CN107239739B - Signal envelope extraction method with adjustable scale parameter control - Google Patents
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Abstract
The invention provides a method for extracting a signal envelope curve with adjustable scale parameter control. The method has the main advantages that the method has the capability of continuously controlling the smoothness of the envelope by only adjusting a single scale parameter, and overcomes the defects of the traditional envelope extraction method. The method comprises the steps of firstly, extracting extreme points of original signals as a characteristic point sequence; then circularly eliminating partial points which meet the conditions in the characteristic sequence until the length of a new characteristic point sequence formed when two continuous circulations are finished is not more than a given number, or the number of points of the newly formed characteristic point sequence is not more than three; and finally, connecting the reserved characteristic point sequences by using a proper interpolation method to obtain an envelope curve. The elimination condition of the characteristic points can be controlled by adjusting the single-scale parameters, and the smoothness of the envelope curve is further controlled. The excellent characteristic of envelope smoothness can be controlled only by a single scale parameter, and various requirements on envelope linear performance in actual signal processing can be met.
Description
Technical Field
The invention relates to a signal envelope extraction method, in particular to a signal envelope extraction method with adjustable scale parameter control.
Background
The envelope of the signal is the outer contour of the signal, and the envelope analysis method is a signal analysis method which is commonly used and effective in engineering signal processing, and has very important roles in reciprocating mechanical vibration signal analysis and mechanical failure diagnosis analysis in particular. Many engineering actual signals (especially reciprocating mechanical vibration signals) are very complex in waveform, mostly include a plurality of local impact non-stationary signals, and the difficulty of directly analyzing and processing the signals is large, but the envelope curve of the signals has a certain rule or a certain trend, and further analysis on the envelope curve can obtain a lot of useful information. For example, the vibration signal of the cylinder cover of the internal combustion engine belongs to a typical quasi-periodic non-stationary signal, wherein the vibration signal comprises a plurality of local impacts, the complexity of time domain analysis, frequency domain analysis, even time frequency analysis and the like of the signal is high, intuitive and effective regular characteristics are difficult to obtain, but the envelope curve of the whole period of the vibration signal has clear and intuitive waveform characteristics, the envelope curves of the vibration signal of each period have obvious similarity, the abnormal vibration impact occurrence and the impact characteristic change can be conveniently detected, and in addition, the phase position of each impact occurrence and the impact energy can be effectively obtained through further analysis of the envelope curves.
The drawing of a proper envelope is the key point of performing the envelope analysis and is a precondition for ensuring the effectiveness of the envelope analysis. The difficulty is how to automatically draw the envelope line meeting the processing requirement of engineering signals through an algorithm, and the envelope line characteristics can be controlled through a small number of parameters, such as the smoothness degree and other characteristics of the envelope line are controlled through only one parameter in the method.
The current methods for extracting signal envelope mainly include two categories: one is a method of directly extracting feature points of an original signal and then connecting the feature points by an interpolation method to form an envelope, such as a method of obtaining a signal envelope by using a first-order extreme point adopted in the EMD decomposition, i.e., a method of obtaining an upper (lower) envelope of a signal by a cubic spline interpolation method after extracting a maximum (small) value point in the signal, and further, using a second-order extreme value or a multi-order extreme value as a feature point and connecting the feature points by other various interpolation methods. The second type is a method of separating low-frequency signals in the signals by a demodulation method to be used as envelope lines of original signals, such as a method of carrying out envelope demodulation by Hilbert transform and wavelet transform to obtain low-frequency envelope lines. In the two methods, the first method is simple and direct, the calculated amount is small, the adaptability to various signals is strong, but the obvious defect problems of poor envelope smoothness (such as 'break point') or poor close fitting performance (such as 'overshoot' distortion) and the like often occur, and more importantly, after the problems occur, the purpose of continuously adjusting the envelope linear performance is difficult to achieve by only controlling a certain parameter under the condition of not changing an envelope algorithm in the conventional method. In the second method, the envelope of the mechanical shock signal extracted by directly using Hilbert transform is not smooth enough, and a large number of burrs exist and contain a large number of high-frequency components; although the envelope calculating method by wavelet transform can obtain envelope curves with different smoothness degrees by adjusting scale parameters, the self-adaptive capacity of the envelope calculating method is poor due to the fact that the basis function with an exact expression is provided, and the processing capacity of any non-stationary and non-linear signal is limited; in addition, the second method is complex in calculation and large in calculation amount, and is difficult to be effectively applied to occasions with large data volume and requirements for calculating the envelope line in real time for multiple times or in a circulating manner.
The invention fully analyzes the advantages and disadvantages of the prior traditional method for obtaining the envelope curve, and provides a signal envelope curve extraction method with adjustable scale parameter control.
Disclosure of Invention
The invention aims to provide a simple and effective method for extracting a signal envelope with adjustable scale parameter control, aiming at the defects and the defects of the traditional method for extracting the signal envelope. The method is simple in calculation and strong in adaptability, and has the capability of continuously controlling the smoothness of the envelope curve only by adjusting a single scale parameter.
The purpose of the invention is realized by the following technical scheme (the above envelope is taken as an example, and the lower envelope is the same as the above envelope): extracting maximum value points (first-order maximum value points or multi-order maximum value points) in an original signal to form a group of characteristic points; then, the minimum value of the group of feature points is obtained, one or more feature values at each minimum value point are calculated, and if the feature values meet preset conditions, the feature values are removed from the group of feature points to obtain a new feature point sequence; repeating the previous step for the new characteristic point sequence, and circularly eliminating partial characteristic points until the difference of the number of the characteristic points obtained by two continuous circulations is not more than 1 (or other positive integers); and finally, connecting the finally obtained characteristic point sequences by an interpolation method to obtain an upper envelope curve of the signal. The elimination condition of the characteristic points is controlled by the scale parameters, so that the aim of continuously controlling the smoothness of the envelope curve by adjusting a single parameter is fulfilled.
1. A method for extracting signal envelope lines with adjustable scale parameter control is characterized by comprising the following steps:
(1) extracting maximum value points in the original signal to form a group of characteristic point sequences;
(2) extracting all minimum value points in the characteristic point sequence, and calculating the characteristic value of each minimum value point; removing the minimum value points of which the characteristic values meet given conditions from the characteristic point sequence to form a new characteristic point sequence;
(3) searching minimum value points in the new characteristic point sequence again, and eliminating the minimum value points of which the characteristic values meet set conditions; circularly eliminating partial points in the characteristic point sequence until a circular termination condition is met to obtain a final characteristic point sequence;
(4) and interpolating the finally obtained new characteristic point sequence in the original signal, and connecting the characteristic point sequence with the interpolation point to obtain an upper envelope curve.
Or
(1) Extracting minimum value points in the original signal to form a group of characteristic point sequences;
(2) extracting all maximum value points in the characteristic point sequence, and calculating the characteristic value of each maximum value point; removing the maximum value points of which the characteristic values meet given conditions from the characteristic point sequence to form a new characteristic point sequence;
(3) searching maximum value points in the new characteristic point sequence again, and eliminating the maximum value points of which the characteristic values meet set conditions; circularly eliminating partial points in the characteristic point sequence until a circular termination condition is met to obtain a final characteristic point sequence;
(4) and interpolating the finally obtained new characteristic point sequence in the original signal, and connecting the characteristic point sequence with the interpolation point to obtain a lower envelope curve.
Characteristic value char in step (2)(a)(k) The calculation formula of (2) is as follows:
char(a)(k)＝C(a)(k)-D(a)(k)
wherein, C(a)(k) And (b) a circle center ordinate obtained by rounding three points under the condition that the abscissa has a stretching and contracting scale of a, wherein the three points are as follows: and (3) the extreme point in the step (2) and two points of the extreme value which are adjacent in front and back in the characteristic point sequence in the step (1). D(a)(k) And (3) linear interpolation at the extreme point of the connecting line of the extreme point in the step (2) between the two points before and after the feature point sequence in the step (1) is shown when the abscissa scaling is a.
And the characteristic value char(a)(k) Not greater than 0.
The cycle termination conditions in the step (3) are as follows: the difference between the lengths of the new feature point sequences formed twice consecutively is not more than a given number N _ stop. N _ stop typically takes positive integers between 1-10, including 1-10.
The present invention is further described below, including the following steps (again, the above envelope is taken as an example, and the following envelope is the same):
first, extracting maximum value points (first-order maximum value points or multi-order maximum value points) in original signals s (i) to form a group of characteristic point sequences y1(j) And recording the position sequence x of the original signal1(j)；
Second, calculate y1(j) Sequence of minima y of2(k) And recording it in x1(j) Position sequence x in (1)2(k) Then its position sequence x in the original signal s (i)1(x2(k) Calculate point (x)1(x2(k)),y2(k) Char) of the feature value(a)(k)：
char(a)(k)＝C(a)(k)-D(a)(k) (1)
Wherein C is(a)(k) To representPoint (x)2(k),y2(k) And in (x)1(j),y1(j) Two points in front and back of the sequence adjacent to the point in the sequence are used for obtaining a center ordinate by drawing a circle by three points under the condition that the expansion ratio of the abscissa is a; d (a), (k) shows that when the abscissa scaling is a, the point (x) is represented by using the position sequence of the feature point in the original signal s (i) as the abscissa2(k),y2(k) In (x)1(j),y1(j) A line connecting two points in the sequence adjacent to the sequence is in x1(x2(k) Linear interpolation at).
If char(a)(k)<0, then the point (x)2(k),y2(k) From (x)1(j),y1(j) ) sequences are deleted.
Here, C is given(a)(k) And D(a)(k) The expression of (a) and the change rule of the expansion coefficient a along the horizontal axis give the following calculation process:
let the three-point coordinates in the plane be (x1, y1), (x2, y2), (x3, y3) respectively, wherein x1<x2<x3，y1>y2,y2<y3, the coordinates of the center of the circle defined by the three points are (x)c,yc) (ii) a The linear interpolation of the two-point connecting line of (x1, y1), (x3, y3) at x2 is yIAnd then:
taking:
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)
bringing the formula in (4) into (2) to obtain:
from (5), it can be seen that:
Yc>0
(8)
if x' is a.x (a)>0) Then obtain the new longitudinal coordinate Y of the circle centerc' and the ordinate Y of the interpolation pointI′:
YI′＝YI
(10)
Obtained from (5):
thus: when a is 1, Yc′＝Yc>0；
a>1 time, Yc′>Yc>0；
0<a<1 time, 0<Yc′<Yc；
From the above calculations: on one hand, the position of the center of a circle of the three points can be adjusted by adjusting the scale parameter a (a >0), and when the scale parameter a is larger than 1, the position of the center of the circle is increased along with the increase of a; when the scale parameter a is smaller than 1, the circle center position is lowered along with the reduction of the scale parameter a. On the other hand, the ordinate of the interpolation point does not change with the change of the scale parameter a, and therefore the interpolation point can be used as a stationary reference point.
For subsequent analysis, it is necessary here to demonstrate: whether a (a)>0) What value is taken, Y is presentc' always greater than YI。
Represented by Y in formula (9)cThe expression of' indicates that although the case of a being 0 results in the denominator of some equations being zero during the derivation process, the final result can be obtained by subtracting a from the denominator, and since in the case of the subject setting, Y is used to approximate the denominatorc' is an increasing function of a, so can be at Yc' where Y is obtained when a is directly 0 and approaches zeroc' minimum value.
Substituting 0 for a into equation (9), and Yc' and YISubtraction can give:
as can be seen from equation (5): the denominator on the right side of the equal sign of formula (11) is always less than zero if Y is to be proved to existc'>YIIf it is always true, then only the presence (X) needs to be verified1,Y1) And (X)2，Y2) So that (X)1Y3 2+X3Y1 2)(X3+X1)-4X1X3Y1Y3<0 is required.
According to (5), the following can be set: x1＝-αX3；Y1＝βY3In which α is>0，β>0, since in random signals, X1，Y1，X2，Y2Is four independent variables, then α, β can take any positive real number. Then the right-hand numerator portion of equation (11) equal sign can be simplified as:
it is easy to see that between alpha and beta2And 1, and β is small enough (tends to be 0) (e.g., β ═ 0.1, α ═ 0.5) or β is large enough (tends to be positive infinity) (e.g., β ═ 10, α ═ 5), equation (12) can both be less than 0. As can be seen from the above, there are (x1, y1), (x2, y2), (x3, y3) (x 1)<x2<x3，y1>y2,y2<y3) such that y varies regardless of the scaling factor ac>yIThis is always true.
Based on the above calculation process, and to facilitate the calculation, let:
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))
can obtain Ca(k) And Da(k) Expression (c):
thirdly, the sequence y1(j) And (3) after the characteristic points meeting the condition of the formula (1) are removed, forming a new group of sequences, repeating the second step, and circularly removing the points meeting the condition until the number of the points removed twice continuously is not more than N _ stop.
And fourthly, connecting the points remained after the second step and the third step by an interpolation method to be used as an upper envelope curve of the signal.
In the present invention, Ca(k) Is a scale parameter a (a)>0) Function of Da(k) Independent of a. Whether some characteristic points in the signal are eliminated or not can be controlled by adjusting the scale parameters, and when a is increased, C isa(k) The number of the kicked feature points is reduced, and the obtained curve is smoother (namely closer to the envelope curve of the extreme point); when a decreases, then Ca(k) The number of the kicked feature points is increased, the obtained curve is smoother, and feature points which can not be removed forever exist, namely the limit condition of the 'smoothest' envelope line exists in a family of envelope lines obtained by changing the scale parameter a. Meanwhile, the same parameter a ensures that the envelope extraction is carried out on the signal in the same scale in the whole signal length range.
Drawings
FIG. 1 original waveform of vibration of internal combustion engine
FIG. 2a is an envelope of the present invention with a scale parameter of 10
FIG. 2b is a diagram showing a waveform of envelope refinement with a scale parameter of 10 according to the present invention
FIG. 3a is an envelope of the present invention with a scale parameter of 1
FIG. 3b is a diagram illustrating a waveform of envelope refinement with a scale parameter of 1 according to the present invention
FIG. 4a is an envelope of the present invention with a scale parameter of 0.1
FIG. 4b is a diagram illustrating a waveform of envelope refinement with a scale parameter of 0.1 according to the present invention
FIG. 5a is a diagram illustrating an envelope curve with a scale parameter of 0 and a waveform refined therefrom according to the present invention
FIG. 5b is a diagram illustrating a waveform of envelope refinement with a scale parameter of 0 according to the present invention
FIG. 6a first order extremum envelope
FIG. 6b first order extremum envelope refinement waveform
FIG. 7a packet line for Hilbert transform
FIG. 7b is a refined waveform of a envelope of the Hilbert transform
Detailed Description
In order to better understand the technical solution of the present invention, the following detailed description is made with reference to the accompanying drawings.
Firstly, extracting a signal s (i) of the whole period of vibration of the cylinder cover of the internal combustion engine, as shown in fig. 1, and extracting maximum (small) value points of s (i) to form a group of characteristic point sequences y1(j) And recording the position sequence x of the original signal s (i)1(j)；
Second, calculate y1(j) Sequence of very small (large) values y2(k) And recording it in x1(j) Position sequence x in (1)2(k) Then its position sequence x in the original signal s (i)1(x2(k) Calculate point (x)1(x2(k)),y2(k) Char) of the feature value(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 it satisfies char(a)(k)<Condition 0, then the point (x)2(k),y2(k) From (x)1(j),y1(j) Removing the sequences to form a new characteristic point sequence;
thirdly, searching minimum (large) value points in the new characteristic point sequence obtained in the second step again, eliminating the minimum (large) value points of which the characteristic values meet the set conditions, forming a new characteristic point sequence again, and circularly eliminating the minimum (large) value points which meet the char requirement(a)(k)<0 condition point until the difference between the lengths of the new feature point sequences formed two consecutive times is not more than a given number N _ stop.
And fourthly, connecting the points remained after the step (2) and the step (3) by an interpolation method to be used as the upper (lower) envelope curve of the signal.
Setting the scale parameter as a to 10, a to 1, a to 0.1, and a to 0, respectively, to obtain waveforms of four envelopes, as shown in fig. 2 to 5; fig. 6 shows an envelope obtained by a first-order extremum envelope method, and fig. 7 shows an envelope obtained by a Hilbert transform envelope method, which are easy to see: compared with the traditional envelope line calculation method, the envelope line extraction method is simple and flexible, and the smoothness of the envelope line can be controlled only by modifying a single scale parameter according to the purpose and smoothness requirement of calculating the envelope line.
Claims (1)
1. A method for extracting signal envelope lines with adjustable scale parameter control is characterized by comprising the following steps:
(1) extracting maximum value points in the original signal to form a group of characteristic point sequences;
(2) extracting all minimum value points in the characteristic point sequence, and calculating characteristic values of all the minimum value points; removing the minimum value points of which the characteristic values meet set conditions from the characteristic point sequence to form a new characteristic point sequence;
(3) searching minimum value points in the new characteristic point sequence again, and eliminating the minimum value points of which the characteristic values meet set conditions; circularly eliminating partial points in the characteristic point sequence until a circular termination condition is met to obtain a final new characteristic point sequence;
(4) interpolating the finally obtained new characteristic point sequence in an original signal, and connecting the new characteristic point sequence with an interpolation point to obtain an upper envelope curve;
or (1) extracting minimum value points in the original signal to form a group of characteristic point sequences;
(2) extracting all maximum value points in the characteristic point sequence, and calculating the characteristic values of all the maximum value points; removing the maximum value point with the characteristic value meeting the set condition from the characteristic point sequence to form a new characteristic point sequence;
(3) searching maximum value points in the new characteristic point sequence again, and eliminating the maximum value points of which the characteristic values meet set conditions; circularly eliminating partial points in the characteristic point sequence until a circular termination condition is met to obtain a final new characteristic point sequence;
(4) interpolating the finally obtained new characteristic point sequence in an original signal, and connecting the new characteristic point sequence with an interpolation point to obtain a lower envelope curve;
characteristic value char in step (2)(a)(k) The calculation formula of (2) is as follows:
char(a)(k)＝C(a)(k)-D(a)(k)
wherein, C(a)(k) And (b) a circle center ordinate obtained by rounding three points under the condition that the abscissa has a stretching and contracting scale of a, wherein the three points are as follows: the extreme point in the step (2) and two points of the extreme value which are adjacent in the front and back in the characteristic point sequence in the step (1); d(a)(k) A linear interpolation is shown in the step (2) when the abscissa scaling is a, and the line connecting two points before and after the feature point sequence in the step (1) of the extreme point is at the extreme point;
setting conditions: char(a)(k) Not more than 0;
the cycle termination conditions in the step (3) are as follows: the difference between the lengths of the new feature point sequences formed twice consecutively is not more than a given number N _ stop, or the number of points of the feature point sequences is not more than three.
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