CN107941511A - A kind of implementation method of the frequency based on signal Time-frequency Decomposition-kurtosis figure - Google Patents

Abstract

The invention discloses a realization method of a frequency-kurtosis graph based on time-frequency decomposition of a signal. Firstly, the frequency slice wavelet transform is performed on the signal to obtain its time-frequency decomposition result. Based on this, a signal component is selected for reconstruction With a certain frequency interval as the step size, the time-frequency subspace is selected in the time-frequency decomposition space, and the time-frequency space of the signal is divided into a series of subspaces with the same bandwidth and overlapping with each other. Then, the frequency slice wavelet transform inverse transform is used to extract the time domain components of the signal in these subspaces, and the kurtosis values of the time domain components of these subspaces are calculated, and then the kurtosis value sequence of the signal in the entire analysis frequency band is obtained; The center frequency of each time-frequency subspace is taken as the abscissa value, and the kurtosis of the corresponding signal component is taken as the ordinate value, and the frequency-kurtosis curve of the signal can be obtained, and the frequency corresponding to the peak value on the frequency-kurtosis curve is the mechanism or the resonant frequency of the component.

Description

A Realization Method of Frequency-Kurtosis Diagram Based on Signal Time-Frequency Decomposition

technical field

The invention belongs to the field of mechanical equipment signal processing, and in particular relates to a method for realizing a frequency-kurtosis diagram based on signal time-frequency decomposition.

Background technique

Bearings, gears, etc. are the most commonly used parts in mechanical equipment, and more than 30% of mechanical equipment failures are related to them. When these components are damaged or faulty, the structural components will be excited to resonate during their rotation. Due to the repeated shock response, the amplitude modulation phenomenon will appear in the vibration signal with the repeated impact. The frequency of the amplitude modulation is related to the fault characteristics. These features are submerged in the noise at the initial stage of the fault. Therefore, selecting the resonant frequency band to separate out the repetitive shock features can effectively determine the fault type.

Kurtosis is a dimensionless index commonly used in mechanical equipment fault diagnosis, which can be used to measure the strength of the impact component in the signal. It is a statistical indicator. If it is calculated based on the sampling signal of a certain period of time, this kurtosis is a time-domain indicator. For working mechanical equipment, when a component fails, its dynamic performance changes and the vibration intensifies. Therefore, in the field of mechanical equipment condition monitoring and fault diagnosis, kurtosis is often used to evaluate the state of mechanical equipment or components.

Literature [1] is based on the short-time Fourier transform, after selecting the window function, the vibration signal is filtered with a certain bandwidth, and then the kurtosis of the envelope of the filtered signal in each frequency band is calculated, and the resonance frequency band is determined by the maximum kurtosis value To extract the damage features of the bearing. Literature [2] uses the narrowband filtering method to filter the signal to obtain a series of signal components. On the basis of obtaining the spectrum of the envelope of these signal components, the resonance frequency band is determined by calculating the kurtosis of these spectrum amplitude sequences. Bearing damage characteristics. Literature [3] uses the frequency slice wavelet transform to decompose the time-frequency of the vibration signal to obtain the time-frequency energy distribution of the signal, and then divides the time-frequency space of the signal with a given frequency bandwidth, and calculates these based on the time-frequency energy distribution. The time-frequency kurtosis index of the time-frequency subspace is used to determine the resonance frequency band and extract the damage characteristics of the bearing.

The above method has the following problems in the application process:

(1) To adopt the short-time Fourier transform filtering and narrow-band filtering methods, the bandwidth and center frequency of the window function need to be set in advance, which requires prior knowledge.

(2) Using a given bandwidth to divide the frequency band or time-frequency space of the signal in a non-overlapping, equal-width form often misses the best frequency band, because the characteristic frequency band does not necessarily fall exactly within the artificially divided frequency band or time-frequency interval .

(3) The selection of the width of the filter frequency band has a great influence on the calculation of the kurtosis value in the time domain and frequency domain based on the signal envelope. If the bandwidth selection is too large, the envelope components of the filtered signal are complex, and the kurtosis value cannot reflect the signal well. If the bandwidth selection is too small, the envelope component of the filtered signal is single, the envelope changes slowly, and the impact characteristics cannot be displayed.

The following are relevant references searched by the applicant:

[1] J.Antoni and R.B.Randall, The spectral kurtosis: application to the vibratory surveillance and diagnostics of rotating machines [J]. Mechanical Systems and Signal Processing, 2006, 20: 308-331.

[2] T. Barszcz, A. Jabtoński. A novel method for the optimal band selection for vibration signal demodulation and comparison with the Kurtogram [J]. Mechanical Systems and Signal Processing, 2011, 25: 431–451.

[3] Duan Chendong, Gao Peng, Gao Qiang, A method for diagnosis of rolling bearing damage based on time-frequency kurtosis spectrum, Chinese Journal of Mechanical Engineering, 2015, 51(11): 78-83.

Contents of the invention

In view of the defects or deficiencies in the above-mentioned prior art, the purpose of the present invention is to provide a method for realizing frequency-kurtosis curve based on the frequency slice wavelet transform method of signals.

In order to realize above-mentioned task, the present invention adopts following technical solution:

A method for realizing a frequency-kurtosis diagram based on time-frequency decomposition of a signal, characterized in that firstly, the signal is subjected to frequency-slicing wavelet transform to obtain its time-frequency decomposition result, and based on this, a signal component is selected for reconstruction With a certain frequency interval as the step size, the time-frequency subspace is selected in the time-frequency decomposition space, and the time-frequency space of the signal is divided into a series of subspaces with the same bandwidth and overlapping with each other. Then, the frequency slice wavelet transform inverse transform is used to extract the time domain components of the signal in these subspaces, and the kurtosis values of the time domain components of these subspaces are calculated, and then the kurtosis value sequence of the signal in the entire analysis frequency band is obtained; The center frequency of each time-frequency subspace is taken as the abscissa value, and the kurtosis of the corresponding signal component is taken as the ordinate value, and the frequency-kurtosis curve of the signal can be obtained, and the frequency corresponding to the peak value on the frequency-kurtosis curve is the mechanism or the resonant frequency of the component; where:

The frequency slice wavelet transform is a signal time-frequency decomposition method. Before the signal transform, a frequency slice function is selected, and its transform result is the energy mapping of the signal in time-frequency space;

The analysis frequency band refers to the Nyquist band of the signal, its lower limit frequency is 0 Hz, and its upper limit frequency is half of the sampling frequency of the signal.

The specific implementation method is as follows:

(1) Select a frequency slice function;

(2) Determine the bandwidth of the reconstructed signal component. For the analysis of bearing or gear vibration signals, the bandwidth should be 3 to 5 times the maximum damage characteristic frequency.

(3) Determine the frequency step size. For the analysis of bearing or gear vibration signals, the frequency step size should not be greater than its rotation frequency.

(4) remove the DC component in the vibration signal collected;

(5) Carry out frequency slice wavelet transform to the signal that removes DC component;

(6) Extract the signal components of the subspaces by inverse transformation, and calculate the kurtosis values of the time domain components of these subspaces, and then obtain the kurtosis value sequence of the signal in the entire analysis frequency band;

(7) Calculate the center frequency of each subspace;

(8) Taking the center frequency of the subspace as the abscissa and the kurtosis of the corresponding signal component as the ordinate, draw the frequency-kurtosis curve of the signal; the frequency corresponding to the peak value on the frequency-kurtosis curve is the frequency of the mechanism or component Resonance frequency.

According to the present invention, the signal reconstruction refers to the process of performing frequency slice wavelet inverse transform or Fourier transform on the selected frequency band to separate the signal components of the frequency band.

The realization method of the frequency-kurtosis diagram based on signal time-frequency decomposition of the present invention adopts the method of dividing the time-frequency space of the analyzed signal into a series of subspaces with the same bandwidth and overlapping each other, so that the original signal information is Redundant application can fully and effectively extract the shock feature information contained in the vibration signal, and can reflect the kurtosis change trend in the entire analysis frequency band of the signal, which is conducive to the extraction of fault features. In engineering applications, the frequency corresponding to the peak value can be selected. Neighborhood intervals are used as frequency bands for demodulation analysis.

Description of drawings

Fig. 1 is a flow chart of the frequency-kurtosis curve based on signal time-frequency decomposition in the present invention.

The time-domain waveform diagram of Fig. 2 signal y (t);

Fig. 3 is a sinusoidal signal component waveform diagram;

Figure 4 is a waveform diagram of repetitive shock components;

Fig. 5 is an amplitude modulation component waveform diagram;

Fig. 6 is the obtained frequency-kurtosis curve diagram based on signal time-frequency decomposition;

The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

Detailed ways

This embodiment presents a method for realizing the frequency-kurtosis curve based on time-frequency decomposition of the signal. Its purpose is to find the resonance frequency in the signal, which is used to determine the resonance frequency band to extract the amplitude modulation characteristics in the signal. , the neighborhood interval corresponding to the peak frequency can be selected as the frequency band for demodulation analysis.

Firstly, the frequency slice wavelet transform is performed on the signal to obtain its time-frequency decomposition result. Based on this, a bandwidth of signal component reconstruction is selected, and a certain frequency interval is used as the step size, and the time-frequency sub-components are selected in the time-frequency decomposition space. Space, the time-frequency space of the signal is divided into a series of subspaces with the same bandwidth and overlapping with each other. Then, the frequency slice wavelet transform inverse transform is used to extract the time domain components of the signal in these subspaces, and the kurtosis values of the time domain components of these subspaces are calculated, and then the kurtosis value sequence of the signal in the entire analysis frequency band is obtained; The center frequency of each time-frequency subspace is taken as the abscissa value, and the kurtosis of the corresponding signal component is taken as the ordinate value, and the frequency-kurtosis curve of the signal can be obtained, and the frequency corresponding to the peak value on the frequency-kurtosis curve is the mechanism or the resonant frequency of the component; where:

The frequency slice wavelet transform is a signal time-frequency decomposition method. Before the signal transform, a frequency slice function is selected, and its transform result is the energy mapping of the signal in time-frequency space;

The analysis frequency band refers to the Nyquist band of the signal, its lower limit frequency is 0 Hz, and its upper limit frequency is half of the sampling frequency of the signal.

In this example:

The frequency slice wavelet transform is a signal time-frequency decomposition method. Before the signal transform, a frequency slice function needs to be selected, and its transform result is the energy mapping of the signal in time-frequency space.

The kurtosis is a dimensionless statistical index describing the signal in the time domain, which is sensitive to the impact component in the signal.

The frequency-kurtosis curve is a trend diagram showing the time-domain kurtosis value of the signal component in the sub-band (sub-time-frequency space) of the analysis frequency band changing with frequency.

In engineering applications, the neighborhood interval corresponding to the peak frequency can be selected as the frequency band for demodulation analysis.

The specific implementation method is as follows:

(1) Select a frequency slice function;

(2) Determine the bandwidth of the reconstructed signal component. For the analysis of bearing or gear vibration signals, the bandwidth should be 3 to 5 times the maximum damage characteristic frequency.

(3) Determine the frequency step size. For the analysis of bearing or gear vibration signals, the frequency step size should not be greater than its rotation frequency.

(4) remove the DC component in the vibration signal collected;

(5) Carry out frequency slice wavelet transform to the signal that removes DC component;

(6) Extract the signal components of the subspaces by inverse transformation, and calculate the kurtosis values of the time domain components of these subspaces, and then obtain the kurtosis value sequence of the signal in the entire analysis frequency band;

(7) Calculate the center frequency of each subspace;

(8) Taking the center frequency of the subspace as the abscissa and the kurtosis of the corresponding signal component as the ordinate, draw the frequency-kurtosis curve of the signal.

Wherein, the signal reconstruction refers to the process of performing frequency slice wavelet inverse transform or Fourier transform on the selected frequency band to separate the signal components of the frequency band.

The specific implementation process is given below.

For the time domain signal f(t), let its Fourier transform be If the frequency slice function is p(t), then the frequency slice wavelet transform of the signal is:

In the formula, κ>0, for the conjugate function of is the Fourier transform of p(t).

Since ω=2πf, when κ is a constant, the transformation result W(t,ω,κ) can be written as W(t,f), which is an energy mapping of the signal in time-frequency space.

The signal component y(t) of [t ₁ ,t ₂ ,f ₁ ,f ₂ ] on the time-frequency subspace can be obtained by inverse transformation:

Suppose the vibration signal s(t) is sampled with f _s as the sampling frequency, and the signal sequence S={s _i , i=1～N} with a length of N is obtained, and its corresponding time interval is [0,...,t _j ,. ..,t _N-1 ], wherein, t _j =j/f _s , j=0˜N-1.

Remove the DC component from the vibration signal:

in, is the mean value of s(t) in the time interval [0,t _N-1 ].

Using the formula (1) to transform the signal x(t), the transformation result of x(t) in the time-frequency interval [0,t _N-1 ,0,f _s /2] is: W(t,f)={ W(t _k , f _k ), t _k =0˜t _N-1 , f _k =0˜f _s /2}.

In the time-frequency space of the signal, define the frequency bandwidth as ΔW and the step size as f _p , then at step i, the reconstructed signal component y _i (t) from the time-frequency subspace is:

i=1,2,...,M, M is the integer part of f _s /2f _p .

Calculate the kurtosis of the signal component y _i (t):

L is the length of y _i (t), is the mean of y _i (t).

When i=1,2,...,M, the kurtosis value sequence of the signal s(t) in the frequency band [0, f _s /2] is obtained:

K _R ＝{K _r (i),i=1,2,...,M}

make: but:

F _c ={f _c (i),i=1,2,...,M}

Using K _R ={K _r (i),i=1,2,...,M} as the ordinate, F _c ={f _c (i),i=1,2,.... .., M} as the abscissa, the frequency-kurtosis curve is obtained, and the realization process of the frequency-kurtosis curve is shown in Figure 1. Its peak can characterize the resonant frequency of a structure or component.

Engineering application example:

A time-domain signal y(t) is shown in Figure 2, the sampling frequency is 20kHz, and the sampling length is 2048. It is constructed by adding the three components in Figure 2, Figure 3, and Figure 4, and then superimposing a certain amount of white noise. The frequency of the sinusoidal signal component in Fig. 3 is f ₁ = 500 Hz, the repetition frequency of the repetitive impact component in Fig. 4 is 100 Hz, the resonance frequency of the structure is 3000 Hz, the amplitude modulation frequency of the amplitude modulation component in Fig. 5 is 100 Hz, and the carrier The frequency is 1500Hz.

Figure 6 shows the frequency-kurtosis curve of the signal y(t). The selected bandwidth is 300Hz and the step size is 100Hz. Two peaks appear on the curve indicating 1500Hz and 3000Hz. These two frequencies are the carrier frequency and the structural resonance frequency respectively.

Claims (3)

1. A method for realizing a frequency-kurtosis graph based on signal time-frequency decomposition, characterized in that, at first the signal is subjected to frequency slice wavelet transform to obtain its time-frequency decomposition result, based on this, a signal component is selected The reconstructed bandwidth takes a certain frequency interval as the step size, selects the time-frequency subspace in the time-frequency decomposition space, and divides the time-frequency space of the signal into a series of overlapping subspaces with the same bandwidth. Then, the frequency slice wavelet transform inverse transform is used to extract the time domain components of the signal in these subspaces, and the kurtosis values of the time domain components of these subspaces are calculated, and then the kurtosis value sequence of the signal in the entire analysis frequency band is obtained; The center frequency of each time-frequency subspace is taken as the abscissa value, and the kurtosis of the corresponding signal component is taken as the ordinate value, and the frequency-kurtosis curve of the signal can be obtained, and the frequency corresponding to the peak value on the frequency-kurtosis curve is the mechanism or the resonant frequency of the component; where: The frequency slice wavelet transform is a signal time-frequency decomposition method. Before the signal transform, a frequency slice function is selected, and its transform result is the energy mapping of the signal in time-frequency space; The analysis frequency band refers to the Nyquist band of the signal, its lower limit frequency is 0 Hz, and its upper limit frequency is half of the sampling frequency of the signal. 2. The method according to claim 1, wherein the specific implementation method is as follows: (1) Select a frequency slice function; (2) Determine the bandwidth of the reconstructed signal component. For the analysis of bearing or gear vibration signals, the bandwidth should be 3 to 5 times the maximum damage characteristic frequency. (3) Determine the frequency step size. For the analysis of bearing or gear vibration signals, the frequency step size should not be greater than its rotation frequency. (4) remove the DC component in the vibration signal collected; (5) Carry out frequency slice wavelet transform to the signal that removes DC component; (6) Extract the signal components of the subspaces by inverse transformation, and calculate the kurtosis values of the time domain components of these subspaces, and then obtain the kurtosis value sequence of the signal in the entire analysis frequency band; (7) Calculate the center frequency of each subspace; (8) Taking the center frequency of the subspace as the abscissa and the kurtosis of the corresponding signal component as the ordinate, draw the frequency-kurtosis curve of the signal; the frequency corresponding to the peak value on the frequency-kurtosis curve is the frequency of the mechanism or component Resonance frequency. 3. The method according to claim 1 or 2, wherein said signal reconstruction refers to the process of performing frequency slice wavelet inverse transform or Fourier transform on the selected frequency band to separate the signal components of the frequency band.