A rotating equipment rotating speed estimation method based on hill identification combined with correlation analysis
By combining peak identification with correlation analysis, vibration signals of rotating equipment are automatically identified, solving the problems of large speed measurement errors and high hardware costs, and achieving low-cost, rapid speed estimation and fault diagnosis.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- BEIJING AEROSPACE ZHIKONG MONITORING TECH INST
- Filing Date
- 2023-12-14
- Publication Date
- 2026-07-14
AI Technical Summary
Existing technologies for monitoring the condition of rotating equipment suffer from large instantaneous speed measurement errors, high costs, and numerous hardware requirements. Time-frequency analysis methods involve large computational loads and poor noise resistance, making it difficult to achieve real-time fault diagnosis.
A method combining peak identification and correlation analysis was adopted. By using Fourier transform, Hilbert transform and Savitzky-Golay smoothing filter, peaks in vibration signals were automatically identified, envelope signals were extracted and autocorrelation coefficients were calculated, and fundamental frequency and rotational speed were estimated.
It achieves low-cost, fast, and noise-resistant speed estimation, suitable for real-time online monitoring, reduces hardware requirements, and improves the accuracy and efficiency of fault diagnosis.
Smart Images
Figure CN117708573B_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of mechanical vibration signal processing, specifically, it relates to a method for estimating the rotational speed of rotating equipment based on peak identification combined with correlation analysis. Background Technology
[0002] In the condition monitoring of large rotating equipment, fault diagnosis is often carried out using methods based on equipment mechanisms. This method requires accurate measurement of the instantaneous rotation speed of the equipment, and then obtaining the equipment's fundamental frequency through the rotation speed, thereby combining the equipment parameters to predict the type of fault.
[0003] Currently, the commonly used method for measuring instantaneous rotational speed of equipment is the key phase measurement method. The key phase measurement method determines the rotor's position within one rotation cycle by detecting the moment when the key phase pulse signal is generated. This method obtains the rotor's average rotational speed, but the measurement error is large when the rotational speed changes. At the same time, key phase measurement requires additional hardware equipment, resulting in high measurement costs. Moreover, using a speed sensor increases the testing process, requiring the data acquisition system to reserve a channel for rotational speed measurement. In some application scenarios, it is very inconvenient to install a speed sensor on-site, or there is simply no space available for installation.
[0004] Another commonly used method is the instantaneous frequency estimation method based on time-frequency analysis. Common methods such as short-time Fourier transform, wavelet transform, and Wegener's distribution are all instantaneous speed estimation methods. The instantaneous speed estimation method automatically identifies the order curve in the three-dimensional spectral vibration analysis plot, filters the original signal through this curve to obtain a set of narrowband signals, and then estimates the instantaneous speed from the instantaneous frequency of the narrowband signals. However, the disadvantages of this method are: poor time-frequency concentration, cross-term interference, large computational load, poor noise resistance, and many hyperparameters, which is not conducive to real-time calculation. Summary of the Invention
[0005] To address the aforementioned problems and technical deficiencies, this application adopts the following technical solution: a method for estimating the rotational speed of rotating equipment based on hill peak identification combined with correlation analysis, comprising the following steps:
[0006] Step 1: Collect vibration signals and calculate the spectrum of the vibration signals using the Fourier transform method;
[0007] Step 2: Automatically identify whether there are peaks in the spectrum using the peak identification method. If peaks exist, use Hilbert transform to extract the envelope signal from the vibration signal, and then use correlation analysis to calculate the autocorrelation coefficient of the envelope signal. If there are no peaks, directly use correlation analysis to calculate the autocorrelation coefficient of the vibration signal.
[0008] Step 3: Use the Savitzky-Golay smoothing filter to fit the autocorrelation coefficients to obtain new autocorrelation coefficients;
[0009] Step 4: Take the two largest values in the new autocorrelation coefficient, obtain the two index positions corresponding to the two maximum value points, and calculate the position difference between the two index positions.
[0010] Step 5: Calculate the fundamental frequency based on the position difference, and then calculate the rotational speed based on the fundamental frequency.
[0011] Preferably, the calculation of the spectrum of the vibration signal using the Fourier transform method involves using continuous Fourier transform and its inverse transform to achieve mutual conversion between the time domain and frequency domain of the vibration signal, thereby obtaining the spectrum of the vibration signal.
[0012] Preferably, the process for automatically identifying the presence of peaks in the spectrum using the peak identification method is as follows:
[0013] S211. A new spectrum is obtained by fitting the spectrum using the Savitzky-Golay smoothing filter;
[0014] S212. Obtain multiple local maxima in the new spectrum, and then obtain eight spectral lines based on the maxima.
[0015] S213. Calculate based on the frequencies of the two largest values in the spectrum to determine whether there is a peak at the center frequency of the maximum value point.
[0016] Furthermore, the process of extracting the envelope signal from the vibration signal using Hilbert transform is as follows:
[0017] S221. First, assume the vibration signal is a real-valued signal. Perform a Hilbert transform on the real-valued signal. The amplitude remains unchanged after the transformation, and the phase shift is obtained.
[0018] S221. Based on the phase shift, phase shifts are generated on the positive frequency part and the negative frequency part of the real-valued signal respectively, so that the real-valued signal is orthogonal to the Hilbert transform signal;
[0019] S221. The defined analytic signal is obtained based on the real-valued signal and the Hilbert transform signal;
[0020] S221. According to the definition, the envelope signal of the real-valued signal is obtained by analyzing the polar coordinates of the signal.
[0021] Furthermore, the Hilbert transform signal The calculation formula is as follows:
[0022]
[0023] Where f(t) is a real-valued signal.
[0024] Furthermore, the formula for calculating the analytic signal z(t) is as follows:
[0025]
[0026] The formula for calculating the envelope signal A(t) is as follows:
[0027]
[0028] Furthermore, the autocorrelation coefficient calculated using correlation analysis is the short-time autocorrelation function of the envelope signal or vibration signal. The autocorrelation function has the same periodicity as the envelope signal or vibration signal. The autocorrelation function reaches its maximum value at integer multiples of the period of the envelope signal or vibration signal. The period of the envelope signal or vibration signal can be estimated based on the position of the first maximum value of the autocorrelation function.
[0029] Preferably, the filter used in fitting the autocorrelation coefficient using the Savitzky-Golay smoothing filter is a filter based on the least squares algorithm. Before fitting the autocorrelation coefficient, it is necessary to smooth the autocorrelation coefficient to remove irrelevant noise.
[0030] Preferably, the formula for calculating the fundamental frequency ff is as follows:
[0031] ff = f s / pd
[0032] Among them, f s Let X be the sampling frequency of the vibration signal X, and pd be the position difference.
[0033] Furthermore, the formula for calculating the rotational speed is as follows:
[0034] speed = ff·60
[0035] Compared with the prior art, the beneficial effects of the embodiments of this application are as follows:
[0036] This application only requires setting three parameters for the collected vibration signal samples; all other intermediate parameters are adaptive. It automatically identifies the "peak" modulation signals generated by gear and bearing faults, and automatically demodulates and analyzes the envelope signal based on the identification results. This avoids the deviation in speed estimation caused by traditional methods, has low computational load, strong noise resistance, facilitates real-time calculation, and has a fast processing speed, making it suitable for online processing. It can be effectively applied to real-time monitoring scenarios such as rotational equipment speed estimation, fault diagnosis, and equipment health management. The calculation process has a certain degree of universality, and it does not require a large number of other hardware acquisition devices, reducing measurement costs. It also requires less installation space, is easy to install, and has high loading and unloading efficiency. Attached Figure Description
[0037] To more clearly illustrate the technical solutions in the embodiments or examples of this application, the accompanying drawings used in the embodiments or examples will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other drawings can be obtained according to these drawings without creative effort.
[0038] Figure 1 This is a schematic diagram of the method steps in this application;
[0039] Figure 2 This is a schematic diagram of the method flow of this application;
[0040] Figure 3 This is a time-domain waveform diagram of Embodiment 1 of this application;
[0041] Figure 4 This is a frequency domain feature map of Embodiment 1 of this application;
[0042] Figure 5 This is a graph of the autocorrelation function of Embodiment 1 of this application;
[0043] Figure 6 This is a time-domain waveform diagram of Embodiment 2 of this application;
[0044] Figure 7 This is the frequency domain feature map of Embodiment 2 of this application;
[0045] Figure 8 This is a spectrum signal diagram of Embodiment 2 of this application;
[0046] Figure 9 This is an envelope signal diagram of Embodiment 2 of this application;
[0047] Figure 10 This is the autocorrelation function graph of Embodiment 2 of this application. Detailed Implementation
[0048] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of this application, but not all embodiments. Generally, the components of the embodiments of this application described and shown in the accompanying drawings can be arranged and designed in various different configurations.
[0049] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.
[0050] Example 1
[0051] like Figure 1 As shown, a method for estimating the rotational speed of rotating equipment based on hill peak identification and correlation analysis includes the following steps:
[0052] Collect vibration signals X = [x1, x2, x3... x L The spectrum F(w) of the vibration signal X is calculated using the Fourier transform method. The calculation of the spectrum F(w) of the vibration signal X is achieved by using the continuous Fourier transform and its inverse transform to realize the mutual conversion between the time domain and the frequency domain of the vibration signal, thus obtaining the spectrum F(w) of the vibration signal.
[0053] The formula for continuous conversion is as follows:
[0054]
[0055] The inverse conversion formula is as follows:
[0056]
[0057] The presence of peaks in the frequency spectrum F(w) is automatically identified using a peak identification method. If peaks are found, the envelope signal Xe from the vibration signal X is extracted using Hilbert transform. e Then, the envelope signal X is calculated using correlation analysis. e The autocorrelation coefficient R = [y1, y2, y3...y 2L-1 If no peaks exist, the autocorrelation coefficient R = [y1, y2, y3...y] of the vibration signal X can be calculated directly using correlation analysis. 2L-1 ];
[0058] The method of automatically identifying whether there are peaks in the spectrum F(w) is to first fit the spectrum F(w) with a Savitzky-Golay smoothing filter to obtain a new spectrum. Obtaining a new spectrum K local maxima in For each w i As the center, with w i The four spectral lines on each side are spaced apart, denoted as:
[0059]
[0060] Pick The two largest values in the range are denoted as the frequencies corresponding to these two values. and
[0061] If |w im -w k |=|w in -w k | indicates that w i There is a peak at the center frequency, and the original vibration signal contains modulation. If |w im -w k |≠|w in -w k | indicates that w i There are no peaks at the center frequency.
[0062] Extracting the envelope signal X from the vibration signal X using Hilbert transform. e First, let the vibration signal X be a real-valued signal f(t), where t∈(+∞, -∞). Perform a Hilbert transform on the real-valued signal f(t). The amplitude remains unchanged after the transform, and the phase shift is obtained. A phase shift is introduced into the positive frequency portion of the real-valued signal f(t), and a phase shift is introduced into the negative frequency portion of the real-valued signal f(t), so that the real-valued signal f(t) and the Hilbert transform signal are phase-shifted. Orthogonal, and then based on the real-valued signal f(t) and the Hilbert transform signal The analytic signal z(t) is defined, and the envelope signal A(t) of the real-valued signal f(t) is obtained from the polar coordinates of the analytic signal z(t).
[0063] Hilbert transform signal The calculation formula is as follows:
[0064]
[0065] in, The Fourier transform formula is as follows:
[0066]
[0067] Where w is the frequency;
[0068] F[f(t)*g(t)]=F[f(t)]F[g(t)]
[0069]
[0070] The formula for calculating the analytic signal z(t) is defined as follows:
[0071]
[0072] The formula for calculating the envelope signal A(t) is as follows:
[0073]
[0074] The autocorrelation coefficient R = [y1, y2, y3...y] was calculated using correlation analysis. 2L-1 ] is the envelope signal X e Or the short-time autocorrelation function of the vibration signal X, the autocorrelation function and the envelope signal X e Or the periodicity of the vibration signal X is the same, in the envelope signal X e The autocorrelation function reaches its maximum value at integer multiples of the period of the vibration signal X, and the envelope signal X can be estimated based on the location of the first maximum value of the autocorrelation function. e Or the period of the vibration signal X.
[0075] The new autocorrelation coefficient is obtained by fitting the autocorrelation coefficient R using the Savitzky-Golay smoothing filter. The Savitzky-Golay smoothing filter used to fit the autocorrelation coefficient R is based on the least squares algorithm. Before fitting the autocorrelation coefficient R, it needs to be smoothed to remove irrelevant noise.
[0076] Take the new autocorrelation coefficient The two largest values in and Obtain the index positions index1 and index2 corresponding to the two maximum value points, calculate the position difference pd = |index1-index2| between the two index positions, calculate the fundamental frequency ff based on the position difference pd, and calculate the rotational speed based on the fundamental frequency ff.
[0077] The formula for calculating the fundamental frequency (ff) is as follows:
[0078] ff = f s / pd
[0079] Among them, f s Let X be the sampling frequency of the vibration signal X, and pd be the position difference.
[0080] The formula for calculating rotational speed is as follows:
[0081] speed = ff·60
[0082] As can be seen from the above description, in this example,
[0083] Example 2
[0084] The number of actual vibration signal sampling points L = 4096, and the sampling frequency fs =2560, actual signal speed 960 RPM.
[0085] Data time-domain waveform as follows Figure 3 As shown.
[0086] The presence of peaks in the frequency spectrum F(w) is automatically identified using a peak identification method. If peaks are found, the envelope signal Xe from the vibration signal X is extracted using Hilbert transform. e Then, the envelope signal X is calculated using correlation analysis. e The autocorrelation coefficient R = [y1, y2, y3...y 2L-1 If no peaks exist, the autocorrelation coefficient R = [y1, y2, y3...y] of the vibration signal X can be calculated directly using correlation analysis. 2L-1 ];
[0087] The method of automatically identifying whether there are peaks in the spectrum F(w) is to first fit the spectrum F(w) with a Savitzky-Golay smoothing filter to obtain a new spectrum. Obtaining a new spectrum K local maxima in For each w i As the center, with w i The four spectral lines on each side are spaced apart, denoted as:
[0088]
[0089] Pick The two largest values in the range are denoted as the frequencies corresponding to these two values. and
[0090] If |w im -w k |=|w in -w k | indicates that w i There is a peak at the center frequency, and the original vibration signal contains modulation. If |w im -w k |≠|w in -w k | indicates that w i There are no peaks at the center frequency.
[0091] Data frequency domain characteristics such as Figure 4 As shown: the dominant frequency is 15.62Hz. The signal spectrum automatically identifies no "peaks," so the autocorrelation of the original time-domain signal is directly calculated, as follows: Figure 5 As shown.
[0092] Calculate the interval between the two maximum values of the autocorrelation value (number of original signal sampling points):
[0093] pd = |index1-index2| = 161
[0094] Estimated fundamental frequency ff = f s / pd = 15.9;
[0095] The estimated rotational speed is speed = ff · 60 = 954 RPM.
[0096] The estimated speed of 954 RPM is close to the actual speed of 960 RPM, indicating that the method is effective.
[0097] Example 3
[0098] The number of actual vibration signal sampling points L = 4096, and the sampling frequency f s =2560, actual signal speed 2490 RPM.
[0099] The time-domain waveform of this data is as follows: Figure 6 As shown.
[0100] The frequency domain characteristics of this data are as follows: Figure 7 As shown.
[0101] The presence of peaks in the frequency spectrum F(w) is automatically identified using a peak identification method. If peaks are found, the envelope signal Xe from the vibration signal X is extracted using Hilbert transform. e Then, the envelope signal X is calculated using correlation analysis. e The autocorrelation coefficient R = [y1, y2, y3...y 2L-1 If no peaks exist, the autocorrelation coefficient R = [y1, y2, y3...y] of the vibration signal X can be calculated directly using correlation analysis. 2L-1 ];
[0102] The method of automatically identifying whether there are peaks in the spectrum F(w) is to first fit the spectrum F(w) with a Savitzky-Golay smoothing filter to obtain a new spectrum. Obtaining a new spectrum K local maxima in For each w i As the center, with w i The four spectral lines on each side are spaced apart, denoted as:
[0103]
[0104] Pick The two largest values in the range are denoted as the frequencies corresponding to these two values. and
[0105] If |w im -w k |=|w in -w k | indicates that w i There is a peak at the center frequency, and the original vibration signal contains modulation. If |w im -w k |≠|w in -w k | indicates that w i There are no peaks at the center frequency.
[0106] The system automatically identifies a "peak" at the 700Hz frequency peak of the signal spectrum. Figure 8 As shown.
[0107] Extracting the envelope signal X from the vibration signal X using Hilbert transform. e First, let the vibration signal X be a real-valued signal f(t), where t∈(+∞, -∞). Perform a Hilbert transform on the real-valued signal f(t). The amplitude remains unchanged after the transform, and the phase shift is obtained. A phase shift is introduced into the positive frequency portion of the real-valued signal f(t), and a phase shift is introduced into the negative frequency portion of the real-valued signal f(t), so that the real-valued signal f(t) and the Hilbert transform signal are phase-shifted. Orthogonal, and then based on the real-valued signal f(t) and the Hilbert transform signal The analytic signal z(t) is defined, and the envelope signal A(t) of the real-valued signal f(t) is obtained from the polar coordinates of the analytic signal z(t).
[0108] Hilbert transform signal The calculation formula is as follows:
[0109]
[0110] in, The Fourier transform formula is as follows:
[0111]
[0112] Where w is the frequency;
[0113] F[f(t)*g(t)]=F[f(t)]F[g(t)]
[0114]
[0115] Hilbert transform demodulation yields the envelope signal as follows: Figure 9 As shown.
[0116] The formula for calculating the analytic signal z(t) is defined as follows:
[0117]
[0118] The formula for calculating the envelope signal A(t) is as follows:
[0119]
[0120] Calculate the autocorrelation of the envelope signal, such as Figure 10 As shown.
[0121] Calculate the interval between the two maximum values of the autocorrelation value (number of original signal sampling points):
[0122] pd = |index1-index2| = 63
[0123] Estimated fundamental frequency ff = f s / pd = 40.63;
[0124] The estimated rotational speed is speed = ff * 60 = 2438 RPM
[0125] The estimated speed of 2438 RPM is close to the actual speed of 2490 RPM, indicating that the method is effective.
[0126] The embodiments described above are merely preferred embodiments of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications, improvements, and substitutions without departing from the concept of this application, and these all fall within the protection scope of this application.
Claims
1. A method for estimating the rotational speed of rotating equipment based on hill peak identification and correlation analysis, characterized in that, Includes the following steps: Step 1: Collect vibration signals and calculate the spectrum of the vibration signals using the Fourier transform method; Step 2: Automatically identify whether there are peaks in the spectrum using the peak identification method. If peaks exist, use Hilbert transform to extract the envelope signal from the vibration signal, and then use correlation analysis to calculate the autocorrelation coefficient of the envelope signal. If there are no peaks, directly use correlation analysis to calculate the autocorrelation coefficient of the vibration signal. The method of automatically identifying the spectrum using peak recognition The process of determining whether a hill peak exists is as follows: S211, Smoothing the spectrum using the Savitzky-Golay filter. The new spectrum was obtained by fitting. ; S212. Obtain the K local maxima in the new spectrum. For each ,Will As the center, with The four spectral lines on each side are spaced apart, denoted as: Eight spectral lines were obtained; S213, Taking Spectral Lines The two largest values in the range are denoted as the frequencies corresponding to these two values. and Calculations are performed based on the frequencies of these two largest values. This indicates that... The presence of a peak at the center frequency indicates modulation in the original vibration signal. This indicates that... There are no peaks at the center frequency; Step 3: Use the Savitzky-Golay smoothing filter to fit the autocorrelation coefficients to obtain new autocorrelation coefficients; Step 4: Take the two largest values in the new autocorrelation coefficient, obtain the two index positions corresponding to the two maximum value points, and calculate the position difference between the two index positions. Step 5: Calculate the fundamental frequency based on the position difference, and then calculate the rotational speed based on the fundamental frequency.
2. The method for estimating the rotational speed of rotating equipment based on hill peak identification and correlation analysis according to claim 1, characterized in that, The method of calculating the spectrum of vibration signal using Fourier transform involves using continuous Fourier transform and its inverse transform to achieve mutual conversion between the time domain and frequency domain of vibration signal, thereby obtaining the spectrum of vibration signal.
3. The method for estimating the rotational speed of rotating equipment based on hill peak identification and correlation analysis according to claim 1, characterized in that, The process of extracting the envelope signal from the vibration signal using Hilbert transform is as follows: S221. First, assume the vibration signal is a real-valued signal. Perform a Hilbert transform on the real-valued signal. The amplitude remains unchanged after the transformation, and the phase shift is obtained. S222. Based on the phase shift, phase shifts are generated on the positive and negative frequency parts of the real-valued signal respectively, so that the real-valued signal is orthogonal to the Hilbert transform signal. S223. The defined analytic signal is obtained based on the real-valued signal and the Hilbert transform signal; S224. According to the definition, the envelope signal of the real-valued signal is obtained by analyzing the polar coordinates of the signal.
4. The method for estimating the rotational speed of rotating equipment based on hill peak identification and correlation analysis according to claim 3, characterized in that, The Hilbert transform signal The calculation formula is as follows: ； in, It is a real-valued signal.
5. The method for estimating the rotational speed of rotating equipment based on hill peak identification and correlation analysis according to claim 4, characterized in that, The definition of the analytical signal The calculation formula is as follows: ； Envelope signal The calculation formula is as follows: 。 6. The method for estimating the rotational speed of rotating equipment based on hill peak identification and correlation analysis according to claim 5, characterized in that, The autocorrelation coefficient calculated using correlation analysis is the short-time autocorrelation function of the envelope signal or vibration signal. The autocorrelation function has the same periodicity as the envelope signal or vibration signal. The autocorrelation function reaches its maximum value at integer multiples of the period of the envelope signal or vibration signal. The period of the envelope signal or vibration signal can be estimated based on the location of the first maximum value of the autocorrelation function.
7. The method for estimating the rotational speed of rotating equipment based on hill peak identification and correlation analysis according to claim 1, characterized in that, The filter used in fitting the autocorrelation coefficients using the Savitzky-Golay smoothing filter is based on the least squares algorithm. Before fitting the autocorrelation coefficients, it is necessary to smooth them to remove irrelevant noise.
8. The method for estimating the rotational speed of rotating equipment based on hill peak identification and correlation analysis according to claim 1, characterized in that, The fundamental frequency The calculation formula is as follows: ;in, Vibration signal sampling frequency, This is the positional difference.
9. The method for estimating the rotational speed of rotating equipment based on hill peak identification and correlation analysis according to claim 8, characterized in that, The speed The calculation formula is as follows: 。