CN-117407686-B - Generalized motion centroid decomposition method based on local centroid and fluctuation rate

CN117407686BCN 117407686 BCN117407686 BCN 117407686BCN-117407686-B

Abstract

The invention belongs to the technical field of fault diagnosis, and discloses a generalized motion centroid decomposition method based on a local centroid and a fluctuation rate, which obtains a signal extremum set based on a vibration signal; calculating local barycenters through a barycenter solving formula based on adjacent signal extreme values, calculating all the local barycenters in a time set to obtain a local barycenter set, calculating through the formula to obtain a slope set, traversing the slope set, obtaining a mapping characteristic point set based on the slope through the formula, generating a mean value curve through fitting all characteristic points with a cubic spline curve, separating the mean value curve from an original signal and fitting to obtain an original separation extremum curve, repeating the local mean value curve data obtained in the steps 1-4 by the original separation extremum curve until the standard deviation of the local mean value curve meets the requirement, stripping the mean value signal corresponding to the mean value curve from the original signal to obtain a barycenter decomposition signal, and performing loop iteration until the barycenter decomposition signal is a monotonic function or a constant function.

Inventors

DAI YUANJUN
HUANG WEIQIANG
SHI KUNJU
LI BAOHUA
XU LIJUN
Jiang Jiading

Assignees

上海电机学院

Dates

Publication Date: 20260512
Application Date: 20231027

Claims (6)

1. The generalized motion centroid decomposition method based on the local centroid and the fluctuation rate is characterized by comprising the following steps of: step 1, obtaining a signal extremum set based on a vibration signal; step 2, calculating local barycenters based on signal extremum sets and on adjacent signal extremums through a barycenter solving formula, and counting all the local barycenters in a time set to obtain a local barycenter set; Step 3, calculating the local centroid set through a slope calculation formula to obtain a slope set, wherein the slope set is ; The slope calculation formula is as follows: , ; Wherein, the First, the A local centroid signal; First, the A local centroid signal; First, the The time points corresponding to the local centroid signals; First, the The time points corresponding to the local centroid signals; Traversing a set of slopes, from the slopes Selecting and selecting Slope of minimum difference of (2) Selecting the product to meet A kind of electronic device Order-making ; Traversing the set of slopes from the slopes Selecting and selecting Slope of minimum difference of (2) Selecting the product to meet A kind of electronic device For slope of Performing analog calculation , The slope obtains a mapping characteristic point set through a formula; step 4, fitting all characteristic points through a cubic spline curve to generate a mean value curve, separating the mean value curve from the original signal, and fitting to obtain an original separation extremum curve; step 5, judging whether the standard deviation of the local mean curve meets a preset standard value or not according to the local mean curve data obtained by the original separation extremum curve through the steps 1-4, if not, repeating the steps 1-4 until the requirement is met, and executing the next step 6; Step 6, peeling the mean signal corresponding to the mean curve from the original signal, and obtaining a mass center decomposition signal through a formula, repeating the steps 1-5 on the mass center decomposition signal to obtain a local mean signal, and performing loop iteration until the mass center decomposition signal is a monotonic function or a constant function; Step 7, adaptively decomposing the centroid decomposition signal into a series of AM-FM signals, wherein the AM-FM signals comprise An intrinsic centroid function and 1 residual component.
2. The generalized motion centroid decomposition method based on local centroid and fluctuation rate as set forth in claim 1, wherein the set of signal extrema is labeled as The corresponding time set is marked as ; Wherein, the For a set of signal extrema Is provided for the length of (a), First, a third step Extreme value of each signal The corresponding time point is 。
3. A generalized motion centroid decomposition method based on local centroids and slew rate as recited in claim 2, wherein a set of local centroids is obtained The specific steps of (a) include: in the interval Fitting of internal data to time variable Is the local centroid equation of (2) Time variable Derivation of the derived equation ; Definition of the definition For the point in time And Number of data in between, time set of adjacent extreme points And the corresponding data set is Wherein ; For a pair of And The inner adjacent data carries out centroid operation and rewrites after traversing the whole array And An inner value; Repeating the above operation until And Only one data is left in each of the data, respectively recorded as And ; Traversing all time set intervals to obtain a local centroid set 。
4. A generalized motion centroid decomposition method based on local centroids and wave rate according to claim 3, wherein centroid point coordinates are obtained based on slope and coordinates of feature points are calculated based on linear equation.
5. The generalized motion centroid decomposition method based on local centroid and fluctuation rate as set forth in claim 4, wherein the formula for separating and fitting the mean curve from the raw signal to obtain the raw separation extremum curve is: ; Wherein: Is a curve of the average value of the curve, The sensor is used for collecting the original signal of the vibration operation of the rolling bearing, Is the original separation extremum curve.
6. The generalized motion centroid decomposition method based on local centroid and fluctuation rate of claim 5, wherein the AM-FM signal comprises The specific formulas of the intrinsic centroid function ICF and 1 residual component are as follows: ; Wherein: is the first The intrinsic centroid function ICF, ; Is the first And residual components.

Description

Generalized motion centroid decomposition method based on local centroid and fluctuation rate Technical Field The invention relates to the technical field of fault diagnosis, in particular to a generalized motion centroid decomposition method based on a local centroid and a fluctuation rate. Background Along with the acceleration of informatization process, the requirements of the fields of mechanical equipment and the like on analysis and processing of complex signals are continuously increased, and fault diagnosis is carried out on the mechanical equipment through analysis of the complex signals. In order to better cope with these demands, various time-frequency domain analysis methods have been proposed, including Empirical Mode Decomposition (EMD), local feature scale decomposition (LCD), local Mean Decomposition (LMD), and Ensemble Empirical Mode Decomposition (EEMD), but each has some problems and limitations, which need to be selected according to specific application scenarios. In order to improve the limitations of these methods, and in particular to solve the problem of modal aliasing, a GMCD method was introduced, which is based on the centroid and slope of the signal waveform, and signal continuation was performed by selecting the optimal value to obtain a more accurate decomposition. In view of this, the present invention provides a generalized motion centroid decomposition method based on local centroid and fluctuation rate. Disclosure of Invention In order to overcome the problems in the prior art, the invention provides a generalized motion centroid decomposition method based on local centroid and fluctuation rate, comprehensively considers all data in a signal interval, improves the defects of long calculation time, signal expression requirement and the like of a traditional integral formula, and provides a new idea for limiting mode aliasing. According to one aspect of the present invention, there is provided a generalized motion centroid decomposition method based on a local centroid and a fluctuation rate, comprising the steps of: step 1, obtaining a signal extremum set based on a vibration signal; step 2, calculating local barycenters based on signal extremum sets and on adjacent signal extremums through a barycenter solving formula, and counting all the local barycenters in a time set to obtain a local barycenter set; Step 3, calculating the local centroid set through a formula to obtain a slope set, traversing the slope set, and searching for the slope set to enable A kind of electronic deviceOrder-makingSequentially obtainObtaining a mapping characteristic point set through a formula based on the slope; step 4, fitting all characteristic points through a cubic spline curve to generate a mean value curve, separating the mean value curve from the original signal, and fitting to obtain an original separation extremum curve; step 5, judging whether the standard deviation of the local mean curve meets a preset standard value or not according to the local mean curve data obtained by the original separation extremum curve through the steps 1-4, if not, repeating the steps 1-4 until the requirement is met, and executing the next step 6; Step 6, peeling the mean signal corresponding to the mean curve from the original signal, and obtaining a mass center decomposition signal through a formula, repeating the steps 1-5 on the mass center decomposition signal to obtain a local mean signal, and performing loop iteration until the mass center decomposition signal is a monotonic function or a constant function; step 7 GMCD can adaptively decompose the centroid decomposition signal into a series of AM-FM signals including An Intrinsic Centroid Function (ICF) and 1 residual component. Preferably, the set of signal extrema is marked asThe corresponding time set is marked as; Wherein, the For a set of signal extremaIs provided for the length of (a),First, a third stepExtreme value of each signalThe corresponding time point is。 Preferably, a local centroid set is obtainedThe specific steps of (a) include: in the interval Fitting of internal data to time variableIs the local centroid equation of (2)Time variableDerivation of the derived equation; Definition of the definitionFor the point in timeAndNumber of data in between, time set of adjacent extreme pointsAnd the corresponding data set isWherein; For a pair ofAndThe inner adjacent data carries out centroid operation and rewrites after traversing the whole arrayAndAn inner value; Repeating the above operation until AndOnly one data is left in each of the data, respectively recorded asAnd; Traversing all time set intervals to obtain a local centroid set。 Preferably, the slope calculation formula is as follows: ; Wherein, the First, theA local centroid signal; First, the A local centroid signal; First, the The time points corresponding to the local centroid signals; First, the The time points corresponding to the local centroid signals. Preferably, the c