CN102269644A - 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 and gear impact method for diagnosing faults based on optimum adaptive wavelet wave filter

Technical field

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

Background technology

In the equipment fault diagnosis field, because rolling bearing and gear are very generally to use and crucial parts, and the two all is one of parts of the easiest damage in the mechanized equipment, has great engineering significance so the two is carried out condition monitoring and fault diagnosis.When there were defective in rolling bearing and gear, impaired loci can produce periodic impact when contacting with other element.How effectively extracting from vibration acceleration signal and impact feature, 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 use more quadrature simple harmonic quantity trigonometric function impact signal to approach, unless damage of the bearing is serious, fault signature is very obvious, otherwise for the rolling bearing and the gear vibration signal of complicated component, its fault is impacted feature and is usually flooded by ground unrest and other signal contents in frequency spectrum.Envelope demodulation is a kind of effective rolling bearing and gear failure diagnosing method, but envelope demodulation at first all will be carried out bandpass filtering or high-pass filtering to vibration signal; How reasonably to have selected related parameter at different units, different operating mode, be the difficult problem in the engineering, and the field engineering personnel often are difficult to grasp main points are set, and each concrete versatility that is provided with all has problems.In addition, time frequency analysis such as Wigner branch, EMD-HHT etc., also has report to be used for rolling bearing and gear impact Fault Diagnosis, and calculated amount is big, parameter is selected difficulty and the difficult problem such as monitoring in real time that realizes but these methods exist.Simultaneously, these methods also need the engineering staff to have advanced signal Processing knowledge, and it is relatively more difficult that this makes that equally it is applied in the engineering practice.

Summary of the invention

The objective 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 impact fault signature in the vibration signal is extracted accurately.Its process need not human intervention, and can provide more clearly envelope spectrum, thereby more clearly demonstrates failure symptom.

Concrete technical scheme is as follows:

A kind of rolling bearing and gear impact method for diagnosing faults based on optimum adaptive wavelet wave filter is characterized in that may further comprise the steps:

(1) foundation is used the adaptive wavelet wave filter that mode adaptive small echo generating algorithm generates and this signal model is complementary that Hector Mesa publishes then based on the impact fault-signal model of index attenuation sine;

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

(3) filtering result's kurtosis value described in the calculation procedure (2);

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

Described step (1) may further comprise the steps:

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

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

Wherein, time t is obtained w (n)=w (n Δ t) with sample frequency Fs sampling back discretize, Δ t=1/Fs, used sample frequency when Fs is the actual measurement vibration signal; α is a damped expoential, f ₀Be the preassignment failure-frequency, f _HIt is the 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) that adapts with w (n); Described small echo satisfies the small echo admissible condition, and has time frequency compactly supported property.

Described step (2) may further comprise the steps:

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

x′(n)＝IDFT(DFT(wav ₀(n))·DFT(x(n)))

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

Described step (3) may further comprise the steps:

Calculate described filtering x ' kurtosis value (n) as a result, 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 the expression filtering, x ' _0iThe value of i sample in the sequence after the expression filtering.

Described step (4) may further comprise the steps:

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

(4.2) repeat damped expoential α, preassignment failure-frequency f in described step (2) and (3) the impact fault-signal model ₀With the high frequency modulated frequency f _HThree parameters are optimized; Optimization aim is used the kurtosis value in the step (3), promptly when kurtosis value reaches maximal value, stops to calculate the α after being optimized, f ₀, f _H

(4.3) with α, f after the optimization that obtains in the step (4.2) ₀, f _HIn the described impact fault-signal of the substitution 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 x ' as a result _Opti(n);

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

The step of described general Envelope Analysis is as follows:

To described optimal filtering x ' as a result _Opti(n) carry out the Hilbert envelope, obtain:

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

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

EnvSpectrum(n)＝DFT(Envx′ _opti(n))。

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

In sum, this method has related parameter by the optimization method Automatic Optimal, and its process need not human intervention, and has comprised the filtering with the fault signature phase adjust signal, makes fault signature farthest be reinforced.

Description of drawings

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

Fig. 2 is the coefficient curve figure of the adaptive wavelet wave filter of the signal process method for mode matching generation among Fig. 1 of the present invention.

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

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

Fig. 4 is after the present invention relates to pass through the optimization of certain number of times among the embodiment, the filtered signal graph of optimization adaptive wavelet that finally obtains.

Fig. 5-the 1st the present invention relates to that low signal-to-noise ratio rolling bearing fault signal (signal of Fig. 3-1) directly carries out the demodulation spectrogram that general envelope demodulation analysis obtains among the embodiment.

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

Fig. 6 is the synoptic diagram of the specific implementation method 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 in conjunction with the accompanying drawings: described rolling bearing and gear impact method for diagnosing faults based on optimum adaptive wavelet wave filter may further comprise the steps:

1) foundation is based on the impact fault-signal model of index attenuation sine

Wherein, α is a damped expoential, f ₀Be the preassignment failure-frequency, f _HIt is the high frequency modulated frequency;

Use the disclosed lift technique of Hector Mesa then and generate the adaptive wavelet wave filter wav (n) that is complementary with this signal model;

Concrete steps comprise: initial setting α ₀=2000, f _{H 0}=6000Hz, f ₀₀=50Hz; Generate the 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.

Utilize the disclosed technology of Hector Mesa again, with w ₀(n Δ t) obtains to have time frequency compactly supported property, meet small echo admissibility condition as known mode, and and w ₀The small echo wav that the pattern of (n Δ t) definition adapts ₀(n):

w ₀(n·Δt)＝0，|n|＞n _max (1)

Wherein WAV (Ω) is wav ₀(n) Fourier transform, C _ψThe expression integral result should be finite value.(2) small echo of formula (1) expression generation must satisfy tight property condition, and formula (2) expression small echo must satisfy small echo 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 computation to obtain according to the signal among Fig. 1; Concrete computing method please refer to the paper that Hector Mesa published in 2005.The wav of Sheng Chenging at last ₀(n) do not have an analytical expression, be one group of sequence of real numbers, i.e. wavelet filter coefficient.

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

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

Wherein, DFT () represents discrete Fourier transformation, the discrete inverse Fourier transform of IDFT () expression, and both all can be finished by the standard fft algorithm; Promptly to wav ₀(n) and measured signal x (n) all be DFT, do inverse transformation, the sequence x ' that obtains after multiplying each other again ₀(n) be filtered sequence.

3) calculation of filtered result's kurtosis value, concrete computing formula 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 the formula,

The mean value of sequence after the expression filtering, x ' _0iThe value of i point of sequence after the expression filtering.

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

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

Embodiment:

Present embodiment is used to verify 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 taken place to experimentize.The fault bearing also claims the fault end on the right side of axle when measuring this signal; But the side that bearing does not break down is deliberately chosen in the measuring position when measuring, and is also referred to as non-fault end.At non-fault end, the fault-signal of rolling bearing has passed through transmission course indirectly, big high attenuation; Adopt such metering system, purpose is this method of checking superiority with respect to classic method when low signal-to-noise ratio.

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

Claims (6)

1. rolling bearing and gear impact method for diagnosing faults based on an optimum adaptive wavelet wave filter is characterized in that may further comprise the steps:

(1) foundation is used the adaptive wavelet wave filter that mode adaptive small echo generating algorithm generates and this signal model is complementary that Hector Mesa publishes then based on the impact fault-signal model of index attenuation sine;

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

(3) filtering result's kurtosis value described in the calculation procedure (2);

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

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

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

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

Wherein, time t is obtained w (n)=w (n Δ t) with sample frequency Fs sampling back discretize, Δ t=1/Fs, used sample frequency when Fs is the actual measurement vibration signal; α is a damped expoential, f ₀Be the preassignment failure-frequency, f _HIt is the 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) that adapts with w (n); Described small echo satisfies the small echo admissible condition, and has time frequency compactly supported property.

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

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

x′(n)＝IDFT(DFT(wav ₀(n))·DFT(x(n)))

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

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

Calculate described filtering x ' kurtosis value (n) as a result, 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 the expression filtering, x ' _0iThe value of i sample in the sequence after the expression filtering.

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

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

(4.2) repeat damped expoential α, preassignment failure-frequency f in described step (2) and (3) the impact fault-signal model ₀With the high frequency modulated frequency f _HThree parameters are optimized; Optimization aim is used the kurtosis value in the step (3), promptly when kurtosis value reaches maximal value, stops to calculate the α after being optimized, f ₀, f _H

(4.3) with α, f after the optimization that obtains in the step (4.2) ₀, f _HIn the described impact fault-signal of the substitution model, obtain optimal wavelet wave filter wavo _Pti(n), with described optimal wavelet wave filter wavo _Pti(n) to x (n) filtering, obtain optimal filtering x ' as a result _Opti(n);

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

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

To described optimal filtering x ' as a result _Opti(n) carry out the Hilbert envelope, obtain:

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

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

EnvSpectrum(n)＝DFT(Envx′ _opti(n))。

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

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