Bearing fault diagnosis method based on S transform and inverse Fourier transform

Abstract

The invention provides a bearing fault diagnosis method based on S transform and inverse Fourier transform. The method comprises the following steps: acquiring a vibration signal of a bearing; discretizing the vibration signal and then performing S transformation to obtain a two-dimensional time-frequency matrix; extracting diagonal elements of the two-dimensional time-frequency matrix to obtain a diagonal sequence of the two-dimensional time-frequency matrix; inverse Fourier transform is carried out on the diagonal sequence to obtain a time domain signal; and performing spectral analysis on the time domain signal to obtain a characteristic frequency component, and then identifying the bearing fault according to the relationship between the characteristic frequency component and the bearing fault characteristic frequency. According to the bearing fault diagnosis method, while noise reduction is carried out on the signal, the characteristics of the signal can be enhanced, and extraction of the characteristic frequency corresponding to the fault and judgment of the bearing fault type can be realized.

Description

Technical Field

[0001] This invention belongs to the field of fault diagnosis technology, and specifically designs a bearing fault diagnosis method based on S-transform and inverse Fourier transform. Background Technology

[0002] Bearings are crucial components of large rotating machinery, and their health status affects the stability and safety of the entire mechanical system. Due to the complexity of rotating machinery systems and the diversity of operating conditions, signals from various excitation sources couple with each other, often causing the impact characteristics of bearing fault signals to be submerged in strong background signals and noise, making timely detection and handling difficult. Over time, this can lead to equipment damage, even resulting in significant personal injury and substantial economic losses. Furthermore, due to the interrelationships between various components, bearing faults manifest in multiple forms. Therefore, bearing fault diagnosis helps prevent equipment accidents and ensures the safe operation of mechanical systems. Effectively detecting and enhancing fault impulse responses and extracting fault characteristics has always been a focus in bearing fault diagnosis.

[0003] Currently, many signal analysis algorithms have been successfully applied in the field of bearing fault diagnosis, such as singular value decomposition, wavelet transform, deconvolution, short-time Fourier transform, and stochastic resonance. Among these algorithms, those based on time-frequency analysis can more clearly observe the time-varying characteristics of signals while effectively processing non-stationary signals. The S-transform, based on short-time Fourier transform and wavelet transform, overcomes the limitation of short-time Fourier transform in adjusting the analysis window frequency and introduces multi-resolution analysis from wavelet transform. Therefore, the S-transform is suitable for processing and analyzing non-stationary impact characteristic signals and has certain applications in bearing fault diagnosis. However, while the S-transform method can more significantly highlight the time-frequency characteristics of bearing fault signals, its effect on enhancing the fault characteristics of the fault signal is not ideal. Summary of the Invention

[0004] In view of this, the present invention proposes a bearing fault diagnosis method based on S-transform and inverse Fourier transform to solve the problems existing in the prior art.

[0005] This invention provides a bearing fault diagnosis method based on S-transform and inverse Fourier transform, comprising:

[0006] S1: Obtain the vibration signal x(t) of the bearing;

[0007] S2: Discretize the vibration signal x(t) to obtain a discrete signal x(m). Then, perform an S-transform on the discrete signal x(m) to obtain a two-dimensional time-frequency matrix.

[0008] S3: Extract the two-dimensional time-frequency matrix The diagonal elements are used to obtain the diagonal sequence D of the two-dimensional time-frequency matrix. mn ;

[0009] S4: For the diagonal sequence D mn Perform an inverse Fourier transform to obtain the time-domain signal M. mn (q);

[0010] S5: For the time-domain signal M mn (q) Perform spectral analysis to obtain characteristic frequency components, and then identify bearing faults based on the relationship between the characteristic frequency components and the characteristic frequency of bearing faults.

[0011] Preferably, in S2, the formula for performing the S-transform on the discrete signal x(m) is as follows:

[0012]

[0013] In the formula: T is the sampling period; N is the number of sampling points; m and n correspond to the time sampling point number and the frequency sampling point number, respectively; k is the frequency point of the spectrum; the values ​​of m, n and k are all 1, 2, 3, ..., N; and X[k] is the discrete Fourier transform of the time series x(m).

[0014] Further optimization, in S4, the diagonal element sequence D... mn The formula for performing the inverse Fourier transform is as follows:

[0015]

[0016] In the formula, M mn (q) is the time-domain signal obtained after the inverse Fourier transform, D mn (p) is the two-dimensional time-frequency matrix The p-th diagonal element, where p and q take values ​​of 1, 2, 3, ..., N.

[0017] In a further optimized version, in S5, the bearing failure characteristic frequency is calculated based on the bearing's geometric dimensions and rotational speed.

[0018] The bearing fault diagnosis method based on S-transform and inverse Fourier transform proposed in this invention can enhance the features of the signal while reducing noise, and can extract the feature frequencies corresponding to the fault and determine the bearing fault type. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 A flowchart of the bearing fault diagnosis method based on S-transform and inverse Fourier transform provided by the present invention;

[0021] Figure 2 The bearing fault diagnosis results based on S-transform and inverse Fourier transform provided by the present invention are shown in the following figures: (a) is the time domain diagram of the original vibration signal, (b) is the spectrum of (a), (c) is the inverse Fourier transform result of (a) after S-transform, (d) is the spectrum of (c), (e) is the autocorrelation function diagram of (c), and (f) is the spectrum of (e).

[0022] Figure 3 The diagrams provided by this invention are diagnostic results of bearing faults under different fault types based on S-transform and inverse Fourier transform. In the diagrams, (a) is the time domain diagram of the original vibration signal, (b) is the spectrum of (a), (c) is the inverse Fourier transform result of (a) after S-transform, (d) is the spectrum of (c), (e) is the autocorrelation function diagram of (c), and (f) is the spectrum of (e). Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, to avoid obscuring the invention with unnecessary details, only processing steps closely related to the solution of this invention are shown in the drawings, while other details not closely related to this invention are omitted.

[0024] like Figure 1 As shown, this invention provides a bearing fault diagnosis method based on S-transform and inverse Fourier transform, including the following steps:

[0025] S1: Obtain the vibration signal x(t) of the bearing, where t is a time series, t∈[0,T1], and T1 is the sampling time;

[0026] S2: Discretize the vibration signal x(t) to obtain a discrete signal x(m). Then, perform an S-transform on the discrete signal x(m) to obtain a two-dimensional time-frequency matrix.

[0027] The formula for performing the S-transform on the discrete signal x(m) is as follows:

[0028]

[0029] In the formula: T is the sampling period; N is the number of sampling points; m and n correspond to the time sampling point number and the frequency sampling point number, respectively; k is the frequency point of the spectrum; the values ​​of m, n and k are all 1, 2, 3, ..., N; X[k] is the discrete Fourier transform of the time series x(m);

[0030] The two-dimensional time-frequency matrix obtained after S-transformation It can be represented as:

[0031]

[0032] In the formula, S[1,1] is the S-transform result of the vibration signal when m=1, n=1, and similarly, S[M,N] is the S-transform result of the vibration signal when m=M, n=N;

[0033] S3: Extract the two-dimensional time-frequency matrix The diagonal elements are used to obtain the diagonal sequence D of the two-dimensional time-frequency matrix. mn ;

[0034] Among them, D mn =[D mn (1),D mn (2),…,D mn (p),…,D mn (N)]=[S[1,1],S[2,2],…,S[p,p],…,S[M,N]];

[0035] In the formula, D mn (p) is the two-dimensional time-frequency matrix The p-th diagonal element, where P is the diagonal sequence D. mn Length;

[0036] S4: For the diagonal sequence D mn Perform an inverse Fourier transform to obtain the time-domain signal M. mn (q);

[0037] Among them, the diagonal element sequence D mn The formula for performing the inverse Fourier transform is as follows:

[0038]

[0039] In the formula, M mn (q) is the time-domain signal obtained after the inverse Fourier transform, D mn (p) is the two-dimensional time-frequency matrix The p-th diagonal element, where p and q take values ​​of 1, 2, 3, ..., N;

[0040] S5: For the time-domain signal M mn (q) Perform spectral analysis to obtain characteristic frequency components, and then identify bearing faults based on the relationship between the characteristic frequency components and the characteristic frequency of bearing faults.

[0041] Among them, the characteristic frequency of bearing failure can be calculated based on the bearing's geometric dimensions and rotational speed.

[0042] This bearing fault diagnosis method based on S-transform and inverse Fourier transform obtains a two-dimensional time-frequency matrix by performing an S-transform on the bearing vibration signal, thus improving the time-frequency characteristics of the bearing vibration signal. By combining the S-transform and inverse Fourier transform, the prominent characteristic frequency components corresponding to the bearing fault can be extracted more completely and accurately, thereby achieving accurate judgment of the bearing fault type. Since the energy of the signal after the S-transform is mainly concentrated in the diagonal position of the two-dimensional time-frequency matrix, this invention extracts the diagonal sequence and performs an inverse Fourier transform on the diagonal sequence to obtain a new time-domain signal, which can effectively reduce noise and enhance the signal characteristics. By performing spectral analysis on the new time-domain signal (such as analyzing the Fourier spectrum of the autocorrelation function of the new time-domain signal), the extraction of characteristic frequencies corresponding to the fault can be made more accurate.

[0043] The bearing fault diagnosis method proposed in this invention can enhance the characteristics of the signal while reducing noise, making it easier to extract the characteristic frequencies corresponding to the fault.

[0044] For the sake of simplicity, in Examples 1 and 2: f r Representing the rotational frequency, in f n Represents rotational speed; in f i Represents the characteristic frequency of inner ring faults; denoted by f o Represents the characteristic frequency of outer ring faults; denoted by f b Represents the characteristic frequency of rolling element failure; denoted by f c This represents the characteristic frequency of cage failure.

[0045] Example 1

[0046] The bearing fault diagnosis method proposed in this invention is verified and analyzed using Case 1 in Table 1 as an example. Case 1 corresponds to the data collected by the acceleration sensor when the bearing experiences a combined inner and outer ring fault.

[0047] This set of data shows the rotational speed f. n =1823 r / min, the characteristic frequencies of bearing failure are shown in Table 1. Specifically: f r =30.39Hz, f i =134.75Hz, f o =78.01Hz, f b=52.93Hz, f c =11.14Hz.

[0048] Table 1. Case 1 Experimental Data Information Table

[0049]

[0050] The bearing fault in Case 1 is identified below using the method proposed in this invention. The time domain of the original vibration signal is as follows: Figure 2 As shown in (a). Figure 2 (b) is Figure 2 The spectrum of (a). Figure 2 The time domain of the signal after performing the inverse Fourier transform of the s-transform shown in (a) is as follows: Figure 2 As shown in (c) Figure 2 (d) is Figure 2 The spectrum of (c) Figure 2 (e) is Figure 2 The autocorrelation function of (c), Figure 2 (f) is Figure 2 (e) spectrum.

[0051] analyze Figure 2 (b) It can be found that:

[0052] (1) In the spectrum of the original signal, only the 9th harmonic of the bearing outer ring fault characteristic frequency (78.01Hz) can be extracted, 714.11Hz (714.11 / 9=79.34Hz);

[0053] (2) No typical characteristic frequencies corresponding to the bearing inner ring fault were found in the original signal spectrum.

[0054] analyze Figure 2 (f) and with Figure 2 (b) By comparison, it can be found that the spectrum of the signal obtained based on the method of the present invention has the following characteristics:

[0055] (1) Noise components are significantly reduced;

[0056] (2) It can extract prominent characteristic frequency components corresponding to the bearing inner ring fault characteristic frequency (134.75Hz), including:

[0057] ① 832.5Hz, this frequency corresponds to 6f i With 2f c The sum of ((832.5-2*11.14) / 6=135.03);

[0058] ②1137.7Hz, this frequency corresponds to 8f i With 2f cThe sum of ((1138-2*11.14) / 8=134.65);

[0059] ③ 1450.2Hz, this frequency corresponds to 11f i with f c The difference, ((1450.2+11.14) / 11=134.58);

[0060] ④ 2390.14Hz, this frequency corresponds to 18f i with f r The difference, ((2390.14+30.39) / 18=134.47);

[0061] (3) It can extract the 23rd harmonic of the prominent bearing outer ring fault characteristic frequency (78.01Hz), 1762.7Hz, (1762.7 / 23=76.65);

[0062] It can be seen that the method proposed in this invention effectively suppresses noise while extracting characteristic frequencies corresponding to bearing fault types, and each fault characteristic frequency is relatively prominent, thus achieving accurate identification of bearing fault types.

[0063] Example 2

[0064] The sensitivity of the bearing fault diagnosis method proposed in this invention to different fault types was verified. The specific parameters of randomly selected typical data correspond to Case 2 in Table 1. Data of different fault types were randomly selected to verify the sensitivity of the method proposed in this invention under different bearing fault types. A combined outer ring and rolling element fault (Case 2) was randomly selected, and the results are as follows... Figure 3 As shown. The rotational speed f corresponding to this embodiment. n The speed is 1818 r / min. The calculated characteristic frequencies are: f r =30.30Hz, f i =134.34Hz, f o =77.77Hz, f b =52.77Hz, f c =11.11Hz.

[0065] The time domain of the original vibration signal in Case 2 is as follows: Figure 3 As shown in (a). Figure 3 (b) is Figure 3 The spectrum of (a). Figure 3 The time domain of the signal after performing the inverse Fourier transform of the s-transform shown in (a) is as follows: Figure 3 As shown in (c) Figure 3 (d) is Figure 3 The spectrum of (c) Figure 3 (e) is Figure 3The autocorrelation function of (c), Figure 3 (f) is Figure 3 (e) spectrum.

[0066] analyze Figure 3 (f) and with Figure 3 (b) By comparison, it can be found that the spectrum of the signal obtained based on the method of the present invention has the following characteristics:

[0067] (1) Feature enhancement was achieved while significantly reducing noise components;

[0068] (2) It can extract the 13th harmonic of the prominent bearing rolling element fault characteristic frequency component (52.77Hz), 686Hz, (686 / 13=52.77);

[0069] (3) It can extract prominent frequency components corresponding to the characteristic frequency of bearing outer ring failure (77.77Hz), including:

[0070] ①1025Hz, this frequency corresponds to 13f o (1025 / 13 = 78.84);

[0071] ②1340Hz, this frequency corresponds to 17f o (1340 / 17=78.82);

[0072] ③ 1658Hz, this frequency corresponds to 21f o (1658 / 21=78.95);

[0073] ④2280Hz, this frequency corresponds to 29f o , (2280 / 29=78.62).

[0074] In summary, it can be seen that the method proposed in this invention is insensitive to bearing fault types. Regardless of whether the fault type is a combined outer ring and inner ring fault or a combined outer ring and rolling element fault, the method proposed in this invention can effectively extract very prominent characteristic frequencies corresponding to the bearing fault type, enabling accurate determination of the bearing fault type.

[0075] It should be noted that the purpose of disclosing the embodiments is to help further understand the present invention; however, those skilled in the art will understand that various substitutions and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the present invention should not be limited to the content disclosed in the embodiments, and the scope of protection of the present invention is defined by the scope of the claims.

Claims

1. A bearing fault diagnosis method based on S-transform and inverse Fourier transform, characterized in that, include: S1: Obtain the vibration signal x(t) of the bearing; S2: Discretize the vibration signal x(t) to obtain a discrete signal x(m). Then, perform an S-transform on the discrete signal x(m) to obtain a two-dimensional time-frequency matrix. S3: Extract the two-dimensional time-frequency matrix The diagonal elements are used to obtain the diagonal sequence D of the two-dimensional time-frequency matrix. mn ; S4: For the diagonal sequence D mn Perform an inverse Fourier transform to obtain the time-domain signal M. mn (q); S5: For the time-domain signal M mn (q) Perform spectral analysis to obtain characteristic frequency components, and then identify bearing faults based on the relationship between the characteristic frequency components and the characteristic frequency of bearing faults.

2. The bearing fault diagnosis method based on S-transform and inverse Fourier transform according to claim 1, characterized in that, In S2, the formula for performing the S-transform on the discrete signal x(m) is as follows: In the formula: T is the sampling period; N is the number of sampling points; m and n correspond to the time sampling point number and the frequency sampling point number, respectively; k is the frequency point of the spectrum; the values ​​of m, n and k are all 1, 2, 3, ..., N; and X[k] is the discrete Fourier transform of the time series x(m).

3. The bearing fault diagnosis method based on S-transform and inverse Fourier transform according to claim 1, characterized in that, In S4, the diagonal element sequence D mn The formula for performing the inverse Fourier transform is as follows: In the formula, M mn (q) is the time-domain signal obtained after the inverse Fourier transform, D mn (p) is the two-dimensional time-frequency matrix The p-th diagonal element, where p and q both take values ​​of 1, 2, 3, ..., N.

4. The bearing fault diagnosis method based on S-transform and inverse Fourier transform according to claim 1, characterized in that, In S5, the characteristic frequency of bearing failure is calculated based on the bearing's geometry and rotational speed.

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