described as:
Figure BDA0002844046290000055
where x (t) represents an m-dimensional discrete-time signal received at time t, and x (t) ([ x ])1(t),x2(t),···,xm(t)]T(ii) a s (t) represents an n-dimensional discrete time signal emitted at time t, and s (t) is s1(t),s2(t),···,sn(t)]T；HpAn mxn-dimensional hybrid coefficient matrix representing a time delay of p; v (t) represents the noise signal at time t; denotes the convolution operator.
For simplicity of operation, equation (5) is usually transformed into the z-domain:
x(z)＝H(z)s(z)+v(z) (6)
where H (z) is an m × n order matrix.
Figure BDA0002844046290000056
Wherein h isji(p) represents filter coefficients of the hybrid filter from the ith source to the jth observation, i being 1 to n, and j being 1 to m.
Converting the denoised mixture signal x (t) from the time domain to the frequency domain using a Short Time Fourier Transform (STFT), and if the STFT window is long enough to contain the major part of the impulse response, the convolutional mixture model can be approximated as a linear instantaneous mixture model at each frequency:
x(t,f)＝H(f)s(t,f) (8)
wherein H (f) [ < h >1(f),h2(f),···,hN(f)]Is a frequency domain filter.
And step 3: the single source point extraction method based on sparse coding and the vibration source number identification method based on the density peak value clustering method realize effective estimation of the mixing matrix.
And extracting the single source point by adopting a sparse coding method. When a certain time frequency point is a single source point, the time frequency vector of the time exists in the one-dimensional space. All time-frequency vectors are combined to form a matrix U (t, f) ═ x1(t,f),···,xK(t,f)]Then xi(t, f) x can be divided by U (t, f)iVectors other than (t, f) are encoded, i.e.:
xi(t,f)＝U(f)c,s.t.ci＝0 (9)
the identification problem of a single source point can be translated into the following l0Norm optimization problem:
min||c||0,s.t.xi(t,f)＝U(f)c,ci＝0 (10)
when c is sufficiently sparse, it can be converted to l1Norm optimization problem, and in turn translates into:
Figure BDA0002844046290000061
after the single source point is obtained, clustering the single source point to obtain the estimation of the mixed matrix, wherein the information expressed by each clustering center is the estimation of one column vector of the mixed matrix, namely:
Figure BDA0002844046290000062
wherein, yi(i ═ 1,2, ·, K) denotes the extracted single source points, and the number of classes is the number of source signals. The basis of this algorithm is to assume that the cluster center is surrounded by a neighborhood with a lower local density and is at a greater distance from a point with a higher local density.
Using Euclidean distance, yi，yjThe distance between is expressed as:
dij＝||yi-yj||2,1≤i,j≤K and i≠j (13)
data point distance dijSatisfying the triangle inequality.
Local density ρ of data point iiIs defined as:
Figure BDA0002844046290000071
wherein, when x<When 0, x (x) is 1, otherwise, x (x) is 0; dcIs the cut-off distance. RhoiIndicating small distance from point iAt dcThe number of points of (2). The algorithm is sensitive only to the relative size of the different points, which means that for large data the analysis results are for dcIs robust.
Local density ρ for each data point i by probability density methodiCalculated and sorted in descending order and using subscript q1,q2,···,qKIdentification, i.e.
Figure BDA0002844046290000072
For each data point i, the distance between the point and all points with a density greater than the density is calculated, wherein the minimum distance δ between the data point i and other points with a higher density is calculatediIs obtained by calculating the minimum distance between point i and other points of higher density:
Figure BDA0002844046290000073
so that each data point has two distances d from the data point onlyijThe relevant characteristic attributes: local density ρiThe minimum distance delta between the point i and other points of higher densityi. These two attributes are presented in the form of a decision graph, as shown in fig. 2 and 3, the decision graph can divide data points into three categories: density peak points, normal points and outliers. Some data points, e.g., points 2, 11, have larger ρiAnd a larger deltaiValues, indicating that there are no more dense data points than they are in the larger neighborhood range, and thus such points belong to the density peak points, suitably defined as cluster centers. Having a large rhoiAnd a smaller deltaiValues, indicating that there are more dense data points than they are in a smaller neighborhood, and thus such points do not belong to the density peak points, nor are they suitable to be defined as cluster centers. Yet another type of dots, such as dots 1,9,12, has a smaller ρiAnd a larger deltaiValues, such points are less dense and no more dense data points than they are in a larger neighborhood, and thus belong to outliers.
DPC pair dcIs robust, d can be selectedcSuch that the average number of clusters is about 1% -2% of the total number of data points. In this item, the ratio is set to 2%. In addition, the cluster can be identified regardless of the shape of the cluster and the dimension of the embedding space, and the distance in equation (13) needs to be calculated only once. Therefore, DPC has the advantages of few parameters, high efficiency, easy implementation, etc.
And 4, step 4: restoring the source signal by a compressed sensing method to obtain a separated signal: a norm optimization method based on Gaussian function approximation estimates a source signal, and a smooth parameter selection method is researched, so that the problem of low source estimation precision caused by insufficient sparsity of the signal is solved, and further effective extraction of a fault signal under an underdetermined condition is realized.
The compressed sensing mathematical model is shown as formula (16), and a signal s with the length n can be projected into a sparse space with sparsity through a sparse basis V (n × n). At this time, although the length of the coefficient signal x is still n, due to sparsity, there are only k main elements (k < < n) far greater than zero, and the rest elements are zero or close to zero. The main elements in the source signal are preserved and the length is compressed, as observed by the observation matrix U (m × n).
y(y1,y2,···,yn)T＝Ux＝UVs＝Ws (16)
Wherein y represents a compressed signal of length m, and m < n; the sensing matrix W (m × n) ═ UV. And the compression reconstruction process is the inverse process of the compressed sensing.
Due to the presence of undercharacterization, the number of mixed signals m is smaller than the number of source signals n, which is precisely the prerequisite for solving the underdetermined blind source separation with a compressed perceptual model. Taking m-2 as an example, with the compressed sensing model, a one-dimensional mixed signal must be constructed first. So that two mixed signals of length t can be converted into y ═ (y)11,y12,···,y1t,y21,y22,···,y2t)T。
Next, an estimation matrix obtained by using equation (12)
Figure BDA0002844046290000081
To construct the sensing matrix W. From the compressed sensing model, when the signal y (mt × 1) is mixed, the sensing matrix is W (mt × nt). So using the identity matrix EiTo expand the estimation matrix
Figure BDA0002844046290000082
Of (2), i.e.
Figure BDA0002844046290000083
The specific conversion is as follows:
Figure BDA0002844046290000084
wherein the reconstructed signal x ═ (x)11,x12,···,x1t,···,xn1,xn1,···,xnt)TThe dimension is (nt × 1). To this end, the reconstruction model for underdetermined blind source separation has been fully established.
Smoothing l0Norm is defined as
Figure BDA0002844046290000085
Wherein:
Figure BDA0002844046290000086
the smaller the smoothing parameter σ, the closer F(s) is to l0Norm, but the less smooth the function, the less likely it is to converge when optimizing the parameter using its gradient. Therefore, the initial value of σ is large, and the value of σ gradually decreases with the iterative process. And the source signal is estimated using the following equation:
Figure BDA0002844046290000087
s←s-HT(HHT)(Hs-x) (21)
alternately updating equation (20) and equation (21) results in an estimate of the source signal under-determined conditions.
And 5: and carrying out order and amplitude correction on the acquired separation signals of each frequency band, and then converting the separation signals from a frequency domain into a time domain.
Due to uncertainty in the order of the separated signals within each band and amplitude ambiguities, order and amplitude corrections are made to the separated signals for each band before converting them from the frequency domain to the time domain. And finally, converting the obtained source signal in the time-frequency domain into a time domain through inverse short-time Fourier transform to obtain a time domain form of the source signal.

Claims (4)

1. A gear vibration information source underdetermined blind source separation method based on density and compressed sensing is characterized by comprising the following steps:
(1) carrying out denoising pretreatment on the acquired signal by adopting a wavelet denoising method;
(2) short-time Fourier transform is used for the mixed signals, and a linear convolution mixed model in a time domain is converted into a linear instantaneous mixed model in each frequency band;
(3) the single source point extraction method based on sparse coding and the vibration source number identification method based on the density peak value clustering method realize effective estimation of a mixed matrix;
(4) restoring the source signal by a compressed sensing method to obtain a separated signal:
(5) and (4) carrying out order and amplitude correction on the separated signals of each frequency band acquired in the step (4), and then converting the separated signals from a frequency domain into a time domain.
2. The gear vibration source underdetermined blind source separation method based on density and compressed sensing according to claim 1, wherein the step (2) is implemented as follows:
the linear convolution mixture model is:
Figure FDA0002844046280000011
where x (t) represents an m-dimensional discrete-time signal received at time t, and x (t) ([ x ])1(t),x2(t),…,xm(t)]T(ii) a s (t) represents an n-dimensional discrete time signal emitted at time t, and s (t) is s1(t),s2(t),…,sn(t)]T；HpAn mxn-dimensional hybrid coefficient matrix representing a time delay of p; v (t) represents the noise signal at time t; denotes the convolution operator;
transform equation (5) to the z-domain:
x(z)＝H(z)s(z)+v(z) (6)
where H (z) is an m × n order matrix:
Figure FDA0002844046280000012
wherein h isji(p) represents filter coefficients of the hybrid filter from the ith source to the jth observation, i being 1 to n, and j being 1 to m;
converting the denoised mixture signal x (t) from the time domain to the frequency domain using a short-time fourier transform, approximating a linear convolution mixture model as a linear instantaneous mixture model at each frequency:
x(t,f)＝H(f)s(t,f) (8)
wherein h (f) ═ h1(f),h2(f),…,hN(f)]Is a frequency domain filter.
3. The gear vibration source underdetermined blind source separation method based on density and compressed sensing according to claim 1, wherein the step (3) is implemented as follows:
all time-frequency vectors are combined to form a matrix U (t, f) ═ x1(t,f),…,xK(t,f)]Then xi(t, f) x can be divided by U (t, f)iVectors other than (t, f) are encoded, i.e.:
xi(t,f)＝U(f)c,s.t.ci＝0 (9)
the problem of identifying a single source point translates to0Norm optimization problem:
min||c||0,s.t.xi(t,f)＝U(f)c,ci＝0 (10)
when c is sufficiently sparse, it is converted to l1Norm optimization problem, and in turn translates into:
Figure FDA0002844046280000021
after the single source point is obtained, clustering the single source point to obtain the estimation of the mixed matrix, wherein the information expressed by each clustering center is the estimation of one column vector of the mixed matrix, namely:
Figure FDA0002844046280000022
wherein, yi(i ═ 1,2, …, K) denotes the extracted single source points, and the number of classes is the number of source signals.
4. The gear vibration source underdetermined blind source separation method based on density and compressed sensing according to claim 1, wherein the step (4) is implemented as follows:
the compressed sensing mathematical model is as follows:
y(y1,y2,…,yn)T＝Ux＝UVs＝Ws (16)
wherein y represents a compressed signal with a length of m, m is less than n, a sensing matrix W (m × n) is UV, and a compression reconstruction process is an inverse process of obtaining a compressed sensing;
two mixed signals of length t can be converted into y ═ (y)11,y12,…,y1t,y21,y22,…,y2t)T；
Using estimation matrices
Figure FDA0002844046280000023
To construct a sensing matrix W, which is W (m) when the signal y (mt × 1) is mixed according to the compressed sensing modelt × nt), using an identity matrix EiTo expand the estimation matrix
Figure FDA0002844046280000031
Of (2), i.e.
Figure FDA0002844046280000032
The specific conversion is as follows:
Figure FDA0002844046280000033
wherein the reconstructed signal x ═ (x)11,x12,…,x1t,…,xn1,xn1,…,xnt)TDimension is (nt × 1);
smoothing l0Norm is defined as
Figure FDA0002844046280000034
Wherein:
Figure FDA0002844046280000035
the smaller the smoothing parameter σ, the closer F(s) is to l0Norm, the initial sigma value is large, the sigma value is gradually reduced along with the iteration process, and the source signal is estimated by adopting the following formula:
s←s-μ▽sF(s) (20)
s←s-HT(HHT)(Hs-x) (21)
alternately updating equation (20) and equation (21) results in an estimate of the source signal under-determined conditions.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113095394A (en) * 2021-04-07 2021-07-09 深圳大学 Underdetermined blind source separation method based on robust clustering particle swarm optimization
CN113252929A (en) * 2021-07-05 2021-08-13 格创东智(深圳)科技有限公司 Rotating speed determination method and device, electronic equipment and computer readable storage medium
CN113406441A (en) * 2021-07-27 2021-09-17 天津大学 Flexible direct-current power grid fault location method based on clustering and iterative algorithm

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107301434A (en) * 2017-07-28 2017-10-27 西安交通大学 Blind separation hybrid matrix method of estimation based on synchronous compression Short Time Fourier Transform
CN109711468A (en) * 2018-12-27 2019-05-03 西安交通大学 A kind of complex value blind separation hybrid matrix estimation method based on single source point
WO2019169544A1 (en) * 2018-03-06 2019-09-12 大连理工大学 Sparse component analysis method for structural modal identification during quantity insufficiency of sensors

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107301434A (en) * 2017-07-28 2017-10-27 西安交通大学 Blind separation hybrid matrix method of estimation based on synchronous compression Short Time Fourier Transform
WO2019169544A1 (en) * 2018-03-06 2019-09-12 大连理工大学 Sparse component analysis method for structural modal identification during quantity insufficiency of sensors
CN109711468A (en) * 2018-12-27 2019-05-03 西安交通大学 A kind of complex value blind separation hybrid matrix estimation method based on single source point

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
王飞宇;胡志祥;黄潇;: "基于密度峰值聚类算法的模态参数识别", 振动与冲击, no. 02, 28 January 2019 (2019-01-28) *

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113095394A (en) * 2021-04-07 2021-07-09 深圳大学 Underdetermined blind source separation method based on robust clustering particle swarm optimization
CN113095394B (en) * 2021-04-07 2023-09-22 深圳大学 Underdetermined blind source separation method based on robust cluster particle swarm optimization
CN113252929A (en) * 2021-07-05 2021-08-13 格创东智(深圳)科技有限公司 Rotating speed determination method and device, electronic equipment and computer readable storage medium
CN113406441A (en) * 2021-07-27 2021-09-17 天津大学 Flexible direct-current power grid fault location method based on clustering and iterative algorithm
CN113406441B (en) * 2021-07-27 2022-07-05 天津大学 Flexible direct-current power grid fault location method based on clustering and iterative algorithm

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