CN102269644B - Diagnosis method for impact type failure between rolling bearing and gear based on optimal self-adaptive wavelet filter - Google Patents

Abstract

The invention relates to a diagnosis method for impact type failure between a rolling bearing and a gear based on an optimal self-adaptive wavelet filter, which comprises the following steps: firstly establishing an exponentially damped sinusoidal impact type failure signal model, using a mode self-adaptive wavelet generation algorithm publicly disclosed by Hector Mesa to generate a self-adaptive wavelet filter which is matched with the signal model, then utilizing a fast FIR (finite impulse response) filtering algorithm to execute the wavelet filter to obtain the filtering result, then calculating the kurtosis value of the filtering result, and using an evolution differential algorithm to repeat the steps so as to finally obtain an optimized envelope spectrum. By adopting the method, impact failure characteristics in vibration signals can be precisely extracted, and a clearer envelope spectrum can be given out, thereby ensuring that failure symptoms can be displayed more clearly.

Description

Rolling bearing based on optimum adaptive wavelet wave filter and gear impact method for diagnosing faults

Technical field

The invention belongs to field of diagnosis about equipment fault, especially, relate to a kind of rolling bearing and gear impact method for diagnosing faults based on optimum adaptive wavelet wave filter.

Background technology

At field of diagnosis about equipment fault, because rolling bearing and gear are very generally to use and very important parts, and the two is all to hold most one of flimsy part in mechanized equipment, so being carried out to condition monitoring and fault diagnosis, the two there is great engineering significance.When rolling bearing and gear exist defect, impaired loci can produce periodic impact while contact with other element.How from vibration acceleration signal, effectively extracting shock characteristic, is the key issue that rolling bearing and gear defects position and the extent of damage are passed judgment on.

Traditional rolling bearing and gear failure diagnosing method have spectrum analysis, envelope demodulation and time frequency analysis etc.But spectrum analysis need to be used more orthogonal simple harmonic quantity trigonometric function impact signal to approach, unless damage of the bearing is serious, fault signature is very obvious, otherwise for rolling bearing and the Gearbox vibration signal of complicated component, its fault shock characteristic is usually flooded by ground unrest and other signal contents in frequency spectrum.Envelope demodulation is a kind of effectively rolling bearing and gear failure diagnosing method, but envelope demodulation first all will be carried out bandpass filtering or high-pass filtering to vibration signal; How reasonably to select relevant parameters for different units, different operating mode, be the difficult problem in engineering, and field engineering personnel are often difficult to grasp main points are set, and each concrete versatility arranging all has problems.In addition, time frequency analysis, such as Wigner branch, EMD-HHT etc., also has the diagnosis of report for rolling bearing and gear impact fault, but these methods exist, calculated amount is large, parameter is selected difficulty and the more difficult problems such as Real-Time Monitoring that realize.Meanwhile, these methods also need engineering staff to have more advanced signal processing knowledge, and it is more difficult that this makes it be applied in engineering practice equally.

Summary of the invention

The object of the invention is to, rolling bearing and gear impact method for diagnosing faults based on optimum adaptive wavelet wave filter have been proposed, by vibration signals measured is carried out carrying out suitable filtering according to the sef-adapting filter after the highest optimization of kurtosis, realize the impulse fault feature in vibration signal is extracted accurately.Its process is without human intervention, and can provide more clearly envelope spectrum, thereby more clearly demonstrates failure symptom.

Concrete technical scheme is as follows:

Rolling bearing based on optimum adaptive wavelet wave filter and a gear impact method for diagnosing faults, is characterized in that comprising the following steps:

(1) set up the impact fault-signal model based on index attenuation sine, then apply the adaptive wavelet wave filter that mode adaptive small echo generating algorithm generates and this signal model matches that Hector Mesa publishes;

(2) utilize quick FIR filtering algorithm to carry out described adaptive wavelet wave filter, the acceleration vibration signal of rolling bearing or gear is carried out to filtering and obtain filtering result;

(3) kurtosis value of filtering result described in calculation procedure (2);

(4) use evolution difference algorithm repeating step (2) to step (3), the parameter in described impact fault-signal model is optimized; Optimization aim is used the kurtosis in step (3); Finally obtain optimization envelope spectrum.

Described step (1) comprises the following steps:

(1.1) set up impact fault-signal model as follows:

$w\left(t\right)=\exp \left(\frac{-\mathrm{\αt}}{f_0}\right)\·\sin \left(2\mathrm{\π}{f}_{H}t\right)$

Wherein, time t is obtained to w (n)=w (n Δ t), Δ t=1/Fs, sample frequency used when Fs is actual measurement vibration signal by discretize after sample frequency Fs sampling; α is damped expoential, f ₀preassignment failure-frequency, f _hit is high frequency modulated frequency;

(1.2) the mode adaptive small echo generating algorithm that adopts French scholar Hector Mesa to publish, generates the small echo wav (n) adapting with w (n); Described small echo meets small echo admissible condition, and has time frequency compactly supported property.

Described step (2) comprises the following steps:

Described wav (n) is considered as to the unit impact response of a FIR wave filter, and with fast convolution algorithm general in digital signal processing, the sampling x (n) of vibration signals measured x (t) is carried out to filtering, algorithm is as follows:

x′(n)＝IDFT(DFT(wav ₀(n))·DFT(x(n)))

Wherein, x ' is (n) filtering result, and DFT represents discrete Fourier transformation, and IDFT represents discrete inverse Fourier transform.

Described step (3) comprises the following steps:

Calculate described filtering result x ' kurtosis value (n), computing formula is:

$\mathrm{kurtosis}\left\{x^{\′}\left(n\right)\right\}=\frac{\frac{1}{\mathrm{Ns}}\underset{i=1}{\overset{\mathrm{Ns}}{\mathrm{\Σ}}}{(x_{0i}^{\′}-{\stackrel{\‾}{x}}_0^{\′})}^4}{{\left(\frac{1}{\mathrm{Ns}}\underset{i=1}{\overset{\mathrm{Ns}}{\mathrm{\Σ}}}{(x_{0i}^{\′}-{\stackrel{\‾}{x}}_0^{\′})}^2\right)}^2}$

Wherein, Ns represents sampling number,

the mean value of sequence after expression filtering, x ' _0ithe value of i sample in sequence after expression filtering.

Described step (4) comprises the following steps:

(4.1) the optimization number of times of setting differential evolution algorithm, step-length, damped expoential α, preassignment failure-frequency f ₀with high frequency modulated frequency f _hthe scope of three parameters and variation crossover probability parameter;

(4.2) repeat damped expoential α, the preassignment failure-frequency f in described step (2) and (3) impact fault-signal model ₀with high frequency modulated frequency f _hthree parameters are optimized; Optimization aim is used the kurtosis value in step (3),, in the time that kurtosis value reaches maximal value, stops calculating α, f after being optimized ₀, f _h;

(4.3) by α, f after the optimization obtaining in step (4.2) ₀, f _hdescribed in substitution, in impact fault-signal model, obtain optimal wavelet wave filter wav _opti(n), with described optimal wavelet wave filter wav _opti(n) to x (n) filtering, obtain optimal filtering result x ' _opti(n);

(4.4) to optimal filtering result x ' _opti(n) carry out general Envelope Analysis, finally obtain optimization envelope spectrum.

The step of described general Envelope Analysis is as follows:

To described optimal filtering result x ' _opti(n) carry out Hilbert envelope, obtain:

Envx′ _opti(n)＝abs(Hilbert(x′ _opti(n)))

To Envx ' _opti(n) carry out spectrum analysis and obtain optimization envelope spectrum:

EnvSpectrum(n)＝DFT(Envx′ _opti(n))。

Wherein, Envx ' _opti(n) envelope spectrum of signal after expression optimal filtering, the envelope spectrum of signal after EnvSpectrum (n) expression optimal filtering.

In sum, this method is by optimization method Automatic Optimal relevant parameters, and its process is without human intervention, and comprised the filtering adapting with fault characteristic signals, and fault signature is farthest reinforced.

Brief description of the drawings

Fig. 1 is the signature tune line chart going out according to impact fault-signal modeling rendering in the present invention; In optimizing process, can produce many categories likelihood signal, as example, this is wherein one group.

Fig. 2 is the charts for finned heat of the adaptive wavelet wave filter of the signal process method for mode matching generation in Fig. 1 of the present invention.

Fig. 3-1st, the present invention relates to the vibration signal figure of rolling bearing in embodiment.

Fig. 3-2nd, the signal graph of the vibration signal in Fig. 3-1 after by the adaptive wavelet filter filtering in Fig. 2.

Fig. 4 the present invention relates in embodiment after the optimization of certain number of times, the filtered signal graph of optimization adaptive wavelet finally obtaining.

Fig. 5-1st, the present invention relates to low signal-to-noise ratio rolling bearing fault signal (signal of Fig. 3-1) in embodiment and directly carries out the demodulation spectrogram that general Envelope Demodulation Analysis obtains.

Fig. 5-2nd, the present invention relates to the demodulation spectrogram that in embodiment, low signal-to-noise ratio rolling bearing fault signal obtains after the filtering of optimization adaptive wavelet.

Fig. 6 is the schematic diagram of the concrete methods of realizing of step 4 of the present invention.

Embodiment

Further describe the present invention below in conjunction with embodiment.Scope of the present invention is not limited by these embodiment.Be described in further detail as follows to content of the present invention by reference to the accompanying drawings: described rolling bearing and gear impact method for diagnosing faults based on optimum adaptive wavelet wave filter comprises the following steps:

1) set up the impact fault-signal model based on index attenuation sine

wherein, α is damped expoential, f ₀preassignment failure-frequency, f _hit is high frequency modulated frequency;

Then apply the disclosed lift technique of Hector Mesa and generate the adaptive wavelet wave filter wav (n) matching with this signal model;

Concrete steps comprise: initial setting α ₀=2000, f _{h 0}=6000Hz, f ₀₀=50Hz; Generate primary fault signal model with Computer Simulation:

$w_0(n\·\mathrm{\Δt})=\exp \left(\frac{-\mathrm{\αn}\·\mathrm{\Δt}}{f_0}\right)\·\sin (2\mathrm{\π}{f}_{H}n\·\mathrm{\Δt})$

Wherein, Δ t=1/Fs value, and the span of n must be identical with measured signal; Here suppose that sampling number is Ns.

The disclosed technology of recycling Hector Mesa, by w ₀(n Δ is t) as known mode, and acquisition has time frequency compactly supported property, meets admissibility condition, and and w ₀(the small echo wav that the pattern that n Δ t) defines adapts ₀(n):

w ₀(n·Δt)＝0，|n|＞n _max (1)

wherein WAV (Ω) is wav ₀(n) Fourier transform, C _ψrepresent integral result, should be finite value.(2) formula (1) represents that the small echo generating must meet tight property condition, and formula (2) represents that small echo must meet admissibility condition.Fig. 1 is the curve map of initialize signal model, and Fig. 2 is the small echo signal graph that adopts Hector Mesa algorithm to calculate according to the signal in Fig. 1; Circular please refer to the paper that Hector Mesa published in 2005.The wav finally generating ₀(n) there is no an analytical expression, be one group of sequence of real numbers, i.e. wavelet filter coefficient.

2) then utilize quick FIR filtering algorithm to carry out this wave filter, the acceleration vibration signal of rolling bearing or gear is carried out to filtering; FIR filtering algorithm is classical wave filter execution algorithm fast, and its realization please refer to general digital signal processing books; Circular summary is following formula:

x′ ₀(n)＝IDFT(DFT(wav ₀(n))·DFT(x(n))) (3)

Wherein, DFT () represents discrete Fourier transformation, and IDFT () represents discrete inverse Fourier transform, and both all can be completed by standard fft algorithm; To wav ₀(n) and measured signal x (n) be all DFT, after multiplying each other, do again inverse transformation, the sequence x ' obtaining ₀(n) be filtered sequence.

3) kurtosis value of calculation of filtered result, specific formula for calculation is as follows:

$\mathrm{kurtosis}\left\{x_0^{\′}\left(n\right)\right\}=\frac{\frac{1}{\mathrm{Ns}}\underset{i=1}{\overset{\mathrm{Ns}}{\mathrm{\Σ}}}{(x_{0i}^{\′}-{\stackrel{\‾}{x}}_0^{\′})}^4}{{\left(\frac{1}{\mathrm{Ns}}\underset{i=1}{\overset{\mathrm{Ns}}{\mathrm{\Σ}}}{(x_{0i}^{\′}-{\stackrel{\‾}{x}}_0^{\′})}^2\right)}^2},---\left(4\right)$

In formula, the mean value of sequence after expression filtering, x ' _0ithe value of i point of sequence after expression filtering.

4) with evolution difference algorithm, said process is repeated to certain number of times (experiment finds that general 50 left and right can obtain good result), damped expoential α, preassignment failure-frequency f in impact fault-signal signal model ₀, high frequency modulated frequency f _hthree parameters are optimized; Optimization aim is used in step (3) and obtains kurtosis value,, in the time that kurtosis value reaches maximal value, stops calculating, and obtains the filtering result that kurtosis is the highest.

5) the highest filtering result of kurtosis is carried out after Hilbert envelope, then carry out the frequency spectrum that discrete Fourier transformation (DFT) obtains and be optimization envelope spectrum, the step comprising as shown in Figure 6.

Embodiment:

The present embodiment is for verifying the performance of the method that the present invention is based on optimum adaptive wavelet wave filter.Adopt signal one group of actual measurement, that the rolling bearing of known fault has occurred to test.While measuring this signal, fault bearing, on the right side of axle, also claims fault end; But while measurement, the side that bearing does not break down is deliberately chosen in measuring position, also referred to as non-fault end.At non-fault end, the fault-signal of rolling bearing has passed through transmitting procedure indirectly, large high attenuation; Adopt such metering system, object is checking the method superiority with respect to classic method in the time of low signal-to-noise ratio.

Fig. 3-1st, the present invention relates to the vibration signal figure of rolling bearing in embodiment.Fig. 3-2nd, the vibration signal in Fig. 3-1 is by the filtered signal graph of the adaptive wavelet in Fig. 2.Fig. 4 the present invention relates in embodiment after the optimization of certain number of times, the filtered signal graph of optimization adaptive wavelet finally obtaining.What Fig. 5-1 provided is in embodiment, to adopt traditional envelope demodulation method, i.e. high-pass filtering adds the demodulation spectrogram that Hilbert envelope demodulation method obtains, Fig. 5-2nd, the demodulation spectrogram that adopts method of the present invention to obtain.Contrasting above-mentioned two figure can find out, because fault-signal is buried in oblivion by noise, classic method cannot extract fault signature, even and if method of the present invention still can clearly extract the fault-signal of rolling bearing in the situation that of this low signal-to-noise ratio.

Claims (5)

1. the rolling bearing based on optimum adaptive wavelet wave filter and a gear impact method for diagnosing faults, is characterized in that comprising the following steps:

(1) set up the impact fault-signal model based on index attenuation sine, then apply the adaptive wavelet wave filter that mode adaptive small echo generating algorithm generates and this signal model matches that Hector Mesa publishes;

(2) utilize quick FIR filtering algorithm to carry out described adaptive wavelet wave filter, the acceleration vibration signal of rolling bearing or gear is carried out to filtering and obtain filtering result;

(3) kurtosis value of filtering result described in calculation procedure (2);

(4) use evolution difference algorithm repeating step (2) to step (3), the parameter in described impact fault-signal model is optimized; Optimization aim is used the kurtosis in step (3); Finally obtain optimization envelope spectrum; Described step (1) comprises the following steps:

(1.1) set up impact fault-signal model as follows:

$w\left(t\right)=\exp \left(\frac{-\mathrm{\αt}}{f_0}\right)\·\sin \left(2\mathrm{\π}{f}_{H}t\right)$

Wherein, time t is obtained to w (n)=w (n Δ t), Δ t=1/Fs, sample frequency used when Fs is actual measurement vibration signal by discretize after sample frequency Fs sampling; α is damped expoential, f ₀preassignment failure-frequency, f _hit is high frequency modulated frequency; Primary fault signal model:

$w_0(n\·\mathrm{\Δt})=\exp \left(\frac{-\mathrm{\αn}\·\mathrm{\Δt}}{f_0}\right)\·\sin (2\mathrm{\π}{f}_{H}n\·\mathrm{\Δt})$

(1.2) the mode adaptive small echo generating algorithm that adopts French scholar Hector Mesa to publish, by w ₀(n Δ is t) as known mode, and acquisition has time frequency compactly supported property, meets admissibility condition, and and w ₀(the small echo wav that the pattern that n Δ t) defines adapts ₀(n): w ₀(n Δ t)=0, | n|>n _max(1)

$C_{\mathrm{\&psi;}}={\&Integral;}_0^{\&infin;}\frac{{\left|\mathrm{WAV}\left(\mathrm{\&Omega;}\right)\right|}^2}{\mathrm{\&Omega;}}\mathrm{d\&Omega;}<\&infin;---\left(2\right)$

Wherein WAV (Ω) is wav ₀(n) Fourier transform, C _ψrepresent integral result, should be finite value; W (n) is by the result that after w (t) sample frequency Fs sampling, discretize obtains, Δ t=1/Fs.

2. rolling bearing and the gear impact method for diagnosing faults based on optimum adaptive wavelet wave filter according to claim 1, is characterized in that, described step (2) comprises the following steps:

Described wav (n) is considered as to the unit impact response of a FIR wave filter, and with fast convolution algorithm general in digital signal processing, the sampling x (n) of vibration signals measured x (t) is carried out to filtering, algorithm is as follows:

x′(n)＝IDFT(DFT(wav ₀(n))·DFT(x(n)))

Wherein, x ' is (n) filtering result, and DFT represents discrete Fourier transformation, and IDFT represents discrete inverse Fourier transform.

3. rolling bearing and the gear impact method for diagnosing faults based on optimum adaptive wavelet wave filter according to claim 2, is characterized in that: described step (3) comprises the following steps:

Calculate described filtering result x ' kurtosis value (n), computing formula is:

$\mathrm{Kurtosis}\left\{x^{\&prime;}\left(n\right)\right\}=\frac{\frac{1}{\mathrm{Ns}}\underset{i=1}{\overset{\mathrm{Ns}}{\mathrm{\&Sigma;}}}{(x_{0_i}^{\&prime;}-{\stackrel{\&OverBar;}{x}}_0^{\&prime;})}^4}{{\left(\frac{1}{\mathrm{Ns}}\underset{i=1}{\overset{\mathrm{Ns}}{\mathrm{\&Sigma;}}}{(x_{0_i}^{\&prime;}-{\stackrel{\&OverBar;}{x}}_0^{\&prime;})}^2\right)}^2}$

Wherein, Ns represents sampling number,

the mean value of sequence after expression filtering, the value of i sample in sequence after expression filtering.

4. rolling bearing and the gear impact method for diagnosing faults based on optimum adaptive wavelet wave filter according to claim 3, is characterized in that: described step (4) comprises the following steps:

(4.1) the optimization number of times of setting differential evolution algorithm, step-length, damped expoential α, preassignment failure-frequency f ₀with high frequency modulated frequency f _hthe scope of three parameters and variation crossover probability parameter;

(4.2) repeat damped expoential α, the preassignment failure-frequency f in described step (2) and (3) impact fault-signal model ₀with high frequency modulated frequency f _hthree parameters are optimized; Optimization aim is used the kurtosis value in step (3),, in the time that kurtosis value reaches maximal value, stops calculating α, f after being optimized ₀, f _h;

(4.3) by α, f after the optimization obtaining in step (4.2) ₀, f _hdescribed in substitution, in impact fault-signal model, obtain optimal wavelet wave filter wav _opti(n), with described optimal wavelet wave filter wav _opti(n) to x (n) filtering, obtain optimal filtering result x ' _opti(n);

(4.4) to optimal filtering result x ' _opti(n) carry out general Envelope Analysis, finally obtain optimization envelope spectrum.

5. rolling bearing and the gear impact method for diagnosing faults based on optimum adaptive wavelet wave filter according to claim 4, is characterized in that: the step of described general Envelope Analysis is as follows:

To described optimal filtering result x ' _opti(n) carry out Hilbert envelope, obtain:

Envx′ _opti(n)＝abs(Hilbert(x′ _opti(n)))

To Envx ' _opti(n) carry out spectrum analysis and obtain optimization envelope spectrum:

EnvSpectrum(n)＝DFT(Envx′ _opti(n))。

Wherein, Envx ' _opti(n) envelope spectrum of signal after expression optimal filtering, the envelope spectrum of signal after EnvSpectrum (n) expression optimal filtering.

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