CN102539150B - Self-adaptive failure diagnosis method of rotary mechanical component based on continuous wavelet transformation - Google Patents

Abstract

The invention relates to a self-adaptive failure diagnosis method of a rotary mechanical component based on continuous wavelet transformation. The method comprises the following steps of: 1, performing zero-mean preprocessing on an acquired discrete initial vibration signal to obtain a preprocessed signal from which a direct-current component is eliminated; 2, performing continuous wavelet transformation on the preprocessed signal obtained in the step 1 to obtain a wavelet coefficient which corresponds to each scale parameter; 3, calculating the kurtosis of the wavelet coefficient which corresponds to each scale parameter in the step 2 respectively; 4, searching for a wavelet scale parameter which corresponds to large kurtosis in the wavelet scale parameter obtained in the step 3 with a self-adaptive algorithm to configure an optimal analysis signal; and 5, performing envelope demodulation on the optimal analysis signal obtained in the step 4 to obtain an envelope signal. The method has the beneficial effects that: the accuracy of failure diagnosis is increased, and the method is particularly suitable for failure diagnosis of mechanical parts with impact damages.

Description

The adaptive failure diagnostic method of the rotary mechanical part based on continuous wavelet transform

Technical field

The present invention relates to technology for mechanical fault diagnosis field, relate in particular to the fault diagnosis technology to rotary mechanical part (as bearing or gear etc.).

Background technology

While there is local fault (as peel off, spot corrosion, crack etc.) in rotary mechanical part (as rolling bearing), its vibration signal is accompanied by the generation of impact conventionally, and the low frequency impact signal of these low-frequency ranges is by resonance generation high-frequency vibration signal occurring with the high band that is activated at of mechanical system and sensor.Therefore,, by can effectively carrying out fault diagnosis to bearing to the analysis of high-frequency vibration signal, also eliminated the interference of low-frequency noise simultaneously.In a very long time, high frequency resonance demodulation technology (being called again envelope demodulation technology) becomes the effective ways of rotary mechanical part fault diagnosis in the past, and it can obtain the fault characteristic frequency of rotary mechanical part more accurately.

In actual fault diagnosis, high frequency resonance demodulation technology often requires to obtain accurately high-frequency resonance frequency band, also determine centre frequency and the bandwidth of bandpass filter, yet determining of centre frequency and bandwidth is more difficult often, this is because the centre frequency of high frequency resonance demodulation technology medium-high frequency resonance bands is normally unknown in advance, this has just caused, and obtaining of high-frequency resonance frequency band is incomplete or bandwidth is excessive, thereby has influence on the accuracy of final fault diagnosis.

Summary of the invention

The object of the invention is to be difficult to definite problem for bandpass filter centre frequency in existing high frequency resonance demodulation technology, proposed the adaptive failure diagnostic method of the rotary mechanical part based on continuous wavelet transform, the method is especially applicable to the fault diagnosis with the rotary mechanical part of impact damage.

Content of the present invention is: the adaptive failure diagnostic method of the rotary mechanical part based on continuous wavelet transform, and as shown in Figure 1, its step comprises:

Step 1: the discrete initial vibration signal s (n) obtaining is carried out to zero-mean pre-service, the preprocessed signal s of the DC component that is eliminated ₁(n);

Step 2: by resulting preprocessed signal s in step 1 ₁(n) carry out continuous wavelet transform, obtain the wavelet coefficient WT that each scale parameter is corresponding _a(n);

Step 3: the corresponding wavelet coefficient WT of each scale parameter in difference calculation procedure 2 _a(n) kurtosis;

Step 4: utilize a kind of adaptive algorithm to find out in step 3 the corresponding wavelet scale parameter of larger kurtosis in small echo scale parameter, optimal wavelet yardstick, then selects the corresponding wavelet coefficient structure of these scale parameters optimum analysis signal s _a(n);

Step 5: to the optimum analysis signal s obtaining in step 4 _a(t) carry out envelope demodulation, obtain its envelope signal s _e(t);

Step 6: by the envelope signal s in step 5 _e(t) do FFT conversion, obtain its envelope frequency spectrum S _e(f), by the analysis to envelope spectrum, realize the fault diagnosis to rotary mechanical part.

The invention has the beneficial effects as follows: owing to not needing to pre-estimate centre frequency and the bandwidth of wave filter, avoided the impact of evaluated error on diagnostic result, therefore compare with traditional high frequency resonance demodulation technology, the present invention has improved the accuracy of fault diagnosis, is especially applicable to the fault diagnosis with the component of machine of impact damage.

Accompanying drawing explanation

Fig. 1 is main flow chart of the present invention.

Fig. 2 is the time-domain diagram of the preprocessed signal after zero-mean is processed.

Fig. 3 is the schematic flow sheet that self-adaptation is obtained optimal scale coefficient.

Fig. 4 is each yardstick a=[1,2 ..., 32] corresponding kurtosis value.

Fig. 5 is that self-adaptation is obtained scale coefficient result a _opt=[7,8 ..., 16] corresponding kurtosis value.

Fig. 6 is the time-domain diagram of the analytic signal that obtains of reconstruct optimal scale coefficient.

Fig. 7 is the envelope signal time-domain diagram after analytic signal demodulation.

Fig. 8 is the envelope spectrum of analytic signal.

Fig. 9 is the envelope time-domain diagram of the preprocessed signal after zero-mean processing in Fig. 2.

Figure 10 is the FFT spectrum of envelope signal in Fig. 9

Embodiment

Below in conjunction with specific embodiments and the drawings, the present invention is described further.

As shown in Figure 1, the adaptive failure diagnostic method of the rotary mechanical part based on continuous wavelet transform, as shown in Figure 1, its step comprises:

Step 1: the discrete initial vibration signal s (n) obtaining is carried out to zero-mean pre-service, the preprocessed signal s of the DC component that is eliminated ₁(n).

The present embodiment is usingd the object of gear case as fault diagnosis, the vibration signal of this gear case gathers by acceleration transducer, after being utilized to signal conditioner, analog to digital conversion, the vibration signal collecting obtains discrete initial vibration signal s (n), and this signal is sent into computing machine and carry out zero-mean pre-service, zero-mean pre-service is in order to eliminate the impact of DC component in initial vibration signal s (n), here initial vibration signal is carried out to the preprocessed signal s1 (n) that zero-mean is processed the DC component that is eliminated, its specific algorithm is as follows:

$s_1\left(n\right)=s\left(n\right)-\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}s\left(n\right)---\left(1\right)$

Here s (n) is discrete initial vibration signal, and n is discrete time point, and N is that signal sampling is counted, s ₁(n) be the preprocessed signal after zero-mean processing.

As shown in Figure 2, be the time domain figure of the preprocessed signal after zero-mean processing, this signal has been eliminated DC component.

Step 2: by resulting preprocessed signal s in step 1 ₁(n) carry out continuous wavelet transform, obtain the wavelet coefficient WT that each scale parameter is corresponding _a(n);

Continuous wavelet transform is defined as follows:

Wherein x (t) is signal function, and t is time independent variable; for wavelet mother function, the wavelet mother function using in the present invention is Morlet wavelet function; A is wavelet scale parameter; B is small echo time parameter.The wavelet coefficient WT (a, b) is here a binary function, and when wavelet scale parameter a gives regularly, its corresponding wavelet coefficient just becomes WT _a(b), b discretize can be expressed as to WT _a(n), n is natural number; From equation (2), can find out, continuous wavelet transform is equivalent to signal function x (t) and wavelet function make convolution, subscript ^*expression is got conjugation to wavelet mother function, the character of convolution theorem in technology in processing according to signal, and continuous wavelet transform can be expressed as again:

Wherein X (f), ψ (f) be respectively x (t), fourier transform, F ^-1[ ] represents the inverse transformation of Fourier transform, and b is the time parameter after inverse transformation.From equation (3), continuous wavelet transform is equivalent to utilize one group of bandpass filter to carry out bandpass filtering to signal, and each yardstick a is corresponding to a bandpass filter the bandwidth and the centre frequency that are single filter are determined by scale parameter a.Take Morlet small echo as example:

Wherein for wavelet mother function, σ is attenuation parameter constant, f ₀for wavelet mother function centre frequency, its frequency domain representation:

$\mathrm{\ψ}\left(f\right)=e^{-({\mathrm{\π}}^2/{\mathrm{\σ}}^2){(f-f_0)}^2}---\left(5\right)$

Therefore its half-power bandwidth can be calculated as: ; Therefore the filter transmission band that, wavelet mother function ψ (f) is corresponding is: the small echo bandpass filter of corresponding wavelet scale parameter a is:

$\mathrm{\ψ}\left(\mathrm{af}\right){=e}^{-({\mathrm{\π}}^2/{\mathrm{\σ}}^2){\left(a(f-\frac{f_0}{a})\right)}^2}---\left(6\right)$

Therefore by the preprocessed signal s obtaining in step 2 ₁(n) make continuous wavelet transform and can obtain being distributed in the wavelet coefficient WT in different frequency bands _a(n), these wavelet coefficients are corresponding one by one with scale parameter a and each frequency band of wavelet transformation, and in invention, the scale parameter of wavelet transformation is expressed as a=[a ₁, a ₂..., a _l], l is the number of wavelet transformation mesoscale parameter.

Step 3: l the corresponding wavelet coefficient WT of scale parameter in difference calculation procedure 2 _a(n) kurtosis (kurtosis);

Since the concept of the proposition kurtosis (kurtosis) such as Stewart in 1970 rises, in a very long time in past, it was used to weigh the order of severity of mechanical fault always.Kurtosis ku _abe a highstrung statistic of impact signal, its size has been weighed the impact strength of signal, and its impact that is worth large-signal is more just stronger, otherwise more weak.Therefore, the present invention utilizes this impact of adding up to weigh each yardstick wavelet coefficient in step 2 strong and weak, is calculated as follows:

${\mathrm{ku}}_a=\frac{E\left[{\mathrm{WT}}_a{\left(n\right)}^4\right]}{{\left\{E\right[{\mathrm{WT}}_a{\left(n\right)}^2\left]\right\}}^2}---\left(7\right)$

WT wherein _a(n) wavelet coefficient for obtaining in step 2, E[ ] represent to ask expectation.

Step 4: utilize a kind of adaptive algorithm to find out small echo scale parameter a=[a in step 3 ₁, a ₂..., a _l] in larger kurtosis ku _acorresponding wavelet scale parameter a _opt=[a _n, a _n+1..., a _m], optimal wavelet yardstick, then selects the corresponding wavelet coefficient structure of these scale parameters optimum analysis signal s _a(n);

In step 2, mention and utilize different scale small echo to do wavelet transformation to signal to be equivalent to utilize a bank of filters to signal filtering, and include the signal of bearing fault characteristics, often kurtosis ku is larger, therefore can select the corresponding coefficient of several yardsticks that ku value is larger to carry out component analysis signal s _a(n) carry out fault diagnosis, s _a(n) for having the stack of the wavelet coefficient of larger kurtosis, its computing method are as follows:

$s_a=\underset{a=a_m}{\overset{a_n}{\mathrm{\Σ}}}\mathrm{WT}(a,b)=\underset{a=a_m}{\overset{a_n}{\mathrm{\Σ}}}\sqrt{a}{F}^{-1}\left[X\left(f\right){\mathrm{\ψ}}^{*}\left(\mathrm{af}\right)\right]=F^{-1}\left[X\left(f\right)\underset{a=a_m}{\overset{a_n}{\mathrm{\Σ}}}\sqrt{a}{\mathrm{\ψ}}^{*}\left(\mathrm{af}\right)\right]=F^{-1}\left[X\left(f\right)\mathrm{\φ}\left(f\right)\right]---\left(8\right)$

In formula, φ (f) is equivalent to a new wave filter, optimal scale a _opt=[a _m, a _m+1..., a _n] selection utilized a kind of adaptive algorithm, its flow process as shown in Figure 3, in order to select the analytic signal s with maximum kurtosis ku _a(n), here by the wavelet coefficient s after merging _aas analytic signal, and its kurtosis ku is compared, its specific algorithm is: select i scale coefficient as a upper coefficient WT _pre, and i scale coefficient (n) with i+1 scale coefficient merge coefficient WT _cur(n) compare (i is natural number, and initial value is 1), i.e. WT _preand WT (n) _cur(n) compare, if merge coefficient WT _cur(n) ku _curvalue is greater than a scale coefficient WT _pre(n) ku _prevalue, so by current scale coefficient WT _cur(n) as a upper scale coefficient WT _pre(n), by current scale coefficient WT _cur(n) with the merge coefficient of i+2 scale coefficient as current scale coefficient WT _cur, and compare (n); Otherwise, reselect i+1 scale coefficient as a upper scale coefficient WT _pre, and and the merge coefficient WT of i+1 scale coefficient and i+2 scale coefficient (n) _cur(n) compare.By that analogy, until all scale coefficients are all merged completeer, select the merge coefficient of maximum ku value as analytic signal, the yardstick of respectively organizing coefficient merging is as optimal scale a _opt=[a _m, a _m+1..., a _n].

Adaptive algorithm by this step is from yardstick a=[a ₁, a ₂..., a _l] in choose the wavelet coefficient WT with larger kurtosis _a(n) corresponding wavelet scale parameter a _opt=[a _n, a _n+1..., a _m] as optimum yardstick, the merging wavelet coefficient s of the scale parameter that this is optimum _a(n) be exactly the high-frequency resonance band signal that we need, this process is equivalent to several wavelet filters to screen, leave the real corresponding wavelet filter of resonance bands in most likely the present invention, like this, in the process that high-frequency resonance band signal is extracted with regard to unnecessary centre frequency and the bandwidth of first determining wave filter, thereby improved the accuracy of diagnosis.

As shown in Figure 4 and Figure 5, for this step is chosen larger kurtosis ku _aa specific embodiment, in Fig. 4, the yardstick a=[1 that horizontal ordinate is wavelet transformation, 2 ..., 32], ordinate is the corresponding wavelet coefficient WT of each yardstick _a(n) kurtosis ku, can find that at yardstick be 12 left and right, and the kurtosis of wavelet coefficient is larger.After processing by above-mentioned adaptive approach, what in Fig. 5, show is the kurtosis of wavelet coefficient and the corresponding relation of yardstick after merging, and can find yardstick a _opt=[7,8 ..., 16] the corresponding kurtosis of merge coefficient obtain maximal value.So selecting scale a _opt=[7,8 ..., 16] be optimal scale, and through type (8) structure optimum analysis signal s _a(n), optimum analysis signal s _a(n) time-domain diagram as shown in Figure 6.As can be seen from Figure 6, this Optimal Signals has obvious periodic impulse, and the impact producing with bearing local damage is consistent, and has realized the extraction to high-frequency resonance band.

Step 5: to the optimum analysis signal s obtaining in step 4 _a(t) carry out envelope demodulation, obtain its envelope signal s _e(t); Its circular is as follows:

$s_e\left(t\right)=\sqrt{s_a^2\left(t\right)+H^2\left[s_a\left(t\right)\right]}---\left(9\right)$

$H\left[s_a\left(t\right)\right]=\frac{1}{\mathrm{\π}}{\∫}_{-\∞}^{+\∞}\frac{s_a\left(\mathrm{\τ}\right)}{t-\mathrm{\τ}}\mathrm{d\τ}---\left(10\right)$

H[ wherein] represent Hilbert transform, τ is transformation parameter.Envelope demodulation is prior art, no longer describes in detail here.

As shown in Figure 7, be optimum analysis signal s after demodulation _a(t) envelope signal, its cycle is consistent with the inner ring fault characteristic frequency BPFI=257Hz of bearing.

Step 6: by the envelope signal s in step 5 _e(t) do FFT conversion, obtain its envelope frequency spectrum s _e(f), by the analysis to envelope spectrum, realize the fault diagnosis to rotary mechanical part (as components of machine such as bearing, gears).

Because FFT is transformed to prior art, no longer describe in detail here.By step 6, obtained the envelope spectrum of optimum analysis signal, envelope spectrum has been analyzed, if it includes the fault characteristic frequency of bearing, gear, shown that fault has occurred for bearing, gear; Otherwise normal operation.

In the present embodiment, we have provided respectively by direct demodulation preprocessed signal s ₁(n) envelope time domain figure and frequency domain figure, as shown in Figure 9 and Figure 10.Although the envelope signal after direct demodulation also has obvious periodicity as can be seen from Figure 9, can find this cycle T ₁the 2 frequency multiplication 2f that turn frequency of=0.0075s and bearing inner race _r=133.33Hz is consistent, from the frequency domain figure of Figure 10, can be verified, and therefore can not reflect the fault signature of bearing.The result (as shown in Figure 8) so obtaining from step 6 can find out, the resulting result of the present invention obviously comprised the fault characteristic frequency BPFI=257Hz of bearing and harmonic frequency thereof (2BPFI, 3BPFI ...).

Those of ordinary skill in the art will appreciate that, embodiment described here is in order to help reader understanding's principle of the present invention, should be understood to that protection scope of the present invention is not limited to such special statement and embodiment.Those of ordinary skill in the art can make various other various concrete distortion and combinations that do not depart from essence of the present invention according to these technology enlightenments disclosed by the invention, and these distortion and combination are still in protection scope of the present invention.

Claims (2)

1. the adaptive failure diagnostic method of the rotary mechanical part based on continuous wavelet transform, is characterized in that, its step comprises:

Step 1: the discrete initial vibration signal s (n) obtaining is carried out to zero-mean pre-service, the preprocessed signal s of the DC component that is eliminated ₁(n);

Step 2: by resulting preprocessed signal s in step 1 ₁(n) carry out continuous wavelet transform, obtain the wavelet coefficient WT that each scale parameter is corresponding _a(n);

Step 3: the corresponding wavelet coefficient WT of each scale parameter in difference calculation procedure 2 _a(n) kurtosis;

Step 4: utilize a kind of adaptive algorithm to find out in step 3 the corresponding wavelet scale parameter of larger kurtosis in small echo scale parameter, optimal wavelet yardstick, then selects the corresponding wavelet coefficient structure of each scale parameter optimum analysis signal s in step 2 _a(n);

The idiographic flow of the adaptive algorithm in this step is: select i scale coefficient as a upper coefficient WT _pre, and i scale coefficient (n) with i+1 scale coefficient merge coefficient WT _cur(n) compare, i.e. WT _preand WT (n) _cur(n) compare, if merge coefficient WT _cur(n) ku _curvalue is greater than a scale coefficient WT _pre(n) ku _prevalue, so by current scale coefficient WT _cur(n) as a upper scale coefficient WT _pre(n), by current scale coefficient WT _cur(n) with the merge coefficient of i+2 scale coefficient as current scale coefficient WT _cur, and compare (n); Otherwise, reselect i+1 scale coefficient as a upper scale coefficient WT _pre, and and the merge coefficient WT of i+1 scale coefficient and i+2 scale coefficient (n) _cur(n) compare, i is natural number here, and initial value is 1; By that analogy, until all scale coefficients are all merged completeer, select the merge coefficient of maximum ku value as analytic signal, the yardstick of respectively organizing coefficient merging is as optimal scale a _opt=[a _m, a _m+1..., a _n];

Step 5: to the optimum analysis signal s obtaining in step 4 _a(t) carry out envelope demodulation, obtain its envelope signal s _e(t);

Step 6: by the envelope signal s in step 5 _e(t) do FFT conversion, obtain its envelope frequency spectrum S _e(f), by the analysis to envelope spectrum, realize the fault diagnosis to rotary mechanical part.

2. according to the adaptive failure diagnostic method of the rotary mechanical part based on continuous wavelet transform shown in claim 1, it is characterized in that the s of optimum analysis signal described in described step 4 _a(n) computing method are as follows:

$s_a=\underset{a=a_m}{\overset{a_n}{\mathrm{\Σ}}}\mathrm{WT}(a,b)=\underset{a=a_m}{\overset{a_n}{\mathrm{\Σ}}}\sqrt{a}{F}^{-1}\left[X\left(f\right){\mathrm{\ψ}}^{*}\left(\mathrm{af}\right)\right]=F^{-1}\left[X\left(f\right)\underset{a=a_m}{\overset{a_n}{\mathrm{\Σ}}}\sqrt{a}{\mathrm{\ψ}}^{*}\left(\mathrm{af}\right)\right]=F^{-1}\left[X\left(f\right)\mathrm{\φ}\left(f\right)\right]---\left(8\right)$

In formula, wherein X (f), Ψ (f) be respectively x (t), fourier transform, F ^-1[] represents the inverse transformation of Fourier transform, and a is wavelet scale parameter, and b is the time parameter after inverse transformation, and φ (f) is equivalent to a new wave filter, optimal scale a _opt=[a _m, a _m+1..., a _n] selection utilized a kind of adaptive algorithm, in order to select the analytic signal s with maximum kurtosis ku _a(n), here by the wavelet coefficient s after merging _aas analytic signal, and its kurtosis ku is compared.