CN102176678A - Wavelet packet decomposition node and corresponding frequency band researching and programming method - Google Patents

Wavelet packet decomposition node and corresponding frequency band researching and programming method Download PDF

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CN102176678A
CN102176678A CN2011100348552A CN201110034855A CN102176678A CN 102176678 A CN102176678 A CN 102176678A CN 2011100348552 A CN2011100348552 A CN 2011100348552A CN 201110034855 A CN201110034855 A CN 201110034855A CN 102176678 A CN102176678 A CN 102176678A
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node
frequency
wavelet packet
layer
band limits
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CN102176678B (en
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吝伶艳
宋建成
田慕琴
耿蒲龙
郑丽君
谢特列
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Taiyuan University of Technology
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Abstract

The invention relates to a wavelet packet decomposition node and corresponding frequency band researching and programming method, having the aims of quickly determining the frequency band according to the given frequency, locating the relation between the wavelet packet decomposition node and the frequency band, and finally programming for realization. The researching and programming method comprises the steps of: firstly, determining the sampling frequency fs and the frequency resolution delta f according to the engineering practical requirements, determining the number n of wavelet packet decomposition layers according to the fs and delta f of the processed signals; determining the maximum frequency range fmax according to the Shannon's sampling theorem, taking (0-fmax) as the frequency band corresponding to the initial node (0-0), then performing decomposition layer by layer; deriving the relation between the node number NNo and the frequency band range number fNo; programming the relation between the node number NNo and the frequency band range number fNo, analyzing the variables in the relation, determining and defining which types of data or characters the variables are; and applying conditional statements and loop statements in a program language, arrays, subprograms and call knowledge thereof to realize the retrieval function in the program by a short program.

Description

A kind of WAVELET PACKET DECOMPOSITION node and corresponding frequency band retrieval and programmed method
Technical field
Decompose the method that node and corresponding frequency band are retrieved and programmed when the present invention relates to a kind of wavelet packet analysis signal, be specially adapted to detection the fault-signal characteristic frequency.
Background technology
In recent years, the wavelet packet analysis technology so that it was had-frequency analysis characteristic and be widely used in the signal processing field, people's research concentrates on aspects such as the energy, probability calculation of the decomposition and reconstruction of the determining of selection, wavelet packet level, wavelet packet of Wavelet Entropy and different frequency range mostly, above content is all extremely important undoubtedly when this technology of utilization, yet, when utilizing wavelet package transforms to carry out the fault-signal extraction, the fault signature frequency range but occurred and be difficult to the accurately problem of location.When the decomposition number of plies is low, often can find the node of the frequency range and the correspondence thereof at fault characteristic frequency place by observation according to the manual frequency range of decomposing; When decomposing the every increase one deck of the number of plies, resolution can improve 50%, and the node number can double than last layer.Therefore work as the number of plies more for a long time, if still utilize the manual frequency range of decomposing, observe the frequency range and the node at trouble-shooting characteristic frequency place then, both time-consuming, effort is also inaccurate again.At present, correspondence problem for frequency range and node, in " based on the squirrel cage induction motor rotor fault diagnosis of wavelet package transforms " literary composition of 2008 02 phases " big motor technology ", once adopted " filter paths " to solve, by distinguishing low pass filter and two kinds of paths of high pass filter, they are designated as 0 and 1 respectively, then obtain a binary digit; And then a binary digit is set represents frequency range, investigate from left to right along filter paths at last, determine the corresponding relation of WAVELET PACKET DECOMPOSITION node and frequency range with this.But the defective of this method is to find frequency range position under it fast according to given frequency.
Summary of the invention
The present invention seeks to overcome the deficiency of above-mentioned prior art, propose a kind of WAVELET PACKET DECOMPOSITION node and corresponding frequency band retrieval and the programmed method that can determine the also last programming realization of relation of affiliated frequency range, location WAVELET PACKET DECOMPOSITION node and frequency range according to given frequency fast.
The inventive method comprises the steps:
(1) according to the actual requirement of engineering, the number of times that per second need be gathered when determining acquired signal, promptly sample frequency is made as f with it s, unit is Hz; Wish to reach the minimum number of bits to frequency discrimination when determining analytic signal then, promptly frequency resolution is made as Δ f, and unit is Hz;
(2) according to processing signals sampling frequency f sAnd frequency resolution Δ f requirement, signal is carried out wavelet packet analysis.During wavelet packet analysis, one of top priority is to determine the WAVELET PACKET DECOMPOSITION number of plies, represents with n; Corresponding interstitial content is 2 nIndividual.Decompose number of plies difference, then decompose the interstitial content difference of coming out, their relation is shown in Table 1.By relational expression
Figure BSA00000431221500011
Determine the number of plies n of WAVELET PACKET DECOMPOSITION;
Table 1: the WAVELET PACKET DECOMPOSITION number of plies and node number
Figure BSA00000431221500021
(3) determine maximum frequency range f according to Shannon's sampling theorem MaxAfter, with (0～f Max) as the corresponding frequency range of start node (0-0), successively decompose then, each node includes low-frequency range and high band two parts when decomposing again.
Low-frequency range and high band resolution model are analyzed, determining to decompose on the basis of number of plies n, sort as index to decompose node serial number (corresponding in the table 1), list the actual corresponding information slip of WAVELET PACKET DECOMPOSITION node and frequency range, be called for short table 2, wherein n is made as 11, the node sequencing label is 11-0,11-1,11-2,11-3......, the band limits of corresponding node is (0～0.61), (0.61～1.221), (1.831～2.441), (1.221～1.83) ..., this moment, band limits had the aliasing crossover phenomenon to occur;
Table 2: the actual corresponding situation (f of WAVELET PACKET DECOMPOSITION node (only listing 14 nodes) and frequency range s=2500Hz, n=11)
Node serial number Band limits (Hz) Node serial number Band limits (Hz)
11-0 (0～0.61) 11-7 (3.052～3.662)
11-1 (0.61～1.221) 11-8 (9.155～9.766)
11-2 (1.831～2.441) 11-9 (8.545～9.155)
11-3 (1.221～1.83) 11-10 (7.324～7.935)
11-4 (4.272～4.883) 11-11 (7.935～8.545)
11-5 (3.662～4.272) 11-12 (4.883～5.493)
11-6 (2.441～3.052) 11-13 (5.493～6.104)
At the band limits of corresponding node in the table 2 situation of aliasing crossover phenomenon appears, to 0～f MaxScope is equidistantly decomposed by decomposing number of plies n and frequency resolution Δ f, and the corresponding frequency band scope is numbered by frequency order from small to large, lists band limits serial number table from small to large, is called for short table 3;
In table 2, search the band limits at the characteristic frequency place that needs detection, write down its node serial number, represent with NNo; In table 3, go again to seek characteristic frequency place band limits, search the signal collected middle band limits that needs the characteristic frequency place of detection, write down its reference numeral, represent with fNo; In table 2, remove to seek the node of characteristic frequency place band limits correspondence then again, write down its reference numeral, represent with NNo; List the mapping table between NNo and the fNo, be called for short table 4, can retrieve WAVELET PACKET DECOMPOSITION node and corresponding frequency band thereof in view of the above;
Table 3: band limits serial number (f from small to large s=2500Hz, n=11)
Figure BSA00000431221500031
Table 4: the corresponding relation between node serial number and the band limits numbering
fNo 0 1 3 2 6 7 5 4 12 13 15 14 10 11 9 8 24 …
11-NNo 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 …
(4) derivation node serial number NNo and band limits numbering fNo relation.In table 4, when the WAVELET PACKET DECOMPOSITION number of plies was n, node serial number NNo numbered to 2 from 0 n-1; FNo is 0 to 2 for the band limits numbering nIn-1 the scope, but the number order corresponding with NNo is: the band limits numbering fNo of the first half of n layer and whole frequency segment numbers of n-1 layer are identical, and the band limits numbering fNo of latter half is that all frequency segment numbers of n-1 layer add 2 simultaneously N-1, and then inverted sequence is connected synthetic n layer, the order of all band limits numbering of n layer with the first half band limits number order of n layer.
I represents NNo with integer variable, and variable a represents fNo, and the band limits numbering rule of n layer latter half is:
a(i)＝a(i-2 n-1)+2 n-1(n＝2、3、4......)
Wherein, the band limits numbering of i node serial number correspondence of a (i) expression n layer, i span [2 N-1, 2 n-1]; After "+" 2 N-1Be the numerical value that needs to add on n-1 layer all elements, the situation of n=1 is given in advance;
(6) node serial number NNo and band limits numbering fNo relation are programmed.Why type data or character of the variable that occurs in the analyze relationship formula, decision and defined variable.Conditional statement, Do statement, array, the subprogram of application program language and knowledge such as call fully neatly, with brief program realize the search function in being programme.
The node that utilization has been derived and the relation of frequency range are determined the upper and lower rank of Do statement, and coding:
(1) cyclic program is:
For?i＝2^(n-1)To?2^n-1
a(i)＝a(i-2^(n-1))+2^(n-1)
Next?i
(2) the inverted sequence program is:
For?i＝2^(n-1)To?3*2^(n-2)-1
t＝a(i)
a(i)＝a(3*2^(n-1)-1-j)
a(3*2^(n-1)-1-i)＝t
Next?i
Band limits numbering after the inverted sequence is connected with the first half band limits number order of n layer, the order of all band limits numberings of synthetic n layer.
The quick location of fault characteristic frequency and the extraction of associated eigenvalue when the inventive method is suitable for the wavelet packet analysis fault-signal.The present invention has analyzed the corresponding relation of WAVELET PACKET DECOMPOSITION node and frequency range, low frequency and high frequency distribution rule from every level decomposition, frequency range under can determining fast according to given frequency, the relation of location WAVELET PACKET DECOMPOSITION node and frequency range, the method of retrieval of respective nodes and frequency and programming has been proposed, efficiently solve the quick positioning question of characteristic frequency place frequency range in the WAVELET PACKET DECOMPOSITION, and the band limits problem identificatioin of specified node, the further application of wavelet packet analysis method can be promoted.
Description of drawings
Fig. 1 is the programming block diagram of WAVELET PACKET DECOMPOSITION node and frequency range.
Embodiment
The signal of WAVELET PACKET DECOMPOSITION is the stator current of threephase asynchronous behind rotor generation broken bar fault in the present embodiment, and its fault characteristic frequency is (1 ± 2kS) f 1, f 1Be the power supply frequency, i.e. power frequency 50Hz, S is a motor slip ratio, general value between 0.01～0.06,2Sf then 1Numerical value be 1～6.Therefore, if require to detect dominant frequency 2Sf on every side 1Component should require to detect frequency resolution and be not more than 1.In order to reach the requirement of resolution, under the situation that sample frequency fs selectes, can be by relational expression
Figure BSA00000431221500041
Determine the number of plies of WAVELET PACKET DECOMPOSITION, for example, when sample frequency was 5000Hz, the WAVELET PACKET DECOMPOSITION number of plies was taken as 12 layers, decomposed the node number and reached 2 12Individual, frequency resolution Δ f is 0.61; If sample rate is 2500Hz, the WAVELET PACKET DECOMPOSITION number of plies is taken as 11 layers, decomposes node and reaches 2 11Individual, frequency resolution Δ f also is 0.61.This shows that what of the WAVELET PACKET DECOMPOSITION number of plies can be decided by signals sampling rate and frequency resolution.
The signal sampling frequency is 2500Hz in the present embodiment, and the range of initial frequencies of WAVELET PACKET DECOMPOSITION is that (0～1250Hz), resolution is not more than 0.8, and the WAVELET PACKET DECOMPOSITION number of plies is 11 layers, and the node number is 2048.The node and the frequency range of WAVELET PACKET DECOMPOSITION are as shown in table 1.Node sequence is numbered 11-0,11-1,11-2,11-3......, is designated as 11-NNo, is 0,1 respectively, 3......; Band limits by frequency from small to large serial number be 0,1,2,3......, be designated as fNo; The node sequence numbering sees Table 4 with the corresponding situation of frequency range serial number.
The relation of analytical table 4 is found out the contact between them.Decomposing the number of plies is 1 o'clock, and decomposition result is 2; Decomposing the number of plies is 2 o'clock, and decomposition result is 4; Decomposing the number of plies is 3 o'clock, and decomposition result is 8, and the like, when the decomposition number of plies was n, decomposition result was 2 n.Be numbered standard with node sequence, draw the frequency range serial number and be respectively:
1 layer of decomposition: 0-1; 2 layers of decomposition: 0-1-3-2; 3 layers of decomposition: 0-1-3-2-6-7-5-4; 4 layers of decomposition: 0-1-3-2-6-7-5-4-12-13-15-14-10-11-9-8; 5 layers of decomposition: 0-1-3-2-6-7-5-4-12-13-15-14-10-11-9-8-24-25-27-26-30-31-29-28-20-21-23-22-18-19-17-16; ...
Observe above listed content, find that the n layer is 2 times of frequency range number of n-1 layer, and whole frequency segment numbers of the label of the first half of n layer and n-1 layer fit like a glove, the label of the latter half of n layer then is that all frequency segment numbers of n-1 layer add 2 simultaneously N-1, and then inverted sequence, last first half with the n layer is linked in sequence and synthesizes the n layer.
All frequency range serial number fNo of decomposition layer are composed to aray variable a, and the size of array is made as 2 nCrucial part is must be consistent with decomposition node number NNo with the subscript index of a, promptly replaces the position of node with the index of variable a.When programming with co-relation, the frequency range serial number that decomposed the number of plies and be 1 o'clock needs given, i.e. a (0)=0, and a (1)=1 draws according to Do statement then and decomposes the number of plies greater than 2 o'clock latter half frequency range serial number, i.e. a (i)=a (i-2 N-1)+2 N-1(n=2,3,4......)
Wherein, the band limits numbering of i node serial number correspondence of a (i) expression n layer, i represents n layer latter half arbitrary element, span [2 N-1, 2 n-1]; After "+" 2 N-1Be the numerical value that on n-1 layer all elements, needs to add.
Cyclic program is as follows: For i=2^ (n-1) To 2^n-1
a(i)＝a(i-2^(n-1))+2^(n-1)
Next?i
A (2 after will handling then N-1)～a (2 n-1) element inverted sequence exchange is arranged, again as a (2 N-1)～a (2 n-1) element, promptly a (2 n-1) element and a (2 N-1) element exchange, realize that inverted sequence arranges.The inverted sequence program is:
For?i＝2^(n-1)To?3*2^(n-2)-1
t＝a(i)
a(i)＝a(3*2^(n-1)-1-j)
a(3*2^(n-1)-1-i)＝t
Next?i
The retrieval embodiment: incoming frequency, the frequency range serial number fNo at retrieval place, as input 50Hz, getting fNo is 81.FNo belongs to the element of array a, retrieves the call number of this element.FNo is that 81 element index number is 121.The call number of fNo element is consistent with the WAVELET PACKET DECOMPOSITION node number, draws the node NNo at given frequency place thus.50Hz is on node 11-121, and band limits is 49.438～50.049.If want to retrieve the frequency range of given node, then carry out above-mentioned inverse process and get final product.
The programming implementation method is: 1) give title difference, big or small two identical aray variables respectively with frequency range serial number fNo related in the WAVELET PACKET DECOMPOSITION retrieving and band limits, node serial number NNo is 0～2 n-1 integer, i represents NNo with integer variable; 2) adopt Do statement to carry out assignment, comprehensively programme in conjunction with conditional statement and subprogram.During programming, the number of plies of WAVELET PACKET DECOMPOSITION limits by conditional statement, and aforementioned circulation and inverted sequence program are called in order to main program as subprogram; The loop nesting problem that is run in the method realization programming process by main program recursive call subprogram.3) utilize the relation of the node derived and frequency range to determine the upper and lower rank of Do statement.The element of each amount of correspondence is left in each variable of same call number, so just can realize result's correct output easily.

Claims (2)

1. retrieval of WAVELET PACKET DECOMPOSITION node and corresponding frequency band and programmed method is characterized in that:
(1) according to the actual requirement of engineering, the number of times that per second need be gathered when determining acquired signal, promptly sample frequency is made as f with it s, unit is Hz; Wish to reach the minimum number of bits to frequency discrimination when determining analytic signal then, promptly frequency resolution is made as Δ f, and unit is Hz;
(2) according to processing signals sampling frequency f sAnd frequency resolution Δ f requirement, determine the WAVELET PACKET DECOMPOSITION number of plies, represent with n; Corresponding interstitial content is 2 nIndividual; By relational expression
Figure FSA00000431221400011
Determine the number of plies n of WAVELET PACKET DECOMPOSITION;
(3) determine maximum frequency range f according to Shannon's sampling theorem MaxAfter, with (0～f Max) as the corresponding frequency range of start node (0-0), successively decompose then, each node includes low-frequency range and high band two parts when decomposing again;
Low-frequency range and high band resolution model are analyzed, on the basis of determine decomposing number of plies n, sorted as index, list the actual corresponding information slip of WAVELET PACKET DECOMPOSITION node and frequency range, abbreviation table 2 to decompose node serial number; At the band limits of corresponding node in the table 2 situation of aliasing crossover phenomenon appears, to 0～f MaxScope by decompose the number of plies or node number, frequency resolution is equidistantly decomposed, and lists band limits serial number table from small to large, is called for short table 3; In table 2, search the band limits at the characteristic frequency place that needs detection, write down its node serial number, represent with NNo; In table 3, go again to seek characteristic frequency place band limits, write down its reference numeral, represent with fNo; List the mapping table between NNo and the fNo, be called for short table 4; Can retrieve WAVELET PACKET DECOMPOSITION node and corresponding frequency band thereof in view of the above;
(4) derivation node serial number NNo and band limits numbering fNo relation; In table 4, when the WAVELET PACKET DECOMPOSITION number of plies was n, node serial number NNo numbered to 2 from 0 n-1; FNo is 0 to 2 for the band limits numbering nIn-1 the scope, but the number order corresponding with NNo is: the band limits numbering fNo of the first half of n layer and whole frequency segment numbers of n-1 layer are identical, and the band limits numbering fNo of latter half is that all frequency segment numbers of n-1 layer add 2 simultaneously N-1, and then the first half of inverted sequence and the n layer synthetic n layer that is linked in sequence;
I represents NNo with integer variable, and aray variable a represents fNo, and the band limits numbering rule of n layer latter half is:
a(i)＝a(i-2 n-1)+2 n-1(n＝2、3、4......)
Wherein, the band limits numbering of i node serial number correspondence of a (i) expression n layer, i span [2 N-1, 2 n-1]; After "+" 2 N-1Be the numerical value that needs to add on n-1 layer all elements, the situation of n=1 is given in advance;
(5) node serial number NNo and band limits numbering fNo relation is programmed why type data or character of the variable that occurs in the analyze relationship formula, decision and defined variable; The conditional statement of application program language, Do statement, array and subprogram and call knowledge, with brief program realize the search function in being programme.
2. retrieval of WAVELET PACKET DECOMPOSITION node as claimed in claim 1 and corresponding frequency band and programmed method is characterized in that utilizing the relation of the node of having derived and frequency range to determine the upper and lower rank of Do statement, and coding:
(1) cyclic program is:
For?i＝2^(n-1)To?2^n-1
a(i)＝a(i-2^(n-1))+2^(n-1)
Next?i
(2) the inverted sequence program is:
For?i＝2^(n-1)To?3*2^(n-2)-1
t＝a(i)
a(i)＝a(3*2^(n-1)-1-j)
a(3*2^(n-1)-1-i)＝t
Next?i
Band limits numbering after the inverted sequence is connected with the first half band limits number order of n layer, the order of all band limits numberings of synthetic n layer.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102914362A (en) * 2012-10-12 2013-02-06 宁夏电力公司电力科学研究院 Separating method for vibration signals of transformer winding and iron core
CN103471703A (en) * 2013-09-30 2013-12-25 中国人民解放军国防科学技术大学 Non-aliasing reconstruction method of high-speed leaf undersampled leaf apex vibration signals
CN110786851A (en) * 2019-10-31 2020-02-14 长春理工大学 Method for improving wavelet packet decomposition speed based on Mallat algorithm

Citations (2)

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Publication number Priority date Publication date Assignee Title
CN85103579A (en) * 1985-05-08 1986-11-05 索尼公司 The interpretation method of error correcting code and system
US5359606A (en) * 1992-02-12 1994-10-25 Storage Technology Corporation Data quality analysis in a data signal processing channel

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN85103579A (en) * 1985-05-08 1986-11-05 索尼公司 The interpretation method of error correcting code and system
US5359606A (en) * 1992-02-12 1994-10-25 Storage Technology Corporation Data quality analysis in a data signal processing channel

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102914362A (en) * 2012-10-12 2013-02-06 宁夏电力公司电力科学研究院 Separating method for vibration signals of transformer winding and iron core
CN102914362B (en) * 2012-10-12 2015-05-06 宁夏电力公司电力科学研究院 Separating method for vibration signals of transformer winding and iron core
CN103471703A (en) * 2013-09-30 2013-12-25 中国人民解放军国防科学技术大学 Non-aliasing reconstruction method of high-speed leaf undersampled leaf apex vibration signals
CN110786851A (en) * 2019-10-31 2020-02-14 长春理工大学 Method for improving wavelet packet decomposition speed based on Mallat algorithm

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