CN102176678B - A kind of wavelet packet decomposition node and corresponding frequency band are retrieved and programmed method - Google Patents

Abstract

A kind of wavelet packet decomposition node and corresponding frequency band are retrieved and programmed method, and object to determine the relation also last programming realization of affiliated frequency range, location wavelet packet decomposition node and frequency range fast; The present invention is first according to engineering requirements determination sample frequency f _swith frequency resolution Δ f, according to the f of handled signal _sand Δ f requires to determine WAVELET PACKET DECOMPOSITION number of plies n; According to Shannon's sampling theorem determination maximum frequency range f _maxafter, by (0 ~ f _max) as frequency range corresponding to start node (0-0), then successively decompose; Derivation node serial number NNo and band limits numbering fNo relation; Node serial number NNo and band limits numbering fNo relation are programmed, analyzes in relational expression the variable occurred, determine and the defined variable why data of type or character; The condition of application program language and Do statement, array and subprogram and call knowledge, with brief program realize the search function in programming.

Description

A kind of wavelet packet decomposition node and corresponding frequency band are retrieved and programmed method

Technical field

Decompose the method that node and corresponding frequency band carry out retrieving and programming when the present invention relates to a kind of wavelet packet analysis signal, be specially adapted to the detection to fault-signal characteristic frequency.

Background technology

In recent years, Wavelet Packet Analysis with its have time-frequency analysis characteristic and be widely used in signal transacting field, the research of people concentrates on the aspect such as energy, probability calculation of the selection of Wavelet Entropy, the determination of wavelet packet level, the decomposition and reconstruction of wavelet packet and different frequency range mostly, when using this technology, above content is all extremely important undoubtedly, but, when utilizing wavelet package transforms to carry out fault-signal extraction, but occur that fault signature frequency range is difficult to the problem of accurately location.When Decomposition order is lower, often can decomposes frequency range according to manual, finding the frequency range at fault characteristic frequency place and the node of correspondence thereof by observing; When Decomposition order often increases one deck, resolution can improve 50%, and nodes can comparatively double by last layer.Therefore when the number of plies is more, decompose frequency range by hand if still utilized, then observe frequency range and the node at trouble-shooting characteristic frequency place, both time-consuming, require great effort again, also inaccurate.At present, for the correspondence problem of frequency range and node, in " Fault Detection of Rotor Bar Breaking for Squirrel Cage Asynchronous based on wavelet package transforms " literary composition of 02 phase in 2008 " heavy motor technology ", once " filter paths " was adopted to solve, by distinguishing low pass filter and high pass filter two kinds of paths, they are designated as 0 and 1 respectively, then obtain a binary digit; And then a binary digit is set represents frequency range, finally investigate from left to right along filter paths, determine the corresponding relation of wavelet packet decomposition node and frequency range with this.But the defect of the method can not find frequency range position belonging to it fast according to given frequency.

Summary of the invention

The present invention seeks to the deficiency overcoming above-mentioned prior art, propose a kind of can according to given frequency determine fast affiliated frequency range, location wavelet packet decomposition node and frequency range relation and finally the wavelet packet decomposition node of programming realization and corresponding frequency band are retrieved and programmed method.

The inventive method comprises the steps:

(1) according to engineering requirements, determine the number of times of needs collection per second during collection signal, i.e. sample frequency, is set to f _s, unit is Hz; Wish when then determining analytic signal to reach the minimum number of bits to frequency discrimination, i.e. frequency resolution, be set to Δ f, unit is Hz;

(2) according to the sample frequency f of handled signal _sand frequency resolution Δ f requirement, wavelet packet analysis is carried out to signal.During wavelet packet analysis, one of top priority determines the WAVELET PACKET DECOMPOSITION number of plies, represents with n; Corresponding interstitial content is 2 ⁿindividual.Decomposition order is different, then the interstitial content decomposing out is different, and their relation is shown in Table 1.By relational expression determine the number of plies n of WAVELET PACKET DECOMPOSITION;

Table 1: the WAVELET PACKET DECOMPOSITION number of plies and nodes

(3) according to Shannon's sampling theorem determination maximum frequency range f _maxafter, by (0 ~ f _max) as frequency range corresponding to start node (0-0), then successively decompose, 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 determining Decomposition order n, sort to decompose node serial number (corresponding in table 1) as index, list the actual corresponding information slip of wavelet packet decomposition node and frequency range, be called for short table 2, wherein n is set to 11, 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) ..., now band limits has 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)

The situation of aliasing crossover phenomenon is there is, to 0 ~ f for the band limits of corresponding node in table 2 _maxscope is equidistantly decomposed by Decomposition order n and frequency resolution Δ f, and 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;

Search the band limits at the characteristic frequency place that need detect in table 2, record its node serial number, represent with NNo; Go again in table 3 to find characteristic frequency place band limits, search the band limits at the signal collected middle characteristic frequency place that need detect, record its reference numeral, represent with fNo; Then go again in table 2 to find node corresponding to characteristic frequency place band limits, record its reference numeral, represent with NNo; List the mapping table between NNo and fNo, be called for short table 4, wavelet packet decomposition node and corresponding frequency band thereof can be retrieved accordingly;

Table 3: band limits serial number (f from small to large _s=2500Hz, n=11)

Table 4: node serial number and band limits number between corresponding relation

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 is n, node serial number NNo is from 0 numbering to 2 ⁿ-1; Band limits numbering fNo is 0 to 2 ⁿin the scope of-1, but the number order corresponding with NNo is: the band limits numbering fNo of the first half of n-th layer and whole frequency ranges of the (n-1)th floor are number identical, and the band limits numbering fNo of latter half is that all frequency ranges number of the (n-1)th floor add 2 simultaneously ^n-1, and then inverted sequence is connected with the first half band limits number order of n-th layer and synthesizes n-th layer, the order of all band limits numberings of n-th layer.

Represent NNo with integer variable i, variable a represents fNo, and the band limits numbering rule of n-th layer latter half is:

a(i)＝a(i-2 ^n-1)+2 ^n-1(n＝2、3、4......)

Wherein, a (i) represents the band limits numbering that n-th layer i-th node serial number is corresponding, i span [2 ^n-1, 2 ⁿ-1]; After "+" 2 ^n-1for needing the numerical value added on (n-1)th layer of all elements, the situation of n=1 is given in advance;

(6) node serial number NNo and band limits numbering fNo relation are programmed.Analyze in relational expression the variable occurred, determine and the defined variable why data of type or character.Fully neatly application program language conditional statement, Do statement, array, subprogram and the knowledge such as to call, with brief program realize the search function in programming.

Utilize the upper and lower rank of the relation determination Do statement of node and the frequency range of having derived, and coding:

(1) cyclic program is:

Fori＝2^(n-1)To2^n-1

a(i)＝a(i-2^(n-1))+2^(n-1)

Nexti

(2) inverted sequence program is:

Fori＝2^(n-1)To3*2^(n-2)-1

t＝a(i)

a(i)＝a(3*2^(n-1)-1-j)

a(3*2^(n-1)-1-i)＝t

Nexti

Band limits numbering after inverted sequence is connected with the first half band limits number order of n-th layer, the order of all band limits numberings of synthesis n-th layer.

The quick position of fault characteristic frequency and the extraction of associated eigenvalue when the inventive method is suitable for wavelet packet analysis fault-signal.The present invention analyzes the corresponding relation of wavelet packet decomposition node and frequency range, from low frequency and the high frequency distribution rule of every hierachical decomposition, affiliated frequency range can be determined fast according to given frequency, the relation of location wavelet packet decomposition node and frequency range, propose the method for respective nodes and frequency retrieval and programming, efficiently solve the quick positioning question of characteristic frequency place frequency range in WAVELET PACKET DECOMPOSITION, and the band limits problem identificatioin of specified node, the further application of wavelet packet analysis method can be promoted.

Accompanying drawing explanation

Fig. 1 is the programming block diagram of wavelet packet decomposition node and frequency range.

Embodiment

In the present embodiment, the signal of WAVELET PACKET DECOMPOSITION is the stator current of threephase asynchronous after rotor generation broken bar fault, and its fault characteristic frequency is (1 ± 2kS) f ₁, f ₁for power supply frequency, namely power frequency 50Hz, S are motor slip ratio, general value between 0.01 ~ 0.06, then 2Sf ₁numerical value be 1 ~ 6.Therefore, to ask the 2Sf detected around dominant frequency ₁component, should require that detecting frequency resolution is not more than 1.In order to reach the requirement of resolution, when sample frequency fs is selected, can by relational expression determine the number of plies of WAVELET PACKET DECOMPOSITION, such as, when sample frequency is 5000Hz, the WAVELET PACKET DECOMPOSITION number of plies is taken as 12 layers, decomposes nodes and reaches 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 is also 0.61.As can be seen here, the number of the WAVELET PACKET DECOMPOSITION number of plies can be decided by the sample rate of signal and frequency resolution.

In the present embodiment, signal sampling frequency is 2500Hz, and the range of initial frequencies of WAVELET PACKET DECOMPOSITION is (0 ~ 1250Hz), and resolution is not more than 0.8, and the WAVELET PACKET DECOMPOSITION number of plies is 11 layers, and nodes is 2048.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, be 0 respectively, 1,3......; Band limits by frequency from small to large serial number be 0,1,2,3......, be designated as fNo; Node sequence is numbered with the corresponding situation of frequency range serial number in table 4.

The relation of analytical table 4, finds out the contact between them.When Decomposition order is 1, decomposition result is 2; When Decomposition order is 2, decomposition result is 4; When Decomposition order is 3, decomposition result is 8, the like, when Decomposition order is n, decomposition result is 2 ⁿ.Be numbered standard with node sequence, show that frequency range serial number is 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 n-th layer is 2 times of the band number of (n-1)th layer, and whole frequency ranges number of the label of the first half of n-th layer and the (n-1)th floor fit like a glove, the label of the latter half of n-th layer is then that all frequency ranges number of the (n-1)th floor add 2 simultaneously ^n-1, and then inverted sequence, first half that is last and n-th layer is linked in sequence synthesis n-th layer.

All frequency range serial number fNo of decomposition layer are assigned to aray variable a, and the size of array is set to 2 ⁿ.Crucial part is must be consistent with decomposition node number NNo by the subscript index of a, namely replaces the position of node with the index of variable a.To when programming with co-relation, frequency range serial number when Decomposition order is 1 needs given, i.e. a (0)=0, a (1)=1, latter half frequency range serial number when then showing that Decomposition order is greater than 2 according to Do statement, i.e. a (i)=a (i-2 ^n-1)+2 ^n-1(n=2,3,4......)

Wherein, a (i) represents the band limits numbering that n-th layer i-th node serial number is corresponding, and i represents n-th layer latter half arbitrary element, span [2 ^n-1, 2 ⁿ-1]; After "+" 2 ^n-1for needing the numerical value added on (n-1)th layer of all elements.

Cyclic program is as follows: Fori=2^ (n-1) To2^n-1

a(i)＝a(i-2^(n-1))+2^(n-1)

Nexti

Then by a (2 after process ^n-1) ~ a (2 ⁿ-1) element inverted sequence exchanges arrangement, again as a (2 ^n-1) ~ a (2 ⁿ-1) element, i.e. a (2 ⁿ-1) element and a (2 ^n-1) element exchange, realize inverted sequence arrangement.Inverted sequence program is:

Fori＝2^(n-1)To3*2^(n-2)-1

t＝a(i)

a(i)＝a(3*2^(n-1)-1-j)

a(3*2^(n-1)-1-i)＝t

Nexti

Retrieval embodiment: incoming frequency, the frequency range serial number fNo at retrieval place, as input 50Hz, obtaining fNo is 81.FNo belongs to an element of array a, retrieves the call number of this element.FNo be 81 element index number be 121.The call number of fNo element and wavelet packet decomposition node are number consistent, draw the node NNo at given frequency place thus.50Hz is on node 11-121, and band limits is 49.438 ~ 50.049.Retrieve the frequency range of given node if want, then carry out above-mentioned inverse process.

Programming implementation method is: 1) frequency range serial number fNo involved in WAVELET PACKET DECOMPOSITION retrieving and band limits are given respectively title difference, two aray variables that size is identical, node serial number NNo is 0 ~ 2 ⁿthe integer of-1, represents NNo with integer variable i; 2) adopt Do statement to carry out assignment, conjugation condition statement and subprogram are comprehensively programmed.During programming, the number of plies of WAVELET PACKET DECOMPOSITION is limited by conditional statement, and aforementioned circulation and inverted sequence program are called in order to main program as subprogram; The loop nesting problem run in programming process is realized by the method for main program cycle call subroutine.3) the upper and lower rank of the relation determination Do statement of node and the frequency range of having derived are utilized.Element correspondence respectively measured leaves in each variable of same call number, this makes it possible to the correct output realizing result easily.

Claims (2)

1. wavelet packet decomposition node and corresponding frequency band are retrieved and a programmed method, it is characterized in that:

(1) according to engineering requirements, determine the number of times of needs collection per second during collection signal, i.e. sample frequency, is set to

F _s, unit is Hz; Wish when then determining analytic signal to reach the minimum number of bits to frequency discrimination, i.e. frequency resolution, is set to

Δ f, unit is Hz;

(2) according to the sample frequency f of handled signal _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 △ f= determine the number of plies n of WAVELET PACKET DECOMPOSITION;

(3) according to Shannon's sampling theorem determination maximum frequency range f _maxafter, by (0 ~ f _max) as frequency range corresponding to start node (0-0), then successively decompose, 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 determining Decomposition order n, sorts as index to decompose node serial number, list wavelet packet decomposition node and the actual corresponding information slip of frequency range, be called for short table 2; The situation of aliasing crossover phenomenon is there is, to 0 ~ f for the band limits of corresponding node in table 2 _maxscope is equidistantly decomposed by Decomposition order or nodes, frequency resolution, lists band limits serial number table from small to large, is called for short table 3; Search the band limits at the characteristic frequency place that need detect in table 2, record its node serial number, represent with NNo; Go again in table 3 to find characteristic frequency place band limits, record its reference numeral, represent with fNo; List the mapping table between NNo and fNo, be called for short table 4; Wavelet packet decomposition node and corresponding frequency band thereof can be retrieved accordingly;

(4) derivation node serial number NNo and band limits numbering fNo relation; In table 4, when the WAVELET PACKET DECOMPOSITION number of plies is n, node serial number NNo is from 0 numbering to 2 ⁿ-1; Band limits numbering fNo is 0 to 2 ⁿin the scope of-1, but the number order corresponding with NNo is: the band limits numbering fNo of the first half of n-th layer and whole frequency ranges of the (n-1)th floor are number identical, and the band limits numbering fNo of latter half is that all frequency ranges number of the (n-1)th floor add 2 simultaneously ^n-1, and then the first half of inverted sequence and n-th layer is linked in sequence synthesis n-th layer;

Represent NNo with integer variable i, aray variable a represents fNo, and the band limits numbering rule of n-th layer latter half is:

a(i)＝a(i-2 ^n-1)+2 ^n-1(n＝2、3、4......)

Wherein, a (i) represents the band limits numbering that n-th layer i-th node serial number is corresponding, i span [2 ^n-1, 2 ⁿ-1]; After "+" 2 ^n-1for needing the numerical value added on (n-1)th layer of all elements, the situation of n=1 is given in advance;

(5) node serial number NNo and band limits numbering fNo relation are programmed, analyze in relational expression the variable occurred, determine and the defined variable why data of type or character; Conditional statement, Do statement, array and the subprogram of application program language and call knowledge, with program realize the search function in programming.

2. wavelet packet decomposition node as claimed in claim 1 and corresponding frequency band are retrieved and programmed method, it is characterized in that the upper and lower rank of the relation determination Do statement utilizing node and the frequency range of having derived, and coding:

(1) cyclic program is:

Fori＝2^(n-1)To2^n-1

a(i)＝a(i-2^(n-1))+2^(n-1)

Nexti

(2) inverted sequence program is:

Fori＝2^(n-1)To3*2^(n-2)-1

t＝a(i)

a(i)＝a(3*2^(n-1)-1-j)

a(3*2^(n-1)-1-i)＝t

Nexti

Band limits numbering after inverted sequence is connected with the first half band limits number order of n-th layer, the order of all band limits numberings of synthesis n-th layer.