Circuit breaker vibration signal noise reduction method based on VMD-DTW
Technical Field
The invention relates to the technical field of high-voltage circuit breaker vibration signal processing, in particular to a VMD-DTW-based circuit breaker vibration signal noise reduction method.
Background
The circuit breaker is a basic element in a power system and plays a role in protection and control. It is the only element in the power system that allows changing the electrical topology in normal and abnormal modes (short circuit, asynchronous mode, equipment overload). Therefore, the operation state of the circuit breaker directly affects the safe and stable operation of the power system. At present, faults caused by various reasons can not be completely avoided in long-term operation of a circuit breaker, so that the operating state of the circuit breaker needs to be monitored and faults are found early, an effective high-voltage circuit breaker state evaluation system is developed and becomes an important task in power system management of power generation enterprises and power grid companies, and in recent years, a circuit breaker intelligent fault diagnosis system based on vibration signals gradually becomes a mainstream, and state-related features are extracted from the vibration signals and input into a trained diagnosis model to judge the operating state of the circuit breaker. The vibration signal is used as a non-invasive signal, is easy to obtain, contains state information of each part in the action process of the circuit breaker, and is easy to realize on-line monitoring. However, the vibration signal is easily interfered by a low-frequency local oscillator and a high-frequency electromagnetic of the circuit breaker in the acquisition and transmission process, and the acquired vibration signal is inevitably mixed with noise, which brings difficulty to feature extraction.
Therefore, a circuit breaker vibration signal noise reduction method based on the VMD-DTW is needed, and noise reduction processing is carried out before the vibration signal characteristic is extracted.
Disclosure of Invention
Therefore, the present invention is directed to a method for reducing noise of a circuit breaker vibration signal based on VMD-DTW, so as to solve the above problems occurring in the prior art.
A circuit breaker vibration signal noise reduction method based on VMD-DTW comprises the following steps:
s1: collecting vibration signals in the action process of the circuit breaker;
s2: decomposing the vibration signal into a plurality of bandwidth-limited modal components by the VMD;
s3: calculating the DTW distance between the modal component and the original signal, and selecting a related modal component according to the DTW distance;
s4: and accumulating all the selected related modal components to obtain a noise-reduced signal.
Further, the S2 specifically includes the following steps:
s21: the decomposition process of the VMD is to solve the following constrained variational problem:
in the formula ukDenotes the K-th modal component obtained by decomposition, K is 1,2, …, K, wkRepresents ukDelta (t) represents the dirac function, x (t) represents the vibration signal during the action of the circuit breaker,
introducing a quadratic penalty function term and Lagrange multipliers to convert the constrained variation problem into an unconstrained variation problem, and constructing an expression as follows:
wherein α represents a penalty factor, λ (t) represents a Lagrange multiplier;
the above variation problem is solved by using a multiplier alternation method, in the process, the modal component and the center frequency are continuously updated, and the expression of the updating process is as follows:
the update stops until the following convergence condition is satisfied:
where ε is the set convergence threshold,
s22: determining the number of VMD decomposition modal components according to a central frequency method, firstly setting the decomposition number as K-2, comparing the difference value of the central frequencies of the two decomposed modal components, and stopping decomposition if the difference value is less than a threshold value f (t), wherein the optimal modal component number is K-1; if the difference is greater than f (t), K is K +1, the original signal is decomposed again, and the difference of the center frequencies of two adjacent modal components, namely u, is continuously compared1And u2,u2And u3Difference between center frequencies; if the difference value of the central frequencies of the adjacent modal components is smaller than a threshold value f (t), the optimal modal component number is K-1; otherwise, decomposing the signal again until the central frequency difference is less than f (t), and decomposing the optimal modal component number K-1 by the VMD.
Further, the calculating the DTW distance between the modal component and the original signal specifically includes:
s31 constructing modal component u obtained by VMD decompositionkCost matrix D with the original signal:
wherein the elements of the matrix
Is the modal component u
kThe Euclidean distance between the ith element and the jth element in the original signal x;
s32, finding the optimal path DTW:
the optimal path can be found using the following equation:
where R (i, j) is the cumulative distance:
where i is 1,2, …, n, j is 1,2, as, n, R (0,0) is 0, and R (i,0) is R (0, j) is + ∞.
Further, the selecting of the relevant modal component according to the DTW distance specifically includes:
and sequencing the DTW distances of the modal components and the original signal in an ascending order, selecting the top K-2 modal components which are reordered as related modal components, and adding the selected related modal components, namely the signals subjected to noise reduction.
Compared with the prior art, the invention has the beneficial effects that:
before extracting the characteristics of the vibration signal of the circuit breaker, the vibration signal in the action process of the circuit breaker is collected, the vibration signal of the circuit breaker is decomposed into a plurality of modal components with limited bandwidth through the VMD, the number of the modal components is determined by a central frequency method, the DTW distance between the modal components and the original signal is calculated, relevant modal components are selected according to the DTW distance, all the selected relevant modal components are accumulated, and then the signal after noise reduction is obtained. The extraction of signal characteristics can be better carried out through making an uproar is fallen, help carrying out accurate monitoring to the running state of circuit breaker.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is apparent that the drawings in the following description are only preferred embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained based on these drawings without inventive efforts.
Fig. 1 is a flowchart of a circuit breaker vibration signal noise reduction method based on VMD-DTW according to an embodiment of the present invention.
Fig. 2 is a diagram of a circuit breaker normal state vibration signal of a circuit breaker vibration signal noise reduction method based on VMD-DTW according to an embodiment of the present invention.
Fig. 3 is a diagram of a vibration signal of loosening a screw of a base in a VMD-DTW-based method for reducing noise of a vibration signal of a circuit breaker according to an embodiment of the present invention.
Fig. 4 is a mode component diagram after decomposition of a vibration signal in a normal state of a circuit breaker based on a vibration signal noise reduction method of a circuit breaker of a VMD-DTW according to an embodiment of the present invention.
Fig. 5 is a mode component diagram of a circuit breaker base screw loosening vibration signal after decomposition according to a circuit breaker vibration signal noise reduction method based on VMD-DTW provided in an embodiment of the present invention.
Fig. 6 is a signal diagram after noise reduction of a circuit breaker normal state vibration signal of the circuit breaker vibration signal noise reduction method based on VMD-DTW according to the embodiment of the present invention.
Fig. 7 is a signal diagram after noise reduction of a base screw loosening vibration signal of a VMD-DTW-based breaker vibration signal noise reduction method according to an embodiment of the present invention.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, the illustrated embodiments are provided to illustrate the invention and not to limit the scope of the invention.
Example one
Referring to fig. 1, the present invention provides a circuit breaker vibration signal noise reduction method based on VMD-DTW,
the method comprises the following steps:
s1: collecting vibration signals in the action process of the circuit breaker;
s2: decomposing the vibration signal into a plurality of bandwidth-limited modal components by the VMD;
s3: calculating the DTW distance between the modal component and the original signal, and selecting a related modal component according to the DTW distance;
s4: and accumulating all the selected related modal components to obtain a noise-reduced signal.
Specifically, vibration signals in the action process of the circuit breaker are collected through a vibration sensor, vibration signals in the normal state and under the loosening of a base screw in the closing process of the 35kV circuit breaker are collected, the vibration sensor is installed at the position of a cross beam of the circuit breaker, and a data acquisition card works at the speed of 10kHz in each collection process300ms, the number of VMD decomposition modal components is determined according to the center frequency method, in this example, f (t) 300 Hz. Table 1 and table 2 show the modal component center frequency distributions obtained by decomposing the vibration signal under the normal state and the fault state under different K values, and it can be seen that when K is 8, u obtained by decomposing the vibration signal under the normal state5And u6The difference value of the base screw loosening vibration signal is 298.57Hz, and the u is obtained by decomposing the base screw loosening vibration signal1And u2The difference of (a) is 270.28Hz, and is less than f (t), therefore, the optimal K value should be set to be 7.
TABLE 1 centre frequency of modal component obtained by decomposing vibration signal in normal state at different K values
TABLE 2 centre frequency of modal component obtained by decomposing base screw loosening vibration signal at different K values
Fig. 4 is a modal component of the signal of fig. 2 after decomposition, and fig. 5 is a modal component of the signal of fig. 3 after decomposition.
The DTW distance of the component from the original signal is calculated and the result is shown in table 3, where the number in parentheses is the ordering result.
TABLE 3 normalized DTW distance of modal component from original signal
The first 5 signals are selected according to the ascending order of DTW distance for reconstruction, and the signals after noise reduction are obtained as shown in fig. 6 and 7, and compared with the original signals as shown in fig. 2 and 3, the noise is relieved, and the wave crest is more obvious.
The S2 specifically includes the following steps:
s21: the decomposition process of the VMD is to solve the following constrained variational problem:
in the formula ukDenotes the K-th modal component obtained by decomposition, K is 1,2, …, K, wkRepresents ukDelta (t) represents the dirac function, x (t) represents the vibration signal during the action of the circuit breaker,
introducing a quadratic penalty function term and Lagrange multipliers to convert the constrained variation problem into an unconstrained variation problem, and constructing an expression as follows:
wherein α represents a penalty factor, λ (t) represents a Lagrange multiplier;
the above variation problem is solved by using a multiplier alternation method, in the process, the modal component and the center frequency are continuously updated, and the expression of the updating process is as follows:
the update stops until the following convergence condition is satisfied:
where ε is the set convergence threshold,
s22: determination from the center frequency methodThe VMD decomposes the number of modal components, firstly setting the decomposition number as K-2, comparing the difference value of the center frequencies of the two modal components after decomposition, and stopping decomposition if the difference value is less than a threshold value f (t), wherein the optimal modal component number is K-1; if the difference is greater than f (t), K is K +1, the original signal is decomposed again, and the difference of the center frequencies of two adjacent modal components, namely u, is continuously compared1And u2,u2And u3Difference between center frequencies; if the difference value of the central frequencies of the adjacent modal components is smaller than a threshold value f (t), the optimal modal component number is K-1; otherwise, decomposing the signal again until the central frequency difference is less than f (t), and decomposing the optimal modal component number K-1 by the VMD.
The calculating the DTW distance between the modal component and the original signal specifically includes:
s31 constructing modal component u obtained by VMD decompositionkCost matrix D with the original signal:
wherein the elements of the matrix
Is the modal component u
kThe Euclidean distance between the ith element and the jth element in the original signal x;
s32, finding the optimal path DTW:
the DTW distance is obtained under the best match of the two signals, the best match can be obtained by converting the best match into finding an optimal path, that is, finding a path from the cost matrix D, so that the cumulative distance of elements in the two signals along the path is the minimum, the smaller the DTW distance is, the higher the similarity between the two time series is, and based on the idea of dynamic warping, the optimal path can be obtained by using the following formula:
where R (i, j) is the cumulative distance:
where i is 1,2, …, n, j is 1,2, as, n, R (0,0) is 0, and R (i,0) is R (0, j) is + ∞.
The selecting of the relevant modal component according to the DTW distance specifically includes:
and sequencing the DTW distances of the modal components and the original signal in an ascending order, selecting the top K-2 modal components which are reordered as related modal components, and adding the selected related modal components, namely the signals subjected to noise reduction. The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.