Short-time difference spectrum analysis method

Abstract

The short-time difference spectrum analysis method characterizes and extracts the transient components in the signal through time-frequency analysis. First, the window signal is intercepted through a sliding window, and then the window signal is discrete Fourier transformed to obtain a short-time Fourier transform matrix, and then the short-time difference spectrum matrix is ​​calculated and the time-frequency diagram of the short-time difference spectrum analysis is drawn. Finally, the short-time difference spectrum matrix is ​​inversely transformed to reconstruct the time domain signal of the transient component in the signal, and the targeted extraction of the transient component by filtering in the time-frequency domain is realized. The present invention can effectively overcome the influence of steady-state harmonic components often faced in engineering signals, characterize the transient components caused by defects, and improve the ability to detect early abnormalities, which has important engineering application value.

Description

Technical Field

[0001] The invention belongs to the field of signal processing analysis and state monitoring, and particularly relates to a short time difference spectrum analysis method. Background Art

[0002] Fourier transform can decompose a signal into different frequency components, but Fourier transform is a holistic transform and cannot analyze the relationship between the frequency components in the signal and time. Time-frequency analysis transforms the one-dimensional time domain signal into a two-dimensional time-frequency plane, which can reveal the change of frequency over time and reflect the transient structure in the signal. It is particularly suitable for the analysis of non-stationary signals. Typical time-frequency analysis methods include short-time Fourier transform, continuous wavelet transform, Wigner-Ville distribution, Hilbert-Huang transform, etc.

[0003] In the field of condition monitoring, transient information caused by defects can be captured by performing time-frequency analysis on sensor signals to achieve the purpose of diagnosis and early warning. In real applications, such as mechanical fault diagnosis and large-scale structural damage monitoring, the transient components caused by early defects in sensor signals are often very weak and easily masked by other normal components. Taking gear condition monitoring as an example, the gear vibration signal includes stable harmonic components such as shaft vibration and gear meshing vibration. The vibration energy caused by early defects is much smaller than these main vibrations, and it is often not found in the time-frequency diagram. Only after the defect expands can its vibration component be found in the time-frequency diagram.

[0004] The current time-frequency analysis method characterizes the relationship between all frequency components of a signal and time, and cannot specifically reveal the relationship between the transient components caused by the frequency components of interest, such as defects, and time. Summary of the invention

[0005] To overcome the above shortcomings, the present invention proposes a short time difference spectrum analysis method, which can effectively suppress irrelevant harmonic components in the signal, perform targeted extraction of transient components caused by defects, and improve the ability to detect early anomalies.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] The short time difference spectrum analysis method comprises the following steps:

[0008] Step 1: Collect the sensor signal x(n) for condition monitoring, the length of the signal is recorded as Nx, and the sampling frequency is recorded as Fs;

[0009] Step 2: Slide the window function g(n) on the signal x(n) to intercept the window signal. The window length is M. The overlap rate between adjacent windows is L, and the interval between adjacent windows is R=ML.

[0010] Step 3: Calculate the short-time Fourier transform matrix X(f), the number of columns of the matrix For floor rounding, the number of rows in the matrix is ​​the number of points N at which the window signal is subjected to the discrete Fourier transform (DFT) DFT Specifically, X(f) = [X 1 (f) X 2 (f) X 3 (f) … X k (f)], where the mth column vector X m (f) is the discrete Fourier transform result of the window signal at time t = mR, which is calculated by formula (1).

[0011]

[0012] Where g(n) is the window function in step 2, and R is the interval between adjacent windows;

[0013] Step 4: Calculate the short-time difference spectrum matrix D(f) = [D 2 (f) D 3 (f) … D k (f)], the number of columns of the matrix is ​​k-1, and the mth column vector D m Each element D in (f) m (f i ) is calculated by formula (2),

[0014]

[0015] When |X m (f i )|greater than|X 1 (f i )|, indicating that there is a corresponding transient component increment, D m (f i ) and X m (f i ) have the same phase and amplitude |X m (f i )|with|X m (f i )|difference;

[0016] Step 5: Draw a time-frequency diagram based on the short-time difference spectrum matrix D(f), and observe the transient components in the signal in the time-frequency diagram. The time-frequency diagram is the analysis result 1 of the short-time difference spectrum analysis method;

[0017] Step 6: Further perform short-time Fourier inverse transform on the short-time difference spectrum matrix D(f) to reconstruct the time domain signal d(n) of the transient component in the signal. d(n) is calculated by formula (3):

[0018]

[0019] Where D m (f) is the column vector of the short-time difference spectrum matrix D(f) in step 4. This step is the targeted extraction of transient components by filtering in the time-frequency domain. The time domain signal d(n) of the transient component is the analysis result 2 of the short-time difference spectrum analysis method.

[0020] The present invention has the following beneficial effects:

[0021] a) Compared with the traditional time-frequency analysis method, the present invention can better meet the demand for time-frequency analysis in the field of condition monitoring, can effectively characterize the transient components in the signal, and has important engineering application value;

[0022] b) The present invention performs targeted extraction of transient components through time-frequency domain filtering and reconstructs the transient components in the signal, which is conducive to further diagnostic information mining of the transient components;

[0023] c) The method of the present invention can help overcome the interference of steady-state harmonic components often encountered in engineering signals, significantly improve signal quality, and increase the detection rate of early defects. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is a flow chart of the present invention.

[0025] Figure 2 The transient component in the simulation signal of the embodiment of the present invention.

[0026] Figure 3 is a simulation signal of an embodiment of the present invention.

[0027] Figure 4 This is a time-frequency diagram obtained by short-time Fourier transform of the simulation signal in the embodiment of the present invention.

[0028] Figure 5 This is a time-frequency diagram obtained by short-time difference spectrum analysis of the simulation signal in an embodiment of the present invention.

[0029] Figure 6 It is a transient signal extracted by short-time difference spectrum analysis of the simulation signal in the embodiment of the present invention.

[0030] Figure 7 It is the error of the transient signal extracted by the short-time difference spectrum analysis of the simulation signal in the embodiment of the present invention. DETAILED DESCRIPTION

[0031] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0032] The method of the present invention is used to perform short-time difference spectrum analysis on the simulation signal. The simulation signal x(t) is composed of x 1(t) and x 2 (t), that is, x(t) = x 1 (t)+x 2 (t), where x 1 (t) is the transient component of interest, and the function expression is Figure 2 is the time domain waveform of the transient component, which is a transient component with a frequency of 65Hz and an amplitude that increases continuously until it becomes stable. 2 (t) is the 40Hz harmonic component in the signal, and the function expression is: Figure 3 The time domain waveform of the simulated signal x(t) is dominated by the 40Hz harmonic component, and the transient component x cannot be observed. 1 (t).

[0033] Short-time difference spectrum analysis methods, such as Figure 1 As shown, the following steps are included:

[0034] Step 1: Sample the simulation signal x(t) to obtain a digital signal x(n), the sampling frequency is 512 Hz, the time length of the signal is 10 seconds, and Nx = 5120 data points;

[0035] Step 2: Slide the Hanning window g(n) on the signal x(n) to intercept the window signal, the window length M = 512 data points, the overlap rate between adjacent windows is length L = 384 data points, then the interval between adjacent windows R = ML = 128 data points;

[0036] Step 3: Calculate the short-time Fourier transform matrix X(f), the number of columns of the matrix For floor rounding, the number of rows in the matrix is ​​the number of points N at which the window signal is subjected to the discrete Fourier transform (DFT) DFT Specifically, X(f) = [X 1 (f) X 2 (f) X 3 (f) …X k (f)], where the mth column vector X m (f) is the discrete Fourier transform result of the window signal at time t = mR, which is calculated by formula (1).

[0037]

[0038] Where g(n) is the window function in step 2, R is the interval between adjacent windows, Figure 4 The time-frequency diagram of the simulation signal of the embodiment obtained by short-time Fourier transform is dominated by the harmonic component of 40 Hz, and the amplitude of the transient component is weak;

[0039] Step 4: Calculate the short-time difference spectrum matrix D(f) = [D 2 (f) D 3 (f) … D k (f)], the number of columns of the matrix is ​​k-1, and the mth column vector D m Each element D in (f) m (f i ) is calculated by formula (2),

[0040]

[0041] When |X m (f i )|greater than|X 1 (f i )|, indicating that there is a corresponding transient component increment, D m (f i ) and X m (f i ) have the same phase and amplitude |X m (f i )|with|X m (f i )|difference;

[0042] Step 5: Draw the time-frequency diagram using the short-time difference spectrum matrix D(f). Figure 5 The time-frequency diagram of the simulation signal of the embodiment obtained by short-time difference spectrum analysis. It can be seen from the time-frequency diagram that the signal only contains the transient component of interest and no 40Hz harmonic component, which indicates that the short-time difference spectrum analysis method effectively filters out the harmonic component in the time-frequency domain;

[0043] Step 6: Further perform short-time Fourier inverse transform on the short-time difference spectrum matrix D(f) to reconstruct the time domain signal d(n) of the transient component in the signal. d(n) is calculated by formula (3):

[0044]

[0045] Where D m (f) is the column vector of the short-time difference spectrum matrix D(f) in step 4. The time domain signal d(n) of the transient component is as follows: Figure 6 As shown, Figure 2 The instantaneous component of the theoretical solution is almost completely consistent. By subtracting d(n) from the theoretical transient component, the error signal can be obtained as Figure 7 As shown, the error amplitude (10 -4 magnitude) is much lower than the transient component amplitude (10 -2 This indicates that the short-time difference spectrum analysis method can perform targeted extraction and high-precision reconstruction of transient components.

[0046] The short-time difference spectrum analysis method proposed in the present invention can effectively overcome the influence of steady-state harmonic components often faced in engineering signals, characterize the transient components caused by defects, and improve the detection capability of early anomalies through targeted extraction of transient components through time-frequency domain filtering, which has important engineering application value.

Claims

1. Short-time difference spectrum analysis method, The following steps are involved: Step 1: Collect the sensor signal x(n) for condition monitoring. The length of the signal is recorded as N. x , the sampling frequency is recorded as Fs; Step 2: Slide the window function g(n) on the signal x(n) to intercept the window signal. The window length is M. The overlap rate between adjacent windows is L, and the interval between adjacent windows is R=ML. Step 3: Calculate the short-time Fourier transform matrix X(f), the number of columns of the matrix For floor rounding, the number of rows in the matrix is ​​the number of points N at which the window signal is subjected to the discrete Fourier transform (DFT) DFT Specifically, X(f) = [X 1 (f) X 2 (f) X 3 (f) … X k (f)], where the mth column vector X m (f) is the discrete Fourier transform result of the window signal at time t = mR, which is calculated by formula (1). Where g(n) is the window function in step 2, and R is the interval between adjacent windows; Step 4: Calculate the short-time difference spectrum matrix D(f) = [D 2 (f) D 3 (f) … D k (f)], the number of columns of the matrix is ​​k-1, and the mth column vector D m Each element D in (f) m (f i ) is calculated by formula (2), When |X m (f i )|greater than|X 1 (f i )|, indicating that there is a corresponding transient component increment, D m (f i ) and X m (f i ) have the same phase and amplitude |X m (f i )|with|X m (f i )|difference; Step 5: Draw a time-frequency diagram based on the short-time difference spectrum matrix D(f), and observe the transient components in the signal in the time-frequency diagram. The time-frequency diagram is the analysis result 1 of the short-time difference spectrum analysis method; Step 6: Further perform short-time Fourier inverse transform on the short-time difference spectrum matrix D(f) to reconstruct the time domain signal d(n) of the transient component in the signal. d(n) is calculated by formula (3): Where D m (f) is the column vector of the short-time difference spectrum matrix D(f) in step 4. This step is the targeted extraction of transient components by filtering in the time-frequency domain. The time domain signal d(n) of the transient component is the analysis result 2 of the short-time difference spectrum analysis method.

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