Rotating machinery fault diagnosis method based on frequency domain adaptive Kaiser convolution window Fourier transform

Abstract

The invention discloses a rotating machinery fault diagnosis method based on frequency domain adaptive Kaiser convolution window Fourier transform, which comprises the following steps: constructing a frequency domain adaptive Kaiser window function for an acquired discrete vibration signal containing multi-harmonic fault information, and reducing the influence of frequency aliasing in different frequency domain intervals; a frequency domain adaptive Kaiser convolution window model is established by applying self-convolution operation, and the influence of spectrum leakage and noise interference is reduced; calculating the Fourier transform of the signal based on an adaptive Kaiser convolution window, establishing a time-frequency (IKTF) model of an improved Kaiser window base, and carrying out model solution calculation to obtain the time-frequency distribution of the signal; and determining selection of frequency domain adaptive parameter values, and identifying fault characteristic frequency information in time-frequency distribution. According to the innovative method, the weak fault features of the rotating machinery can be extracted, and the influence of factors such as background noise, harmonic interference and random impact is effectively overcome, so that the accuracy of fault detection is improved.

Description

Technical Field

[0001] The invention belongs to the field of rotating machinery fault diagnosis, and in particular relates to a rotating machinery fault diagnosis method based on frequency domain adaptive Kaiser convolution window Fourier transform. Background Art

[0002] Rotating machinery is widely used in a variety of power systems such as engines, fans and diesel engines. These power systems often face a higher risk of failure under harsh operating conditions (such as low-speed heavy load, overload operation, alternating stress and load changes). Research data shows that failures of rotating components such as bearings and gears account for more than 40% of the total number of mechanical failures, highlighting the higher susceptibility of rotating machinery to failures compared to other components. Although the fast Fourier transform (FFT) method is often used to detect fault features in the spectrum, when the fault signal is relatively weak, the FFT method is difficult to capture the instantaneous characteristics of non-stationary weak fault signals.

[0003] The classical Fourier transform occupies a core position in the analysis of stable signals due to its comprehensive coverage of the frequency domain. When processing stable signals, the asynchronous sampling and non-complete cycle truncation of the Fourier transform will lead to spectrum leakage problems. To reduce this error, researchers have adopted the Fourier transform method combined with the window function and achieved corresponding results. However, for non-stable signals, it is necessary to obtain the frequency characteristics of any time point. At this time, the classical Fourier transform that can only describe the signal in the frequency domain shows obvious limitations. In order to cope with the processing challenges of non-stable signals, the short-time Fourier transform (STFT) method is proposed. STFT is essentially an optimization of the traditional Fourier transform by incorporating short-time window technology. By intercepting the signal with a short-time window, an approximately stable signal in a short time is formed. Then, the traditional Fourier transform is used to retain the frequency information of the signal and to integrate the time information to a certain extent. That is, the sliding of the window function on the time axis reveals the time-frequency distribution of the signal, thereby effectively reducing spectrum leakage.

[0004] Compared with the classic Fourier transform, STFT has local analysis capabilities, but its window size is fixed, which may lead to limited frequency resolution. To solve the spectrum leakage problem in Fourier transform, a common method is to add a window function. There are various types of window functions, including Hanning window, Hamming window, Blackman window and triangular window, but these window functions all have fixed sidelobe characteristics, resulting in unsatisfactory results. Summary of the invention

[0005] Purpose of the invention: In order to improve the accuracy of Fourier transform time-frequency analysis, the Kaiser window can independently select the main lobe and side lobe widths. The present invention proposes a rotating machinery fault diagnosis method based on frequency domain adaptive Kaiser convolution window Fourier transform, which can effectively improve the spectrum leakage problem of the Fourier transform algorithm and improve the accuracy of rotating machinery fault parameter identification.

[0006] Technical solution: To achieve the above object, the present invention provides a rotation structure fault diagnosis method based on frequency domain adaptive Kaiser convolution window Fourier transform, comprising the following steps:

[0007] S1: Based on the collected discrete vibration signal containing multi-harmonic fault information, a frequency domain adaptive Kaiser window function is constructed to reduce the impact of frequency aliasing in different frequency domain intervals;

[0008] S2: Apply self-convolution operation to establish a frequency-domain adaptive Kaiser convolution window model to reduce the impact of spectrum leakage and noise interference;

[0009] S3: Calculate the Fourier transform of the signal based on the adaptive Kaiser convolution window, establish the time-frequency model of the improved Kaiser window basis (IKTF), carry out model solution calculation, and obtain the time-frequency distribution of the signal;

[0010] S4: Determine the selection of frequency domain adaptive parameter values, identify fault characteristic frequency information in time-frequency distribution, and improve fault detection accuracy.

[0011] Furthermore, the step S1 constructs a frequency-domain adaptive Kaiser window function, and improves the parameter β as a function β(f) of the frequency f, so as to achieve further fine adjustment of the window width:

[0012]

[0013] Then the improved window function can be characterized as:

[0014]

[0015] Among them, λ1, λ2, λ3 are parameters to be determined. It can be seen from the formula that when λ1=1, λ3=0, it degenerates into the traditional Kaiser window function. The discrete form of the proposed frequency domain adaptive Kaiser window can be expressed as:

[0016]

[0017] Among them, N s is the length of the discretized signal

[0018] Furthermore, in step S2, a frequency domain adaptive Kaiser convolution window model is established. The Kaiser window can further reduce the sidelobe peak and accelerate its attenuation while keeping the main lobe width unchanged through self-convolution operation, thereby improving the suppression effect of spectrum leakage, which is characterized by:

[0019]

[0020] The frequency domain expression of the proposed Kaiser convolution window is:

[0021]

[0022] Its discrete form is expressed as:

[0023]

[0024] Furthermore, in step S3, based on the proposed frequency domain adaptive Kaiser convolution window function w con (t,f), establish the improved Kaiser window-based time-frequency (Improved Kaiser window-based Time-frequency, IKTF) model, characterized by:

[0025]

[0026] Perform Fourier transform on discrete signal x[n] to obtain X[l], l=0,...,N s -1, facing the frequency point k, the frequency shift vector can be represented as:

[0027] X[l+k]=[X k X k+1 X k+2 …X Ns-1 X0…X k-1 ]

[0028] Facing the frequency point k, the frequency shift vector X[l+k] is combined with the Kaiser convolution window function W con [l,k] performs Hadamard product operation, using the symbol Represented by, and then performing inverse Fourier transform, the improved Kaiser window-based time-frequency information of the signal can be obtained, which is characterized as:

[0029]

[0030] Furthermore, in the step S4, the selection of the frequency domain adaptive parameter value is determined, and the values ​​of λ1, λ2, and λ3 are determined according to the following formula:

[0031]

[0032] Under discrete signal conditions, the values ​​of λ1,λ2,λ3 can be derived from the discrete time-frequency information:

[0033]

[0034] Beneficial effects: Compared with the prior art, the present invention proposes a method for selective mechanical fault diagnosis based on frequency domain adaptive Kaiser convolution window Fourier transform, which can effectively improve the spectrum leakage problem of Fourier transform algorithm, and is used to accurately detect fault feature information from state monitoring signals. It can extract weak fault features of rotating machinery, and effectively overcome the influence of background noise, harmonic interference, random shock and other factors, thereby improving the accuracy of fault detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a flow chart of the method of the present invention;

[0036] Figure 2 is a display diagram of the rotating machinery fault diagnosis test bench in this embodiment;

[0037] Figure 3 To detect the vibration signal diagram;

[0038] Figure 4 It is the spectrum diagram of STFT;

[0039] Figure 5 It is a time-frequency spectrum diagram based on the traditional Kaiser window;

[0040] Figure 6 This is the IKFT time spectrum diagram obtained by applying the method of the present invention. DETAILED DESCRIPTION

[0041] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0042] like Figure 1 As shown, the present invention provides a method for diagnosing mechanical faults based on frequency domain adaptive Kaiser convolution window Fourier transform, comprising the following steps:

[0043] S1: Based on the collected discrete vibration signal containing multi-harmonic fault information, a frequency domain adaptive Kaiser window function is constructed to reduce the impact of frequency aliasing in different frequency domain intervals;

[0044] For a continuous-time vibration signal x(t), the short-time Fourier transform (STFT) can be characterized as:

[0045]

[0046] Where w(t) is the window function. Different from the Gaussian window function, the window width of the Kaiser window function is adjusted by the parameter β, which is called the window width adjustment factor. By setting the appropriate parameter β, a higher time-frequency resolution can be obtained. If the traditional Kaiser window is used, its time domain expression is:

[0047]

[0048] T is the duration of the window function, I0(β) is the zero-order Bessel function, and its expression is:

[0049]

[0050] In view of the key role of time-frequency resolution in the accuracy of disturbance signal classification, in order to meet the time-frequency characteristics of various disturbance signals, a strategy of setting different window width adjustment factors is adopted to select the appropriate window function for different frequency values. However, once the total length of the Kaiser window function is set, its window width can only be adjusted by parameter β. In order to broaden the adjustment range of the window width and thus improve the time-frequency resolution, the present invention optimizes the Kaiser window function so that it can better adapt to the needs of different frequency intervals. Under the premise of keeping the total length of the window function unchanged, the present invention improves the function β(f) in which the parameter β is the frequency f, so as to achieve further fine adjustment of the window width:

[0051]

[0052] Then the improved window function can be characterized as:

[0053]

[0054] Among them, λ1, λ2, λ3 are parameters to be determined. It can be seen from the formula that when λ1=1, λ3=0, it degenerates into the traditional Kaiser window function.

[0055] In engineering, continuous vibration signals can be sampled to obtain discrete forms with an interval of Δt, where Δt = 1 / f s , f s Assume that N is the sampling frequency and the window function length, then the discrete form of the Kaiser window is characterized as follows:

[0056]

[0057] Then the discrete form of the frequency domain adaptive Kaiser window proposed in the present invention can be expressed as:

[0058]

[0059] Among them, N s is the length of the discretized signal.

[0060] S2: Apply self-convolution operation to establish a frequency-domain adaptive Kaiser convolution window model to reduce the impact of spectrum leakage and noise interference;

[0061] For the Kaiser window function, there is an inherent trade-off between its main lobe width and side lobe performance, which means that it is difficult to achieve both frequency resolution and spectrum leakage suppression capabilities. Specifically, as the β value of the Kaiser window increases, the difference between the side lobe peak value and the main lobe peak value increases, and the attenuation rate of the side lobe is accelerated, thereby enhancing the ability to suppress spectrum leakage. However, this improvement is accompanied by an increase in the main lobe width, which in turn reduces the frequency resolution and has an adverse effect on the detection of broadband harmonics. It is worth noting that the Kaiser window can further reduce the side lobe peak and accelerate its attenuation while keeping the main lobe width unchanged through a self-convolution operation, thereby improving the spectrum leakage suppression effect. Therefore, the present invention proposes a frequency-domain adaptive Kaiser convolution window function, which is characterized by:

[0062]

[0063] The frequency domain expression of the proposed Kaiser convolution window is:

[0064]

[0065] The corresponding discretized convolution form is:

[0066]

[0067] The corresponding frequency domain expression is:

[0068]

[0069] S3: Calculate the Fourier transform of the signal based on the adaptive Kaiser convolution window, establish the time-frequency model of the improved Kaiser window basis (IKTF), carry out model solution calculation, and obtain the time-frequency distribution of the signal;

[0070] Apply the proposed frequency domain adaptive Kaiser convolution window function w con (t,f), the present invention establishes an improved Kaiser window-based time-frequency (ImprovedKaiser window-basedTime-frequency, IKTF) model, which is characterized by:

[0071]

[0072] Perform Fourier transform on discrete signal x[n] to obtain X[l], l=0,...,N s -1, facing the frequency point k, the frequency shift vector can be represented as:

[0073]

[0074] The discrete Kaiser convolution window function obtained at frequency point k is:

[0075]

[0076] Facing the frequency point k, the frequency shift vector X[l+k] is combined with the Kaiser convolution window function W con [l,k] performs Hadamard product operation, using the symbol Represented by, and then performing inverse Fourier transform, the improved Kaiser window-based time-frequency information of the signal can be obtained, which is characterized as:

[0077]

[0078] S4: Determine the selection of frequency domain adaptive parameter values, identify fault characteristic frequency information in time-frequency distribution, and improve fault detection accuracy;

[0079] The values ​​of λ1,λ2,λ3 are determined according to the following formula:

[0080]

[0081] The values ​​of λ1,λ2,λ3 can be derived from the discrete time-frequency information:

[0082]

[0083] Based on the above scheme, the above fault diagnosis method is applied as an example in this embodiment, as follows:

[0084] In this embodiment, the fault diagnosis test bench of the School of Mechanical Engineering of Jiangsu University of Science and Technology is used. Figure 2 As shown, the accuracy and superiority of the proposed algorithm in practical engineering applications are analyzed and verified. The experiment used a sun gear and annular gear with local wear faults. At the same time, there were slight differences between the three planetary gears, which represented the existence of manufacturing error faults. Therefore, there were two types of faults in the experiment:

[0085] 1. The sun gear and the inner ring gear are in a serious wear fault state, which means that wear fault is a strong fault type. In this case, at the meshing frequency f m There is a local fault characteristic frequency f of the sun gear nearby. s , characteristic frequency f of local fault of inner gear ring tand the planet carrier rotation frequency f c The combined frequency components of .

[0086] 2. Compared with the other two normal gears, the mass deviation of one of the planetary gears is within 5%, so the manufacturing error fault is a weak fault type. In this case, the fault signal has the same s / 3(n=1,2) related sideband features, and this weak fault feature can be easily submerged by other vibration signals, making it difficult to detect.

[0087] Figure 3 Displays the fault monitoring signal and the rotation frequency f r The vibration signal is collected by the vibration accelerometer installed on the top of the planetary gearbox at a sampling frequency of 2000 Hz. In the time-frequency spectrum obtained by the traditional STFT method based on Gaussian window, at the meshing frequency f m Nearby, the local fault characteristic frequency f of the sun gear can be detected s and the characteristic frequency f of the local fault of the inner gear ring t and the planet carrier rotation frequency f c The combined frequency components of Figure 4 When applying the time-frequency analysis based on the traditional Kaiser window, the resolution is improved, but the mass deviation fault of the planetary gear cannot be detected, such as Figure 5 shown. Figure 6 The corresponding time-frequency representation (TFR) results obtained by the method of the present invention are shown, from which the characteristic frequency trajectories corresponding to all fault types can be identified. In particular, the trajectory representing the characteristic frequency of the internal gear ring fault is identified, such as f m +f s +f t 、f m +2f t ,ff m -f t ,、f m -f r -f t and f m -f s +f t -f c At the same time, the trajectory representing the characteristic frequency of the sun gear fault is also identified, such as f m +f s +f t 、f m +f s -f r and f m -f s +f t -f cIn addition, the nf s / 3(n=1,2) band-related trajectories, which indicates that there are manufacturing errors in the three planetary gears, such as f m +2 / 3f s +f c 、f m +1 / 3f s +f c ,f m -1 / 3f s and f m -2 / 3f s -f c . Due to the small values, the traces of planetary gear manufacturing faults are faint on the time-frequency diagram. However, these traces are still clearly visible due to the high time-frequency resolution achieved by the proposed method. The results show that the proposed method is able to detect all fault types, including sun gear faults, internal gear ring faults, and very weak manufacturing error faults of planetary gears.

Claims

1. A method for fault diagnosis of rotating machinery based on frequency domain adaptive Kaiser convolution window Fourier transform, characterized in that: The steps include: S1: Construct a frequency domain adaptive Kaiser window function for the collected discrete vibration signal containing multi-harmonic fault information; S2: Apply self-convolution operation to establish frequency domain adaptive Kaiser convolution window model; S3: Calculate the Fourier transform of the signal based on the adaptive Kaiser convolution window, establish the time-frequency model of the improved Kaiser window basis, carry out model solution calculation, and obtain the time-frequency distribution of the signal; S4: Determine the selection of frequency domain adaptive parameter values ​​and identify fault characteristic frequency information in the time-frequency distribution.

2. The method for fault diagnosis of rotating machinery based on frequency domain adaptive Kaiser convolution window Fourier transform according to claim 1, characterized in that: The frequency-domain adaptive Kaiser window function constructed in step S1 improves the function β(f) whose parameter β is the frequency f, so as to achieve further fine adjustment of the window width: The improved window function is characterized as follows: Among them, λ1, λ2, λ3 are parameters to be determined. It can be seen from the formula that when λ1=1, λ3=0, it degenerates into the traditional Kaiser window function.

3. A method for fault diagnosis of rotating machinery based on frequency domain adaptive Kaiser convolution window Fourier transform according to claim 2, characterized in that: In step S1, the proposed frequency domain adaptive Kaiser window function is characterized as a discrete form, which is expressed as: Among them, N s is the length of the discretized signal.

4. A method for fault diagnosis of rotating machinery based on frequency domain adaptive Kaiser convolution window Fourier transform according to claim 3, characterized in that: The frequency domain adaptive Kaiser convolution window model established in step S2 is characterized as follows: The frequency domain expression of the Kaiser convolution window is:

5. A method for fault diagnosis of rotating machinery based on frequency domain adaptive Kaiser convolution window Fourier transform according to claim 4, characterized in that: In step S2, the Kaiser convolution window is characterized as a discrete form, and its discrete form is expressed as:

6. The method for fault diagnosis of rotating machinery based on frequency domain adaptive Kaiser convolution window Fourier transform according to claim 1, characterized in that: In step S3, based on the proposed frequency domain adaptive Kaiser convolution window function w con (t,f), establish the time-frequency model IKTF of the improved Kaiser window basis, which is characterized by:

7. A method for fault diagnosis of rotating machinery based on frequency domain adaptive Kaiser convolution window Fourier transform according to claim 6, characterized in that: In step S3, the discrete signal x[n] is subjected to Fourier transform to obtain X[l], where l=0, ..., N s -1, facing the frequency point k, the frequency shift vector is characterized by: X[l+k]=[X k X k+1 X k+2 …X Ns-1 X0…X k-1 ]。 8. The method for fault diagnosis of rotating machinery based on frequency domain adaptive Kaiser convolution window Fourier transform according to claim 7, characterized in that: In step S3, the method of performing model solution calculation to obtain the time-frequency distribution of the signal is: Facing the frequency point k, the frequency shift vector X[l+k] is convolved with the Kaiser convolution window function W con [l,k] performs Hadamard product operation, using the symbol Represented by, and then performing inverse Fourier transform, the improved Kaiser window-based time-frequency information of the signal can be obtained, which is characterized as:

9. The method for fault diagnosis of rotating machinery based on frequency domain adaptive Kaiser convolution window Fourier transform according to claim 1, characterized in that: In step S4, the selection of frequency domain adaptive parameter values ​​is determined, and the values ​​of λ1, λ2, and λ3 are determined according to the following formula: Under discrete signal conditions, the values ​​of λ1,λ2,λ3 are derived from the discrete time-frequency information:

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