CN115795295A - Rotating machinery characteristic frequency enhancement extraction method based on optimal weighted envelope spectrum - Google Patents
Rotating machinery characteristic frequency enhancement extraction method based on optimal weighted envelope spectrum Download PDFInfo
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Abstract
The invention discloses a rotating machinery characteristic frequency enhancement extraction method based on an optimal weighted envelope spectrum, which comprises the following steps: (1) Collecting vibration or noise data of the rotating machine as a monitoring signal, and calculating a spectrum correlation function; (2) Normalizing the spectrum correlation function to construct an enhanced envelope spectrum; (3) determining a basic modulation frequency; (4) Slicing the spectrum correlation function, and estimating a carrier-to-noise ratio; (5) Constructing a cyclostationary measurement function of the fundamental modulation frequency and harmonic components thereof; (6) Taking the carrier-to-noise ratio as an initial weighting function, and searching by using a cuckoo optimization algorithm to obtain an optimal weighting function; (7) Carrying out weighting processing on the spectrum correlation function by using the optimal weighting function to obtain optimal weighting spectrum correlation; (8) And integrating the optimal weighted spectrum correlation along a spectrum frequency axis to obtain an optimal weighted envelope spectrum. The invention can effectively extract the modulation frequency component in the vibration noise signal of the rotary machine under the complex and strong noise interference.
Description
Technical Field
The invention belongs to the field of signal processing, and particularly relates to a rotating machinery characteristic frequency enhancement extraction method based on an optimal weighted envelope spectrum.
Background
The rotating machinery is widely applied to the fields of industrial production, water conservancy and hydropower, military application and the like, and the extraction of the characteristic frequency of the rotating machinery is beneficial to realizing the state monitoring and fault diagnosis of key rotating machinery equipment. The characteristic frequency extraction method mainly comprises spectrum analysis and demodulation analysis.
The main implementation of spectral analysis is fourier transformation, which can map the amplitude and phase of different frequency signal components. For example, chinese patent publication No. CN112633098A discloses a fault diagnosis method for a rotary machine, which performs spectrum analysis on a vibration signal of a rotary machine to be measured, which is acquired in real time, by using a short-time fourier transform method to obtain a spectrogram of the vibration signal.
The frequency spectrum analysis can completely describe the frequency distribution of a deterministic signal, but is not suitable for the analysis of a random signal, and the rotating mechanical vibration noise signal in practice is basically a random signal, which limits the universal applicability of the frequency spectrum analysis.
Demodulation analysis is another effective way for extracting the characteristic frequency of the rotating machinery, and comprises signal processing methods such as narrow-band envelope demodulation and cyclostationary analysis. For example, chinese patent publication No. CN104596756A discloses a multiband envelope spectrum array for fault diagnosis of rotating machinery.
The narrow-band envelope demodulation firstly locates the optimal filtering frequency band containing the modulation signal, carries out filtering operation on the frequency band to obtain a filtering signal, then constructs the envelope curve of the filtering signal through Hilbert transform, and finally carries out Fourier transform on the envelope curve to obtain an envelope spectrum. The method is suitable for local defect flaw detection and weak fault diagnosis of the rotary machine, and has the defects that the narrow-band envelope demodulation only selects a specific narrow band for analysis, the algorithm robustness is poor, and the method is easy to fail particularly under the condition of low signal-to-noise ratio containing various types of noise, so that the method is limited to a certain extent.
The cyclostationary analysis can fully utilize cyclostationary components in monitoring signals of the rotary machine to effectively extract modulation frequency components, but the method is limited in the application occasion of extracting the characteristic frequency of the rotary machine, mainly because the monitoring signals usually contain cyclostationary noise interference from other mechanical, electrical and communication equipment besides the characteristic modulation frequency caused by fault phenomena and key components, and the traditional cyclostationary analysis can not remove the noise interference, thereby influencing the identification and extraction of the characteristic frequency of the rotary machine.
Disclosure of Invention
The invention provides a rotating machinery characteristic frequency enhancement extraction method based on an optimal weighted envelope spectrum, which can effectively extract modulation frequency components in a rotating machinery vibration noise signal under complex and strong noise interference and can be applied to the fields of state monitoring, fault diagnosis and the like of rotating machinery.
A rotating machinery characteristic frequency enhancement extraction method based on an optimal weighted envelope spectrum comprises the following steps:
(1) Collecting vibration or noise data of the rotary machine as a monitoring signal, and calculating a spectrum correlation function of the monitoring signal;
(2) Normalizing the spectrum correlation function to obtain a spectrum coherence function, and constructing an enhanced envelope spectrum;
(3) Determining a basic modulation frequency according to prior information and a diagnosis task of the rotating machine and characteristic information of the enhanced envelope spectrum;
(4) Slicing the spectrum correlation function at the zero modulation frequency and the basic modulation frequency, and estimating a carrier-to-noise ratio according to a slicing result;
(5) Giving a definition of a weighted spectrum correlation function, constructing a cyclostationary measurement function of the basic modulation frequency and harmonic components thereof from the definition, and taking the cyclostationary measurement function as a target function;
(6) Setting a search space of an optimal weighting function by taking the carrier-to-noise ratio as an initial weighting function, and searching by using a cuckoo optimization algorithm to obtain the optimal weighting function which enables the target function to be maximum;
(7) Carrying out weighting processing on the spectrum correlation function by using the optimal weighting function, and calculating to obtain optimal weighting spectrum correlation;
(8) And integrating the optimal weighted spectrum correlation along a spectrum frequency axis to obtain an optimal weighted envelope spectrum.
The method can overcome the defects that the conventional frequency spectrum analysis and demodulation method cannot accurately and effectively extract the modulation frequency of the rotary machine or the extraction result contains excessive noise interference, has high noise immunity and strong robustness, and can effectively realize the enhanced extraction of the characteristic frequency of the rotary machine under the conditions of low signal-to-noise ratio and complex noise interference.
In the step (1), the specific process of calculating the spectrum correlation function of the monitoring signal is as follows:
(1-1) calculating two narrow-band filtered signals x of the monitor signal x (t) Δf (t；f 1 ) And x Δf (t；f 2 ) Coefficient of correlation between corr x (f 1 ,f 2 ) The calculation formula is as follows:
wherein t represents time, f represents frequency 1 ≥f 2 E is a natural constant, j is an imaginary symbol, i is a conjugate symbol, -T/2 and T/2 are a time lower limit and a time upper limit, Δ f represents the filtering range of the narrow-band filtering signal, x Δf (t；f 1 ) And x Δf (t；f 2 ) Each represents (f) 1 -Δf/2,f 1 + Δ f/2) and (f) 2 -Δf/2,f 2 + Δ f/2) is a narrow band filtered time domain signal in the band pass range;
(1-2) suppose f = (f) 1 +f 2 )/2，α＝f 1 -f 2 Then, a spectral correlation function of the monitoring signal can be obtained, and the calculation formula is as follows:
in the formula, S x And (alpha, f) is a spectrum correlation function, alpha is a modulation frequency, and f is a carrier frequency.
The specific process of the step (2) is as follows:
(2-1) normalizing the spectral correlation function of the monitoring signal to obtain the spectral correlation function gamma of the monitoring signal x (α, f), the calculation formula is as follows:
in the formula (I), the compound is shown in the specification,
representing the result when the modulation frequency of the spectral correlation function is zero, i.e. having
(2-2) integrating the spectrum coherence function along the carrier frequency axis direction, thereby calculating and obtaining an enhanced envelope spectrum EES of the monitoring signal x (α), the calculation formula is as follows:
in the formula (f) 1 And f 2 Lower and upper limits for carrier frequency integration, with default values of 0 and F s /2，F s To monitor the sampling frequency of the signal.
The specific process of the step (3) is as follows:
(3-1) determining the faulty component to be diagnosed of the rotating machine according to the prior information, and then determining the theoretical fundamental modulation frequency alpha according to the corresponding fault mechanism B-T ；
(3-2) since the values of the modulation frequency of the emphasis envelope spectrum are all integer multiples of the modulation frequency resolution delta alpha, the EES of the emphasis envelope spectrum x (alpha) obtaining and theoretically rotating machinery basic modulation frequency alpha B-T Closest modulation frequency value alpha opt = M Δ α, M is some positive integer;
(3-3) modulating the frequency range [ alpha ] opt -NΔα,α opt +NΔα]Determining an alternative range of the basic modulation frequency, wherein N is a positive integer; selecting the modulation frequency corresponding to the maximum value of the amplitude of the enhancement envelope spectrum from the candidate range, and determining the modulation frequency as the basic modulation frequency alpha B 。
The specific process of the step (4) is as follows:
(4-1) a definition of a carrier-to-noise ratio, which is defined as a ratio of a carrier power spectral density of the second-order cyclostationary component to a stationary noise power spectral density, is given:
in the formula, CNR (f) represents a carrier-to-noise ratio, P v (f) The power spectral density of the carrier signal v (t) representing the second order cyclostationary component contained in the monitoring signal,
n representing stationary noise contained in the monitoring signal s (t) power spectral density;
(4-2) for a signal containing a second order cyclostationary component and stationary noise:
in the formula (I), the compound is shown in the specification,
a modulation signal representing the second order cyclostationary component, v (t) a carrier signal representing the second order cyclostationary component, n s (t) represents stationary noise; the spectrum correlation theoretical value is as follows:
in the formula, δ (·) represents a kronecker function, which satisfies:
by spectral correlation at α =0 and α = α B The value of (b) estimates the power spectral density of stationary noise:
(4-3) A definition of a second order cyclostationary signal-to-noise ratio, which is defined as a ratio of a spectral correlation absolute value of the monitoring signal to a stationary noise power spectral density, is given:
wherein SNR is CS2 (α, f) represents the second order cyclostationary signal-to-noise ratio;
(4-4) cyclostationary signal-to-noise ratio at α = α by the second order B The values of (b) to estimate the carrier-to-noise ratio:
as can be seen from the above equation, SNR CS2 (α B F) carrier-to-noise ratio approximately equal to a number of weighted frequency shifts
Sum of superpositions, which addsThe weight factor is
The amount of frequency shift is
The frequency shift is obviously smaller than the carrier frequency range, and the carrier distribution estimation is not obviously influenced, so that the second-order cyclostationary signal-to-noise ratio is in the range of alpha = alpha B The values of (b) can describe the carrier to noise ratio distribution.
The specific process of the step (5) is as follows:
(5-1) definition of the weighted envelope spectrum:
in the formula (I), the compound is shown in the specification,
represents a weighted envelope spectrum, w (f) represents a weighting function;
(5-2) determining the alternative range of the cycle frequency corresponding to the basic modulation frequency and the harmonic component thereof as follows:
FB k ＝[kα B -mΔα,kα B +mΔα]
in the formula, FB k Representing a cycle frequency alternative range corresponding to the kth harmonic of the basic modulation frequency, wherein m delta alpha represents a single-side alternative limit;
(5-3) acquiring a corresponding characteristic modulation frequency peak from the weighted envelope spectrum, wherein the calculation formula is as follows:
in the formula, m k The amplitude of the k-th harmonic of the fundamental modulation frequency,
is shown in FB k Taking the maximum value;
(5-4) assume that the cycle frequency range under consideration is (0, α) max ) Within this range, the highest order harmonic of the fundamental modulation frequency is k max The maximum number of the cycle frequency is n max (ii) a On the basis, an objective function for measuring the magnitude of the cyclostationarity is defined as:
the specific process of the step (6) is as follows:
(6-1) regarding the process of obtaining the optimal weighting function as an optimization problem, and making the carrier-to-noise ratio as the initial weighting function:
in the formula, w b ∈R 1×d A weighting function representing a vector form;
(6-2) setting a search range of the optimal weighting function:
in the formula, w L And w U Respectively represent a lower limit weighting function and an upper limit weighting function, X% represents the unilateral fluctuation percentage of the weighting function, namely:
and (6-3) searching by using a cuckoo optimization algorithm to obtain an optimal weighting function which maximizes the objective function.
In step (7), the formula for obtaining the optimal weighted spectrum correlation by calculation is as follows:
in the formula, w opt (f) In order to optimize the weighting function,
representing the optimal weighted spectral correlation.
In the step (8), the formula for obtaining the optimal weighted envelope spectrum is as follows:
in the formula (I), the compound is shown in the specification,
is an optimal weighted envelope spectrum.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention provides a method for estimating the carrier-to-noise ratio of a monitoring signal by using a spectrum correlation function, which can roughly capture the carrier frequency range corresponding to a modulation signal component.
2. The invention regards the acquisition of the optimal weighting function as an optimization problem, and adopts the cuckoo optimization algorithm to carry out optimization, and the method can effectively acquire the optimal weighting function.
3. The method provided by the invention is used for demodulating signals based on cyclostationary analysis and spectral correlation weighting processing, can accurately and effectively extract the characteristic modulation frequency components of the rotary machine, and the related information can be used for state monitoring and fault diagnosis of the rotary machine.
Drawings
FIG. 1 is a schematic flow chart of a rotating machine characteristic frequency enhancement extraction method based on an optimal weighted envelope spectrum according to the present invention;
FIG. 2 is a time domain diagram of a simulated signal containing Gaussian noise, impulsive noise, and cyclostationary noise in an embodiment of the present invention;
FIG. 3 is a diagram illustrating a narrow-band demodulation result of a kurtosis spectrum of an artificial signal according to an embodiment of the present invention;
FIG. 4 is a cyclostationary analysis demodulation result of an emulation signal in an embodiment of the present invention;
FIG. 5 is a diagram of an optimal weighted spectral correlation result of a simulation signal according to an embodiment of the present invention;
FIG. 6 shows the optimal weighted envelope spectrum demodulation result of the simulation signal according to the embodiment of the present invention;
FIG. 7 is a narrow-band demodulation result of the kurtosis spectrum of the acoustic signal of the rolling bearing in the embodiment of the present invention;
FIG. 8 shows the cyclostationary analysis demodulation results of the acoustic signals of the rolling bearing according to the embodiment of the present invention;
FIG. 9 shows the optimal weighted envelope spectrum demodulation result of the rolling bearing acoustic signal in the embodiment of the present invention;
FIG. 10 is a narrow band demodulation result of a kurtosis spectrum of a vibration signal of a centrifugal pump in an embodiment of the invention;
FIG. 11 is a result of cyclostationary analysis demodulation of a centrifugal pump vibration signal in an embodiment of the present invention;
FIG. 12 shows the optimal weighted envelope spectrum demodulation result of the vibration signal of the centrifugal pump in the embodiment of the invention.
Detailed Description
The invention will be described in further detail below with reference to the drawings and examples, which are intended to facilitate the understanding of the invention without limiting it in any way.
As shown in fig. 1, a method for extracting a rotating machine feature frequency enhancement based on an optimal weighted envelope spectrum includes the following steps:
and S01, collecting vibration or noise data of the rotary machine as a monitoring signal, and calculating a spectrum correlation function of the monitoring signal.
(1-1) calculating two narrow-band filtered signals x of the monitoring signal x (t) Δf (t；f 1 ) And x Δf (t；f 2 ) (wherein f is defined) 1 ≥f 2 ) Coefficient of correlation between corr x (f 1 ,f 2 ) The calculation formula is as follows:
in the formula, T represents time, f represents frequency, e is a natural constant, j is an imaginary symbol, is a conjugate symbol, -T/2 and T/2 are a time lower limit and a time upper limit, Δ f represents the filtering range size of the narrow-band filtering signal, and x Δf (t；f 1 ) And x Δf (t；f 2 ) Each represents (f) 1 -Δf/2,f 1 + Δ f/2) and (f) 2 -Δf/2,f 2 + Δ f/2) is a narrow band filtered time domain signal in the band pass range.
(1-2) suppose f = (f) 1 +f 2 )/2，α＝f 1 -f 2 Then, a spectrum correlation function of the monitoring signal can be obtained, and the calculation formula is as follows:
in the formula, S x (α, f) is the spectral correlation function, α is the cycle frequency (also called modulation frequency) and f is the spectral frequency (also called carrier frequency, or simply frequency).
S02, normalizing the spectrum correlation function to obtain a spectrum coherence function, and constructing an enhanced envelope spectrum.
(2-1) normalizing the spectral correlation function of the monitoring signal to obtain the spectral correlation function gamma of the monitoring signal x (α, f), the calculation formula is as follows:
in the formula (I), the compound is shown in the specification,
representing the result when the modulation frequency of the spectral correlation function is zero, i.e. having
(2-2) integrating the spectrum coherence function along the carrier frequency axis direction, thereby calculating and obtaining an enhanced envelope spectrum EES of the monitoring signal x (α), the calculation formula is as follows:
in the formula (f) 1 And f 2 Lower and upper limits for carrier frequency integration, with default values of typically 0 and F s /2，F s To monitor the sampling frequency of the signal.
And S03, determining the basic modulation frequency according to the prior information and the diagnosis task of the rotary machine and the characteristic information of the enhanced envelope spectrum.
(3-1) determining a fault component to be diagnosed of the rotary machine according to the prior information, and then determining theoretical basic modulation frequency alpha according to a corresponding fault mechanism B-T ；
(3-2) since the values of the modulation frequency of the emphasis envelope spectrum are all integer multiples of the modulation frequency resolution delta alpha, the EES of the emphasis envelope spectrum x (alpha) obtaining and theoretically rotating machinery basic modulation frequency alpha B-T Closest modulation frequency value alpha opt = M Δ α (M is some positive integer);
(3-3) modulating the frequency range [ alpha ] opt -NΔα,α opt +NΔα](N is positive integer) is determined as the alternative range of the basic modulation frequency, the corresponding modulation frequency when the amplitude value of the enhanced envelope spectrum is maximum is selected from the alternative range, and the modulation frequency is determined as the basic modulation frequency alpha B 。
And S04, carrying out slicing processing on the spectrum correlation function at the zero modulation frequency and the basic modulation frequency, and estimating the carrier-to-noise ratio according to a slicing result.
(4-1) a definition of a carrier-to-noise ratio, which is defined as a ratio of a carrier power spectral density of the second-order cyclostationary component to a stationary noise power spectral density, is given:
wherein CNR (f) represents a carrier-to-noise ratio, P v (f) The power spectral density of the carrier signal v (t) representing the second order cyclostationary component contained in the monitoring signal,
representing stationary noise n contained in the monitoring signal s (t) power spectral density.
(4-2) for a signal containing a second order cyclostationary component and stationary noise:
in the formula (I), the compound is shown in the specification,
a modulation signal representing the second order cyclostationary component, v (t) a carrier signal representing the second order cyclostationary component, n s (t) represents stationary noise. The spectrum correlation theoretical value is as follows:
in the formula, δ (·) represents a kronecker function, which satisfies:
by spectral correlation at α =0 and α = α B To roughly estimate the power spectral density of stationary noise:
(4-3) giving a definition of a second-order cyclostationary signal-to-noise ratio, which is defined as a ratio of a spectrally-correlated absolute value of the monitoring signal to a stationary noise power spectral density:
wherein SNR is CS2 And (alpha, f) represents a second order cyclostationary signal-to-noise ratio.
(4-4) cyclostationary signal-to-noise ratio at α = α by the second order B The values of (b) to roughly estimate the carrier-to-noise ratio:
as can be seen from the above equation, SNR CS2 (α B F) approximately equal to the carrier-to-noise ratio after a number of weighted frequency shifts
Sum of the superpositions with a weighting factor of
The amount of frequency shift is
(generally the amount of frequency shift is significantly smaller than the carrier frequency range and does not significantly affect the carrier distribution estimation). It follows that the second order cyclostationary signal-to-noise ratio is at α = α B The values of (b) can describe the carrier to noise ratio distribution.
And S05, defining a weighted spectrum correlation function, constructing a cyclostationarity measurement function of the basic modulation frequency and harmonic components thereof from the weighted spectrum correlation function, and regarding the cyclostationarity measurement function as a target function.
(5-1) definition of the weighted envelope spectrum:
in the formula (I), the compound is shown in the specification,
representing the weighting envelope spectrum and w (f) the weighting function.
(5-2) determining alternative ranges of the cycle frequency corresponding to the basic modulation frequency and harmonic components thereof as follows:
FB k ＝[kα B -mΔα,kα B +mΔα]
in the formula, FB k Representing the range of cyclic frequency candidates corresponding to the kth harmonic of the fundamental modulation frequency, and m Δ α represents a single-sided candidate limit.
(5-3) acquiring a corresponding characteristic modulation frequency peak from the weighted envelope spectrum, wherein the calculation formula is as follows:
in the formula, m k The amplitude of the k-th harmonic of the fundamental modulation frequency,
is shown in FB k The maximum value is taken.
(5-4) assume that the cycle frequency range under consideration is (0, α) max ) Within this range, the highest order harmonic of the fundamental modulation frequency is k max The maximum number of the cycle frequency is n max . On the basis, an objective function for measuring the magnitude of the cyclostationarity is defined as:
and S06, setting a search space of the optimal weighting function by taking the carrier-to-noise ratio as an initial weighting function, and searching by using a cuckoo optimization algorithm to obtain the optimal weighting function which maximizes the target function.
(6-1) regarding the process of obtaining the optimal weighting function as an optimization problem, making the carrier-to-noise ratio as the initial value of the weighting function:
in the formula, w b ∈R 1×d Representing a weighting function in the form of a vector.
(6-2) setting a search range of the optimal weighting function:
in the formula, w L And w U Respectively represents a lower limit weighting function and an upper limit weighting function, and X% represents the unilateral fluctuation percentage of the weighting function, namely:
and (6-3) searching to obtain an optimal weighting function by using a cuckoo optimization algorithm. The cuckoo algorithm comprises large-span exploratory walking and small-span random walking.
Large-span exploratory walking is achieved by levy flight:
in the formula (I), the compound is shown in the specification,
respectively represents the value of the ith solution of the cuckoo algorithm after the t iteration and the t +1 iteration, and alpha is more than 0 represents the stepThe long scaling factor, s represents the iteration step size, and Γ (λ) represents the gamma function.
The small-span random walk is realized by the following formula:
in the formula (I), the compound is shown in the specification,
represents a scalar multiplication to be performed on the basis of,
and
two different solutions representing the optimization problem, H (-) representing the Havesedard function, ε i Representative solution
Percentage ranking of all solutions at the t-th iteration (in terms of solutions)
The corresponding objective functions are ranked, the larger the objective function is, epsilon i The smaller).
The process of using the cuckoo optimization algorithm to search for the optimal weighting function is summarized as follows:
and S07, carrying out weighting processing on the spectrum correlation function by using the optimal weighting function, and calculating to obtain the optimal weighting spectrum correlation.
The calculation process for obtaining the optimal weighted spectrum correlation is as follows:
in the formula, w opt (f) In order to optimize the weighting function for the particular application,
representing the optimal weighted spectral correlation.
And S08, integrating the optimal weighted spectrum correlation along a spectrum frequency axis to obtain an optimal weighted envelope spectrum.
The calculation process for obtaining the optimal weighted envelope spectrum comprises the following steps:
in the formula (I), the compound is shown in the specification,
is an optimal weighted envelope spectrum.
In order to verify the effectiveness of the invention, the simulation signal containing Gaussian noise, impact noise and cyclostationary noise is analyzed, and the method specifically comprises the following steps:
the simulation signal x (t) containing Gaussian noise and impact noise is analyzed by the method:
in the formula, n p (t) and n s (t) represents impulsive noise and white gaussian noise, respectively. The parameter settings of the simulated signal are as follows:
the simulated signal is shown in fig. 2, where the modulated signal is completely drowned out by the background noise. Kurtosis spectrum narrow-band demodulation result and cyclostationarity analysis demodulation of simulation signalThe results are shown in fig. 3 and 4, respectively. It can be seen that although the fundamental modulation frequency α is B And its harmonics are extracted, but its demodulation result also contains a lot of white gaussian noise and significant cyclostationary noise interference.
The optimal weighted spectrum correlation and the optimal weighted envelope spectrum corresponding to the simulation signal are respectively shown in fig. 5 and fig. 6, in the optimal weighted spectrum correlation, two carrier frequencies positioned at 2500-7500Hz and 12500-17500Hz are effectively captured, and in the optimal weighted envelope spectrum, the basic modulation frequency alpha is B And its harmonics are clearly prominent and essentially free of other noise, indicating that the modulation frequency is effectively extracted. The results prove that the optimal weighted envelope spectrum provided by the invention can effectively and accurately extract and represent modulation frequency components under the common interference of complex and strong noises such as Gaussian noise, impact noise, cyclostationary noise and the like.
The acoustic signals of the rolling bearing (outer ring pitting failure) are analyzed by the method, and the traditional kurtosis spectrum demodulation result, the cyclostationary analysis demodulation result and the optimal weighted envelope spectrum result provided by the invention are respectively shown in figures 7 to 9. Due to the fact that excitation sources of noise signals of the rolling bearing are various, interference noise is large, transmission paths are complex, the signal to noise ratio is low, outer ring pitting modulation frequency is difficult to extract through traditional methods such as kurtosis spectrum analysis, interference components such as motor shaft frequency and harmonic waves of the motor shaft frequency are only extracted through analysis results, and the pitting failure frequency of the outer ring of the bearing can be extracted through circulation and stability analysis, but a large number of interference components such as the motor shaft frequency and the harmonic waves of the motor shaft frequency are also included. In the optimal weighted envelope spectrum, although a small amount of interference components such as motor shaft frequency and harmonic waves thereof are still contained, the outer ring pitting modulation frequency is effectively extracted and is clear and distinguishable. The results prove that when rolling bearing noise signals containing strong and complex noises are processed, the optimal weighted envelope spectrum provided by the invention can effectively and accurately extract and characterize characteristic frequency components.
The vibration signals of the centrifugal pump (in a cavitation state) are analyzed by the method, and the traditional kurtosis spectrum demodulation result, the cyclostationary analysis demodulation result and the optimal weighted envelope spectrum result provided by the invention are respectively shown in figures 10-12. Due to the fact that excitation sources of vibration signals of the centrifugal pump are various, interference noise is large, transmission paths are complex, the signal-to-noise ratio is extremely low, characteristic frequency components such as rotor frequency and blade passing frequency are difficult to analyze and extract through a kurtosis spectrum, and analysis results of the centrifugal pump basically only include background interference. The cyclostationary analysis can effectively extract characteristic frequency components such as rotor frequency and blade passing frequency, but also comprises a large amount of background interference components. In the optimal weighted envelope spectrum, characteristic frequency components such as rotor frequency, blade passing frequency and the like are effectively extracted and are clear and recognizable, and background noise is suppressed to a low level. The results prove that when the vibration signal of the centrifugal pump containing strong and complex noise is processed, the optimal weighted envelope spectrum provided by the invention can effectively and accurately extract and characterize characteristic frequency components.
The embodiments described above are intended to illustrate the technical solutions and advantages of the present invention, and it should be understood that the above-mentioned embodiments are only specific embodiments of the present invention, and are not intended to limit the present invention, and any modifications, additions and equivalents made within the scope of the principles of the present invention should be included in the scope of the present invention.
Claims (9)
1. A rotating machinery characteristic frequency enhancement extraction method based on an optimal weighted envelope spectrum is characterized by comprising the following steps:
(1) Collecting vibration or noise data of the rotary machine as a monitoring signal, and calculating a spectrum correlation function of the monitoring signal;
(2) Normalizing the spectrum correlation function to obtain a spectrum coherence function, and constructing an enhanced envelope spectrum;
(3) Determining basic modulation frequency according to prior information and a diagnosis task of the rotary machine and characteristic information of the enhanced envelope spectrum;
(4) Slicing the spectrum correlation function at the zero modulation frequency and the basic modulation frequency, and estimating a carrier-to-noise ratio according to a slicing result;
(5) Giving a definition of a weighted spectrum correlation function, constructing a cyclostationary measurement function of the basic modulation frequency and harmonic components thereof from the definition, and taking the cyclostationary measurement function as a target function;
(6) Setting a search space of an optimal weighting function by taking the carrier-to-noise ratio as an initial weighting function, and searching by using a cuckoo optimization algorithm to obtain the optimal weighting function which enables the target function to be maximum;
(7) Carrying out weighting processing on the spectrum correlation function by using the optimal weighting function, and calculating to obtain optimal weighting spectrum correlation;
(8) And integrating the optimal weighted spectrum correlation along a spectrum frequency axis to obtain an optimal weighted envelope spectrum.
2. The rotating machinery feature frequency enhancement extraction method based on the optimal weighted envelope spectrum according to claim 1, wherein in the step (1), the specific process of calculating the spectral correlation function of the monitoring signal is as follows:
(1-1) calculating two narrow-band filtered signals x of the monitoring signal x (t) Δf (t；f 1 ) And x Δf (t；f 2 ) Coefficient of correlation between corr x (f 1 ，f 2 ) The calculation formula is as follows:
wherein t represents time, f represents frequency, f 1 ≥f 2 E is a natural constant, j is an imaginary symbol, i is a conjugate symbol, -T/2 and T/2 are a time lower limit and a time upper limit, Δ f represents the filtering range of the narrow-band filtering signal, x Δf (t；f 1 ) And x Δf (t；f 2 ) Respectively represent (f) 1 -Δf/2，f 1 + Δ f/2) and (f) 2 -Δf/2，f 2 + Δ f/2) is a narrow-band filtered time domain signal of the band-pass range;
(1-2) suppose f = (f) 1 +f 2 )/2，α＝f 1 -f 2 Then, a spectral correlation function of the monitoring signal can be obtained, and the calculation formula is as follows:
in the formula, S x And (alpha, f) is a spectrum correlation function, alpha is a modulation frequency, and f is a carrier frequency.
3. The rotating machinery feature frequency enhancement extraction method based on the optimal weighted envelope spectrum according to claim 2, wherein the specific process of the step (2) is as follows:
(2-1) normalizing the spectral correlation function of the monitoring signal to obtain a spectral correlation function gamma of the monitoring signal x (α, f), the calculation formula is as follows:
in the formula (I), the compound is shown in the specification,
representing the result when the modulation frequency of the spectral correlation function is zero, i.e. having
(2-2) integrating the spectrum coherence function along the direction of the carrier frequency axis, thereby calculating and obtaining an Enhanced Envelope Spectrum (EES) of the monitoring signal x (α), the calculation formula is as follows:
in the formula, f 1 And f 2 Lower and upper limits for carrier frequency integration, with default values of 0 and F s /2，F s To monitor the sampling frequency of the signal.
4. The rotating machinery feature frequency enhancement extraction method based on the optimal weighted envelope spectrum according to claim 3, wherein the specific process of the step (3) is as follows:
(3-1) determining a fault component to be diagnosed of the rotary machine according to the prior information, and then determining theoretical basic modulation frequency alpha according to a corresponding fault mechanism B-T ；
(3-2) since the values of the modulation frequency of the emphasis envelope spectrum are all integer multiples of the modulation frequency resolution delta alpha, the EES of the emphasis envelope spectrum x (alpha) obtaining and theoretically rotating machinery basic modulation frequency alpha B-T Closest modulation frequency value alpha opt = M Δ α, M is some positive integer;
(3-3) modulating the frequency range [ alpha ] opt -NΔα，α opt +NΔα]Determining an alternative range of the basic modulation frequency, wherein N is a positive integer; selecting the modulation frequency corresponding to the maximum value of the amplitude of the emphasis envelope spectrum from the candidate range, and determining the modulation frequency as the basic modulation frequency alpha B 。
5. The rotating machinery feature frequency enhancement extraction method based on the optimal weighted envelope spectrum according to claim 4, wherein the specific process of the step (4) is as follows:
(4-1) a definition of a carrier-to-noise ratio, which is defined as a ratio of a carrier power spectral density of the second-order cyclostationary component to a stationary noise power spectral density, is given:
wherein CNR (f) represents a carrier-to-noise ratio, P v (f) The power spectral density of the carrier signal v (t) representing the second order cyclostationary component contained in the monitored signal,
n representing stationary noise contained in the monitoring signal s (t) power spectral density;
(4-2) for a signal containing a second order cyclostationary component and stationary noise:
in the formula (I), the compound is shown in the specification,
a modulation signal representing the second order cyclostationary component, v (t) a carrier signal representing the second order cyclostationary component, n s (t) represents stationary noise; the spectrum correlation theoretical value is as follows:
in the formula, δ (·) represents a kronecker function, which satisfies:
by spectral correlation at α =0 and α = α B The value of (b) estimates the power spectral density of stationary noise:
(4-3) A definition of a second order cyclostationary signal-to-noise ratio, which is defined as a ratio of a spectral correlation absolute value of the monitoring signal to a stationary noise power spectral density, is given:
wherein SNR is CS2 (α, f) represents the second order cyclostationary signal-to-noise ratio;
(4-4) cyclostationary signal-to-noise ratio at α = α by the second order B The values of (b) to estimate the carrier-to-noise ratio:
as can be seen from the above equation, SNR CS2 (α B F) carrier-to-noise ratio approximately equal to a number of weighted frequency shifts
Sum of the superpositions with a weighting factor of
The amount of frequency shift is
The frequency shift is obviously smaller than the carrier frequency range, and the carrier distribution estimation is not obviously influenced, so that the second-order cyclostationary signal-to-noise ratio is in the range of alpha = alpha B The values of (b) can describe the carrier to noise ratio distribution.
6. The rotating machinery feature frequency enhancement extraction method based on the optimal weighted envelope spectrum according to claim 5, wherein the specific process of the step (5) is as follows:
(5-1) definition of the weighted envelope spectrum:
in the formula (I), the compound is shown in the specification,
represents a weighted envelope spectrum, w (f) represents a weighting function;
(5-2) determining the alternative range of the cycle frequency corresponding to the basic modulation frequency and the harmonic component thereof as follows:
FB k ＝[kα B -mΔα，kα B +mΔα]
in the formula, FB k Representing a cycle frequency alternative range corresponding to the kth harmonic of the basic modulation frequency, wherein m delta alpha represents a single-side alternative limit;
(5-3) acquiring a corresponding characteristic modulation frequency peak from the weighted envelope spectrum, wherein the calculation formula is as follows:
in the formula, m k The amplitude of the k-th harmonic of the fundamental modulation frequency,
is shown in FB k Taking the maximum value;
(5-4) assume that the cycle frequency range under consideration is (0, α) max ) Within this range, the highest order harmonic of the fundamental modulation frequency is k max The maximum number of the cycle frequency is n max (ii) a On this basis, the objective function to measure the magnitude of cyclostationarity is defined as:
7. the rotating machinery feature frequency enhancement extraction method based on the optimal weighted envelope spectrum according to claim 6, wherein the specific process of the step (6) is as follows:
(6-1) regarding the process of obtaining the optimal weighting function as an optimization problem, making the carrier-to-noise ratio as the initial weighting function:
in the formula, w b ∈R 1×d A weighting function representing a vector form;
(6-2) setting a search range of the optimal weighting function:
in the formula, w L And w U Respectively represents a lower limit weighting function and an upper limit weighting function, and X% represents the unilateral fluctuation percentage of the weighting function, namely:
and (6-3) searching by using a cuckoo optimization algorithm and a cuckoo optimization algorithm to obtain an optimal weighting function which maximizes the objective function.
8. The rotating machine feature frequency enhancement extraction method based on the optimal weighted envelope spectrum as claimed in claim 7, wherein in the step (7), the formula related to the optimal weighted spectrum is calculated as:
in the formula, w opt (f) In order to optimize the weighting function,
representing the optimal weighted spectral correlation.
9. The method for enhancing and extracting the characteristic frequency of the rotating machinery based on the optimal weighted envelope spectrum as claimed in claim 8, wherein in the step (8), the formula for obtaining the optimal weighted envelope spectrum is as follows:
in the formula (I), the compound is shown in the specification,
is an optimal weighted envelope spectrum.
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