CN108398260B - Method for quickly evaluating instantaneous angular speed of gearbox based on mixed probability method - Google Patents
Method for quickly evaluating instantaneous angular speed of gearbox based on mixed probability method Download PDFInfo
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Abstract
The invention provides a method for quickly evaluating the instantaneous angular speed of a gearbox based on a mixed probability method, which comprises the following steps of: collecting acoustic emission signals and vibration acceleration signals; denoising the signal by a wavelet threshold; normalizing the denoised signal; performing pre-whitening processing on the normalized signal by adopting a cepstrum editing method; carrying out Gabor conversion to obtain a spectrogram of the mixed signal; regarding each column of the mixed spectrogram as an instantaneous spectrum, and establishing a probability density function of the instantaneous angular velocity at each time step; combining all probability density functions within a given time interval into one; performing Gaussian smoothing processing on the obtained probability density function; and obtaining the change rule of the angular speed along with time. The invention does not need to use a rotating speed measuring instrument, improves the system stability under severe working conditions and saves the cost; the limitation of the rotation speed change on the rotation speed evaluation is separated, and the rotation speed can still be accurately identified under the condition of severe rotation speed change.
Description
Technical Field
The invention relates to the technical field of signal processing of rotating machinery, in particular to a method for quickly evaluating instantaneous angular speed of a gearbox based on a mixed probability method.
Background
The gearbox is an important speed change and power transmission component, is widely applied to modern industrial equipment, and has important significance for safety production of enterprises when condition monitoring and fault diagnosis are carried out on the gearbox. In the fault diagnosis of gearboxes, especially in variable-speed operating conditions, the speed estimation is an indispensable component thereof. The most widely used method for estimating the rotating speed at present is to measure the rotating speed by installing a tachometer. However, for an industrial field with a severe operating environment, the additional installation of a tachometer greatly reduces the reliability of system equipment. In addition, the installation of the tachometer requires additional design of the device and adds considerable cost.
The technical search shows that the existing tachometer-free rotating speed estimation method is based on the analysis of vibration signals of a gearbox body. The frequency domain or time-frequency domain conversion is carried out on the vibration signals, the meshing frequency at each moment is extracted, and the number of teeth of the gear is combined, so that the rotating speed of the gear box is determined. However, the field operation environment of the equipment is generally severe, the vibration signal of the actual measurement gearbox box usually contains a large amount of noise components and other harmonic interference components, and particularly under the working condition of variable rotating speed, the frequency spectrum fuzzy phenomenon is easy to occur when the meshing frequency at each moment is extracted. In addition, the existing method is only suitable for occasions with small fluctuation range of the rotating speed, and some estimation algorithms are complex and cannot meet the requirement of rapidly realizing rotating speed estimation on an industrial field.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the defects of the prior art, the method for rapidly evaluating the instantaneous angular speed of the gearbox based on the mixed probability method is provided, and the angular domain signals are resampled without using complex hardware or even a velocimeter.
Therefore, the invention adopts the following technical scheme: the method for quickly evaluating the instantaneous angular speed of the gearbox based on the mixed probability method comprises the following steps:
(1) respectively placing an acceleration sensor and an acoustic emission sensor on the gearbox body, and acquiring an acceleration signal and an acoustic emission signal of the gearbox body;
(2) denoising and smoothing the acquired acoustic emission signals and vibration acceleration signals by adopting a wavelet threshold method;
(3) respectively carrying out normalization processing on the denoised acoustic emission signal and the denoised vibration acceleration signal;
(4) carrying out pre-whitening treatment on the normalized acoustic emission signal and the vibration acceleration signal, improving the impact characteristic of the signal and removing the resonance of the structure;
(5) after pre-whitening treatment, carrying out Gabor transformation on the acoustic emission signal and the vibration acceleration signal to obtain a spectrogram of a mixed signal;
(6) each column of the mixed spectrogram is considered as a transient spectrum, while taking into account the first 10 harmonic volumes generated by each impulse, in order to establish a probability density function of the instantaneous angular velocity at each time step:
where ω is set as a parameter of the probability density function, Ω is the instantaneous angular velocity, Hi(i∈[1...n]) Is the sequence of impact events, A (H)iω) is the temporal spectrum, ζ, of the signal after pre-whiteningiIs a normalization factor, ΩminAnd ΩmaxIs the minimum and maximum of the apriori instantaneous angular velocity law;
(7) introducing a continuity condition, and combining all probability density functions in a given time interval into one:
(8) carrying out smoothing treatment on the obtained probability density function;
(9) and extracting the expected value of the probability density function in each time step to obtain the final angular speed change rule along with the time.
Further, the sequence of events during operation of the gearbox that can lead to a strong vibratory impulse response is known.
Further, the wavelet threshold denoising main steps in the step 2) are as follows:
(2.1) carrying out wavelet decomposition on the collected acoustic emission signals and acceleration signals to obtain each scale coefficient;
(2.2) processing the threshold value, and determining a high threshold value and a low threshold value;
and (2.3) performing wavelet reconstruction on the signals to obtain the denoised signals.
Further, step 3) adopts 0 mean normalization to normalize the signal, i.e. normalize the original data set into a data set with mean 0 and variance 1.
Further, step 4) uses cepstrum editing to implement pre-whitening of the signal, and the specific implementation steps are as follows:
(4.1) carrying out fast Fourier transform on the normalized acoustic emission signal and the normalized vibration acceleration signal to respectively obtain a logarithmic amplitude spectrum and a phase spectrum;
(4.2) carrying out fast Fourier inverse transformation on the logarithmic magnitude spectrum to obtain a real cepstrum;
(4.3) editing the real cepstrum, namely, setting the corresponding inverse harmonic in the real cepstrum to zero to remove the discrete frequency component in the signal;
(4.4) carrying out fast Fourier transform on the edited real cepstrum to obtain an edited logarithmic amplitude spectrum;
(4.5) recombining the edited log-magnitude spectrum with the original log spectrum to form a complex log spectrum;
and (4.6) carrying out inverse Fourier transform on the complex frequency spectrum to obtain a pre-whitened signal of the original signal.
Further, the normalization factor in step 6) is calculated by the following formula:
further, the continuity condition in step 7) needs to satisfy the following formula:
wherein omegajProbability density function, σ, representing instantaneous angular velocity at the jth time stepk＝|γkΔt|，ΔtIs the time step of the spectrum and gamma is the standard acceleration of the instantaneous angular velocity.
Further, step 8) adopts gaussian smoothing, and the specific calculation formula is as follows:
wherein the setting j and j + k are gearsTwo moments during the operation of the tank, k representing the time interval between the two moments, then the probability density function [ omega ] of the instantaneous angular velocity at moment jj]j+kIs a probability density function [ omega ] of the instantaneous angular velocity through the moment j + kj+k]Convolution with a Gaussian function, so that the probability density function [ omega ] of the instantaneous angular velocity at time jj]j+kIs j + K (K e-K, …, K) before and after time j]) The result of the co-action of the probability density functions at the time of day.
The invention has the beneficial effects that: the method improves the system stability under the severe working condition and saves the cost; the limitation of the rotation speed change on the rotation speed evaluation is separated, and the rotation speed can still be accurately identified under the condition of severe rotation speed change.
Drawings
FIG. 1 is a flow chart of the evaluation method of the present invention.
Fig. 2 is a flow chart of implementing a pre-whitening process using cepstral editing.
FIG. 3 is a collected acceleration signal for a gearbox.
FIG. 4 is an acoustic emission signal of a gearbox collected.
Fig. 5 is a spectral diagram of a mixed signal.
Fig. 6 is a graph of the angular velocity change obtained finally.
Detailed description of the preferred embodiments
The technical solution of the present invention is further described in detail with reference to the following examples, which are carried out under the premise of the technical solution of the present invention, and detailed embodiments and specific procedures are given, but the scope of the present invention is not limited to the following examples.
The embodiment is to evaluate the rotating speed of a large-range rotating speed changing process of a certain spur gear gearbox test bed, wherein the evaluation process is shown in fig. 1 and specifically comprises the following steps:
1) an acceleration sensor and an acoustic emission sensor are respectively arranged on the gearbox body, and acceleration signals and acoustic emission signals of the gearbox body are acquired, as shown in figures 3 and 4.
2) Denoising and smoothing the collected acoustic emission signals and vibration acceleration signals by adopting a wavelet threshold method, and specifically comprising the following steps of: carrying out wavelet decomposition on the collected acoustic emission signals and acceleration signals to obtain each scale coefficient; processing the threshold value, and determining a high threshold value and a low threshold value; and performing wavelet reconstruction on the signal to obtain a denoised signal.
3) And respectively carrying out normalization processing on the denoised acoustic emission signal and the denoised vibration acceleration signal, wherein a 0-mean normalization method is adopted in the invention, namely, an original data set is normalized into a data set with a mean value of 0 and a variance of 1.
4) The normalized acoustic emission signal and the vibration acceleration signal are subjected to pre-whitening processing, the impact characteristic of the signal is improved, and the resonance of the structure is removed, the pre-whitening is realized by adopting cepstrum editing, the flow chart of the method is shown in figure 2, and the method specifically comprises the following steps:
a. carrying out fast Fourier transform on the normalized acoustic emission signal and the vibration acceleration signal to respectively obtain a logarithmic amplitude spectrum and a phase spectrum;
b. carrying out fast Fourier inverse transformation on the logarithmic amplitude spectrum to obtain a real cepstrum;
c. editing the real cepstrum, namely setting corresponding inverse harmonics in the real cepstrum to zero so as to remove discrete frequency components in the signal;
d. carrying out fast Fourier transform on the edited real cepstrum to obtain an edited logarithmic amplitude spectrum;
e. recombining the edited log-amplitude spectrum with the original log spectrum to form a complex log spectrum;
f. the complex spectrum is inverse fourier transformed to obtain a pre-whitened signal of the original signal.
5) After the pre-whitening processing, Gabor conversion is performed on the acoustic emission signal and the vibration acceleration signal to obtain a spectrogram of the mixed signal, as shown in fig. 5.
6) Each column of the spectrogram is considered as an instantaneous spectrum, while taking into account the first 10 harmonic volumes generated by each impulse, in order to establish a probability density function of the instantaneous angular velocity at each time step:
where Ω is the instantaneous angular velocity Hi(i∈[1…n]) Is the sequence of impact events with respect to instantaneous angular velocity, A (f) is the whitened version of the instantaneous spectrum of the response signal, ΩminAnd ΩmaxIs the minimum and maximum values of the law of instantaneous angular velocity a priori, ζiIs a normalization factor and can be calculated by the following formula:
7) introducing a continuity condition, and combining all probability density functions in a given time interval into one:
8) and performing Gaussian smoothing on the obtained probability density function, wherein the specific calculation formula is as follows:
wherein the probability density function [ omega ] of the instantaneous angular velocity at time jj]j+kIs a probability density function [ omega ] of the instantaneous angular velocity through the moment j + kj+k]And convolution with a gaussian function. Therefore, the probability density function [ omega ] of the instantaneous angular velocity at time jj]j+kIs j + K (K e-K, …, K) before and after time j]) The result of the co-action of the probability density functions at the time of day.
9) The expected value of the probability density function is extracted in each time step to obtain the final angular velocity time-dependent law, as shown in fig. 6.
10) The angular velocity variation curve is highly matched with the angular velocity variation curve directly measured by the angular encoder, so that the correctness of the method provided by the invention can be proved.
From the above examples, it can be seen that the method for rapidly estimating the instantaneous angular velocity of the gearbox based on the hybrid probability method provided by the invention is very suitable for rapidly estimating the angular velocity of the gearbox, and can also identify the angular velocity very accurately when the rotating speed is changed in a large range.
Claims (7)
1. The method for quickly evaluating the instantaneous angular speed of the gearbox based on the mixed probability method is characterized by comprising the following steps of: the rapid evaluation method comprises the following steps:
(1) respectively placing an acceleration sensor and an acoustic emission sensor on the gearbox body, and acquiring an acceleration signal and an acoustic emission signal of the gearbox body;
(2) denoising and smoothing the acquired acoustic emission signals and vibration acceleration signals by adopting a wavelet threshold method;
(3) respectively carrying out normalization processing on the denoised acoustic emission signal and the denoised vibration acceleration signal;
(4) carrying out pre-whitening treatment on the normalized acoustic emission signal and the vibration acceleration signal, improving the impact characteristic of the signal and removing the resonance of the structure;
(5) after pre-whitening treatment, carrying out Gabor transformation on the acoustic emission signal and the vibration acceleration signal to obtain a spectrogram of a mixed signal;
(6) each column of the mixed spectrogram is considered as a transient spectrum, while taking into account the first 10 harmonic volumes generated by each impulse, in order to establish a probability density function of the instantaneous angular velocity at each time step:
where ω is set as a parameter of the probability density function, Ω is the instantaneous angular velocity, Hi(i∈[1...n]) Is the sequence of impact events, A (H)iω) is the temporal spectrum, ζ, of the signal after pre-whiteningiIs a normalization factor, ΩminAnd ΩmaxIs the minimum and maximum of the apriori instantaneous angular velocity law;
(7) introducing a continuity condition, and combining all probability density functions in a given time interval into one:
(8) carrying out smoothing treatment on the obtained probability density function;
(9) extracting expected values of the probability density function in each time step to obtain a final angular speed time-varying rule;
the continuity condition needs to satisfy the following formula:
wherein omegajProbability density function, σ, representing instantaneous angular velocity at the jth time stepk＝|γkΔt|，ΔtIs the time step of the spectrum and gamma is the standard acceleration of the instantaneous angular velocity.
2. Method for the rapid evaluation of the instantaneous angular velocity of a gearbox based on a hybrid probability method according to claim 1, characterized in that the sequence of events during the operation of the gearbox that lead to strong vibratory impulse responses is known.
3. The method for rapidly evaluating the instantaneous angular velocity of the gearbox based on the mixed probability method as claimed in claim 1, wherein the wavelet threshold denoising in the step 2) mainly comprises the following steps:
(2.1) carrying out wavelet decomposition on the collected acoustic emission signals and acceleration signals to obtain each scale coefficient;
(2.2) processing the threshold value, and determining a high threshold value and a low threshold value;
and (2.3) performing wavelet reconstruction on the signals to obtain the denoised signals.
4. The method for rapidly estimating the instantaneous angular velocity of a gearbox based on the mixed probability method as claimed in claim 1, wherein step 3) normalizes the signal by 0-mean normalization, i.e. normalizes the original data set into a data set with a mean value of 0 and a variance of 1.
5. The method for rapidly evaluating the instantaneous angular velocity of the gearbox based on the mixed probability method according to the claim 1, characterized in that the step 4) uses cepstrum editing to realize the pre-whitening of the signal, and the specific implementation steps are as follows:
(4.1) carrying out fast Fourier transform on the normalized acoustic emission signal and the normalized vibration acceleration signal to respectively obtain a logarithmic amplitude spectrum and a phase spectrum;
(4.2) carrying out fast Fourier inverse transformation on the logarithmic magnitude spectrum to obtain a real cepstrum;
(4.3) editing the real cepstrum, namely, setting the corresponding inverse harmonic in the real cepstrum to zero to remove the discrete frequency component in the signal;
(4.4) carrying out fast Fourier transform on the edited real cepstrum to obtain an edited logarithmic amplitude spectrum;
(4.5) recombining the edited log-magnitude spectrum with the original log spectrum to form a complex log spectrum;
and (4.6) carrying out inverse Fourier transform on the complex log spectrum to obtain a pre-whitened signal of the original signal.
6. The method for fast estimation of instantaneous angular velocity of a gearbox based on the hybrid probability method as claimed in claim 1, wherein the normalization factor in step 6) is calculated by the following formula:
7. the method for rapidly evaluating the instantaneous angular velocity of a gearbox based on a hybrid probability method according to claim 1, wherein step 8) adopts Gaussian smoothing, and the specific calculation formula is as follows:
wherein j and j + k are two moments in the operation of the gearbox, and k represents the time interval between the two moments, then the probability density function [ omega ] of the instantaneous angular velocity at the moment jj]j+kIs a probability density function [ omega ] of the instantaneous angular velocity through the moment j + kj+k]Convolution with a Gaussian function, so that the probability density function [ omega ] of the instantaneous angular velocity at time jj]j+kIs j + K (K e [ -K., K.) before and after time j]) The result of the co-action of the probability density functions at the time of day.
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