Impulse noise resistant robust DOA (direction of arrival) estimation method and monitoring system for power grid safety

Abstract

The invention discloses a power grid security-oriented anti-impulse noise robust DOA estimation method and monitoring system, and the method comprises the steps: collecting a fault position signal through a nested array antenna, and obtaining the information of a received signal; establishing a p-order bounded nonlinear function, performing exponential kernel operation on received signal information, and calculating an equivalent exponential kernel covariance matrix; vectorizing the covariance matrix to obtain a virtual received signal; and removing redundancy of the virtual received signal, obtaining virtual uniform array information, constructing a spatial smooth matrix, obtaining an estimated value of the DOA by adopting a MUSIC method, and outputting DOA direction angle estimation of a spectral peak position of a fault position signal. According to the invention, the problems of low positioning precision, slow response speed and disjunction with power grid safety protection under impulse noise in a traditional method can be solved.

Description

TECHNICAL FIELD

[0001] The technical field of the present application belongs to the field of power system security and array signal processing, and more specifically, it is a kind of anti-pulse noise robust DOA estimation method and monitoring system for power grid security. BACKGROUND

[0002] As one of the most important infrastructures in modern society, the stability and security of the power grid are crucial for the normal operation of the entire society. Therefore, it is particularly important to monitor various electromagnetic interferences and threats that may occur during the operation of the power grid in real time. These interferences may come from natural phenomena such as lightning, or from internal operations of the power grid, such as switch operations, or from noise generated by industrial equipment. In addition, the power grid also faces the threat of malicious attacks, which may include the access of illegal equipment or the injection of instructions through wireless means, all of which can interfere with or damage the normal operation of the power grid.

[0003] To address these challenges, traditional Direction of Arrival (DOA) algorithms, such as MUSIC (Multiple Signal Classification) and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques), have shown excellent performance in dealing with signal source positioning problems in Gaussian noise environments. However, these traditional algorithms perform significantly worse when faced with the pulse noise commonly found in power grids. Pulse noise usually follows an alpha-stable distribution, which is characterized by a thick tail, meaning it contains more outliers or sudden interferences. Therefore, when using traditional DOA algorithms to process this noise, the positioning of interference sources may be biased, or even missed, which undoubtedly poses a serious threat to the stable operation of the power grid.

[0004] However, there are many limitations in the existing technology:

[0005] In view of the characteristics of pulse noise in power grid security monitoring, traditional DOA estimation methods are obviously unable to meet the actual needs. The high proportion of pulse noise greatly reduces the performance of traditional algorithms based on Gaussian noise assumption. Therefore, it is particularly important to develop a robust DOA estimation algorithm that is resistant to pulse noise. This new algorithm needs to be able to accurately estimate the direction of the signal source in a complex noise environment, while improving the utilization of the array aperture, thereby improving the accuracy and reliability of power grid security monitoring.

[0006] The existing three methods of symbol covariance based on nested array, phase fractional low-order moment and infinite norm rely on low-order statistics or nonlinear transformation, but the covariance matrix is easily polluted by impulse noise, and the direction finding resolution is reduced. SUMMARY

[0007] In order to solve the above-mentioned deficiencies in the prior art, the purpose of the present application is to provide an anti-impulse noise robust DOA estimation method and monitoring system for power grid safety, which solves the problems of low positioning accuracy, slow response speed and disconnection with power grid safety protection of traditional methods under impulse noise.

[0008] The technical scheme adopted by the present application is:

[0009] The anti-impulse noise robust DOA estimation method and monitoring system for power grid safety comprise the following steps:

[0010] Step S1, acquiring fault position signal s(t) by nested array antenna, and obtaining received signal information x(t);

[0011] Step S2, establishing a p-order bounded nonlinear function, performing exponential kernel operation on the received signal information x(t), and calculating the equivalent exponential kernel covariance matrix E EKO ;

[0012] Step S3, vectorizing the E EKO matrix to obtain virtual received signal z;

[0013] Step S4, de-redundantizing the virtual received signal z to obtain virtual uniform array information and constructing a spatial smoothing matrix R o , using the MUSIC method to obtain the estimation value of DOA, and outputting the DOA direction angle estimation of the spectral peak position of s(t).

[0014] The nested array element position set of the nested array antenna is:

[0015]

[0016] Wherein N1 and N2 are the number of elements, the uniform linear array element spacing of the element number N1 is d0, and the element spacing of the element number N2 is (N1+1)d0, wherein d0=λ / 2 is half wavelength;

[0017] Let be the index order of the nested array element position; wherein sort(·) is the small-to-large ordering operation, and P=N1+N2.

[0018] Suppose there are K DOAs respectively θ k ​When the narrowband signal s(t) of k=k,1,2,…,K is incident on the nested array, the array received signal information is represented as:

[0019] x(t)=As(t)+n(t)

[0020] where A=[a(θ1),…,a(θ K )] is the direction matrix, is the direction vector of the kth signal, and j is the imaginary unit; n(t) is the impulse noise obeying the symmetric alpha stable distribution, and s(t) is the signal vector.

[0021] The p-order bounded nonlinear function is represented as:

[0022] f(x)=x|x| p-2 ,x≠0,

[0023] where x is a complex constant, || represents the absolute value operation, and 1<p<2 is the order parameter.

[0024] The (s, r)th element of the equivalent exponential kernel covariance matrix E EKO is represented as:

[0025]

[0026] where s, r=1,…,P, z s (t) represents the s th element of the vector z(t), z r (t) represents the r th element of the vector z(t), and z(t)=f(x(t)), T represents the total number of time-domain snapshots, is the estimated covariance of the signal s(t).

[0027] The E EKO matrix is vectorized by the nested array technology to obtain the virtual received signal z:

[0028]

[0029] where vec(·) represents the vectorization operation, is the virtual array direction matrix, represents the signal energy, represents the approximate covariance of the impulse noise, I P is a P×P unit matrix.

[0030] The virtual received signal z is de-redundant to obtain the virtual uniform array information including:

[0031] The virtual received signal z is de-redundant to obtain the virtual uniform array information

[0032]

[0033] wherein is a virtual uniform array direction matrix, G=N1(N2+1)-1, is a vector with 1 as the center element and 0 at other positions.

[0034] The construction space smoothing matrix R o adopts the MUSIC method to obtain the estimated value of DOA, comprising:

[0035] Constructing a virtual uniform array information smoothing matrix R o :

[0036]

[0037] wherein [ ] H represents a conjugate operation, and Q=N1(N2+1) is the number of array elements of the smoothing subarray, represents a subvector of ;

[0038] After eigenvalue decomposition, the noise subspace U N is obtained; the MUSIC spectrum peak search function is used to obtain the signal DOA estimation:

[0039]

[0040] wherein θ is the spectrum peak search grid value, and the search direction vector a(θ)=[1,e -jπsinθ ,…,e -j(Q-1)πsinθ ] T ;

[0041] Finally, the output s(t) is the DOA direction angle estimation at the spectrum peak position.

[0042] The anti-impulse noise robust DOA estimation method and monitoring system for power grid safety comprise a nested array antenna, a cloud server and an upper computer arranged in a power grid environment;

[0043] The nested array antenna is used for real-time acquisition of fault position signals and conversion into received signal information uploaded to the cloud server;

[0044] The cloud server is provided with a processor and a memory, the memory stores a signal processing program, the processor loads the program to execute the method steps as described above, and the signal DOA direction angle estimation value is sent to the upper computer;

[0045] The upper computer is provided with a power grid monitoring platform, which is used for man-machine interaction to collect user instructions to control the nested array antenna to collect data, control the cloud server to execute a signal processing program to calculate a DOA direction angle estimation value, and display a process and result data, and receive an operation user input fault mark.

[0046] The power grid monitoring platform comprises a front-end interface and a background control end.

[0047] The front-end interface is used for collecting parameters and instructions and sending the parameters and instructions to the background control end, and visualizing and displaying a graph.

[0048] The background control end generates a visualized graph according to process and result data in DOA direction angle estimation calculation of the cloud server.

[0049] The present application has the following advantages and benefits:

[0050] The method can significantly improve the positioning ability in a complex noise environment. Specifically, the method can not only effectively suppress the influence of impulse noise, but also improve the information amount of the array received signal, so that a more accurate DOA estimation value can be obtained under a lower signal-to-noise ratio condition. In addition, by combining with the MUSIC method, the stability and accuracy of the algorithm are further enhanced, and a more reliable guarantee is provided for power grid safety monitoring. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 is a system architecture diagram of the present application.

[0052] Figure 2 is a virtual array structure schematic diagram of the nested array of the present application.

[0053] Figure 3 is a log space spectrum diagram obtained by using the method of the present application.

[0054] Figure 4 is a root mean square error performance comparison diagram of all algorithms under different generalized signal-to-noise ratios.

[0055] Figure 5 is a root mean square error performance comparison diagram of all algorithms under different snapshot numbers.

[0056] Figure 6 is a root mean square error performance comparison diagram of all algorithms under different characteristic exponents. DETAILED DESCRIPTION

[0057] In order to make the above objectives, characteristics and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are described in detail below in conjunction with the drawings. In the following description, a large number of specific details are set forth in order to facilitate a thorough understanding of the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the spirit of the present application, so the present application is not limited to the specific implementations disclosed below.

[0058] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs. The terminology used in the description of the application herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0059] The present application is particularly concerned with an innovative robust direction of arrival (DOA) estimation algorithm and its accompanying monitoring system. This technology is designed to address the challenges posed by impulsive noise environments in power grids. By employing the algorithm and system in the present application, the positioning accuracy of power grid interference sources can be significantly improved, the ability of equipment fault detection can be enhanced, and the monitoring efficiency of security threats can be improved.

[0060] I. Electromagnetic interference noise model

[0061] In traditional direction of arrival (DOA) methods, Gaussian noise assumption is usually adopted to process signals. However, the actual application often does not conform to this assumption, especially in radar electronic countermeasures, underwater acoustic detection and other various signal processing scenarios, where impulsive noise accounts for a considerable proportion. To address this problem, the present application proposes a new method, i.e., using symmetric alpha stable distribution to accurately model impulsive noise. Symmetric alpha stable distribution is a more general noise model that can better describe impulsive noise with heavy-tailed characteristics. The definition of its characteristic function is as follows:

[0062] φ(u) = exp(-γ|u| α )

[0063] In the above definition, u represents the variable of the characteristic function, 0 < α ≤ 2 is the characteristic exponent, which determines the thickness of the tail of the distribution, and γ represents the dispersion parameter, which plays a similar role to the variance in Gaussian distribution in symmetric alpha stable distribution, used to describe the dispersion degree of the signal.

[0064] II. Fault location method

[0065] The present embodiment provides an anti-impulse noise robust DOA estimation algorithm and monitoring system for power grid security, including the following steps:

[0066] (1) Receiving fault position signals through a nested array antenna to obtain received signal information x(t);

[0067] (2) Establishing a p-order bounded nonlinear function, substituting the received signal information x(t) into and performing an exponential kernel operation to calculate an equivalent exponential kernel covariance matrix E EKO ;

[0068] (3) Vectorizing the E EKO matrix to obtain virtual received signal z;

[0069] (4) Removing redundancy from the virtual received signal z to obtain virtual uniform array information and constructing a spatial smoothing matrix R o , and then using a MUSIC method to obtain an estimated value of DOA.

[0070] The specific steps are as follows:

[0071] Step (1): Receiving fault position signals through a nested array antenna to obtain received signal information x(t).

[0072] The nested array element position set adopted by the application is as follows:

[0073]

[0074] Wherein N1 and N2 are the number of elements, the element spacing of the uniform linear array with the number of elements N1 is d0, and the element spacing of the array with the number of elements N2 is (N1+1)d0, wherein d0 = λ / 2 is half the wavelength.

[0075] Let sort(·) is a sorting operation from small to large, and P = N1+N2.

[0076] Suppose that K narrowband signals s(t) with DOAs θ k , k = 1, 2, …, K are incident on the nested array, then the array received signal information is represented as:

[0077] x(t) = As(t) + n(t)

[0078] Wherein A = [a(θ1), …, a(θ K )] is a direction matrix, is the direction vector of the kth signal, j is an imaginary unit; n(t) is impulse noise obeying symmetric alpha stable distribution, and s(t) is a signal vector.

[0079] Step (2): Establishing a p-order bounded nonlinear function, substituting the received signal information x(t) into and performing an exponential kernel operation to calculate an equivalent exponential kernel covariance matrix E EKO .​

[0080] A pth-order bounded nonlinear function can be represented as

[0081] f(x) = x |x| p-2 , x≠0,

[0082] where x is a complex constant, || denotes the absolute value operation, and 1 < p < 2 is the order moment parameter. Next, the equivalent exponential kernel covariance matrix E is calculated EKO , whose (s, r)th element is represented as

[0083]

[0084] where s, r = 1, …, P, and z s (t) represents the sth element of the vector z(t), z r (t) represents the rth element of the vector z(t), and z(t) = f(x(t)), T represents the total number of time-domain snapshots, is the estimated covariance of the signal s(t).

[0085] Step (3): Vectorize the E EKO matrix to obtain the virtual received signal z.

[0086] Process the E EKO matrix through the nested array technique to obtain the virtual received signal z:

[0087]

[0088] where vec(·) represents the vectorization operation, is the virtual array steering matrix, represents the signal energy, represents the impulse noise approximate covariance, I P is a P × P identity matrix.

[0089] Step (4): De-redundant the virtual received signal z to obtain the virtual uniform array information and construct the spatial smoothing matrix R o , and then use the MUSIC method to obtain the estimated value of the DOA.

[0090] For the virtual received signal z, the virtual array information of the continuous array elements is intercepted to obtain the virtual uniform array information with an array element spacing of half a wavelength

[0091]

[0092] where is the virtual uniform array steering matrix, and G = N1(N2+1)-1. A vector with 1 as the center element and 0 at other positions.

[0093] Since the spatial smoothing algorithm usually requires that the array is a uniform linear array, the smoothing matrix R o :

[0094]

[0095] where H represents the conjugate operation, and Q=N1(N2+1) is the number of array elements of the smoothing subarray, represents the subvector of .

[0096] The covariance matrix R o is obtained, and then the noise subspace U N is obtained by eigenvalue decomposition. The signal DOA estimation can be obtained by the MUSIC spectrum peak search function:

[0097]

[0098] where θ is the spectrum peak search grid value, and the search direction vector a(θ)=[1,e -jπsinθ ,…,e -j(Q-1)πsinθ ] T .

[0099] III. Experimental simulation analysis and performance analysis

[0100] 1. Theoretical analysis

[0101] (1) The suppression ability of the method of the application to the diagonal line outliers of the matrix

[0102] Let x s (t) = x r (t) = a + bj, and x (t) = a - bj. The (s,s) element of the matrix E EKO is

[0103]

[0104] For z s (t), there are

[0105]

[0106] Similarly, there are Then the exponential term satisfies

[0107]

[0108] Taking the absolute value, we get

[0109]

[0110] When a or b is an outlier, the exponential term decays rapidly, thus suppressing diagonal outliers.

[0111] (2) The ability of the method of the present invention to suppress matrix off-diagonal outliers

[0112] Let x s (t)=a+bj,x r (t)=c-dj, there is

[0113]

[0114] Then the matrix E EKO The (s,r)th element of is

[0115]

[0116] For z s (t),z r (t), yes Then the exponential term satisfies

[0117]

[0118] It's definitely worth it

[0119]

[0120] Therefore, off-diagonal outliers are also suppressed.

[0121] 2. Experimental Configuration and Evaluation Indicators

[0122] The generalized signal-to-noise ratio under impulse noise is defined as The performance metric is the joint root mean square error (RMSE), which is defined as follows:

[0123]

[0124] in is the precise estimate of the DOA of the kth source in the jth MC trial, K represents the number of sources, and MC represents the number of Monte Carlo trials.

[0125] 3. Key experimental results

[0126] The method of the present invention is compared with existing methods. The existing methods: phase fractional low-order moment method, signed covariance method and infinite norm method, are all based on nested array background.

[0127] like Figure 1The figure shows the system architecture of the present invention. The present invention also provides a robust DOA estimation method and monitoring system for power grid security that is resistant to impulse noise, including: nested array antennas, a cloud server, and a host computer, located within a power grid environment. The nested array antennas are used to collect fault location signals in real time, convert them into received signal information, and upload them to the cloud server. The cloud server is equipped with a processor and memory, wherein the memory stores a signal processing program. The processor loads the program and executes the method steps to obtain a signal DOA direction angle estimate and transmit it to the host computer. The host computer is equipped with a power grid monitoring platform for human-computer interaction to collect user instructions, control the nested array antennas to collect data, control the cloud server to execute the signal processing program to calculate the DOA direction angle estimate, and display the process and result data. After the host computer obtains the DOA estimate, an operator checks the location indicated by the angle to determine whether there is a fault.

[0128] like Figure 2 , which is a schematic diagram of the virtual array structure of the nested array of the present invention (where N1=3, N2=4); it can be seen that the position of the virtual array is located at [-N2(N1+1)+1, N2(N1+1)-1]d0, that is, [-15d_0, 15d_0], and there is no hole.

[0129] like Figure 3 Figure 2 shows the logarithmic-space spectrum obtained using the proposed method when 17 signal sources are incident on a nested array with DOAs of -40°, 5°, and 40° at 5° intervals. The nested array has N1 = 4, N2 = 5 elements, T = 500 snapshots, and GSNR = 10 dB. The moment parameter p = 0.9, and the impulse noise exponent α = 1.5, demonstrates that the proposed method can estimate the DOA of all signals.

[0130] like Figure 4 The figure shows the performance comparison of the algorithms under different GSNR conditions when α = 0.5 and snapshot T = 500. 1000 MC experiments were run with the azimuth angles of the three signal sources at [-10°, 20°, and 30°]. It can be seen that under the same generalized signal-to-noise ratio conditions, the proposed method has better DOA estimation performance.

[0131] like Figure 5 The figure shows a performance comparison of algorithms under different snapshot numbers when α = 0.5 and GSNR = 0dB. 1000 MC experiments were run with three signal sources at azimuth angles of [-10°, 20°, and 30°]. It can be seen that the performance of the proposed method improves with increasing snapshot numbers. Under the same snapshot conditions, the proposed method outperforms other methods in estimation performance.

[0132] like Figure 6It is shown that, in the case of GSNR=0dB and snap T=500, the algorithm performance comparison under different characteristic indexes, 1000 times of MC experiments, and the azimuth angles of 3 sources are [-10°, 20°, 30°]. It can be seen that the performance of the application is improved with the increase of the characteristic index, and under the same characteristic index, the estimation performance of the application is the best.

[0133] In summary, from the analysis of the simulation effect diagram, the method of the application realizes the accurate DOA estimation in the nested array pulse noise environment, improves the degree of freedom, and compared with the existing method, the estimation performance of the method of the application is better.

[0134] The embodiments of the application are described in detail above in combination with the drawings, but the application is not limited to the above-mentioned embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the purpose of the application.

Claims

1. A robust DOA estimation method and monitoring system for power grid security against impulse noise, characterized by: It includes the following steps: Step S1: Collect the fault location signal s(t) through the nested array antenna to obtain the received signal information x(t); Step S2: Establish a p-order bounded nonlinear function, perform an exponential kernel operation on the received signal information x(t), and calculate the equivalent exponential kernel covariance matrix E EKO ; Step S3: E EKO The matrix is ​​vectorized to obtain the virtual received signal z; Step S4: Remove redundancy from the virtual received signal z and obtain virtual uniform array information And construct the spatial smoothing matrix R o , the MUSIC method is used to obtain the estimated value of DOA, and the DOA direction angle estimation of the spectrum peak position of s(t) is output.

2. A robust DOA estimation method and monitoring system for power grid security against impulse noise, characterized by: The nested array element position set of the nested array antenna for: Among them, N1 and N2 are the number of array elements. The element spacing of the uniform linear array with the number of array elements N1 is d0, and the element spacing of the array with the number of array elements N2 is (N1 + 1)d0, where d0 = λ / 2 is the half wavelength; make As the index sorting of the nested array element positions; where sort(·) is an ascending order sorting operation, P=N1+N2.

3. A robust DOA estimation method and monitoring system for power grid security against impulse noise, characterized by: Assume there are K DOAs, each of which is θ k , k=1,2,…,K narrowband signal s(t) is incident on the nested array, then the array received signal information is expressed as: x(t) = As(t) + n(t) where A=[a(θ1),…,a(θ K )] is the direction matrix, is the direction vector of the kth signal, j is the imaginary unit; n(t) is the impulse noise that obeys the symmetric α-stable distribution, and s(t) is the signal vector.

4. A robust DOA estimation method and monitoring system for power grid security against impulse noise, characterized in that: The p-order bounded nonlinear function is expressed as: f(x)=x|x| p-2 ,x≠0, where x is a complex constant, | | represents the absolute value operation, and 1 < p < 2 is the moment parameter.

5. A robust DOA estimation method and monitoring system for power grid security against impulse noise, characterized by: The equivalent exponential kernel covariance matrix E EKO The (s,r)th element of is represented as: where s, r=1,…,P,z s (t) represents the sth element of the vector z(t), z r (t) represents the rth element of the vector z(t), and z(t) = f(x(t)), T represents the total number of time domain snapshots, is the estimated covariance of the signal s(t).

6. A robust DOA estimation method and monitoring system for power grid security against impulse noise, characterized in that: The E EKO The matrix is ​​vectorized by using nested array technology to obtain the virtual received signal z: Where vec(·) represents a vectorized operation, is the virtual array direction matrix, represents the signal energy, represents the approximate covariance of impulse noise, I P is the P×P identity matrix.

7. A robust DOA estimation method and monitoring system for power grid security against impulse noise, characterized in that: The virtual receiving signal z is de-redundant to obtain virtual uniform array information include: For the virtual received signal z, the virtual array information of the continuous array element part is intercepted to obtain the virtual uniform array information with an array element spacing of half a wavelength. in is the virtual uniform array direction matrix, G = N1(N2+1)-1, A vector with a 1 at the center and 0s elsewhere.

8. A robust DOA estimation method and monitoring system for power grid security against impulse noise, characterized in that: The constructed spatial smoothing matrix R o , the MUSIC method is used to obtain the estimated value of DOA, including: Constructing virtual uniform array information The smoothing matrix R o : in[ ] H represents the conjugate operation, and Q = N1(N2+1) is the number of elements of the smoothing sub-matrix, express subvector of ; The noise subspace U is obtained by eigenvalue decomposition N ; Use the MUSIC spectrum peak search function to obtain the signal DOA estimate: Where θ is the peak search grid value, and the search direction vector a(θ) = [1,e -jπsinθ ,…,e -j(Q-1)πsinθ ] T ; Finally, output the DOA direction angle estimation at the spectral peak position of s(t).

9. A robust DOA estimation method and monitoring system for power grid security against impulse noise, characterized in that: It includes: A nested array antenna, a cloud server, and a host computer set in the power grid environment; The nested array antenna is used to collect the fault location signal in real time and convert it into the received signal information and upload it to the cloud server; The cloud server is provided with a processor and a memory. The memory stores a signal processing program. The processor loads the program and executes the method steps described in any one of claims 1-8 to obtain the DOA direction angle estimation value of the signal and send it to the host computer; The host computer is provided with a power grid monitoring platform, which is used for human-computer interaction to collect user instructions to control the nested array antenna to collect data, control the cloud server to execute the signal processing program to calculate the DOA direction angle estimation value, and display the process and result data.

10. The method and monitoring system for robust DOA estimation against impulse noise for power grid security according to claim 9, characterized in that: The power grid monitoring platform includes a front-end interface and a background control end: The front-end interface is used to collect parameters and instructions and send them to the background control end, and visually display the spectrum; The background control end generates a visual spectrum according to the process and result data in the DOA direction angle estimation calculation by the cloud server.

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