CN107239739A - A kind of scale parameter controls adjustable signal envelope extracting method - Google Patents
A kind of scale parameter controls adjustable signal envelope extracting method Download PDFInfo
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Abstract
The present invention provides a kind of scale parameter and controls adjustable signal envelope extracting method.The major advantage of this method is to possess only reaches the ability of continuous control envelope slickness by adjusting single scale parameter, overcomes the shortcoming of existing traditional envelope extracting method.This method extracts the extreme point of original signal as characteristic point sequence first；Then the partial dot that condition is met in characteristic sequence is rejected in circulation, and the length of the new feature point sequence formed at the end of double circulation is not more than given number, or the points of the characteristic point sequence newly formed are not more than three；Appropriate interpolation method is finally utilized, the characteristic point sequence retained is connected, obtains envelope.Can be by adjusting the kick-out condition of single scale parameter controlling feature point, and then control the slickness of envelope curve.Only it is the good characteristic of controllable envelope slickness by single scale parameter, disclosure satisfy that the various demands to envelope performance in actual signal processing.
Description
Technical field
Adjustable signal bag is controlled the present invention relates to a kind of signal envelope extracting method, more particularly to a kind of scale parameter
Winding thread extracting method.
Background technology
The envelope of signal is the outline of signal, and envelope provision of on-line analysis methodology is to be commonly used during Engineering Signal is handled and effective
A kind of signal analysis method, especially reciprocating mechanical vibration signal analysis and mechanical fault diagnosis analysis in have very
Important effect.Many engineering actual signal (especially reciprocating mechanical vibration signal) waveforms are extremely complex, mostly comprising many
The non-stationary signal of individual local assault, the directly difficulty to signal analysis and processing are larger, but its envelope has certain rule
Or certain trend, many useful information can be obtained to the further analysis of envelope.For example, engine cylinder head system vibration signal
Belong to typical non-stationary signal paracycle, wherein containing multiple local assaults, time-domain analysis, frequency domain directly are carried out to signal
The complexity of analysis even time frequency analysis etc. is larger, and is difficult to obtain effective law characteristic directly perceived, but vibration signal complete cycle
Envelope there is clear and intuitive wave character, and the vibration signal envelope in each cycle has significant similitude, is easy to
The appearance and the change of shock characteristic impacted to abnormal vibrations are detected, in addition by that can have to the further analysis of envelope
Effect obtains phase and the energy of impact that each impact occurs.
It is the key point for carrying out Envelope Analysis to depict suitable envelope, is also to ensure before Envelope Analysis validity
Put forward condition.Its difficult point is how to realize that automatic depict meets the envelope that Engineering Signal handles needs by algorithm, and energy
Enough lead in too small amount of state modulator envelope characteristic, such as this method and only pass through the smoothness of a state modulator envelope
Characteristic.
The method to signal envelope line drawing mainly includes two major classes at present：One class is the direct feature for extracting primary signal
Point, then characteristic point is connected by composition envelope by interpolation method, the utilization single order extreme point that such as EMD is used in decomposing is asked
The method for taking signal envelope, that is, ask for signal after extracting very big (small) the value point in signal by the method for cubic spline interpolation
Upper (lower) envelope, also envelope second order extreme value or multistage extreme value, as characteristic point, and pass through other all kinds of interpolation methods in addition
The method for carrying out line.Two classes are the bags that the low frequency signal in signal is isolated as to primary signal by the method for demodulation
Winding thread, such as Hilbert are converted and wavelet transformation carries out the method that lower-frequency envelope line is asked in envelope demodulation.In above-mentioned two classes method,
The first kind is relatively simple, and directly amount of calculation is small, and the adaptability to various types of signal is also very strong, but envelope slickness often occurs not
Good (such as there are problems that " break ") or close fitting bad (such as " overshoot " distortion) notable defect, it is often more important that occurring
After above mentioned problem, existing conventional method is difficult to only reach company by controlling a certain parameter in the case where not changing envelope algorithm
The purpose of continuous adjustment envelope performance.And in Equations of The Second Kind method, the bag of the mechanical shock signal extracted is directly converted with Hilbert
Network is often not smooth enough, and the burr existed is a lot, contains substantial amounts of high fdrequency component；Although and wavelet transformation asks the method for envelope can
To obtain the envelope of different smooth degrees by adjusting scale parameter, but the basic function with exact expression formula causes its adaptive
Should be able to power it is poor so that the disposal ability to any non-stationary, nonlinear properties is limited；In addition, the calculating of Equations of The Second Kind method compared with
For complexity, amount of calculation is larger, big and require repeatedly to calculate in real time or the occasion of cycle calculations envelope is difficult in some data volumes
Effectively applied.
The present invention fully analyzes the advantage and disadvantage that existing conventional method asks for envelope, proposes that a kind of scale parameter control can
The signal envelope extracting method of tune, this method has taken into account the advantage of above-mentioned two classes method simultaneously, and it substantially belongs to above-mentioned the
One class method, but be provided simultaneously with that the ability of continuous control envelope slickness can be reached by adjusting scale parameter.
The content of the invention
It is an object of the invention to the shortcoming and defect existed for existing traditional signal envelope extracting method there is provided
A kind of simple and effective scale parameter controls adjustable signal envelope extracting method.This method not only calculate simply, adapt to
Property it is strong, and possess only adjust single scale parameter can continuous control envelope slickness ability.
The purpose of the present invention is achieved through the following technical solutions (exemplified by above envelope, lower envelope line is similarly)：The present invention
The maximum point (single order maximum point or multistage maximum point) extracted first in original signal constitutes one group of characteristic point；Then ask for
The minimum of this group of characteristic point, and some at each minimum point or multiple characteristic values are calculated, if this feature value meets pre-
If condition then rejects it from this group of characteristic point, new characteristic point sequence is obtained；Upper one is repeated to new characteristic point sequence again
Partial Feature point is rejected in step, circulation, until it is double circulate obtained feature point number it is only poor be not more than 1 (or it is other just
Integer)；Finally the characteristic point sequence finally given is connected by the method for interpolation, the coenvelope line of signal is obtained.Its
In, the kick-out condition of characteristic point by scale parameter control so that reach adjustment single parameter can continuous control envelope it is smooth
The purpose of property.
1st, a kind of scale parameter controls adjustable signal envelope extracting method, it is characterised in that comprise the following steps：
(1) maximum point in original signal is extracted, one group of characteristic point sequence is constituted；
(2) all minimum points in features described above point sequence are extracted, the characteristic value at above-mentioned each minimum point is calculated；And
The minimum point that features described above value is met into specified criteria is rejected from features described above point sequence, forms new features described above point sequence
Row；
(3) find minimum point again in above-mentioned new characteristic point sequence, reject features described above value satisfaction and impose a condition
Minimum point；The partial dot in features described above point sequence is rejected in circulation, until meeting loop termination condition, obtains final spy
Levy point sequence；
(4) the above-mentioned new feature point sequence finally given is entered into row interpolation in primary signal, by features described above point sequence
Coenvelope line is obtained with interpolation point line.
Or
(1) minimum point in original signal is extracted, one group of characteristic point sequence is constituted；
(2) all maximum points in features described above point sequence are extracted, the characteristic value at above-mentioned each maximum point is calculated；And
The maximum point that features described above value is met into specified criteria is rejected from features described above point sequence, forms new features described above point sequence
Row；
(3) find maximum point again in above-mentioned new characteristic point sequence, reject features described above value satisfaction and impose a condition
Maximum point；The partial dot in features described above point sequence is rejected in circulation, until meeting loop termination condition, obtains final spy
Levy point sequence；
(4) the above-mentioned new feature point sequence finally given is entered into row interpolation in primary signal, by features described above point sequence
Lower envelope line is obtained with interpolation point line.
Characteristic value char in step (2)(a)(k) calculation formula is：
char(a)(k)=C(a)(k)-D(a)(k)
Wherein, C(a)(k) represent in the case where abscissa stretches yardstick for a, pass through at three o'clock at 3 points and make the circle that circle is tried to achieve
Heart ordinate, above three point is：Before and after above-mentioned steps (2) extreme point and the extreme value are in step (1) described characteristic point sequence
Two adjacent points.D(a)(k) represent that above-mentioned steps (2) extreme point is in step (1) in the case where abscissa stretches yardstick for a
Linear interpolation of 2 points of the line at above-mentioned extreme point before and after the characteristic point sequence.
And characteristic value char(a)(k) it is not more than 0.
Loop termination condition in step (3) is：The difference of the length of the new feature point sequence of double formation is not more than
Given number N_stop.N_stop typically takes the positive integer between 1-10, including 1-10.
The present invention is further illustrated below, comprises the following steps that (still exemplified by above envelope, lower envelope line is same
Reason)：
The first step, extracts the maximum point (single order maximum point or multistage maximum point) in original signal s (i), constitutes one
Group characteristic point sequence y1(j), and its position sequence x in original signal is recorded1(j)；
Second step, calculates y1(j) minimum sequences y2(k), and it is recorded in x1(j) the position sequence x in2(k), then
Its position sequence x in original signal s (i)1(x2(k) point (x), is calculated1(x2(k)),y2(k)) the characteristic value char at place(a)(k)：
char(a)(k)=C(a)(k)-D(a)(k) (1)
Wherein C(a)(k) point (x is represented2(k),y2(k)) and its in (x1(j),y1(j)) adjacent thereto front and rear two in sequence
Point, in the case where abscissa scaling is a, the center of circle ordinate that circle is tried to achieve is made by 3 points；D (a) (k) represents to sit horizontal
Scaling is marked in the case of a, abscissa, point (x are used as using position sequence of the characteristic point in original signal s (i)2(k),y2(k))
In (x1(j),y1(j)) front and rear 2 lines adjacent thereto in sequence are in x1(x2(k)) the linear interpolation at place.
If char(a)(k)<0, then by the point (x2(k),y2(k)) from (x1(j),y1(j)) rejected in sequence.
It is to provide C herein(a)And D (k)(a)(k) expression formula and its changing rule with transverse axis coefficient of dilatation a, provide with
Lower calculating process：
If three point coordinates are (x1, y1), (x2, y2), wherein (x3, y3), x1 respectively in plane<x2<X3, y1>y2,y2<
Y3, the central coordinate of circle of this 3 points determinations is (xc,yc)；Linear interpolation of 2 lines of (x1, y1), (x3, y3) at x2 is yI,
Then：
Take：
X1=x1-x2, X3=x3-x2, Xc=xc-x2；Y1=y1-y2, Y3=y3-y2, Yc=yc-y2； (4)
Then：
X1<0, X3>0；Y1>0, Y3>0； (5)
Bring into (2), obtain by various in (4)：
From (5)：
Yc>0
(8)
If making x '=ax (a>0) new center of circle ordinate Y, is then obtainedc' and interpolation point ordinate YI′:
YI'=YI
(10)
Obtained by (5)：
Therefore：During a=1, Yc'=Yc>0；
a>When 1, Yc′>Yc>0；
0<a<When 1,0<Yc′<Yc；
Calculate and understand more than：On the one hand, can be by adjusting scale parameter a (a>0) method adjusts 3 points of works
Round home position, and when scale parameter a is more than 1, with a increase, home position is improved；When scale parameter a is less than 1
When, with scale parameter a reduction, home position declines.On the other hand, the ordinate of interpolation point will not be with scale parameter a
Change and change, therefore interpolation point can be used as motionless reference point.
For ease of subsequent analysis, need to prove herein：No matter a (a>0) what value is taken, there is Yc' it is consistently greater than YI。
The Y in formula (9)c' expression formula it is recognized that while a=0 situation can cause during the derivation of equation derive
During the denominators of some formulas be zero, but final result can about fall a from denominator, but due to being set in topic in the case of,
Yc' be a increasing function, so can be in Yc' in directly make a=0 obtain level off to zero when Yc' minimum value.
Bring a=0 into formula (9), and by Yc' and YISubtracting each other to obtain：
From formula (5)：Denominator on the right of formula (11) equal sign is consistently less than zero, to prove there is Yc'>YIIt is permanent into
It is vertical, then it need to only prove there is (X1,Y1) and (X2, Y2) so that (X1Y3 2+X3Y1 2)(X3+X1)-4X1X3Y1Y3<0.
It can be set according to (5)：X1=-α X3；Y1=β Y3, wherein α>0, β>0, due in random signal, X1, Y1, X2, Y2It is
Four independent variables, then α, β can take any arithmetic number.Then on the right of formula (11) equal sign molecular moiety can abbreviation be：
Then it is readily seen in α between β2Between 1, and β sufficiently small (tending to 0) is (for example：β=0.1, α=0.5) or β
Sufficiently large (tending to be just infinite) (such as during β=10, α=5), formula (12) can be less than 0.In summary, exist (x1, y1),
(x2,y2)、(x3,y3)(x1<x2<X3, y1>y2,y2<Y3) such that no matter how zoom factor a changes, yc>yIPerseverance is set up.
Based on above calculating process, and for ease of calculating, order：
X1(x2(k) -1)=x1(x2(k)-1)-x1(x2(k))
X1(x2(k)+1)=x1(x2(k)+1)-x1(x2(k))
Y1(x2(k) -1)=y1(x2(k)-1)-y1(x2(k))
Y1(x2(k)+1)=y1(x2(k)+1)-y1(x2(k))
C can be obtainedaAnd D (k)a(k) expression formula：
3rd step, by sequences y1(j) met in after the characteristic point rejecting of formula (1) condition, form one group of new sequence, lay equal stress on
Multiple second step, the point for the condition that meets is rejected in circulation, until the points of double rejecting are not more than N_stop.
4th step, the point still remained after above-mentioned second step and third step is connected with the method for interpolation,
It is used as the coenvelope line of signal.
In the present invention, Ca(k) it is scale parameter a (a>0) function, Da(k) it is unrelated with a.Can be by adjusting scale parameter
Whether some characteristic points are removed in control signal, when a increases, then Ca(k) increase, the characteristic point quantity kicked out of is reduced,
Obtained curve is more unsmooth (i.e. closer to extreme point envelope)；When a reduces, then Ca(k) reduce, the characteristic point kicked out of
Quantity increase, obtained curve is smoother, and there is the characteristic point that can not be rejected forever, i.e., obtained by changing scale parameter a
To family's envelope in exist " most smooth " envelope limiting case.Meanwhile, same parameters a ensure that in whole Chief Signal Boatswain
In the range of degree, signal carries out envelope extraction under same yardstick.
Brief description of the drawings
Fig. 1 gasoline engine vibration original waveforms
Fig. 2 a mesoscale parameters of the present invention are 10 envelope
Fig. 2 b mesoscale parameters of the present invention are 10 envelope line thinning waveform
Fig. 3 a mesoscale parameters of the present invention are 1 envelope
Fig. 3 b mesoscale parameters of the present invention are 1 envelope line thinning waveform
Fig. 4 a mesoscale parameters of the present invention are 0.1 envelope
Fig. 4 b mesoscale parameters of the present invention are 0.1 envelope line thinning waveform
Envelope and its refinement waveform that Fig. 5 a mesoscale parameters of the present invention are 0
Fig. 5 b mesoscale parameters of the present invention are 0 envelope line thinning waveform
Fig. 6 a single order extreme value envelopes
Fig. 6 b single order extreme value envelope line thinning waveforms
The required envelope of Fig. 7 a Hilbert conversion
The refinement waveform of the required envelope of Fig. 7 b Hilbert conversion
Embodiment
In order to be best understood from technical scheme, below in conjunction with accompanying drawing to the present invention embodiment make into
The detailed description of one step.
The first step, engine cylinder head system vibration signal s complete cycle (i), as shown in figure 1, s (i) very big (small) value point is extracted,
Constitute one group of characteristic point sequence y1(j), and its position sequence x in original signal s (i) is recorded1(j)；
Second step, calculates y1(j) minimum (big) value sequence y2(k), and it is recorded in x1(j) the position sequence x in2
(k), then its position sequence x in original signal s (i)1(x2(k) point (x), is calculated1(x2(k)),y2(k)) the characteristic value at place
char(a)(k),
char(a)(k)=C(a)(k)-D(a)(k)
Wherein：
X1(x2(k) -1)=x1(x2(k)-1)-x1(x2(k))
X1(x2(k)+1)=x1(x2(k)+1)-x1(x2(k))
Y1(x2(k) -1)=y1(x2(k)-1)-y1(x2(k))
Y1(x2(k)+1)=y1(x2(k)+1)-y1(x2(k))
If meeting char(a)(k)<0 condition, then by the point (x2(k),y2(k)) from (x1(j),y1(j)) rejected in sequence,
Form new features described above point sequence；
Found again in 3rd step, the new characteristic point sequence that above-mentioned second step is obtained in minimum (big) value point, rejecting
State characteristic value and meet minimum (big) the value point imposed a condition, form new characteristic point sequence again, circulation rejecting meets char(a)
(k)<The point of 0 condition, until the difference of the length of the new feature point sequence of double formation is not more than given number N_stop.
4th step, the point that will be still remained after above-mentioned (2) step and (3) step is connected with the method for interpolation
Come, be used as the upper (lower) envelope of signal.
Scale parameter is set to a=10, a=1, a=0.1, a=0 respectively, the waveform of four kinds of envelopes is obtained, such as schemed
Shown in 2- Fig. 5；In addition, Fig. 6 is to seek the envelope that the method for envelope is tried to achieve using single order extreme value, Fig. 7 is that bag is sought in Hilbert conversion
The envelope that the method for network is tried to achieve, it is easy to see that：The envelope line drawing side of the present invention compared with traditional method for seeking envelope
Method is succinctly flexible, can according to purpose and the flatness requirement for asking for envelope, only by amendment once scale parameter can be with
Control the flatness of envelope.
Claims (1)
1. a kind of scale parameter controls adjustable signal envelope extracting method, it is characterised in that comprise the following steps：
(1) maximum point in original signal is extracted, one group of characteristic point sequence is constituted；
(2) all minimum points in features described above point sequence are extracted, the characteristic value at above-mentioned each minimum point is calculated；And will be upper
State characteristic value and meet the minimum point of specified criteria and rejected from features described above point sequence, form new features described above point sequence；
(3) find minimum point again in above-mentioned new characteristic point sequence, reject features described above value and meet the pole imposed a condition
Small value point；The partial dot in features described above point sequence is rejected in circulation, until meeting loop termination condition, obtains final characteristic point
Sequence；
(4) the above-mentioned new feature point sequence finally given is entered into row interpolation in primary signal, by features described above point sequence and insert
Value point line obtains coenvelope line；
Or
(1) minimum point in original signal is extracted, one group of characteristic point sequence is constituted；
(2) all maximum points in features described above point sequence are extracted, the characteristic value at above-mentioned each maximum point is calculated；And will be upper
State characteristic value and meet the maximum point of specified criteria and rejected from features described above point sequence, form new features described above point sequence；
(3) find maximum point again in above-mentioned new characteristic point sequence, reject features described above value and meet the pole imposed a condition
Big value point；The partial dot in features described above point sequence is rejected in circulation, until meeting loop termination condition, obtains final characteristic point
Sequence；
(4) the above-mentioned new feature point sequence finally given is entered into row interpolation in primary signal, by features described above point sequence and insert
Value point line obtains lower envelope line；
Characteristic value char in step (2)(a)(k) calculation formula is：
char(a)(k)=C(a)(k)-D(a)(k)
Wherein, C(a)(k) represent in the case where abscissa stretches yardstick for a, make the round center of circle tried to achieve by 3 points at three o'clock and indulge
Coordinate, above three point is：Above-mentioned steps (2) extreme point and the extreme value are front and rear adjacent in step (1) described characteristic point sequence
Two points；D(a)(k) represent that above-mentioned steps (2) extreme point is described in step (1) in the case where abscissa stretches yardstick for a
Linear interpolation of 2 points of the line at above-mentioned extreme point before and after characteristic point sequence；
And characteristic value char(a)(k) it is not more than 0；
Loop termination condition in step (3) is：The difference of the length of the new feature point sequence of double formation is not more than given
Number N_stop, or the points of characteristic point sequence are less than or equal to three.
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| CN113031524A (en) * | 2021-02-07 | 2021-06-25 | 南京航空航天大学 | Cubic spline-based press fitting force envelope generation method |
| CN113191317A (en) * | 2021-05-21 | 2021-07-30 | 江西理工大学 | Signal envelope extraction method and device based on pole construction low-pass filter |
| CN113191317B (en) * | 2021-05-21 | 2022-09-27 | 江西理工大学 | Signal envelope extraction method and device based on pole construction low-pass filter |
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