CN109598255B - Energy operator k-gradient-based self-adaptive extraction method for impact start points of reciprocating mechanical vibration signals - Google Patents
Energy operator k-gradient-based self-adaptive extraction method for impact start points of reciprocating mechanical vibration signals Download PDFInfo
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Abstract
The invention provides a self-adaptive extraction method of the impact starting point of a reciprocating mechanical vibration signal based on an energy operator k-gradient, which solves the problems of unreasonable threshold setting and poor adaptability in the traditional impact starting point extraction technology, and achieves the effects of self-adapting and optimizing the impact starting point of the vibration signal. The method comprises the steps of firstly, carrying out EMD self-adaptive filtering treatment on a vibration signal, removing low-frequency components in the signal, and retaining high-frequency components; then calculating a Teager energy operator, and highlighting transient vibration impact energy; calculating a k-gradient and a k-gradient neighborhood of the Teager energy operator, and taking a first point of the k-gradient neighborhood in a time sequence as an impact starting point; and finally, according to the quasi-periodic characteristic of the vibration signal impact of the reciprocating machine, performing outlier inspection on the calculation result by using a 3-sigma criterion, and optimizing the calculation result of the outlier by automatically adjusting the k value and the set criterion, thereby achieving the purpose of adaptively and accurately extracting the vibration signal impact starting point.
Description
Technical Field
The invention relates to a vibration characteristic processing method for extracting a vibration impact starting point, in particular to a self-adaptive extracting method for a reciprocating mechanical vibration signal impact starting point, which is suitable for the field of state monitoring and fault diagnosis based on vibration signals.
Background
The impact is usually generated by abrupt change of stress of parts caused by contact collision, so that stress imbalance of corresponding mechanical parts is vibrated, and the impact is represented as a local impact which is instantaneously increased and rapidly attenuated on a vibration signal of the equipment. The actual vibration signal of the reciprocating machine is generally mainly composed of local impact with definite physical meaning, for example, the vibration signal of the cylinder cover of the internal combustion engine is generally composed of ignition impact, valve opening and closing impact and the like; the reciprocating compressor cylinder vibration signal is generally composed of valve plate impact vibration. The attack point is an important feature of the local attack signal and can be used as a fault-sensitive feature for equipment fault diagnosis, for example, the attack point feature of valve opening and closing of an internal combustion engine can be used for diagnosing abnormal faults of valve clearance.
Currently, threshold judgment is one of the most commonly used techniques for vibration impact signal origin extraction. For a single local impact signal, the location where the amplitude of the vibration first crosses the threshold line is generally taken as the impact point. However, since the setting of the threshold value is generally empirically determined, there is a general problem that the setting of the threshold value is unreasonable or the adaptation is poor in an actual complex vibration signal composed of a plurality of impacts of different magnitudes. In addition, the method for identifying the impact starting point based on the maximum rising gradient of energy can achieve the purpose of adaptive calculation, but the actual vibration signal is influenced by a plurality of interference factors, the rising gradient of the vibration energy at the impact starting position can be larger in the impact area instead of the largest, and a large error is often caused by the method for identifying the maximum position of the energy gradient.
According to the characteristics of energy change of an impact area, the invention combines the advantages of a Teager energy operator in the aspect of identifying transient vibration change, and provides a novel vibration impact starting point self-adaptive accurate extraction method based on the Teager energy operator ascending gradient by adaptively extracting larger value points of which the energy ascending gradient meets a set condition according to a reasonable design rule, so that the problems of poor threshold value setting self-adaptability and poor calculation accuracy in the traditional method are solved, and the purpose of self-adaptively and accurately extracting the vibration signal impact starting point is achieved.
Disclosure of Invention
The invention aims to provide an impact starting point self-adaptive accurate extraction method based on a Teager energy operator ascending gradient, aiming at the problems of poor adaptability and low accuracy of the existing commonly adopted impact starting point extraction method.
The invention is realized by the following technical scheme: firstly, performing EMD self-adaptive filtering treatment on a vibration signal; then calculating a Teager energy operator, and highlighting transient vibration impact energy; then solving the gradient of the local energy operator to obtain the gradient of the Teager energy operator; the concept of k-gradient and k-gradient neighborhood is put forward, and the first point of the k-gradient neighborhood in the time sequence is taken as an impact starting point; and finally, according to the quasi-periodic characteristic of the vibration signal impact of the reciprocating machine, performing outlier inspection on the calculation result by using a 3-sigma criterion, and optimizing the calculation result of the outlier by automatically adjusting the k value and the set criterion, thereby achieving the purpose of adaptively and accurately extracting the vibration signal impact starting point.
1. A reciprocating mechanical vibration signal impact starting point self-adaptive extraction method based on an energy operator k-gradient is characterized by comprising the following steps:
(1) Performing adaptive filtering pretreatment based on empirical mode decomposition (Empirical Mode Decomposition, EMD) on the actually measured reciprocating mechanical full-period vibration signal;
(2) Angular domain resampling is carried out on the discrete signals after filtering;
(3) Calculating a local Teager energy operator at each data point;
(4) Initially setting a positive integer k, calculating the k-gradient of an energy operator, and extracting the position of the energy gradient which firstly belongs to the k-gradient neighborhood in an energy gradient time sequence as an impact starting point;
(5) According to the stable periodicity of the reciprocating mechanical vibration impact signal, calculating the average value mu and standard deviation sigma of n whole period signal impact starting points, if an outlier which deviates from the average value 3 sigma or more exists, changing the k value to recalculate, and repeatedly adjusting the k value until the termination condition is met, and determining the final impact starting point.
2. In the step (1), after the EMD is adaptively decomposed, each intrinsic mode component (Intrinsic Mode Function, IMF) is obtained, and the Pearson correlation coefficient r between each IMF component and the original signal is calculated by the following formula:
wherein x represents an original signal, j represents a sequence number of an IMF component, IMF (j) represents a j-th IMF component, cov (IMF (j), x) represents covariance of IMF (j) and x, var [ IMF (j) ] and Var [ x ] represent variances of IMF (j) and x, respectively, and r (j) represents correlation coefficients of IMF (j) and x.
And then, selecting each intrinsic mode component with the correlation coefficient not smaller than a threshold value c (taking the number between 0.1 and 0.5) for reconstruction.
2. In the step (2), the angular domain resampling adopts an equal-angle resampling method, and the angle interval d takes a value between 0.1 and 0.5.
3. In the step (3), the local Teager energy operator in the discrete time series vibration signal x is calculated according to the following formula:
ψ d (i)＝|x 2 (i)-x(i-1)x(i+1)|
wherein x represents vibration signals obtained after angular domain resampling, i represents a point sequence number, x (i-1), x (i), and x (i+1) represent values of x at the sequence numbers i-1, i, and i+1, respectively, and ψ d (i) Representing the Teager energy operator at sequence number i.
4. The k-gradient involved in step (4) above is defined as follows: for any natural number k, defining the energy gradient as an energy operator psi d Gradient at i, with dψ d (i) Representing the k-gradient dψ k-grad Representing the energy gradient in the energy gradient sequence satisfying the following two conditions:
(1) In the energy gradient sequence, at least k points p exist to satisfy Dψ d (p)≥Dψ k-grad ；
(2) In the energy gradient sequence, at most k-1 points p exist to satisfy Dψ d (p)＞Dψ k-grad ；
k-gradient dψ k-grad Is calculated by the following steps: first, the energy gradients, dψ, of all locations in the time series are calculated d (i)＝ψ d (i+1)-ψ d (i) The method comprises the steps of carrying out a first treatment on the surface of the The energy gradients at each location are then arranged in descending order, and the k-th value in the resulting sequence is selected as the k-gradient.
5. The k-gradient neighborhood N referred to in step (4) above k The definition is as follows: k-gradient dψ of a given energy operator k-grad K-gradient neighborhood N k To include gradient value not less than Dψ k-grad Is a function of the energy gradient value of the energy gradient.
6. The invention provides two schemes for selecting the initial k value in the step (4), namely, scheme one: directly selecting natural numbers between 5 and 20; scheme II: and determining based on a principle of minimum variance, namely calculating variances of extraction results of a plurality of groups of data under different k values, and selecting a k value corresponding to the minimum variance result as a k initial value.
7. The average value μ and standard deviation σ involved in the above step (5) are calculated from the following formula:
wherein n is the number of groups of the acquired full-period vibration signals; y is an array formed by the impact initial point extraction results of n groups of vibration signals; q represents the sequence number of the y array, and y (q) is the impact start point extraction result of the q-th group full-period vibration signal.
8. The strategy of changing k value for outliers involved in the above step (5) is: setting an adjustment step (taking 1-3), and adjusting the k value to an increasing direction when the calculated result is greater than 3 times of the standard deviation above the average value; when the calculated result is smaller than 3 times of standard deviation below the average value, the k value is adjusted to be smaller. The process of adjusting the k value is terminated when one of the following two conditions is met, namely, the condition one: the new calculation result is judged to be a non-outlier, i.e. the calculation result is within 3 times variance of the average value; condition II: the adjustment is carried out for m times (the value of m is 5-20). If the calculation process finally ends with the second condition, the result closest to the average value in the m calculation results is taken as an impact starting point.
Each step of the present invention is described in further detail below as follows:
the method comprises the steps of firstly, performing EMD self-adaptive filtering pretreatment on a reciprocating mechanical whole-period vibration signal, and selecting a modal component with a Pearson correlation coefficient not smaller than a threshold value c (value of 0.1-0.5) of an original signal to perform signal reconstruction to obtain a signal s (i);
secondly, resampling the angle domain of the same angle as s (i), wherein the sampling angle interval d takes a value of 0.1-0.5 to obtain a signal x (i);
third, calculate the local Teager energy operator ψ of the discrete signal x (i) at each data point i after EMD adaptive filtering and angular domain resampling d (i)＝|x 2 (i)-x(i-1)x(i+1)|；
Fourth step, calculating the local energy operator psi d (i) Energy gradient dψ of (2) d (i)＝ψ d (i+1)-ψ d (i) The method comprises the steps of carrying out a first treatment on the surface of the Then, the energy gradients of all the positions are arranged in a descending order, an initial k value is selected (natural numbers between 5 and 20 are directly selected, or variances of extraction results of a plurality of groups of data under different k values are calculated, the k value corresponding to the smallest variance result is selected as a k initial value), and the k value in a sequence obtained by the descending order of the energy gradients is taken as a k-gradient; and then extracting all values not smaller than k-gradient in the energy gradient sequence to obtain N in the k-gradient field k The method comprises the steps of carrying out a first treatment on the surface of the Finally, extracting the first N belonging to the k-gradient field from the time sequence of the energy operator k As the impact initiation point.
Fifth, using quasi-periodicity of reciprocating mechanical vibration signal, calculating average value of n (number between 20-40) whole period signal impact initial point positions y (q)
Standard deviation->
And 3, judging discrete points by adopting a 3 sigma criterion, and calculating by adopting a method of circularly adjusting k values. The k value adjusting method comprises the following steps: firstly, setting an adjustment step (taking 1-3) and the number of circulation times m (taking 5-20), adjusting the k value and recalculating the extraction result, judging outliers of the new calculation result, and terminating calculation if the new calculation result is judged to be a non-outlier; if the outlier is still judged, the k value is continuously adjusted to repeat the calculation process until the number of times of cyclic calculation reaches a set value m. The adjustment strategy of k value is: if the calculated result is 3 times of standard deviation above the average value, the k value is adjusted to the increasing direction; if the calculated result is less than 3 times of standard deviation below the average value, the k value is reduced toAnd (5) direction adjustment.
Drawings
FIG. 1 shows an original waveform of a full cycle signal of an engine cylinder head
FIG. 2 shows the whole cycle signal of the cylinder head of the internal combustion engine after EMD adaptive filtering and equal angle angular domain resampling
Teager energy operator of FIG. 3 full cycle cylinder head vibration signal
Fig. 4 initial k=15 impact start point extraction results
FIG. 5 impact origin extraction results after outlier processing
Detailed Description
In order to better understand the technical scheme of the present invention, the application of the present invention to the extraction of the valve closing impact initiation phase characteristics of an internal combustion engine is further described in detail below with reference to the accompanying drawings.
Firstly, as shown in fig. 1, performing EMD self-adaptive decomposition on a cylinder cover vibration signal of an internal combustion engine to obtain an intrinsic mode component, and selecting an intrinsic mode component with a Pearson correlation coefficient of not less than a set threshold value c=0.4 of an original vibration signal to reconstruct to obtain a self-adaptive filtered signal s (i);
secondly, resampling the equal angle domain of s (i), wherein the sampling angle interval d takes a value of 0.1-0.5 to obtain a signal x (i), as shown in figure 2;
third, calculating the local Teager energy operator ψ at each data point i of the above-mentioned filtered discrete signal x (i) d (i)＝|x 2 (i) -x (i-1) x (i+1) | and the calculation result is shown in fig. 3;
fourth, this example is described with respect to exhaust valve closing impacts within 0-90 crank angles in the map. Calculating a local energy operator ψ d (i) Energy gradient dψ of (2) d (i)＝ψ d (i+1)-ψ d (i) The method comprises the steps of carrying out a first treatment on the surface of the Setting k=1, k=5, k=10, k=15, k=20, and calculating k-gradients as: dψ 1-grad ＝1.43x10 5 ,Dψ 5-grad ＝7.58x10 4 ,Dψ 10-grad ＝5.69x10 4 ,Dψ 15-grad ＝4.31x10 4 ,Dψ 20-grad ＝2.64x10 4 The method comprises the steps of carrying out a first treatment on the surface of the And then determines the correspondenceK-gradient field N of (2) k The first in the time series belongs to N k The sequence numbers of the points of (a) are respectively: p (P) k＝1 ＝137，P k＝5 ＝120，P k＝10 ＝120P k＝15 ＝120，P k＝20 =109, the above point numbers, i.e. the impact start points for different k values, are converted into angular domain phases as:
the variances corresponding to the k values of each group are selected as follows: sigma (sigma) k＝1 ＝29.65，σ k＝5 ＝11.65，σ k＝10 ＝4.99，σ k＝15 ＝3.61，σ k＝20 =3.94, so k=15 is selected as the initial value. 480 sets of full-period vibration waveforms are selected, and in the case of initial k=15, the extraction calculation results are shown in fig. 4.
Fourth, in the case of initial k=15, the above 480 sets of full-period signal vibration waveforms, the average μ=14.48 and standard deviation σ=3.61 of the target impact start point position y (i), there are 4 outliers whose calculation result is 3 times larger than the average value and 3 outliers whose calculation result is 3 times smaller than the standard deviation below the average value, the k value (step size is 2) is repeatedly adjusted for each outlier, and each outlier satisfies the 3 σ criterion before reaching the set number of cycles m=10, and the result is shown in fig. 5.
Claims (6)
1. A reciprocating mechanical vibration signal impact starting point self-adaptive extraction method based on an energy operator k-gradient is characterized by comprising the following steps:
(1) Performing adaptive filtering pretreatment based on empirical mode decomposition on an actually measured full-period vibration signal of the reciprocating machine;
(2) Angular domain resampling is carried out on the discrete signals after filtering;
(3) Calculating a local Teager energy operator at each data point;
(4) Initially setting a positive integer k, calculating the k-gradient of an energy operator, and extracting the position of the energy gradient which firstly belongs to the k-gradient neighborhood in an energy gradient time sequence as an impact starting point;
(5) Calculating the average value mu and the standard deviation sigma of n whole-period signal impact starting points according to the quasi-periodicity of the reciprocating mechanical vibration impact signals, if an outlier which deviates from the average value 3 sigma or more exists, changing the k value to recalculate, and repeatedly adjusting the k value until the termination condition is met, and determining the final impact starting point;
the k-gradient involved in step (4) above is defined as follows: for any natural number k, defining the energy gradient as an energy operator psi d Gradient at i, with dψ d (i) Representing the k-gradient dψ k-grad Representing the energy gradient in the energy gradient sequence satisfying the following two conditions:
1) In the energy gradient sequence, at least k points p exist to satisfy Dψ d (p)≥Dψ k-grad ；
2) In the energy gradient sequence, at most k-1 points p exist to satisfy Dψ d (p)>Dψ k-grad The method comprises the steps of carrying out a first treatment on the surface of the k-gradient dψ k-grad Is calculated by the following steps: first, the energy gradients, dψ, of all locations in the time series are calculated d (i)＝ψ d (i+1)-ψ d (i) The method comprises the steps of carrying out a first treatment on the surface of the Then, the energy gradients of all the positions are arranged in a descending order, and the kth value in the obtained sequence is selected as the k-gradient;
involving a k-gradient neighborhood N k The definition is as follows: k-gradient dψ of a given energy operator k-grad K-gradient neighborhood N k To include gradient value not less than Dψ k-grad Is determined by the energy gradient values of the energy gradient values;
the initial k value involved in the step (4) is selected by one of the following two schemes, scheme one: directly selecting natural numbers between 5 and 20; scheme II: and determining based on a principle of minimum variance, namely calculating variances of extraction results of a plurality of groups of data under different k values, and selecting a k value corresponding to the minimum variance result as a k initial value.
2. The method according to claim 1, characterized in that: in the step (1), after the EMD self-adaptive decomposition, each intrinsic mode component is obtained, and the Pearson correlation coefficient r between each IMF component and the original signal is calculated, which is obtained by the following formula:
wherein x represents an original signal, j represents a sequence number of an IMF component, IMF (j) represents a j-th IMF component, cov (IMF (j), x) represents covariance of IMF (j) and x, var [ IMF (j) ] and Var [ x ] represent variances of IMF (j) and x, respectively, and r (j) represents correlation coefficients of IMF (j) and x;
and then, selecting each eigenvector component with the correlation coefficient not smaller than a threshold value c to reconstruct, wherein c is a number between 0.1 and 0.5.
3. The method according to claim 1, characterized in that: in the step (2), the angular domain resampling adopts an equal-angle resampling method, and the angle interval d takes a value between 0.1 and 0.5.
4. The method according to claim 1, characterized in that: in the step (3), the local Teager energy operator in the discrete time series vibration signal x is calculated according to the following formula:
ψ d (i)＝|x 2 (i)-x(i-1)x(i+1)|
wherein x represents vibration signals obtained after angular domain resampling, i represents a point sequence number, x (i-1), x (i), and x (i+1) represent values of x at the sequence numbers i-1, i, and i+1, respectively, and ψ d (i) Representing the Teager energy operator at sequence number i.
5. The method according to claim 1, characterized in that: the average value μ and standard deviation σ involved in the above step (5) are calculated from the following formula:
wherein n is the number of groups of the acquired full-period vibration signals; y is an array formed by the impact initial point extraction results of n groups of vibration signals; q represents the sequence number of the y array, and y (q) is the impact start point extraction result of the q-th group full-period vibration signal.
6. The method according to claim 1, characterized in that: the strategy of changing k value for outliers involved in the above step (5) is: setting the adjustment step length to be 1-3, and adjusting the k value to an increasing direction when the calculation result is greater than the average value by 3 times of the standard deviation; when the calculated result is smaller than 3 times of the standard deviation of the average value, the k value is adjusted in the decreasing direction; the process of adjusting the k value is terminated when one of the following two conditions is met, namely, the condition one: the new calculation result is judged to be a non-outlier, i.e. the calculation result is within 3 times variance of the average value; condition II: and (3) adjusting for m times, wherein m is 5-20, and if the calculation process is finally terminated under the second condition, the result closest to the average value in the m calculation results is taken as an impact starting point.
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| CN110514921B (en) * | 2019-07-22 | 2022-07-26 | 华南理工大学 | Method for identifying nonlinear phenomenon in non-stationary signal of power electronic converter |
| CN111104887B (en) * | 2019-12-11 | 2024-03-29 | 北京化工大学 | Full-period keyless phase monitoring method based on vibration mechanism and deep learning technology |
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| CN112183344B (en) * | 2020-09-28 | 2021-06-01 | 广东石油化工学院 | Large unit friction fault analysis method and system based on waveform and dimensionless learning |
| CN116595324B (en) * | 2023-07-19 | 2023-11-10 | 北谷电子股份有限公司 | Method for extracting signal transient impact starting point |
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