Differential Spectrum Analysis and Filtering Method of Vibration Signals

Abstract

Differential spectrum analysis and filtering method for vibration signals, which characterizes and extracts damage components in signals based on the frequency-domain differences between the signal to be evaluated and the reference signal. First, the signal to be evaluated and the reference signal are subjected to discrete Fourier transform, then frequency-domain subtraction is performed to obtain a differential spectrum diagram, and then the damage components in the signal are reconstructed through inverse discrete Fourier transform. Finally, based on the time-domain characteristics of the damage components and the frequency-domain characteristics of the differential spectrum diagram, the occurrence and severity of damage are judged. The present invention can effectively suppress the conventional components in vibration signals, targetedly extract damage information, improve the sensitivity for detecting early damage, and has important engineering application value.

Description

Technical Field

[0001] The present invention belongs to the field of signal processing analysis and condition monitoring, and particularly relates to the differential spectrum analysis and filtering method of vibration signals. Background Art

[0002] Vibration analysis is one of the main means for condition monitoring. When damage occurs to the monitored object, the vibration signal will change in corresponding components compared with the healthy state, mainly manifested as the generation and evolution of damage components in the signal. Time-domain and frequency-domain analysis are two common means for analyzing signals. By comparing the time-domain and frequency-domain differences of vibration signals in normal and damaged states, damage components can often be found. However, for early damage, the vibration components caused by damage usually have weak energy and are not significant enough in the vibration signal. Direct time-domain and frequency-domain analysis often fails to detect them.

[0003] The differential spectrum method generally refers to the appropriate subtraction processing of the absorption spectrum curve in spectral analysis to eliminate the interference of matrix components, and is widely used for the determination of trace components. Similarly, the vibration signal with early damage not only contains weak signal components caused by damage, but is more dominated by vibration components that also exist in the normal state. Taking the vibration of a gearbox as an example, the vibration signals in normal and damaged states both include significant shaft vibration and gear meshing vibration. How to extract the weak damage components in the vibration signal through spectral analysis and filtering means based on the vibration signal in the normal state is an important scientific and engineering problem to be solved urgently. Summary of the Invention

[0004] To overcome the above disadvantages, the present invention draws on the idea of the differential spectrum method in spectral analysis and proposes a differential spectrum analysis and filtering method for vibration signals. This method can effectively suppress the conventional components in the vibration signal, targetedly extract damage information, and improve the sensitivity for detecting early damage.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0006] The differential spectrum analysis and filtering method of vibration signals includes the following steps:

[0007] Step 1: Obtain the vibration signal x 1 (n) of the normal state and the vibration signal x 2 (n) to be evaluated. The vibration signal x 1 (n) of the normal state will be used as the signal reference. The working conditions and sampling parameters of the vibration signal x 2 (n) are consistent with those of the vibration signal x 1 (n). The sampling frequency is denoted as Fs, and the data length is denoted as N;

[0008] Step 2: The vibration signals x 1 (n) and x2 (n) is obtained by discrete Fourier transform (DFT) of formula (1) to get X 1 (k) and X 2 (k);

[0009]

[0010] Step 3: Calculate the difference spectrum D(k) according to formula (2), and draw the difference spectrum diagram. Observe the frequency components in the difference spectrum diagram that the vibration signal x 2 (n) has more than the reference signal x 1 (n) in the frequency domain;

[0011]

[0012] Step 4: Perform inverse discrete Fourier transform on the difference spectrum D(k) to reconstruct the time-domain signal d(n) of the potential damage component in the signal. d(n) is calculated by formula (3),

[0013]

[0014] This step is essentially a filtering process of the signal x 2 (n), achieving the purpose of filtering out the vibration components in the signal x 2 (n) that are the same as x 1 (n);

[0015] Step 5: Analyze the time-domain characteristics of the filtered signal d(n), and combine with the frequency-domain characteristics of the difference spectrum diagram to judge the occurrence and severity of damage.

[0016] The present invention has the following beneficial effects:

[0017] a) The method of the present invention targets and extracts damage information through filtering, improving the sensitivity for detecting early damage, and has important engineering application value.

[0018] b) The subtraction operation object of the present invention is the frequency-domain amplitude of the signal, avoiding the residual problem caused by the inconsistent initial phases directly subtracting in the time domain of the original signal, and can more effectively eliminate the interference of the conventional components of the signal.

[0019] c) The complex operation steps involved in the method of the present invention are discrete Fourier transform and its inverse transform, and now there are mature fast algorithms for both. Therefore, the proposed method has the advantages of high calculation efficiency and saving calculation resources. Description of the Drawings

[0020] Figure 1 is the flow chart of the present invention.

[0021] Figure 2 is the reference vibration signal x of the embodiment of the present invention1 (n).

[0022] Figure 3 is the vibration signal x of the embodiment of the present invention 2 (n) in the damage component.

[0023] Figure 4 is the vibration signal x of the embodiment of the present invention 2 (n).

[0024] Figure 5 is the vibration signal x of the embodiment of the present invention 2 (n) spectrum.

[0025] Figure 6 is the difference spectrum diagram obtained by the difference spectrum analysis of the embodiment of the present invention.

[0026] Figure 7 is the damage component obtained by the difference spectrum filtering of the embodiment of the present invention.

[0027] Figure 8 is the error of the damage component obtained by the difference spectrum filtering of the embodiment of the present invention. Specific implementation manner

[0028] The present invention will be described in detail below with reference to the drawings and embodiments.

[0029] The difference spectrum analysis and filtering method of the vibration signal, as Figure 1 shown, apply this method to analyze the embodiment signal. The embodiment signal includes the reference vibration signal x 1 (n) and the signal to be evaluated x 2 (n). The signal x 1 (n) is a sine wave with a frequency of 1000 Hz and an amplitude of 1 g, as Figure 2 shown. The signal x 2 (n) is composed of two parts. The first part is a sine wave with the same frequency and amplitude as x 1 (n) but with a different initial phase. The second part is a periodic impact component with an oscillation frequency of 8000 Hz caused by damage, as Figure 3 shown. The signal x 2 (n) as Figure 4 shown. It can be seen that the damage component in the signal is affected by the sine wave and becomes indistinguishable in the time domain.

[0030] The method includes the following steps:

[0031] Step 1: Obtain the vibration signal x 1 (n) in the normal state and the vibration signal x 2 (n) to be evaluated. The signal x 1 (n) will be used as the signal reference, and the signal x 1(n) and the signal x 2 (n) of the time domain waveforms are respectively as Figure 2 and Figure 4 shown. The sampling frequency is 24000Hz, the data length is 2400 data points, corresponding to a time length of 0.1 seconds;

[0032] Step two: The vibration signal x 1 (n) and x 2 (n) are obtained as X 1 (k) and X 2 (k) through the discrete Fourier transform (DFT) of formula (1), Figure 5 which is the spectrum of the signal x 2 (n). It can be seen from the spectrum that the signal is dominated by a 1000Hz sine component, while the amplitude of the resonance frequency band at 8000Hz where the fault component is located is relatively weak;

[0033]

[0034] Step three: Calculate the difference spectrum D(k) according to formula (2), and draw the difference spectrum diagram as Figure 6 shown. The difference spectrum diagram can clearly observe the additional frequency components in the frequency domain of the vibration signal x 2 (n) compared with the reference signal x 1 (n), that is, the resonance sideband centered at 8000Hz;

[0035]

[0036] Step four: Perform the inverse discrete Fourier transform on the difference spectrum D(k) to reconstruct the time domain signal d(n) of the potential damage component in the signal. d(n) is calculated through formula (3).

[0037]

[0038] This step is essentially a filtering process of the signal x 2 (n), aiming to filter out the same vibration components (the sine wave at 1000Hz in the embodiment) in the signal x 2 (n) as those in x 1 (n). The damage component d(n) obtained by difference spectrum filtering is as Figure 7 shown. Subtracting this result from the Figure 3 theoretical waveform gives the filtering error as Figure 8 shown. The maximum error amplitude is about 10% of the amplitude of the damage component, indicating that the proposed method has a small filtering error and effectively extracts the damage component;

[0039] Step Five: Analyze the time-domain characteristics of the filtered signal d(n), and combine with the frequency-domain characteristics of the differential spectrum diagram to judge the occurrence and severity of damage. In the embodiment, the filtered signal d(n) is a periodic impact signal caused by a fault in a rotating machine, and the oscillation frequency of the impact is 8000 Hz. The damage location can be traced through the impact period, and the impact amplitude can be used to evaluate the severity of the damage.

[0040] The differential spectrum analysis and filtering method of vibration signals proposed by the present invention can effectively suppress the conventional components in vibration signals, targetedly extract damage information, improve the sensitivity of detecting early damage, and has important engineering application value.

Claims

1. Differential spectrum analysis and filtering method for vibration signals, including the following steps: Step 1: Obtain the vibration signal x under normal conditions 1 (n) and the vibration signal x to be evaluated 2 (n). The vibration signal x under normal conditions 1 (n) will be used as the signal reference. The working conditions and sampling parameters of the vibration signal x 2 (n) are the same as those of the vibration signal x 1 (n). The sampling frequency is denoted as Fs, and the data length is denoted as N; Step 2: Vibration signal x 1 (n) and x 2 (n) are obtained as X 1 (k) and X 2 (k) through the discrete Fourier transform (DFT) of formula (1); Step 3: Calculate the difference spectrum D(k) according to formula (2), and plot the difference spectrum diagram, and observe the vibration signal x in the difference spectrum diagram 2 compared with the reference signal x 1 (n) the extra frequency components in the frequency domain; Step 4: Perform inverse discrete Fourier transform on the differential spectrum D(k) to reconstruct the time-domain signal d(n) of the potential damage component in the signal. d(n) is calculated through formula (3). This step is essentially a filtering process for the signal x 2 (n), aiming to filter out the vibration components in the signal x 2 (n) that are the same as those in x 1 (n); Step 5: Analyze the time-domain characteristics of the filtered signal d(n), and combine with the frequency-domain characteristics of the differential spectrum diagram to judge the occurrence and severity of damage.

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