CN110333071B

CN110333071B - Mechanical vibration signal processing method using narrowband cepstrum transformation

Info

Publication number: CN110333071B
Application number: CN201910571408.7A
Authority: CN
Inventors: 柳亦兵; 滕伟
Original assignee: North China Electric Power University
Current assignee: North China Electric Power University
Priority date: 2019-06-28
Filing date: 2019-06-28
Publication date: 2021-09-10
Anticipated expiration: 2039-06-28
Also published as: CN110333071A

Abstract

A mechanical vibration signal processing method using narrowband cepstrum transformation comprises the following steps: A. collecting a mechanical vibration signal x (t) of periodic motion; B. carrying out spectrum analysis on the vibration signal x (t) to obtain a frequency spectrum X (f) of the signal; C. logarithm of spectrum x (f) is calculated to obtain the logarithm spectrum of the signal: D. and (3) performing narrow-band cepstrum transformation on the logarithmic spectrum Lx (f) of the signal to obtain a narrow-band frequency-cepstrum of the signal. The method can accurately distinguish the same sideband components distributed in different frequency bands, and further distinguish and locate the gear tooth fault and the unbalance fault.

Description

Mechanical vibration signal processing method using narrowband cepstrum transformation

Technical Field

The invention belongs to the technical field of mechanical equipment monitoring and diagnosis based on vibration monitoring and analysis, and particularly relates to a composite fault positioning method for realizing gear transmission through frequency-frequency inversion of vibration monitoring signals.

Background

The transmission structure of the gear box is widely applied to rotary mechanical equipment in many fields, such as a double-fed wind turbine generator, an automobile gear box, a processing machine tool, hoisting machinery, a ship engine, a steel plate hot rolling mill and the like. The gear box is a fault high-occurrence part in rotary mechanical equipment, and particularly, rotary parts such as gear meshing pairs, bearings and the like in the gear box are subjected to alternating load and impact load during operation, so that faults are easy to occur, and the safe and reliable operation of the whole equipment is influenced. The main method for the running health state of the gear transmission is a vibration monitoring method, when parts such as gears, bearings and the like start to have faults, the load change of fault contact parts is caused, additional excitation is generated on the structure, so that the vibration response of the structure is changed, and fault diagnosis can be realized by monitoring the vibration change of the structure.

The basic characteristic of the gear and bearing part failure is that periodic impact excitation is generated, modulated vibration is generated on a structure, and sideband components related to operating parameters and structure characteristics are formed in the frequency spectrum of a vibration signal, wherein the sideband components comprise shaft rotation frequency sideband components, bearing characteristic frequency sideband components and the like. In the currently common vibration signal analysis method, cepstrum analysis is a method for identifying sideband components, and the sideband components in the signal spectrum are subjected to energy concentration in the cepstrum domain to form a single peak value by performing inverse frequency domain transformation on the signal spectrum, namely performing Fourier transformation on the logarithmic spectrum of the signal, so that all sideband information in the signal spectrum can be effectively identified, and fault diagnosis is realized.

However, cepstrum analysis has the following problems: sideband components in the signal spectrum having the same frequency spacing may be distributed over different frequency bands, reflecting different fault signatures. For example, sideband components generated by gear faults are concentrated on two sides of the meshing frequency of the gear pair, and the unbalance fault of the rotating shaft is distributed near a certain stage of natural frequency of a transmission system. The sideband frequencies and the reciprocal frequencies corresponding to the two types of faults are completely the same, but the reciprocal spectrum only has information of the reciprocal frequency (time) and does not have frequency information, so that the same-frequency sideband components of different frequency bands cannot be distinguished.

The patent application No. CN103471848A provides a rolling bearing fault feature extraction method based on independent component analysis and cepstrum theory. Acquiring a vibration acceleration test signal of a rolling bearing by using an acceleration sensor; decoupling and separating the vibration acceleration test signals by adopting FastICA based on negative entropy maximization; selecting a separation signal which can represent fault characteristic information most; performing cepstrum analysis on the selected separated signals and making a cepstrum map; and observing whether the cepstrum has fault characteristic frequency or obvious peak value at the frequency doubling position of the cepstrum, and further judging whether the rolling bearing has fault. The invention can effectively identify the characteristic information of the rolling bearing fault signal from the complex side-band signal, but the invention does not establish a two-dimensional frequency-cepstrum domain function.

The patent application No. CN104006961A provides a cycloidal bevel gear fault diagnosis method based on empirical mode decomposition and cepstrum, which comprises the following steps: 1. measuring the cycloid bevel gear pair by using an acceleration sensor, and collecting an acceleration vibration signal as a signal to be analyzed; 2. introducing the collected signals into Matlab to obtain original signals, and decomposing the original signals into a series of Intrinsic Mode Function (IMF) components by using an Empirical Mode Decomposition (EMD) method; 3. performing cepstrum analysis on the first orders of inherent modal function components to obtain amplitude cepstrum of the inherent modal function components; 4. and drawing an amplitude cepstrum by using a drawing tool of Matlab software, and extracting fault characteristic information according to the distribution of the amplitude in the cepstrum. The method can effectively identify the characteristic information of the fault signal of the cycloidal bevel gear from the complex sideband signal, but the method does not establish a two-dimensional frequency-cepstrum domain function.

The invention is based on a time-frequency analysis method in a modern signal analysis method, takes the frequency spectrum of a signal as an analyzed object, and carries out time-frequency transformation on the logarithmic frequency spectrum of the signal to obtain a two-dimensional frequency-cepstrum domain function. Various sideband components in the spectrum can be identified in the cepstrum domain, while information reflecting the distribution of the individual sideband components in the frequency domain is retained. The method can realize the distinguishing and identification of the components of the same frequency-inverting sideband and provide new information for the positioning of the composite fault.

Disclosure of Invention

The invention provides a Narrow-Band frequency-cepstrum transformation method for vibration signal analysis, which has the core content that the time-frequency transformation method (such as short-time Fourier transformation, Wigner-Weili distribution and the like) in modern signal analysis is adopted to carry out 'time-frequency' transformation on a logarithmic spectrum of a vibration signal, the transformation is defined as 'Narrow-Band Cepstral Transform (NBCT)', and a two-dimensional frequency-cepstrum domain function is obtained. Taking the example of using a short-time fourier transform, the "narrow-band cepstrum transform" of a signal is defined as:

NBCT_x(f,τ)＝∫L_x(λ)H(λ-f)e^-j2πτλdλ (1)

the essence of this transformation is the log spectrum L of the signal_x(f) Adding a moving narrow-band window H (lambda, f), and then performing inverse Fourier transform to obtain a local cepstrum. By changing the center frequency f of the narrow-band moving spectrum window, local cepstrum of different frequency bands can be obtained, and finally a two-dimensional function NBCT is obtained_x(f, τ). The function has two arguments, where the argument f has a frequency dimension in Hz; the argument τ has a time dimension in seconds and is defined as the reciprocal frequency (Quefrency). Thus, a two-dimensional function NBCT_x(f, τ) is a two-dimensional function of frequency domain-inverse frequency domain, defined as the "frequency-cepstrum". The method of the invention transforms one-dimensional signals into two-dimensional 'frequency domain-inverse frequency domain' functions, and can provide richer information about different line spectrum clusters (harmonic formation) in signal frequency spectrums than the inverse frequency spectrumsMinutes, sideband components).

The invention can be realized by the following technical scheme:

the method comprises the following steps: carrying out frequency spectrum analysis on a structural vibration signal x (t) obtained by monitoring the operation of the gear box equipment to obtain a frequency spectrum X (f) of the signal:

step two: logarithm of spectrum x (f) is calculated to obtain the logarithm spectrum of the signal:

L_x(f)＝Log[X(f)] (1)

step three: by adopting a time-frequency Transform method (such as short-time fourier Transform, wigner-willi distribution and the like) in modern signal analysis, a Narrow-Band Cepstral Transform (NBCT) of a signal logarithmic spectrum is obtained to obtain a "Narrow-Band frequency-Cepstral" of the signal:

NBCT_x(f,τ)＝∫L_x(λ)H(λ-f)e^-j2πτλdλ (2)

where H (f) is a narrowband frequency domain window function.

Step four: in "narrowband frequency-cepstrum" NBCT_xAnd (f, tau) carrying out in-depth analysis and feature extraction of the signal features.

The invention has the beneficial effects that:

1) transforming the one-dimensional log spectrum of the signal into the two-dimensional "frequency-cepstrum domain" can provide more information than the one-dimensional cepstrum.

2) The problem that the cepstrum only has information of the cepstrum frequency (time) and does not have frequency information, so that the same-frequency sideband components of different frequency bands cannot be distinguished is solved.

3) The time-frequency analysis method in modern signal analysis is applied to the logarithmic spectrum of signals, and various properties and characteristics of the time-frequency analysis can be transplanted into the Narrow-Band Cepstral Transform (NBCT) of the invention. The 'narrow-band cepstrum transformation' of discrete signals can be realized by directly applying a 'time-frequency analysis' digitization method; the inverse transformation also exists in the narrow-band frequency-cepstrum, and the filtering, noise reduction processing and the like of signals in a frequency-inverse frequency domain can be realized.

Drawings

FIG. 1 is a flow chart of Narrow Band Cepstral Transform (NBCT for short)

FIG. 2 is a schematic diagram of the principle of Narrow-Band Cepstral Transform (NBCT for short)

Fig. 3 vibration signal analysis example: waveform, log spectrum and cepstrum of vibration signal of gearbox

Fig. 4 vibration signal analysis example: the "narrowband frequency-cepstrum" of the gearbox vibration signal.

Detailed Description

The equipment in the embodiment of the invention subsidizes the subsidy project for the national key research and development plan topic (2017YFC 0805905).

A Narrow-Band frequency-cepstrum transformation method for vibration signal analysis is provided, which has the core content that a time-frequency transformation method (such as short-time Fourier transformation, Virgener-Weili distribution and the like) in modern signal analysis is adopted to carry out 'time-frequency' transformation on a logarithmic spectrum of a vibration signal, the transformation is defined as 'Narrow-Band Cepstral Transform (NBCT)', and a two-dimensional frequency-cepstrum domain function is obtained and defined as 'frequency-cepstrum'.

The invention is further described with reference to the following figures and detailed description:

FIG. 1 is a flow chart of Narrow Band Cepstral Transform (NBCT for short). The method comprises five steps:

(1) the vibration signal x (t) is fourier transformed to obtain the frequency spectrum x (f) of the signal.

(2) Calculating the logarithm of the frequency spectrum X (f) to obtain a logarithmic spectrum L of the signal_x(f)。

(3) Logarithm spectrum L_x(f) The Narrow Band Cepstral Transform (NBCT) is obtained to obtain a frequency-Cepstral NBCT of the signal_x(f,τ)。

(4) In "narrowband frequency-cepstrum" NBCT_xAnd (f, tau) carrying out in-depth analysis and feature extraction of the signal features.

Fig. 2 shows a schematic diagram of a principle of narrowband cepstrum transform (NBCT), and a one-dimensional frequency domain function can be transformed to a two-dimensional "frequency-cepstrum domain" through the narrowband cepstrum transform (NBCT), so as to obtain a frequency-cepstrum, and compared with the one-dimensional function cepstrum, more information reflecting the frequency domain characteristics of the signal can be revealed.

Fig. 3 to 4 show an example of vibration signal analysis under the complex fault of the gearbox, which is the signal under the fault of both gear teeth fault of the gearbox and unbalance of the shafting. Three graphs from top to bottom in fig. 3 show the waveform, log spectrum, and cepstrum of the vibration signal, respectively. The vibration signal time domain waveform has a periodic amplitude modulation characteristic, as shown by a dotted line in fig. 3 a); FIG. 3b) shows a logarithmic spectrum of the signal with a large number of sideband components, which are more prominent in the two regions shown by the dashed lines; fig. 3c) shows a signal cepstrum with a prominent peak (arrow a) at the cepstrum frequency of about 0.04s and its cepstrum, indicating that the frequency separation of the sideband components in the log spectrum of the signal is about 25Hz, corresponding to the rotational frequency of the output shaft of the gearbox, indicating that the frequency domain distribution of the sideband components cannot be judged.

Fig. 4 shows a two-dimensional frequency-cepstrum of the vibration signal, wherein the upper diagram is a two-dimensional plan view representation and the lower diagram is a three-dimensional view representation. It can be clearly seen that the distribution of the component at the cepstrum frequency of 0.04s in the frequency domain appears as two prominent peaks in the frequency bands around 1100Hz and 1180Hz, respectively, as shown by the arrow f₁And f₂The meshing frequency and the inherent frequency of a certain order of the gear box are respectively corresponding to the shown structure, which shows that the gear box structure can accurately distinguish the same sideband components distributed in different frequency bands, and further distinguish and locate the gear tooth fault and the unbalance fault.

As can be seen from the contents of fig. 3 and 4, the two-dimensional frequency-cepstrum is substantially different from the spectral analysis and the cepstrum analysis; through two-dimensional frequency-cepstrum analysis, the same sideband components distributed in different frequency bands can be accurately distinguished, and then the gear tooth fault and the unbalance fault are distinguished and positioned. This is not achievable and can be replaced by spectral analysis and cepstral analysis.

Some specific embodiments have been described above. It will be appreciated that modifications may be made to the embodiments. For example, elements of different embodiments may be combined, supplemented, modified, and deleted to yield yet further embodiments. Further, those of ordinary skill in the art will appreciate that other structures and process flows may be substituted for those disclosed above to achieve other embodiments. The other embodiments achieve substantially the same function in at least substantially the same way to achieve substantially the same result as provided by the embodiments disclosed herein. Accordingly, these and other embodiments are intended to be within the scope of the present invention.

Claims

1. A method of processing a mechanical vibration signal during operation of a gear box apparatus using narrowband cepstrum conversion, comprising the steps of:

A. collecting a mechanical vibration signal x (t) of periodic motion;

B. carrying out spectrum analysis on the vibration signal x (t) to obtain a frequency spectrum X (f) of the signal;

C. logarithm of spectrum x (f) is calculated to obtain the logarithm spectrum of the signal:

L_x(f)＝Log[X(f)] (1)；

subsequent log spectrum L of the signal_x(f) Adding a narrow-band moving window H (lambda, f), and obtaining a local cepstrum after solving Fourier transform;

D. for logarithmic spectrum L of signal_x(f) Performing narrow-band cepstrum transformation to obtain narrow-band frequency-cepstrum of the signal, changing the center frequency f of a narrow-band moving spectrum window to obtain local cepstrum of different frequency bands, and finally obtaining a two-dimensional function NBCT_x(f,τ)：

NBCT_x(f,τ)＝∫L_x(λ)H(λ-f)e^-j2πτλdλ (2)

In formula (2), h (f) is a narrowband frequency domain window function where the argument f has a frequency dimension in Hz; the argument τ has a time dimension in seconds, defined as the reciprocal frequency.

2. The method of claim 1, NBCT for narrowband frequency-cepstrum_xAnd (f, tau) analyzing to obtain a fault characteristic signal of the mechanical vibration.

3. Method according to claim 1, for a logarithmic spectrum L of a signal_x(f) The transformation mode adopted by the narrow-band cepstrum transformation is short-time Fourier transformation and Vigrena-Weili distribution.