CN107783938B - Method for estimating instantaneous rotating speed of rotating equipment - Google Patents

Method for estimating instantaneous rotating speed of rotating equipment Download PDF

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CN107783938B
CN107783938B CN201710781137.9A CN201710781137A CN107783938B CN 107783938 B CN107783938 B CN 107783938B CN 201710781137 A CN201710781137 A CN 201710781137A CN 107783938 B CN107783938 B CN 107783938B
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彭志科
陈是扦
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Abstract

The invention provides an instantaneous rotating speed estimation method of rotating equipment. The method comprises the steps of roughly estimating the instantaneous frequency of a vibration signal by using a parameterized time-frequency analysis method, accurately correcting an initial estimation result by using a new envelope tracking filter, directly reflecting the instantaneous rotating speed of equipment by using the finally obtained instantaneous frequency of the signal, describing the envelope of the signal by using a Fourier series model by using the envelope tracking filter, and optimally solving envelope parameters by using a least square method. The invention adopts an instantaneous rotating speed estimation method combining parameterized time-frequency transformation and an envelope tracking filter, can overcome the defect that the estimation precision of the traditional technology is limited by time-frequency resolution, and has the advantages of high estimation precision and simple realization.

Description

Method for estimating instantaneous rotating speed of rotating equipment
Technical Field
The invention relates to the field of signal processing, in particular to a method for estimating the instantaneous rotating speed of rotating equipment, and specifically relates to an instantaneous rotating speed estimation method based on parameterized time-frequency transformation and envelope tracking filtering.
Background
In large rotating equipment condition monitoring, fault diagnosis and other applications, it is often necessary to accurately measure the instantaneous rotational speed of the equipment. Key phase measurement is one of the currently used methods for measuring the instantaneous rotational speed of equipment. The key phase measurement method determines the position of the rotor within one rotation cycle by detecting the timing at which the key phase pulse signal is generated. The method obtains the average rotating speed of the rotor, and when the rotating speed changes, the measurement error is large. Meanwhile, the key phase measurement needs additional hardware equipment, and the measurement cost is high. The frequency information of the rotor vibration signal is directly related to the instantaneous rotor speed. Therefore, by analyzing the vibration signal, the instantaneous rotational speed of the rotating device can be accurately estimated.
When the rotational speed of the rotating device is changed, the frequency component of the rotor vibration signal exhibits a time-varying characteristic. The instantaneous frequency is often used to characterize such instantaneous changes in the signal. The time-frequency analysis technique is an effective tool for estimating the instantaneous frequency of a signal, and can be divided into a non-parametric time-frequency method and a parametric time-frequency method according to whether an analysis parameter is related to the signal. Common methods such as short-time Fourier transform, wavelet transform, Weignenwell distribution and the like belong to non-parametric time-frequency methods. The disadvantages of these methods are: poor time-frequency concentration, cross item interference and the like. In order to improve the resolution of the non-parametric time-frequency method, some researchers have proposed time-frequency rearrangement and synchronous compression methods. The methods move the value of each point on the time frequency distribution to the center of gravity of the signal energy through a post-processing means so as to compress a time frequency energy band and improve the time frequency resolution, but the methods have large calculation amount and poor noise resistance. Another class of unparameterized time-frequency methods utilizes advanced mathematical optimization methods to improve the signal instantaneous frequency estimation accuracy, such as the data-driven time-frequency analysis methods proposed in the prior art. The method is sensitive to optimizing initial values, and when the initial values are not properly selected, the algorithm is difficult to converge. The parameterized time-frequency method adopts the kernel function matched with the signal model, so that the time-frequency resolution can be effectively improved, and the instantaneous frequency estimation deviation is reduced. Chirp wavelet transform is a parameterized time-frequency method for processing chirp signals. The existing technology expands the linear frequency modulation wavelet transform and provides various time-frequency analysis methods for processing non-linear frequency modulation signals. Although the parameterized time-frequency analysis method improves the energy aggregation of time-frequency distribution, the time-frequency resolution is still limited, and a high-precision instantaneous frequency estimation value is difficult to obtain.
So far, no parametric time-frequency method and envelope tracking filtering are combined for estimating the instantaneous rotating speed of the rotating equipment.
Disclosure of Invention
In order to overcome the defect that the estimation precision of the traditional technology is limited by time-frequency resolution, the invention provides a method for realizing high-precision estimation of the instantaneous rotating speed of rotating equipment based on the combination of parameterized time-frequency transformation and envelope tracking filtering: firstly, roughly estimating the instantaneous frequency of a vibration signal by adopting parameterized time-frequency transformation with Fourier series as a kernel function; estimating the complex envelope of the signal by using a new envelope tracking filter by taking the initial estimation value of the instantaneous frequency as input; the instantaneous frequency estimation result is accurately corrected by utilizing the phase information of the signal envelope, and the obtained instantaneous frequency of the vibration signal can directly reflect the instantaneous rotating speed of the equipment. The envelope tracking filtering algorithm provided by the invention describes signal complex envelope by utilizing a Fourier series model, and estimates envelope model parameters by utilizing a regularization least square method. The envelope tracking algorithm can effectively inhibit noise and accurately extract various complex signal envelope information.
The invention is realized according to the following technical scheme:
a method for estimating the instantaneous rotational speed of a rotating device, comprising the steps of:
step S1, estimating the instantaneous frequency of the equipment vibration signal by using parameterized time-frequency transformation;
step S2, estimating signal complex envelope by using envelope tracking filter;
in step S3, the obtained signal envelope is used to accurately correct the initial estimation result of the instantaneous frequency, and the instantaneous frequency of the signal directly reflects the instantaneous rotation speed of the device.
In the above technical solution, step S1 estimates the instantaneous frequency of the signal by a method of iteratively fitting a parameterized time-frequency distribution ridge, and the process includes:
s101: initializing parameters to make kernel parameter alpha(i)Setting a Fourier order M, a convergence threshold epsilon and an iteration number i as 1;
s102: with a nuclear parameter alpha(i)Calculating a parameterized time-frequency distribution TF (t, f; alpha)(i))；
S103: from the time-frequency distribution TF (t, f; alpha)(i)) Middle extraction time-frequency ridge line
Figure BDA0001397010300000021
S104: using M-th order Fourier series approximation
Figure BDA0001397010300000023
Updating the nuclear parameter alpha(i+1)；
S105: computing iteration end conditions
Figure BDA0001397010300000024
S106: xi is a(i)If is greater than epsilon, let i equal to i +1 and go to step S102; otherwise, executing step S107;
s107: returning instantaneous frequency estimation results
Figure BDA0001397010300000025
In the above technical solution, the parameterized time-frequency transformation in step S1 specifically includes:
defining:
Figure BDA0001397010300000026
wherein
Figure BDA0001397010300000031
z (t) is an analytic form of the vibration signal obtained by Hilbert transform, gσ(t) is a Gaussian window function, α ═
Figure BDA0001397010300000032
To transform the kernel parameters, F0＝FsFrequency resolution (F) with/2N being a Fourier seriessFor signal sampling frequency), parameterized time-frequency transform utilization operator
Figure BDA0001397010300000033
And reducing the frequency modulation degree of the target signal to obtain concentrated time-frequency representation.
In the above technical solution, the envelope tracking filter algorithm in step S2 specifically includes:
assuming that the rotor vibration signal model is described by an amplitude modulation-frequency modulation model when the rotating equipment rotating speed changes:
Figure BDA0001397010300000034
where t is t0，…tN-1At the sampling time, A (t), f (t),
Figure BDA0001397010300000035
Respectively, the instantaneous amplitude, instantaneous frequency and initial phase of the fundamental frequency component of the vibration signal, and n (t) represents noise and other uncorrelated harmonic components. The instantaneous frequency f (t) corresponds directly to the instantaneous speed of rotation of the rotating device.
The instantaneous frequency estimated value obtained by the parameterized time-frequency transformation is assumed to be
Figure BDA0001397010300000036
The vibration signal model is rearranged into:
Figure BDA0001397010300000037
wherein
Figure BDA0001397010300000038
Estimation error of complex phase and instantaneous frequency of a (t) for complex envelope of signal
Figure BDA0001397010300000039
Accordingly, the instantaneous frequency estimation result can be accurately corrected using the phase information of a (t). To extract a (t) accurately, a (t) is characterized by a K-order fourier series model:
Figure BDA00013970103000000310
substituting the above equation into the signal model yields the following regression equation:
z＝Ga+n
wherein z ═ z (t)0)…z(tN-1)]T，a＝[a0…aKb1…bK]T，n＝[n(t0)…n(tN-1)]TThe dimension of the G matrix is N (2K +1), and its elements are:
Figure BDA00013970103000000311
wherein
Figure BDA00013970103000000312
The signal envelope coefficient vector a is estimated by a regularized least squares method:
Figure BDA00013970103000000313
wherein alpha is a regularization parameter, I represents an identity matrix, superscript H represents a matrix conjugate transpose, and a signal envelope estimate can be obtained from the estimated coefficient vector
Figure BDA00013970103000000411
Further extracting the fundamental frequency component of the signal
Figure BDA0001397010300000041
The envelope tracking filter may be considered a time-frequency filter, the center frequency of which is the instantaneous frequency obtained by a parameterized time-frequency transform
Figure BDA0001397010300000042
Having a bandwidth of 2KF0。
In the above technical solution, the instantaneous frequency correction process in step S3 specifically includes:
s301: the instantaneous frequency estimated in step S1
Figure BDA0001397010300000043
As an envelope tracking filter in step S2Inputting, extracting complex envelope of signal
Figure BDA0001397010300000044
Specifically, a signal envelope Fourier series model needs to be established, and model parameters are optimized and solved;
s302: extracting envelope signals
Figure BDA0001397010300000045
Plural phase of
Figure BDA0001397010300000046
Deriving the phase function to obtain the envelope instantaneous frequency
Figure BDA0001397010300000047
Using pairs of Fourier series models
Figure BDA0001397010300000048
Fitting to obtain instantaneous frequency correction
Figure BDA0001397010300000049
S303: correcting instantaneous frequency estimates
Figure BDA00013970103000000410
Compared with the prior art, the invention has the following beneficial effects:
1. compared with the traditional polynomial model, the Fourier series instantaneous frequency model is adopted, so that the invention can process more complex equipment instantaneous rotating speed change conditions.
2. The invention adopts the envelope tracking filter to correct the instantaneous frequency estimation result, can overcome the defect that the estimation precision of the traditional technology is limited by time-frequency resolution, and can obtain the high-precision instantaneous rotating speed estimation.
3. The algorithm is simple to implement, stable in performance and applicable to various application fields.
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Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a schematic flow chart of an instantaneous rotational speed estimation method according to the present invention;
FIG. 2 is a schematic diagram of a time-frequency representation of an emulation signal according to the present invention;
FIG. 3 is a diagram illustrating an estimation result of an instantaneous frequency of a simulation signal according to the present invention;
FIG. 4 is a schematic diagram of the instantaneous frequency estimation error of the simulation signal under different SNR according to the present invention;
FIG. 5 is a schematic view of a rotor test stand of the present invention;
FIG. 6 is a schematic time-frequency representation of a rotor vibration signal in accordance with the present invention;
FIG. 7 is a schematic diagram illustrating the estimation result of the instantaneous rotor speed according to the present invention.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
Fig. 1 is a schematic overall flow chart of the instantaneous speed estimation method of the present invention, as shown in fig. 1, which is characterized by comprising the following steps:
step S1, estimating the instantaneous frequency of the equipment vibration signal by using parameterized time-frequency transformation;
step S2, estimating signal complex envelope by using envelope tracking filter;
in step S3, the obtained signal envelope is used to accurately correct the initial estimation result of the instantaneous frequency, and the instantaneous frequency of the signal directly reflects the instantaneous rotation speed of the device.
Step S1 is an iterative fitting of a parameterized time-frequency distribution ridge in the estimation process, which includes:
s101: initializing parameters to make kernel parameter alpha(i)Set to {0, …, 0}, settingA Fourier order M, a convergence threshold epsilon and an iteration number i equal to 1;
s102: with a nuclear parameter alpha(i)Calculating a parameterized time-frequency distribution TF (t, f; alpha)(i))；
S103: from the time-frequency distribution TF (t, f; alpha)(i)) Middle extraction time-frequency ridge line
Figure BDA0001397010300000058
S104: fitting by M-th Fourier series
Figure BDA0001397010300000051
Updating the nuclear parameter alpha(i+1)；
S105: computing iteration end conditions
Figure BDA0001397010300000052
S106: xi is a(i)If is greater than epsilon, let i equal to i +1 and go to step S102; otherwise, executing step S107;
s107: returning instantaneous frequency estimation results
Figure BDA0001397010300000053
In the above technical solution, the parameterized time-frequency transformation in step S1 specifically includes:
defining:
Figure BDA0001397010300000059
wherein
Figure BDA0001397010300000054
z (t) is an analytic form of the vibration signal obtained by Hilbert transform, gσ(t) is a Gaussian window function,
Figure BDA0001397010300000055
Figure BDA0001397010300000056
to transform the kernel parameters, F0＝FsFrequency resolution (F) with/2N being a Fourier seriessFor signal sampling frequency), parameterized time-frequency transform utilization operator
Figure BDA0001397010300000057
And reducing the frequency modulation degree of the target signal to obtain concentrated time-frequency representation.
The process of estimating the signal envelope by the envelope tracking filter algorithm in step S2 specifically includes:
assuming that the rotor vibration signal model can be described by an am-fm model when the rotational speed of the rotating equipment changes:
Figure BDA0001397010300000061
where t is t0，…tN-1At the sampling time, A (t), f (t),
Figure BDA00013970103000000619
Respectively, the instantaneous amplitude, instantaneous frequency and initial phase of the fundamental frequency component of the vibration signal, and n (t) represents noise and other uncorrelated harmonic components. The instantaneous frequency f (t) corresponds directly to the instantaneous speed of rotation of the rotating device.
The instantaneous frequency estimated value obtained by the parameterized time-frequency transformation is assumed to be
Figure BDA0001397010300000062
The vibration signal model is rearranged into:
Figure BDA0001397010300000063
wherein
Figure BDA0001397010300000064
Estimation error of complex phase and instantaneous frequency of a (t) for complex envelope of signal
Figure BDA0001397010300000065
Accordingly, the instantaneous frequency estimation result can be accurately corrected using the phase information of a (t). To extract a (t) accurately, a (t) is characterized by a K-order fourier series model:
Figure BDA0001397010300000066
substituting the above equation into the signal model yields the following regression equation:
z＝Ga+n
wherein z ═ z (t)0)…z(tN-1)]T，a＝[a0…aKb1…bK]T，n＝[n(t0)…n(tN-1)]TThe dimension of the G matrix is N (2K +1), and its elements are:
Figure BDA0001397010300000067
wherein
Figure BDA0001397010300000068
The signal envelope coefficient vector a is estimated by a regularized least squares method:
Figure BDA0001397010300000069
wherein alpha is a regularization parameter, I represents an identity matrix, superscript H represents a matrix conjugate transpose, and a signal envelope estimate can be obtained from the estimated coefficient vector
Figure BDA00013970103000000610
Further extracting the fundamental frequency component of the signal
Figure BDA00013970103000000611
The envelope tracking filter may be considered a time-frequency filter, the center frequency of which is the instantaneous frequency obtained by a parameterized time-frequency transform
Figure BDA00013970103000000612
Having a bandwidth of 2KF0。
The instantaneous frequency correction process in step S3 specifically includes:
s301: the instantaneous frequency estimated in step S1
Figure BDA00013970103000000613
Extracting the signal complex envelope as an envelope tracking filter input in step S2
Figure BDA00013970103000000620
S302: extracting envelope signals
Figure BDA00013970103000000614
Plural phase of
Figure BDA00013970103000000615
Deriving the phase function to obtain the envelope instantaneous frequency
Figure BDA00013970103000000616
Using pairs of Fourier series models
Figure BDA00013970103000000617
Fitting to obtain instantaneous frequency correction
Figure BDA00013970103000000618
S303: correcting instantaneous frequency estimates
Figure BDA0001397010300000071
Example 1
FIG. 2 is a time-frequency representation of a simulated signal with a signal-to-noise ratio of 0dB and a sampling frequency of 100 Hz. The order M of the parameterized time-frequency transform Fourier kernel is set to be 6, and the iteration convergence threshold epsilon is set to be 1 e-3. The parameterized time-frequency transformation is iterated for 3 times in total to reach the convergence condition, and the relative errors of the instantaneous frequency estimation in each iteration are-43.9 dB, -44.9dB, -45.0dB respectively. The instantaneous frequency estimate is corrected using an envelope tracking filter, setting the filter bandwidth to 1Hz (i.e., fourier order K15), the regularization parameter α to 0.5, and the corrected instantaneous frequency has a relative error of-64.9 dB, as shown in fig. 3. FIG. 4 is a diagram of the parameterized time-frequency transform and the relative error of the instantaneous frequency estimation under different SNR conditions according to the method of the present invention. The result shows that the invention can obtain accurate instantaneous frequency estimation under the condition of strong noise.
Example 2
The method provided by the invention is used for estimating the instantaneous rotating speed of the actual equipment. FIG. 5 is a schematic view of a rotor test bed in which the motor is speed regulated by a speed reducer to drive a loaded rotor to move, and an accelerometer collects vibration signals at a bearing for analysis and processing. FIG. 6 is a time-frequency representation of rotor vibration signals actually measured at the start-stop stage of the test bed, and the sampling frequency is 100 Hz. The order M of the parameterized time-frequency transform Fourier kernel is set to be 30, and the iteration convergence threshold epsilon is set to be 1 e-3. The parameterized time-frequency transform iterates 3 times in total. The instantaneous frequency estimate is modified using an envelope tracking filter to set the filter bandwidth to 1Hz (i.e., fourier order K15) and the regularization parameter α to 0.5. The final estimated instantaneous rotor speed is shown in fig. 7.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.

Claims (1)

1. A method for estimating the instantaneous rotational speed of a rotating device, comprising the steps of:
step S1, estimating the instantaneous frequency of the equipment vibration signal by using parameterized time-frequency transformation;
step S2, estimating signal complex envelope by using envelope tracking filter;
step S3, the obtained signal envelope is used for accurately correcting the initial estimation result of the instantaneous frequency, and the instantaneous frequency of the signal directly reflects the instantaneous rotating speed of the equipment;
the envelope tracking filter in step S2 specifically includes:
when the rotating speed of the rotating equipment changes, the rotor vibration signal model is described by an amplitude modulation-frequency modulation model:
Figure FDA0002774878150000011
where t is t0,…tN-1At the sampling time, A (t), f (t),
Figure FDA0002774878150000012
Respectively representing the instantaneous amplitude, instantaneous frequency and initial phase of the fundamental frequency component of the vibration signal, wherein n (t) represents noise and other irrelevant harmonic components, and the instantaneous frequency f (t) directly corresponds to the instantaneous rotating speed of the rotating equipment;
the instantaneous frequency estimated value obtained by the parameterized time-frequency transformation is assumed to be
Figure FDA0002774878150000013
The vibration signal model is rearranged into:
Figure FDA0002774878150000014
wherein
Figure FDA0002774878150000015
Estimation error of complex phase and instantaneous frequency of a (t) for complex envelope of signal
Figure FDA0002774878150000016
In this regard, the instantaneous frequency estimation result can be accurately corrected using the phase information of a (t), and in order to accurately extract a (t), a (t):
Figure FDA0002774878150000017
substituting the above equation into the signal model yields the following regression equation:
z＝Ga+n
wherein z ═ z (t)0) … z(tN-1)]T，a＝[a0 … aK b1 … bK]T，n＝[n(t0) … n(tN-1)]TThe dimension of the G matrix is N (2K +1), and its elements are:
Figure FDA0002774878150000018
wherein
Figure FDA0002774878150000021
The signal envelope coefficient vector a is estimated by a regularized least squares method:
Figure FDA0002774878150000022
wherein alpha is a regularization parameter, I represents an identity matrix, superscript H represents a matrix conjugate transpose, and a signal envelope estimate can be obtained from the estimated coefficient vector
Figure FDA0002774878150000023
Further extracting the fundamental frequency component of the signal
Figure FDA0002774878150000024
Figure FDA0002774878150000025
The envelope tracking filter may be considered a time-frequency filter, the center frequency of which is the instantaneous frequency obtained by a parameterized time-frequency transform
Figure FDA0002774878150000026
Having a bandwidth of 2KF0；
F0Is the frequency resolution of a fourier series.
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