CN114152837B - Wave head identification method and device under multi-scale wavelet transform - Google Patents

Wave head identification method and device under multi-scale wavelet transform Download PDF

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CN114152837B
CN114152837B CN202010943842.6A CN202010943842A CN114152837B CN 114152837 B CN114152837 B CN 114152837B CN 202010943842 A CN202010943842 A CN 202010943842A CN 114152837 B CN114152837 B CN 114152837B
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reference point
wavelet transform
wave head
point
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CN114152837A (en
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黄涛
徐晓春
谢华
赵青春
陈玉林
谈浩
戴光武
陆金凤
王玉龙
李奔
张洪喜
徐海洋
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NR Electric Co Ltd
NR Engineering Co Ltd
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    • G01R31/081—Locating faults in cables, transmission lines, or networks according to type of conductors
    • G01R31/085—Locating faults in cables, transmission lines, or networks according to type of conductors in power transmission or distribution lines, e.g. overhead
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Abstract

The invention discloses a wave head identification method under multi-scale wavelet transform, which comprises the following steps: acquiring fault traveling wave current data, performing multi-scale wavelet transformation on the traveling wave current data, and solving a modulus maximum value set under each scale; searching in a small scale longitudinally layer by taking the first mode maximum value of the maximum scale as a reference point, and sequentially obtaining the reference point of each scale in a wave head credible interval; each scale calculates a transverse credibility index from each datum point; and finding the minimum scale of the comprehensive credibility of the reference points according to the reference points of all scales and the transverse credibility index, and locally correcting the reference points, wherein the time corresponding to the locally corrected reference points is used as the wave head time. The invention also discloses a corresponding recognition device. The invention can obviously improve the wave head moment extraction precision when the wave head change of the traveling wave is flat.

Description

Wave head identification method and device under multi-scale wavelet transform
Technical Field
The invention relates to the field of relay protection of power systems, in particular to a wave head identification method and device under multi-scale wavelet transformation.
Background
The fault location and traveling wave protection technology can be realized by using transient traveling waves generated on the line when the transmission line fails. The identification of the traveling wave head is a key link for extracting the characteristics of the transient traveling wave, the wavelet transformation has good time-frequency localization capability, singular signals can be quickly and accurately detected, meanwhile, the multi-scale singularity detection of the signals can be realized through the change of scale factors, and the method is the most effective mathematical tool for analyzing the traveling wave.
In actual engineering, due to the influence of factors such as transition resistance, fault distance and the like, a traveling wave may be seriously attenuated, a traveling wave head detected by a measuring point is relatively gentle, singularity characteristics are not obvious, and the precision of traveling wave head identification is seriously influenced by considering the interference of noise. The multi-scale wavelet transform has obvious filtering characteristic difference under different scales, small scales are sensitive to high-frequency signals, traveling wave detection with obvious singularity characteristics is very accurate, but the influence of noise is large, the sensitive frequency of the wavelet transform is continuously reduced along with the increase of the scales, the influence of noise is also obviously reduced, the detection of the traveling wave signals with gentle wave heads is facilitated, and the identification precision of the large-scale downlink wave head at the moment is deficient.
Disclosure of Invention
The present application aims to provide a method and an apparatus for identifying a wave head under multi-scale wavelet transform, which comprehensively utilize multi-scale wavelet transform information to identify a traveling wave head, and implement adaptive identification of traveling wave heads with different change characteristics, thereby improving the accuracy of extracting a traveling wave arrival time, especially the accuracy of identifying a traveling wave head when the traveling wave head is relatively flat.
In order to achieve the above purpose, the solution of the application is:
on one hand, the application provides a wave head identification method under multi-scale wavelet transform, which comprises the following steps:
step 1: acquiring fault traveling wave current data, performing multi-scale wavelet transformation on the traveling wave current data, and solving a modulus maximum value set under each scale;
step 2: searching in a small scale longitudinally layer by taking the first mode maximum value of the maximum scale as a reference point, and sequentially obtaining the reference point of each scale in a wave head credible interval;
and step 3: each scale calculates a transverse credibility index from each datum point;
and 4, step 4: and finding the minimum scale of the comprehensive credibility of the reference points according to the reference points of all scales and the transverse credibility index, and locally correcting the reference points, wherein the time corresponding to the locally corrected reference points is taken as the wave head time.
Preferably, in the step 1, the multi-scale wavelet transform method is n (n ≧ 3) scale dyadic wavelet transform.
Preferably, in step 1, the modulus maximum value set at each scale is obtained by the following formula:
Figure BDA0002671507730000021
in the formula, k is the scale of wavelet transformation, k =1, 2, \8230;, n; n is the maximum scale of wavelet transform; i represents the serial number of the wavelet transformation result; m is a unit of k,i-1 、m k,i 、m k,i+1 Absolute values of wavelet transformation results of ith-1, ith and i +1 points of the kth scale respectively;
Figure BDA0002671507730000022
is the maximum value of the absolute value of the k-th scale wavelet transform result,
Figure BDA0002671507730000023
n is the total number of the traveling wave current data; l is coefficient, and the value range is [0.2,0.5 ]]。
Preferably, in step 2, the wave head confidence interval in each scale is:
Figure BDA0002671507730000024
in the formula, n is the maximum scale of wavelet transformation; i is n A set of modulus maxima at the nth scale; k is the scale of wavelet transformation;
Figure BDA0002671507730000025
is a reference point at the k +1 th scale; c k And the wave head confidence interval at the k-th scale.
Preferably, in step 2, the method for calculating the reference points of each scale is as follows:
Figure BDA0002671507730000026
in the formula, k is the scale of wavelet transformation; j. the design is a square k A modulus maximum value set in a credible interval of a kth scale wave head; n is the maximum scale of wavelet transformation; i is k A set of modulus maxima at the k-th scale; i is k,j Is I k The jth element of (1); c k Is a wave head credible interval under the k-th scale;
Figure BDA0002671507730000027
is a reference point at the k-th scale; min (J) k ) Is a set J k Minimum of all elements in (c).
Preferably, in step 3, the transverse reliability index in each scale is the number of elements in the modulus maximum value set in the scale, which are smaller than the reference point in the scale, and the calculation formula is as follows:
Figure BDA0002671507730000028
in the formula, k is the scale of wavelet transformation; i is k A set of mode maximum values at the kth scale; I.C. A k,j Is I k The jth element of (1);
Figure BDA0002671507730000031
is a reference point at the k-th scale; n is a radical of an alkyl radical k And the k-th scale is a transverse reliability index.
Preferably, in the step 4, the confidence point is integrated with the smallest scale k min The judging method comprises the following steps:
Figure BDA0002671507730000032
in the formula, k is the scale of wavelet transformation; n is k The transverse reliability index under the k scale is obtained; j. the design is a square k A modulus maximum value set in a credible interval of a kth scale wave head;
Figure BDA0002671507730000033
indicating an empty set.
Preferably, in the step 4, the step of locally correcting the reference point includes: at the k-th min Results of scale wavelet transform
Figure BDA0002671507730000034
From the second place to
Figure BDA0002671507730000035
The point starts searching forward until finding less than
Figure BDA0002671507730000036
The first point of (2), the latter point of the point is taken as the reference point after the local correction; wherein k is min Is the minimum scale of the reference point for comprehensive credibility, N is the total number of the traveling wave current data,
Figure BDA0002671507730000037
is the k-th min The ith point of the scale wavelet transform result,
Figure BDA0002671507730000038
is the k-th min A reference point on a scale.
On the other hand, the application provides a wave head identification device under multi-scale wavelet transform, which comprises a modulus maximum value set calculation unit, a datum point calculation unit, a transverse reliability index calculation unit and a correction identification unit which are sequentially connected; wherein:
the modulus maximum value set calculation unit: the system is used for acquiring fault traveling wave current data, performing multi-scale wavelet transformation on the traveling wave current data and solving a modulus maximum value set under each scale;
the reference point calculating unit: the device is used for searching layer by layer in the longitudinal direction of the small scale by taking the first mode maximum value with the maximum scale as a reference point, and sequentially solving the reference point of each scale in a wave head credible interval;
the lateral reliability index calculation unit: the device is used for solving the transverse credibility index of each reference point according to each scale;
the correction recognition unit: and the minimum scale which is used for finding the comprehensive credibility of the reference points according to the reference points of all scales and the transverse credibility index, and locally correcting the reference points, wherein the time corresponding to the locally corrected reference points is the wave head time.
Preferably, in the above apparatus, in the module maximum value set calculating unit, the multi-scale wavelet transform method is n (n ≧ 3) scale dyadic wavelet transform.
Preferably, in the apparatus, in the modulus maximum value set calculation unit, a modulus maximum value set at each scale is obtained by the following formula:
Figure BDA0002671507730000041
in the formula, k is the scale of wavelet transformation, k =1, 2, \8230;, n; n is the maximum scale of wavelet transform; i represents the serial number of the wavelet transformation result; m is a unit of k,i-1 、m k,i 、m k,i+1 Absolute values of wavelet transformation results of the ith-1, ith and ith +1 points of the kth scale respectively;
Figure BDA0002671507730000042
is the maximum value of the absolute value of the kth-scale wavelet transform result,
Figure BDA0002671507730000049
n is the total number of the traveling wave current data; l is a coefficient and has a value range of [0.2,0.5 ]]。
Preferably, in the above apparatus, the reference point calculation means may calculate the wave head confidence interval at each scale as follows:
Figure BDA0002671507730000043
in the formula, n is the maximum scale of wavelet transformation; i is n A set of modulus maxima at the nth scale; k is the scale of wavelet transformation;
Figure BDA0002671507730000044
is a reference point at the k +1 th scale; c k And the wave head credibility interval at the k-th scale is shown.
Preferably, in the above apparatus, the reference point calculation means calculates the reference points for each scale by:
Figure BDA0002671507730000045
in the formula, k is the scale of wavelet transformation; j is a unit of k A module maximum value set in a credible interval of the kth scale wave head; n is the maximum scale of wavelet transformation; I.C. A k A set of modulus maxima at the k-th scale; i is k,j Is shown as I k The jth element of (1); c k A wave head credible interval under the k scale;
Figure BDA0002671507730000046
is a reference point at the k-th scale; min (J) k ) Is a set J k The minimum value of all elements in (c).
Preferably, in the above apparatus, the lateral reliability index at each scale in the lateral reliability index calculation unit is the number of elements smaller than the reference point at the scale in the set of modulo maximum values at the scale, and the calculation formula is as follows:
Figure BDA0002671507730000047
in the formula, k is the scale of wavelet transformation; i is k A set of modulus maxima at the k-th scale; I.C. A k,j Is shown as I k The jth element of (1);
Figure BDA0002671507730000048
is a reference point at the k-th scale; n is a radical of an alkyl radical k And the k-th scale is a transverse reliability index.
Preferably, in the above apparatus, the correction recognition means may recognize a minimum scale k in which the reference points are integrated with confidence min The judging method comprises the following steps:
Figure BDA0002671507730000051
in the formula, k is the scale of wavelet transformation; n is a radical of an alkyl radical k The k-th scale is a transverse reliability index; j. the design is a square k A modulus maximum value set in a credible interval of a kth scale wave head;
Figure BDA0002671507730000052
indicating an empty set.
Preferably, in the above apparatus, the correction identifying means locally corrects the reference point by: at the k-th min Scale wavelet transform results
Figure BDA0002671507730000053
From the second place to
Figure BDA0002671507730000054
The point starts searching until finding less than
Figure BDA0002671507730000055
The first point of (2), the latter point of the point is taken as the reference point after the local correction; wherein k is min Is the minimum scale of the reference point for comprehensive credibility, N is the total number of the traveling wave current data,
Figure BDA0002671507730000056
is the kth min The ith point of the scale wavelet transform result,
Figure BDA0002671507730000057
is the k-th min A reference point on a scale.
The beneficial effect of this application is:
after the scheme is adopted, on the basis of acquiring traveling wave sampling data, the method and the device position the reference point of the traveling wave head to the minimum scale which is comprehensively credible by carrying out longitudinal credible interval search and transverse credibility judgment on a multi-scale wavelet transformation result, ensure the optimization of the wave head identification precision from the minimum wave transformation scale, and then solve the problem that the identification of the wave head time possibly lags when the minimum scale which is comprehensively credible is still larger by carrying out local correction on the reference point of the wave head, thereby effectively improving the traveling wave head identification precision when the wave head changes slowly.
Drawings
Fig. 1 is a flowchart of an embodiment of a method for identifying a wave head under multi-scale wavelet transform according to the present application.
Fig. 2 is a first specific embodiment of a method for identifying a wave head under multi-scale wavelet transform according to the present application.
Fig. 3 is a second specific embodiment of a method for identifying a wave head under multi-scale wavelet transform according to the present application.
Fig. 4 is an embodiment of an apparatus for wave head recognition under multi-scale wavelet transform according to the present application.
Detailed Description
The following detailed description of the present application will be provided in conjunction with the accompanying drawings and specific examples to enable those skilled in the art to better understand the present application and to practice the present application, but the examples are not intended to limit the present application.
As shown in fig. 1, an embodiment of a method for identifying a wave head under multi-scale wavelet transform includes the following steps:
step 1: acquiring fault traveling wave current data, performing multi-scale wavelet transformation on the traveling wave current data, and solving a modulus maximum value set under each scale;
step 2: searching in a small scale longitudinally layer by taking the first mode maximum value of the maximum scale as a reference point, and sequentially obtaining the reference point of each scale in a wave head credible interval;
and 3, step 3: each scale calculates a transverse credibility index from each reference point;
and 4, step 4: and finding the minimum scale of the comprehensive credibility of the reference points according to the reference points of all scales and the transverse credibility index, and locally correcting the reference points, wherein the time corresponding to the locally corrected reference points is taken as the wave head time.
In a preferred embodiment, in step 1, the multi-scale wavelet transform method is an n (n ≧ 3) scale dyadic wavelet transform.
In a preferred embodiment, in step 1, the modulus maximum value set at each scale is obtained by the following formula:
Figure BDA0002671507730000061
in the formula, k is the scale of wavelet transformation, k =1, 2, \8230, n; n is the maximum scale of wavelet transform; i represents the serial number of the wavelet transformation result; m is a unit of k,i-1 、m k,i 、m k,i+1 Absolute values of wavelet transformation results of ith-1, ith and i +1 points of the kth scale respectively;
Figure BDA0002671507730000062
is the maximum value of the absolute value of the kth-scale wavelet transform result,
Figure BDA0002671507730000063
n is the total number of the traveling wave current data; l is a coefficient and has a value range of [0.2,0.5 ]]。
In a preferred embodiment, in step 2, the wave head confidence interval in each scale is:
Figure BDA0002671507730000064
in the formula, n is the maximum scale of wavelet transformation; i is n A set of modulus maxima at the nth scale; k is the scale of wavelet transformation;
Figure BDA0002671507730000065
is a reference point at the k +1 th scale; c k And the wave head confidence interval at the k-th scale.
In a preferred embodiment, in step 2, the calculation method of the reference points of each scale is as follows:
Figure BDA0002671507730000066
in the formula, k is the scale of wavelet transformation; j. the design is a square k A module maximum value set in a credible interval of the kth scale wave head; n is the maximum scale of wavelet transform; I.C. A k A set of modulus maxima at the k-th scale; I.C. A k,j Is shown as I k The jth element of (1); c k Is a wave head credible interval under the k-th scale;
Figure BDA0002671507730000067
is a reference point at the k-th scale; min (J) k ) Is a set J k The minimum value of all elements in (c).
In a preferred embodiment, in step 3, the transverse reliability index in each scale is the number of elements in the modulus maximum value set in the scale that are smaller than the reference point in the scale, and the calculation formula is as follows:
Figure BDA0002671507730000071
in the formula, k is the scale of wavelet transformation; i is k A set of modulus maxima at the k-th scale; i is k,j Is I k The jth element of (1);
Figure BDA0002671507730000072
is a reference point at the k-th scale; n is k And the k-th scale is a transverse reliability index.
In a preferred embodiment, in the step 4, the confidence points are integrated into the smallest k scale min The judging method comprises the following steps:
Figure BDA0002671507730000073
in the formula, k is the scale of wavelet transformation; n is k The transverse reliability index under the k scale is obtained; j. the design is a square k A module maximum value set in a credible interval of the kth scale wave head;
Figure BDA0002671507730000074
indicating an empty set.
In a preferred embodiment, in the step 4, the step of locally correcting the reference point includes: at the k-th min Scale wavelet transform results
Figure BDA0002671507730000075
From the second place to
Figure BDA0002671507730000076
The point starts searching until finding less than
Figure BDA0002671507730000077
The first point of (2), the latter point of the point is taken as the reference point after the local correction; wherein k is min Is the minimum scale of the reference point for comprehensive credibility, N is the total number of the traveling wave current data,
Figure BDA0002671507730000078
is the k-th min The ith point of the scale wavelet transform result,
Figure BDA0002671507730000079
is the k-th min A reference point on a scale.
The method of the present application is described below by way of example of a four-scale dyadic wavelet transform.
Step 1: and acquiring fault traveling wave current data, performing four-scale wavelet transformation on the traveling wave current data, and solving a modulus maximum value set under each scale.
The modulus maximum value set at each scale is calculated as follows:
Figure BDA00026715077300000710
in the formula, k is the scale of wavelet transformation, and k is more than or equal to 1 and less than or equal to 4; m is k,i-1 、m k,i 、m k,i+1 Absolute values of wavelet transformation results of the ith-1, ith and ith +1 points of the kth scale respectively;
Figure BDA00026715077300000711
is the maximum value of the absolute value of the k-th scale wavelet transform result,
Figure BDA00026715077300000712
and N is the total number of the traveling wave current data.
In the step 2, the wave head confidence interval under each scale is as follows:
Figure BDA0002671507730000081
in the formula I 4 A set of modulus maxima at scale 4; k is the scale of wavelet transform;
Figure BDA0002671507730000082
is a reference point at the k +1 th scale; c k And the wave head credibility interval at the k-th scale is shown.
Step 2: and taking the first mode maximum value of the maximum scale as a reference point, searching the small scale longitudinally layer by layer, and sequentially obtaining the reference point of each scale in the wave head credible interval.
The calculation method of the reference points of each scale is as follows:
Figure BDA0002671507730000083
in the formula I k,j Is I k The jth element of (1); c k Is a wave head credible interval under the k-th scale;
Figure BDA0002671507730000084
is a reference point at the k-th scale; min (J) k ) Is a set J k The minimum value of all elements in (c).
And step 3: the lateral reliability index is obtained from the respective reference points by each scale.
The transverse credibility index under each scale is the maximum value set I of the scale modulus k Middle ratio
Figure BDA0002671507730000085
The small number of elements, the calculation formula is as follows:
Figure BDA0002671507730000086
in the formula, k is the scale of wavelet transformation; I.C. A k A set of modulus maxima at the k-th scale; i is k,j Is I k The jth element of (1);
Figure BDA0002671507730000087
is a reference point at the k-th scale; n is k And the k-th scale is a transverse reliability index.
And 4, step 4: and finding the minimum scale of the comprehensive credibility of the reference points according to the reference points of all scales and the transverse credibility index, and locally correcting the reference points, wherein the time corresponding to the locally corrected reference points is taken as the wave head time.
The minimum scale judgment method for comprehensively credible reference points comprises the following steps:
Figure BDA0002671507730000088
in the formula, k is the scale of wavelet transformation; n is a radical of an alkyl radical k The k-th scale is a transverse reliability index; j. the design is a square k A modulus maximum value set in a credible interval of a kth scale wave head;
Figure BDA0002671507730000089
indicating an empty set.
To the benchmarkThe steps of locally correcting the points are as follows: at the k-th min Scale wavelet transform results
Figure BDA0002671507730000091
From the second
Figure BDA0002671507730000092
The point starts searching until finding less than
Figure BDA0002671507730000093
The first point of (2) is set as a reference point after the local correction.
FIG. 2 shows a traveling wave current data, wavelet analysis results and modulus maxima at various scales, where the singularity of traveling wave head is very obvious when the traveling wave current data is viewed, and according to the method of the present application, the first modulus maximum point under the 4 th scale wavelet transform is
Figure BDA0002671507730000094
Longitudinally searching layer by taking the point as a reference point, and respectively finding the reference point under the 3 rd scale, the 2 nd scale and the 1 st scale according to the wave head credible interval
Figure BDA0002671507730000095
And the transverse reliability index n under each scale k All are 0, so the smallest scale of the finally found reference points which can be comprehensively found is the 1 st scale, and then the reference points are locally corrected under the scale, namely the reference points are found from the 273 rd point until less than 0.5m is found 1,273 The first point of the mark =128.6, which is the 271 th point in the figure, and then the latter point of the mark, namely the 272 th point, is taken as the reference point after the local correction, and the real traveling wave arrives at the 271 th point, it can be seen that the wave head arrival time can be identified relatively accurately by using the method of the present application.
FIG. 3 is another embodiment of the present application showing traveling wave current data and wavelet analysis results and modal maxima at various scales, the implementation being seen from the traveling wave current dataThe traveling wave head of the example is very flat, and according to the method of the application, the first module maximum value point under the 4 th scale wavelet transformation is
Figure BDA0002671507730000096
Longitudinally searching layer by taking the point as a reference point, and respectively finding the reference point under the 3 rd scale, the 2 nd scale and the 1 st scale according to the wave head credible interval
Figure BDA0002671507730000097
Figure BDA0002671507730000098
Wherein the transverse reliability index of the 3 rd scale is 0, the transverse reliability index of the 2 nd scale is 2, the transverse reliability index of the 1 st scale is obviously larger than 5, so the finally found minimum comprehensive credibility scale of the reference point is the 2 nd scale, and then the reference point is locally corrected under the scale, namely the reference point is found from the 183 th point to the front until the reference point is found to be less than 0.5m 2,183 The first point of =14.97, which is the 181 th point in the figure, and the subsequent point of the point, namely the 182 th point, is taken as the reference point after local correction, the reference point is converted into the traveling wave current data to be the 364 th point, and the actual traveling wave arrival is at the 365 th point, so that the wave head arrival time can be accurately identified even if the wave head change is relatively smooth after the method of the application is adopted.
Fig. 4 shows an embodiment of a wave head recognition device under multi-scale wavelet transform according to the present application, which includes a modulus maximum value set calculation unit, a reference point calculation unit, a lateral reliability index calculation unit, and a correction recognition unit, which are connected in sequence. Wherein:
the modulus maximum value set calculation unit: the method is used for acquiring fault traveling wave current data, performing multi-scale wavelet transformation on the traveling wave current data and solving a modulus maximum value set under each scale.
The reference point calculating unit: and the method is used for searching layer by layer in the longitudinal direction of the small scale by taking the first mode maximum value of the maximum scale as a reference point, and sequentially obtaining the reference point of each scale in the wave head credible interval.
The lateral reliability index calculation unit: and the device is used for solving the transverse credibility index of each reference point according to each scale.
The correction recognition unit: and the method is used for finding the minimum scale of the comprehensive credibility of the reference points according to the reference points of all scales and the transverse credibility index, and performing local correction on the reference points, wherein the time corresponding to the locally corrected reference points is taken as the wave head time.
In a preferred embodiment of the apparatus, in the module maximum value set calculation unit, the multi-scale wavelet transform method is n (n ≧ 3) scale dyadic wavelet transform.
In an embodiment of the preferred apparatus, in the module maximum set calculating unit, a module maximum set calculation formula at each scale is as follows:
Figure BDA0002671507730000101
in the formula, k is the scale of wavelet transformation, k =1, 2, \8230, n; n is the maximum scale of wavelet transform; i represents the serial number of the wavelet transformation result; m is k,i-1 、m k,i 、m k,i+1 Absolute values of wavelet transformation results of ith-1, ith and i +1 points of the kth scale respectively;
Figure BDA0002671507730000102
is the maximum value of the absolute value of the k-th scale wavelet transform result,
Figure BDA0002671507730000103
n is the total number of the traveling wave current data; l is coefficient, and the value range is [0.2,0.5 ]]。
In an embodiment of the preferred apparatus, in the reference point calculating unit, the wave head confidence interval at each scale is:
Figure BDA0002671507730000104
in the formula, n is the maximum scale of wavelet transformation; i is n A set of modulus maxima at the nth scale; k is smallThe scale of the wave transform;
Figure BDA0002671507730000105
is a reference point at the k +1 th scale; c k And the wave head confidence interval at the k-th scale.
In a preferred embodiment of the apparatus, in the reference point calculating unit, a method of calculating reference points of each scale is as follows:
Figure BDA0002671507730000106
in the formula, k is the scale of wavelet transformation; j. the design is a square k A module maximum value set in a credible interval of the kth scale wave head; n is the maximum scale of wavelet transformation; I.C. A k A set of modulus maxima at the k-th scale; I.C. A k,j Is I k The jth element of (1); c k Is a wave head credible interval under the k-th scale;
Figure BDA0002671507730000111
is a reference point at the k-th scale; min (J) k ) Is a set J k Minimum of all elements in (c).
In a preferred embodiment of the apparatus, in the horizontal reliability index calculation unit, the horizontal reliability index in each scale is the number of elements in the modulus maximum value set in the scale that are smaller than the reference point in the scale, and the calculation formula is as follows:
Figure BDA0002671507730000112
in the formula, k is the scale of wavelet transformation; i is k A set of modulus maxima at the k-th scale; I.C. A k,j Is shown as I k The jth element of (1);
Figure BDA0002671507730000113
is a reference point at the k-th scale; n is a radical of an alkyl radical k And the k-th scale is a transverse reliability index.
In a preferred embodiment of the device, the repair isMinimum k for confidence in integration of reference points in positive identification cells min The judging method comprises the following steps:
Figure BDA0002671507730000114
in the formula, k is the scale of wavelet transformation; n is k The k-th scale is a transverse reliability index; j. the design is a square k A module maximum value set in a credible interval of the kth scale wave head;
Figure BDA0002671507730000115
indicating an empty set.
In a preferred embodiment of the apparatus, the step of locally correcting the reference point in the correction recognition unit is as follows: at the k-th min Results of scale wavelet transform
Figure BDA0002671507730000116
From the second place to
Figure BDA0002671507730000117
The point starts searching forward until finding less than
Figure BDA0002671507730000118
The first point of (2), the latter point of the point is taken as the reference point after the local correction; wherein k is min Is the minimum scale of the reference point for comprehensive credibility, N is the total number of the traveling wave current data,
Figure BDA0002671507730000119
is the kth min The ith point of the scale wavelet transform result,
Figure BDA00026715077300001110
is the k-th min A reference point on a scale.
The method adopts multiple comprehensive technologies such as longitudinal credibility interval searching, transverse feasibility judgment, datum point local correction and the like under multi-scale wavelet transformation, wherein the longitudinal credibility interval searching ensures that the optimal scale of the arrival of the traveling wave head can be represented, the transverse credibility judgment can eliminate the scale with larger noise and serious interference, the datum point local correction realizes fine adjustment of the datum point, and the wave head identification result is closer to the actual wave head arrival time. The method has obvious effect of improving the traveling wave identification precision with gentle wave head change.
The present application is not limited to the above embodiments, and the above embodiments are only used for facilitating the understanding of the core idea of the present application, and any modification made to the present application or equivalent substitution made according to the idea of the present application and the modification made within the scope of the present application shall fall within the protection scope of the present application.

Claims (14)

1. A wave head identification method under multi-scale wavelet transform is characterized by comprising the following steps:
step 1: acquiring fault traveling wave current data, performing multi-scale wavelet transformation on the traveling wave current data, and solving a modulus maximum value set under each scale;
and 2, step: searching in a small scale longitudinally layer by taking the first mode maximum value of the maximum scale as a reference point, and sequentially obtaining the reference point of each scale in a wave head credible interval;
and step 3: each scale calculates a transverse credibility index from each datum point;
and 4, step 4: finding the minimum scale of the comprehensive credibility of the reference points according to the reference points of all scales and the transverse credibility indexes, and locally correcting the reference points, wherein the time corresponding to the locally corrected reference points is taken as the wave head time;
the step of locally correcting the reference point is as follows: at the k-th min Results of scale wavelet transform
Figure FDA0003863433400000011
From the second
Figure FDA0003863433400000019
The point starts searching until finding less than
Figure FDA0003863433400000013
The first point of (2), the latter point of the first point is taken as the reference point after local correction; wherein k is min Is the minimum scale of the reference point for comprehensive credibility, N is the total number of the traveling wave current data,
Figure FDA0003863433400000014
is the k-th min The ith point of the scale wavelet transform result,
Figure FDA0003863433400000015
is the k-th min A reference point on a scale.
2. The method for identifying the wave head under the multi-scale wavelet transform as claimed in claim 1, wherein: in the step 1, the multi-scale wavelet transform method is n-scale dyadic wavelet transform, wherein n is more than or equal to 3.
3. The method for wave-head recognition under multi-scale wavelet transform as claimed in claim 1, wherein: in step 1, the modulus maximum value set at each scale is calculated as follows:
Figure FDA0003863433400000016
in the formula, k is the scale of wavelet transformation, k =1, 2, \8230;, n; n is the maximum scale of wavelet transform; i represents the serial number of the wavelet transformation result; m is k,i-1 、m k,i 、m k,i+1 Absolute values of wavelet transformation results of ith-1, ith and i +1 points of the kth scale respectively;
Figure FDA0003863433400000017
is the maximum value of the absolute value of the k-th scale wavelet transform result,
Figure FDA0003863433400000018
n is the number of travelling wave currentsThe total number of the data; l is coefficient, and the value range is [0.2,0.5 ]]。
4. The method for identifying the wave head under the multi-scale wavelet transform as claimed in claim 1, wherein: in the step 2, the wave head confidence interval under each scale is as follows:
Figure FDA0003863433400000021
in the formula, n is the maximum scale of wavelet transformation; I.C. A n A set of modulus maxima at the nth scale; k is the scale of wavelet transform;
Figure FDA0003863433400000022
is a reference point at the k +1 th scale; c k And the wave head credibility interval at the k-th scale is shown.
5. The method for identifying the wave head under the multi-scale wavelet transform as claimed in claim 1, wherein: in the step 2, the calculation method of the reference points of each scale is as follows:
Figure FDA0003863433400000023
in the formula, k is the scale of wavelet transformation; j. the design is a square k A modulus maximum value set in a credible interval of a kth scale wave head; n is the maximum scale of wavelet transform; i is k A set of mode maximum values at the kth scale; I.C. A k,j Is I k The jth element of (1); c k A wave head credible interval under the k scale;
Figure FDA0003863433400000025
is a reference point at the k-th scale; min (J) k ) Is a set J k The minimum value of all elements in (c).
6. The method for identifying the wave head under the multi-scale wavelet transform as claimed in claim 1, wherein: in step 3, the transverse reliability index at each scale is the number of elements in the modulus maximum value set at the scale, which are smaller than the reference point at the scale, and the calculation formula is as follows:
Figure FDA0003863433400000024
in the formula, k is the scale of wavelet transformation; I.C. A k A set of modulus maxima at the k-th scale; I.C. A k,j Is I k The jth element of (1);
Figure FDA0003863433400000026
is a reference point at the k-th scale; n is k And the k-th scale is a transverse reliability index.
7. The method for identifying the wave head under the multi-scale wavelet transform as claimed in claim 1, wherein: in the step 4, the smallest scale k for the reference points to be comprehensively credible min The judging method comprises the following steps:
Figure FDA0003863433400000031
in the formula, k is the scale of wavelet transformation; n is k The k-th scale is a transverse reliability index; j. the design is a square k A modulus maximum value set in a credible interval of a kth scale wave head;
Figure FDA0003863433400000032
indicating an empty set.
8. A wave head recognition device under multi-scale wavelet transform is characterized by comprising a modulus maximum value set calculation unit, a datum point calculation unit, a transverse reliability index calculation unit and a correction recognition unit which are sequentially connected; wherein:
the modulus maximum value set calculation unit: the system is used for acquiring fault traveling wave current data, performing multi-scale wavelet transformation on the traveling wave current data and solving a modulus maximum value set under each scale;
the reference point calculating unit: the device is used for searching layer by layer in the longitudinal direction of the small scale by taking the first mode maximum value with the maximum scale as a reference point, and sequentially solving the reference point of each scale in a wave head credible interval;
the lateral reliability index calculation unit: the device is used for solving the transverse credibility index of each reference point according to each scale;
the correction recognition unit: the device is used for finding the smallest comprehensively credible scale of the reference point according to the reference point of each scale and the transverse credibility index, and performing local correction on the reference point, wherein the time corresponding to the locally corrected reference point is taken as the wave head time; in the correction recognition unit, the step of locally correcting the reference point is as follows: at the k-th min Scale wavelet transform results
Figure FDA0003863433400000033
From the second
Figure FDA0003863433400000034
The point starts searching forward until finding less than
Figure FDA0003863433400000035
The first point of (2), the latter point of the first point is taken as the reference point after local correction; wherein k is min Is the minimum scale of the reference point for comprehensive credibility, N is the total number of the traveling wave current data,
Figure FDA0003863433400000036
is the k-th min The ith point of the scale wavelet transform result,
Figure FDA0003863433400000037
is the k-th min A reference point on a scale.
9. The apparatus for wave-front recognition under multi-scale wavelet transform according to claim 8, wherein: in the module maximum value set calculation unit, the multi-scale wavelet transformation method is n-scale dyadic wavelet transformation, wherein n is more than or equal to 3.
10. The apparatus for wave-front recognition under multi-scale wavelet transform according to claim 8, wherein: in the module maximum value set calculation unit, the module maximum value set under each scale is calculated according to the following formula:
Figure FDA0003863433400000038
in the formula, k is the scale of wavelet transformation, k =1, 2, \8230, n; n is the maximum scale of wavelet transformation; i represents the serial number of the wavelet transformation result; m is a unit of k,i-1 、m k,i 、m k,i+1 Absolute values of wavelet transformation results of ith-1, ith and i +1 points of the kth scale respectively;
Figure FDA0003863433400000041
is the maximum value of the absolute value of the kth-scale wavelet transform result,
Figure FDA0003863433400000042
n is the total number of the traveling wave current data; l is coefficient, and the value range is [0.2,0.5 ]]。
11. The apparatus for recognizing a wave head under the multi-scale wavelet transform according to claim 8, wherein: in the reference point calculation unit, the wave head confidence interval under each scale is as follows:
Figure FDA0003863433400000043
in the formula, n is the maximum scale of wavelet transformation; I.C. A n A set of mode maximum values at the nth scale; k is the scale of wavelet transformation;
Figure FDA0003863433400000044
is a reference point at the k +1 th scale; c k And the wave head confidence interval at the k-th scale.
12. The apparatus for wave-front recognition under multi-scale wavelet transform according to claim 8, wherein: in the reference point calculation unit, the calculation method of the reference points of each scale is as follows:
Figure FDA0003863433400000045
in the formula, k is the scale of wavelet transformation; j. the design is a square k A module maximum value set in a credible interval of the kth scale wave head; n is the maximum scale of wavelet transformation; I.C. A k A set of modulus maxima at the k-th scale; I.C. A k,j Is shown as I k The jth element of (1); c k Is a wave head credible interval under the k-th scale;
Figure FDA0003863433400000046
is a reference point at the k-th scale; min (J) k ) Is a set J k Minimum of all elements in (c).
13. The apparatus for wave-front recognition under multi-scale wavelet transform according to claim 8, wherein: in the transverse reliability index calculation unit, the transverse reliability index under each scale is the number of elements in the modulus maximum value set under the scale, which are smaller than the reference point under the scale, and the calculation formula is as follows:
Figure FDA0003863433400000047
in the formula, k is the scale of wavelet transformation; I.C. A k A set of mode maximum values at the kth scale; I.C. A k,j Is I k The jth element of (1); i is k b is a radical on the k-th scaleA quasi point; n is k And the k-th scale is a transverse reliability index.
14. The apparatus for wave-front recognition under multi-scale wavelet transform according to claim 8, wherein: in the correction identification unit, the minimum scale k with credible integrated reference points min The judging method comprises the following steps:
Figure FDA0003863433400000051
in the formula, k is the scale of wavelet transformation; n is a radical of an alkyl radical k The k-th scale is a transverse reliability index; j. the design is a square k A modulus maximum value set in a credible interval of a kth scale wave head;
Figure FDA0003863433400000052
indicating an empty set.
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