CN103033663A - Anomaly detection method for three-dimensional waveform data - Google Patents

Anomaly detection method for three-dimensional waveform data Download PDF

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CN103033663A
CN103033663A CN201210566432XA CN201210566432A CN103033663A CN 103033663 A CN103033663 A CN 103033663A CN 201210566432X A CN201210566432X A CN 201210566432XA CN 201210566432 A CN201210566432 A CN 201210566432A CN 103033663 A CN103033663 A CN 103033663A
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amplitude
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张沁川
曾浩
蒋俊
赵勇
杜兴批
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University of Electronic Science and Technology of China
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Abstract

The invention discloses an anomaly detection method for three-dimensional waveform data. In a three-dimensional data processing system, multi-amplitude waveform data collected in a certain period of time are mapped to a three-dimensional database and to be used as samples, and value range of amplitude of each sampling point is calculated to form an anomaly detection template of amplitude valuing. Each amplitude of the waveform data collected soon afterwards is compared with the anomaly detection template of the amplitude valuing in real time, and when the sampling point is located beyond a corresponding value range, whether abnormal events happen or not can be judged, and the amplitude waveform data are mapped and displayed. A digital three-dimensional oscilloscope, which adopts the anomaly detection method of the three-dimensional waveform data, is capable of through ignoring a large number of mapping operations of normal waveforms, increasing capture speed of waveforms, strengthening capability of capturing accidental abnormal signals, and overcoming the defect that low-probability accidental abnormal signals can not be captured because of existence of dead time in the prior art.

Description

A kind of method for detecting abnormality of three-dimensional waveform data
Technical field
The invention belongs to digital three-dimensional oscillograph technical field, more specifically say, relate to a kind of method for detecting abnormality of three-dimensional waveform data.
Background technology
Digital three-dimensional oscillograph (Digital Three-dimensional Oscilloscope, abbreviation DTO) adopts the waveform mapping techniques based on parallel organization, can collect at short notice more waveform, produce the quite abundant three-dimensional waveform database of details, comprise time, amplitude and amplitude temporal evolution relation (being the waveform probabilistic information).The digital three-dimensional oscillograph is mapped to the three-dimensional waveform database with several waveforms that collect in the refresh cycle, and by brightness or colouring information waveform is presented on the lcd screen by three-dimensional mapping block.
Although three-dimensional oscillograph once can be processed several shape informations, improved waveform capture rate, but after each data acquisition is finished, before entering the new data acquisition of next round, digital storage oscilloscope need to be processed, analyze and shine upon current collection the data obtained, during this period of time can't image data, therefore there is Dead Time.The oscillographic acquisition time of digital three-dimensional is too short with respect to Dead Time, and system almost can miss 90% signal.If the user wants to catch the accidental abnormal signal of low probability, may need a very long time, even catch less than abnormal signal.
Such as announcement on 05 02nd, 2012, publication No. was the implementation method that CN102435808A, name are called the Chinese invention patent application announcement of " the oscillographic method for displaying waveform of a kind of digital three-dimensional ".Conventional three-dimensional oscillograph abnormal signal detects the low characteristics of probability that normally occur according to accidental abnormal signal, and several Wave datas that waveform was each time collected in the refresh cycle are added in the three-dimensional waveform database, according to user's needs, a threshold value N are set SetIf sampled point x in the three-dimensional data base iHit-count N i≤ N Set, then think sampled point x iOccurred unusually, in display system, with special brightness or color these abnormal signals and normal waveform have been carried out differential display.
For example, when detecting abnormal signal with the digital three-dimensional oscillograph, if measured signal repeats 1 time unusual with per second, the cycle of effectively the catching 10us of system, waveform capture rate is 10,000wfms/s, in testing process, the waveform of catching all is repetition or similar normal information mostly, if adopt above-mentioned method for detecting abnormality, the normal waveform of " meaningless " that then at every turn captures all can shine upon demonstration, thereby needs to consume a large amount of data processing and analysis time, might just in this section Dead Time, occur by abnormal signal, but oscillograph can't catch.Therefore, capture the interested per second appearance of user abnormal signal once, need long time.Like this, significantly reduce the degree of accuracy that abnormal signal detects, and increased the difficulty that detects.
Summary of the invention
The object of the invention is to overcome the deficiencies in the prior art, a kind of method for detecting abnormality of three-dimensional waveform data is provided, reduce the mapping time of three-dimensional data, improve capture ability and the efficient of accidental abnormal signal.
For achieving the above object, the method for detecting abnormality of three-dimensional waveform data of the present invention is characterized in that may further comprise the steps:
(1), to adopt vertical resolution be the ADC collection signal of dbit, each sampling number that gathers is k, each sampled point has m=2 d Individual amplitude value 0,1 ..., 2 d-1, in hardware system, the N amplitude wave graphic data that collects in the time T is mapped to three-dimensional data base as sample, this three-dimensional data base is expressed as the two-dimensional matrix A of m * k:
A = a 11 , a 12 , · · · , a 1 k a 21 , a 22 , · · · a 2 k · · · · · · · · · · · · · · · · · · a m 1 , a m 2 , · · · , a mk = B 1 B 2 · · · B m = ( A 1 , A 2 , · · · , A k )
Wherein, a IjJ sampled point amplitude value is 2 in the collection of expression N amplitude wave graphic data dThe hit-count of-i, the vectorial B of row i=(a I1, a I2..., a Ik), the amplitude value that 1≤i≤m is corresponding is 2 d-i, column vector A j=(a 1j, a 2j..., a Mj) I, 1≤j≤k represents the mapping vector of j sampled point;
(2), sensitivity parameter η is set, 0<η≤1, structure point set K jFor:
K j={2 d-i|a ij≥N×η}
K jJ sampled point hit-count a during expression N amplitude wave graphic data gathers IjThe amplitude value point set of 〉=N * η; Change sensitivity parameter η and can change the accuracy that abnormal signal detects;
(3), hit probability matrix P corresponding to Two-dimensional matrix A:
P = A N = p 11 , p 12 , · · · , p 1 k p 21 , p 22 , · · · , p 2 k · · · · · · · · · · · · · · · · · · p m 1 , p m 2 , · · · , p mk
Wherein, p Ij=a Ij/ N, 1≤i≤m, 1≤j≤k represent that j sampled point amplitude value is 2 in the collection of N amplitude wave graphic data dThe hit probability of-i;
(4), according to the hit probability p of each amplitude value of j sampled point among the hit probability matrix P 1j, p 2j..., p Mj, with point set K jIn element be divided into R sub-range:
K j = ∪ n = 1 R K n sub = ∪ n = 1 R ( a n , b n )
Wherein,
Figure BDA00002639480900032
Represent n sub-range, a nAnd b n, 0≤a n≤ b n≤ 2 dThe end points of sampled point amplitude span in-1 expression is interval, and K n 1 sub ∩ K n 2 sub = 0,1 ≤ n 1 ≠ n 2 ≤ R ;
The sub-range
Figure BDA00002639480900034
Corresponding interval hit probability is
Figure BDA00002639480900035
Equal the subspace
Figure BDA00002639480900036
In each amplitude value hit probability sum;
If two or more continuous sub-ranges are arranged
Figure BDA00002639480900037
Corresponding interval hit probability
Figure BDA00002639480900038
Equate, then with these sub-ranges Merge into a sub-range;
(5), by interval hit probability
Figure BDA000026394809000310
Order from big to small is successively with each sub-range in j sampled point interval Interval amplitude span end points a nAnd b nStore in the register, as the template of the amplitude value abnormality detection of j sampled point;
(6), waveform to be collected is carried out the waveform acquisition that sampling number is similarly k, the wave-shape amplitude value representation that collects is W=(w 1, w 2..., w k), 0≤w i≤ 2 d-1,1≤j≤k is with the range value w of j sampled point jCompare with the amplitude value abnormality detection template of j sampled point, if there is a sampled point to drop on outside the interval range, then anomalous event occurs, and this Wave data is shone upon and shows; If the range value w of all sampled points 1, w 2..., w kAll drop in the amplitude value abnormality detection template interval range, then waveform is normal, signal is not shone upon and shows.
Goal of the invention of the present invention is achieved in that
The method for detecting abnormality of three-dimensional waveform data of the present invention directly is mapped to three-dimensional data base as sample with several waveforms that gather in the time T, and it is expressed as two-dimensional matrix A in hardware system.Sensitivity parameter η is set, determines amplitude value point set K according to two-dimensional matrix A and sensitivity parameter η jWith point set K jIn element be divided into R sub-range with different amplitude value hit probabilities
Figure BDA000026394809000312
The sub-range
Figure BDA000026394809000313
In the summation of each element probability obtain the probability in sub-range
Figure BDA000026394809000314
And press
Figure BDA000026394809000315
Descending order is with the interval amplitude span end points (a in each sub-range n, b n) be stored in the register as wave-shape amplitude value abnormality detection template.Then each amplitude wave graphic data and the abnormality detection template of system acquisition are compared, if there is a sampled point to drop on amplitude value point set K jOutward, represent anomalous event and occur, this Wave data is shone upon and show.If all sampled points all drop on span K jIn, think that then this amplitude wave shape is normal waveform, this amplitude wave graphic data is not shone upon and show.
Therefore, adopt the present invention to carry out the abnormality detection of three-dimensional waveform data, the number of times that can greatly reduce the mapping of ordinary wave graphic data and show shortens the time that data are processed and analyzed, and improves the abnormal signal capture rate.
Description of drawings
Fig. 1 is the three-dimensional data base sample that 3bitADC gathers in the method for detecting abnormality of three-dimensional waveform data of the present invention;
Fig. 2 is the oscillogram that adopts digital three-dimensional oscillograph observed anomaly signal of the present invention.
Embodiment
Below in conjunction with accompanying drawing the specific embodiment of the present invention is described, so that those skilled in the art understands the present invention better.What need to point out especially is that in the following description, when perhaps the detailed description of known function and design can desalinate main contents of the present invention, these were described in here and will be left in the basket.
Embodiment
To be example describe the embodiment of the method for detecting abnormality of three-dimensional waveform data of the present invention for the existing ADC collection signal take vertical resolution as 3bit, the sample points k=10 that once gathers.Its implementation step is as follows:
Step 1: adopting vertical resolution is the ADC collection signal of d bit, and each sampling number that gathers is k, and each sampled point has m=2 d Individual amplitude value 0,1 ..., 2 d-1, in hardware system, the N amplitude wave graphic data that collects in the time T is mapped to three-dimensional data base as sample, this three-dimensional data base is expressed as the two-dimensional matrix A of m * k:
A = a 11 , a 12 , · · · , a 1 k a 21 , a 22 , · · · , a 2 k · · · · · · · · · · · · · · · · · · a m 1 , a m 2 , · · · , a mk = B 1 B 2 · · · B m = ( A 1 , A 2 , · · · , A k )
Wherein, a IjJ sampled point amplitude value is 2 in the collection of expression N amplitude wave graphic data dThe hit-count of-i, the vectorial B of row i=(a I1, a I2..., a Ik), the amplitude value that 1≤i≤m is corresponding is 2 d-i, column vector A j=(a 1j, a 2j..., a Mj) T, 1≤j≤k represents the mapping vector of j sampled point, such as a 1jThat j sampled point amplitude value is 2 d-1 hit-count, a 2jThat j sampled point amplitude value is 2 d-2 hit-count, a MjThat j sampled point amplitude value is 0 hit-count.
It is the ADC collection signal of 3bit that present embodiment adopts vertical resolution, and then each sampled point has 2 3Individual amplitude value (0 ..., 7), i.e. m=8.In hardware system, adopt parallel mapping structure, in time T, collect N=8 amplitude wave graphic data and be mapped to three-dimensional data base as sample.
Fig. 1 is the three-dimensional data base sample of 3bitADC sampling in the method for detecting abnormality of three-dimensional waveform data of the present invention.As shown in Figure 1, the size of each element represented 8 amplitude wave graphic data gather in this sampled point at the hit-count of this amplitude value.
In the present embodiment, the three-dimensional data base schedule of samples is shown 8 * 10 two-dimensional matrix A, 0 of matrix left side sign ..., the 7th, the amplitude value of sampled point:
A = 7 6 5 4 3 2 1 0 0,0,0,0,0,8,0,0,0,0 0,0,0,0,7,0,5,0,0,0 0,0,0,6,1,0,2,2,0,0 0,0,1,2,0,0,1,4,0,0 0,0,4,0,0,0,0,2,3,0 0,4,3,0,0,0,0,0,3,0 5,4,0,0,0,0,0,0,2,4 3,0,0,0,0,0,0,0,0,4 = ( A 1 , A 2 · · · A 10 )
A j, the mapping vector of 1≤j≤j sampled point of 10 expressions.
Step 2: sensitivity parameter η is set, 0<η≤1, structure point set K jFor:
K j={2 d-i|a ij≥N×η}
K jJ sampled point hit-count a during expression N amplitude wave graphic data gathers IjThe amplitude value point set of 〉=N * η; Wherein, sensitivity parameter η is that the user is adjustable, changes η and can change the accuracy that abnormal signal detects.
Sensitivity parameter η=0.2 is set, then effective hit-count a in the present embodiment e=N * η=8 * 0.2=1.6.With column vector A 1=(0,0,0,0,0,0,5,3) TBe example, sampled point amplitude value is that 0 hit-count is 3, and sampled point amplitude value is that 1 hit-count is 5.Therefore, according to K 1={ 2 d-i|a I1〉=1.6} can determine the amplitude span K of the 1st sampled point 1=(a 1, b 1)=(0,1).In like manner, the amplitude span that can determine the 2nd sampled point is K 2=(1,2), the amplitude span of the 3rd sampled point is K 3=(2,3), the amplitude span of the 4th sampled point is K 4=(4,5), the amplitude span of the 5th sampled point is K 5=(6,6), the amplitude span of the 6th sampled point is K 6=(7,7), the amplitude span of the 7th sampled point is K 7=(5,6), the amplitude span of the 8th sampled point is K 8=(3,5), the amplitude span of the 9th sampled point is K 9=(1,3), the amplitude span of the 10th sampled point is K 10=(0,1).
Step 3: the hit probability matrix P that the Two-dimensional matrix A is corresponding:
P = A N = p 11 , p 12 , · · · , p 1 k p 21 , p 22 , · · · , p 2 k · · · · · · · · · · · · · · · · · · p m 1 , p m 2 , · · · , p mk
Wherein, p Ij=a Ij/ N, 1≤i≤m, 1≤j≤k represent that j sampled point amplitude value is 2 in the collection of N amplitude wave graphic data dThe hit probability of-i.
In the present embodiment, the hit probability matrix P that two-dimensional matrix A is corresponding is:
P = A 8 = 0,0,0,0,0,1,0,0,0,0 0,0,0,0 , 7 8 , 0 , 5 8 , 0,0,0 0,0,0 , 6 8 , 1 8 , 0 , 2 8 , 2 8 , 0,0 0,0 , 1 8 , 2 8 , 0,0 , 1 8 , 4 8 , 0,0 0,0 , 4 8 , 0,0,0,0 , 2 8 , 3 8 , 0 0 , 4 8 , 3 8 , 0,0,0,0,0 , 3 8 , 0 5 8 , 4 8 , 0,0,0,0,0,0 , 2 8 , 4 8 3 8 , 0,0,0,0,0,0,0,0 , 4 8
Step 4: in actual applications, the Wave data value of each row often drops on (0,2 d-1) in 1~3 of scope sub-interval range.Therefore, according to the hit probability p of each amplitude value of j sampled point among the hit probability matrix P 1j, p 2j..., p Mj, with point set K jIn element be divided into R sub-range:
K j = ∪ n = 1 R K n sub = ∪ n = 1 R ( a n , b n )
Wherein
Figure BDA00002639480900064
Represent n sub-range, a nAnd b n(0≤a n≤ b n≤ 2 d-1) end points of the interval interior sampled point amplitude value of expression, and K n 1 sub ∩ K n 2 sub = 0,1 ≤ n 1 ≠ n 2 ≤ R ; The sub-range
Figure BDA00002639480900066
Corresponding interval hit probability is
Figure BDA00002639480900067
Equal the subspace
Figure BDA00002639480900068
In each amplitude value hit probability sum;
If two or more continuous sub-ranges are arranged Corresponding interval hit probability
Figure BDA000026394809000610
Equate, then with these sub-ranges
Figure BDA000026394809000611
Merge into a sub-range.
In the present embodiment, with the amplitude span K of the 1st sampled point 1=(0,1) is divided into two sub-range K with different amplitude value hit probabilities 1 Sub=(0,0) and K 2 Sub=(1,1), corresponding amplitude value hit probability is respectively p 1 sub = 3 / 8 , p 2 sub = 5 / 8 , Be that the hit probability that sampled point is got 0 value is p 1 sub = 3 / 8 , The hit probability of getting 1 value is
Figure BDA00002639480900073
The amplitude span K of the 2nd sampled point 2=(1,2) is divided into two sub-range K 1 Sub=(1,1) and K 2 Sub=(2,2), corresponding amplitude value hit probability
Figure BDA00002639480900074
And two sub-ranges are continuous, therefore with two sub-range K 1 Sub=(1,1) and K 2 SubK is merged into in=(2,2) 1 Sub=(1,2).In like manner can get the sub-range of other sampled points.
Step 5: by interval hit probability Order from big to small is successively with each sub-range in j sampled point interval
Figure BDA00002639480900076
Interval range end points a nAnd b nStore in the register, as the template of the amplitude value abnormality detection of j sampled point.
Still take the 1st sampled point as example, amplitude span K 1=(0,1) can be divided into sub-range K 1 Sub=(0,0) and K 2 Sub=(1,1), corresponding amplitude probability is respectively p 1 sub = 3 / 8 , p 2 sub = 5 / 8 , p 2 sub ≥ p 1 sub . By interval hit probability
Figure BDA00002639480900078
Order from big to small is respectively with the interval Interval range a 2=1 and b 2=1,
Figure BDA000026394809000710
Interval range a 1=0 and b 1=0 stores in the register, and the amplitude value abnormality detection template of constructing the 1st sampled point is as follows:
1 1
0 0
According to said method, construct the amplitude value abnormality detection template of the 2nd sampled point:
1 2
Construct the amplitude value abnormality detection template of the 3rd sampled point:
3 3
2 2
Construct the amplitude value abnormality detection template of the 4th sampled point:
5 5
4 4
Construct the amplitude value abnormality detection template of the 5th sampled point:
6 6
Construct the amplitude value abnormality detection template of the 6th sampled point:
7 7
Construct the amplitude value abnormality detection template of the 7th sampled point:
6 6
5 5
Construct the amplitude value abnormality detection template of the 8th sampled point:
4 4
5 5
3 3
Construct the amplitude value abnormality detection template of the 9th sampled point:
2 3
1 1
Construct the amplitude value abnormality detection template of the 10th sampled point:
0 1
Step 5: waveform to be collected is carried out the waveform acquisition that sampling number is similarly k, and the wave-shape amplitude value representation that collects is W=(w 1, w 2..., w k), 0≤w i≤ 2 d-1,1≤j≤k is with the wave-shape amplitude value w of j sampled point jCompare with the amplitude value abnormality detection template of j sampled point, if there is a sampled point to drop on outside the interval range, then anomalous event occurs, and this Wave data is shone upon and shows; If the wave-shape amplitude value w of all sampled points 1, w 2..., w kAll drop in the amplitude value abnormality detection template interval range, then waveform is normal, signal is not shone upon and shows.
In the present embodiment, as k=10 the sampled point range value that gathers an amplitude wave shape is for { 1,2,3,5,6,7,3,4,3,0} carries out order comparison with corresponding abnormality detection template successively with 10 sampled points.As seen, the amplitude value of the 7th sampled point is 3, drops on outside the amplitude value abnormality detection template of the 7th sampled point.Therefore waveform has occurred unusually, this amplitude wave shape is shone upon, and with different wave brightness or color the unusual waveforms signal is shown on the LCD.
Fig. 2 is the oscillogram that adopts digital three-dimensional oscillograph observed anomaly signal of the present invention.As shown in Figure 2, with sampling number k=800, vertical resolution is that the repetition period signal with abnormal signal that the ADC of 8bit gathers is sent into the oscillographic passage 1 of digital three-dimensional.Belt waveform is amplitude value abnormality detection template, and the wire waveform is the abnormal signal waveform that detects, and as shown in Figure 2, the abnormal signal that adopts digital three-dimensional oscillograph of the present invention to detect is high-visible.
Adopt the three-dimensional oscillograph of above-mentioned method for detecting abnormality, when carrying out abnormality detection, can ignore the normal waveform of a large amount of repetitions or similar " meaningless ", it is not done mapping and show; Simultaneously, the compare operation of waveform mapping and Wave data and template all is to finish in hardware system, realizes parallel data processing structure, thereby has reduced the time that the three-dimensional waveform data are processed and analyzed, and improves accidental abnormal signal capture ability and accuracy.
Although the above is described the illustrative embodiment of the present invention; so that those skilled in the art understand the present invention; but should be clear; the invention is not restricted to the scope of embodiment; to those skilled in the art; as long as various variations appended claim limit and the spirit and scope of the present invention determined in, these variations are apparent, all utilize innovation and creation that the present invention conceives all at the row of protection.

Claims (1)

1. the method for detecting abnormality of three-dimensional waveform data is characterized in that, may further comprise the steps:
(1), to adopt vertical resolution be the ADC collection signal of dbit, each sampling number that gathers is k, each sampled point has m=2 dIndividual amplitude value 0,1 ..., 2 d-1, in hardware system, the N amplitude wave graphic data that collects in the time T is mapped to three-dimensional data base as sample, this three-dimensional data base is expressed as the two-dimensional matrix A of m * k:
A = a 11 , a 12 , · · · , a 1 k a 21 , a 22 , · · · , a 2 k · · · · · · · · · · · · · · · · · · a m 1 , a m 2 , · · · , a mk = B 1 B 2 · · · B m = ( A 1 , A 2 , · · · , A k )
Wherein, a IjJ sampled point amplitude value is 2 in the collection of expression N amplitude wave graphic data dThe hit-count of-i, the vectorial B of row i=(a I1, a I2..., a Ik), the amplitude value that 1≤i≤m is corresponding is 2 d-i, column vector A j=(a j, a 2j..., a Mj), 1≤j≤k represents the mapping vector of j sampled point;
(2), sensitivity parameter η is set, 0<η≤1, structure point set K jFor:
K j={2 d-i|a ij≥N*η}
K jJ sampled point hit-count a during expression N amplitude wave graphic data gathers IjThe amplitude value point set point set of 〉=N* η; Change sensitivity parameter η and can change the accuracy that abnormal signal detects;
(3), hit probability matrix P corresponding to Two-dimensional matrix A:
P = A N = p 11 , p 12 , · · · , p 1 k p 21 , p 22 , · · · , p 2 k · · · · · · · · · · · · · · · · · · p m 1 , p m 2 , · · · , p mk
Wherein, p Ij=a Ij/ N, 1≤i≤m, 1≤j≤k represent that j sampled point amplitude value is 2 in the collection of N amplitude wave graphic data dThe hit probability of-i;
(4), according to the hit probability p of each amplitude sample value of j sampled point among the hit probability matrix P 1j, p 2j..., p Mj, with point set K jIn element be divided into R sub-range:
K j = ∪ n = 1 R K n sub = ∪ n = 1 R ( a n , b n )
Wherein
Figure FDA00002639480800014
Represent n sub-range, a nAnd b nThe end points of sampled point amplitude value in expression is interval, and K n 1 sub ∩ K n 2 sub = 0,1 ≤ n 1 ≠ n 2 ≤ R ;
The sub-range
Figure FDA00002639480800021
Corresponding interval hit probability is
Figure FDA00002639480800022
Equal the subspace
Figure FDA00002639480800023
In each amplitude value hit probability sum;
If two or more continuous sub-ranges are arranged
Figure FDA00002639480800024
Corresponding interval hit probability
Figure FDA00002639480800025
Equate, then with these sub-ranges Merge into a sub-range;
(5), by interval hit probability Order from big to small is successively with each sub-range in j sampled point interval Interval range a nAnd b nStore in the register, as the template of the amplitude value abnormality test of j sampled point;
(6), waveform to be collected is carried out the waveform acquisition that sampling number is similarly k, the wave-shape amplitude value representation that collects is W=(w 1, w 2..., w k), 0≤w i≤ 2 d-1,1≤j≤k is with the range value w of j sampled point jCompare with the amplitude value abnormality test template of j sampled point, if there is a sampled point to drop on outside the interval range, then anomalous event occurs, and this Wave data is shone upon and shows; If the wave-shape amplitude value w of all sampled points 1, w 2..., w kAll drop on outside the amplitude value abnormality test template interval range, then waveform is normal, signal is not shone upon and shows.
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CN105403747A (en) * 2015-11-04 2016-03-16 中国电子科技集团公司第四十一研究所 Multi-template synchronous test method and oscilloscope
CN106896250A (en) * 2015-12-17 2017-06-27 北京航天测控技术有限公司 A kind of display methods of three-dimensional waveform data
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Application publication date: 20130410