CN102539150A - 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

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

Technical field

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

Background technology

When local fault (as peel off, spot corrosion, crack etc.) takes place in rotary mechanical part (like rolling bearing); Its vibration signal is accompanied by the generation of impact usually, and the low frequency impact signal of these low-frequency ranges through the high band that is activated at mechanical system and sensor resonance generation high-frequency vibration signal takes place.Therefore, can effectively carry out fault diagnosis, also eliminate the interference of low-frequency noise simultaneously bearing through analysis to high-frequency vibration signal.In a very long time, high frequency resonance demodulation technology (being called the envelope demodulation technology again) 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 the fault diagnosis of reality; The high frequency resonance demodulation technology often requires to obtain accurately the high-frequency resonance frequency band; Also promptly confirm the centre frequency and the bandwidth of BPF., however centre frequency and bandwidth confirm often difficulty relatively, this is because the normally the unknown in advance of the centre frequency of high frequency resonance demodulation technology medium-high frequency resonance bands; This has just caused obtaining not exclusively of high-frequency resonance frequency band or bandwidth excessive, thereby has influence on the accuracy of final fault diagnosis.

Summary of the invention

The objective of the invention is to be directed against the problem that the BPF. centre frequency is difficult to confirm in the existing high frequency resonance demodulation technology; Proposed the adaptive failure diagnostic method based on the rotary mechanical part of continuous wavelet transform, this method especially is fit to have the fault diagnosis of the rotary mechanical part of impact damage.

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

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

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

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

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

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

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

The invention has the beneficial effects as follows: owing to need not pre-estimate the centre frequency and the bandwidth of wave filter; Avoided the influence of evaluated error to diagnostic result; Therefore with traditional high frequency resonance demodulation compared with techniques; The present invention has improved the accuracy of fault diagnosis, especially is fit to have the fault diagnosis of the component of machine of impact damage.

Description of drawings

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

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

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

Fig. 4 be each yardstick a=[1,2 ..., 32] pairing kurtosis value.

Fig. 5 is that self-adaptation is obtained scale coefficient a as a result _Opt=[7,8 ..., 16] pairing 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 the analytic signal demodulation.

Fig. 8 is the envelope demodulation spectrum of analytic signal.

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

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

Embodiment

Below in conjunction with specific embodiment and accompanying drawing the present invention is done further explanation.

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

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

Present embodiment is with the object of gear case as fault diagnosis; The vibration signal of this gear case is gathered through acceleration transducer; The vibration signal that collects utilized obtain discrete initial vibration signal s (n) after signal conditioner, the analog to digital conversion; And this signal is sent into computing machine carry out the zero-mean pre-service; The zero-mean pre-service is in order to eliminate the influence of DC component among the initial vibration signal s (n), the initial vibration signal to be carried out the preprocessed signal s1 (n) that zero-mean is handled the DC component that is eliminated here, and its specific algorithm is following:

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

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

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

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

Continuous wavelet transform defines as follows:

Wherein x (t) is a signal function, and t is the time independent variable;

is wavelet mother function, and the wavelet mother function that uses among the present invention is the Morlet wavelet function; A is the wavelet scale parameter; B is the small echo time parameter.(a b) is a binary function to the wavelet coefficient WT here, and when wavelet scale parameter a gives regularly, its corresponding wavelet coefficient just becomes WT _a(b), the b discretize can be expressed as WT _a(n), n is a natural number; Can find out that from equality (2) continuous wavelet transform is equivalent to signal function x (t) and wavelet function Make convolution, subscript ^*Expression is got conjugation to wavelet mother function, and according to the character of convolution theorem in the technology in the signal Processing, continuous wavelet transform can be expressed as again:

Wherein X (f), ψ (f) be respectively x (t), Fourier transform, F ^-1The inverse transformation of [ ] expression Fourier transform, b is the time parameter after the inverse transformation.Visible by equality (3); Continuous wavelet transform is equivalent to utilize one group of BPF. that signal is carried out bandpass filtering, and each yardstick a is that the bandwidth and the centre frequency of single filter determined by scale parameter a corresponding to a BPF.

.With the Morlet small echo is example:

Wherein Be wavelet mother function, σ is the attenuation parameter constant, f ₀Be wavelet mother function

Centre frequency, its frequency domain representation:

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

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

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

Since the notion of proposition kurtosis (kurtosis) such as Stewart in 1970 rises, it was used to weigh the order of severity of mechanical fault always in a very long time in past.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 more is just strong more, on the contrary then more a little less than.Therefore, it is strong and weak that the present invention utilizes this to add up the impact of weighing each yardstick wavelet coefficient in the step 2, calculates 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 the step 2, expectation is asked in E [ ] expression.

Step 4: utilize a kind of adaptive algorithm to find out small echo scale parameter a=[a in the step 3 ₁, a ₂..., a _l] in big kurtosis ku _aPairing wavelet scale parameter a _Opt=[a _n, a _N+1..., a _m], promptly the optimal wavelet yardstick is selected the pairing wavelet coefficient structure of these scale parameters optimum analysis signal s then _a(n);

Mention in the step 2 and utilize the different scale small echo that signal is done wavelet transformation to be equivalent to utilize a bank of filters signal filtering; Often kurtosis ku is bigger and include the signal of bearing fault characteristic, therefore can select the pairing coefficient of the bigger several scales of ku value to come component analysis signal s _a(n) carry out fault diagnosis, s _a(n) for having the stack of the wavelet coefficient of kurtosis greatly, its computing method are following:

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

In the 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 is as shown in Figure 3, in order to select the analytic signal s with maximum kurtosis ku _a(n), the wavelet coefficient s after will merging here _aAs analytic signal, and its kurtosis ku compared, its specific algorithm is: select the i scale coefficient

As a last coefficient WT _Pre(n) and the i scale coefficient With the i+1 scale coefficient

Merge coefficient WT _Cur(n) compare (i is a natural number, and initial value is 1), i.e. WT _Pre(n) and WT _Cur(n) compare, if merge coefficient WT _Cur(n) ku _CurValue is greater than a last scale coefficient WT _Pre(n) ku _PreValue is so with current scale coefficient WT _Cur(n) as a last scale coefficient WT _Pre(n), with current scale coefficient WT _Cur(n) with the merge coefficient of i+2 scale coefficient as current scale coefficient WT _CurAnd compare (n); Otherwise, then reselect the i+1 scale coefficient as a last scale coefficient WT _Pre(n), and with the merge coefficient WT of i+1 scale coefficient and i+2 scale coefficient _Cur(n) compare.By that analogy, all merged up to all scale coefficients, the merge coefficient of selecting maximum ku value is as analytic signal, and the yardstick of respectively organizing coefficient that is merged is as optimal scale a _Opt=[a _m, a _M+1..., a _n].

Adaptive algorithm through this step is from yardstick a=[a ₁, a ₂..., a _l] in choose wavelet coefficient WT with big kurtosis _a(n) pairing 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 are screened; Stay the real pairing wavelet filter of resonance bands among most likely the present invention; Like this, in the process that the high-frequency resonance band signal is extracted with regard to unnecessary centre frequency and the bandwidth of at first confirming wave filter, thereby improved the accuracy of diagnosis.

Like Fig. 4 and shown in Figure 5, for this step is chosen big kurtosis ku _aA specific embodiment, among Fig. 4, horizontal ordinate be wavelet transformation yardstick a=[1,2 ..., 32], ordinate is the pairing wavelet coefficient WT of each yardstick _a(n) kurtosis ku can find that at yardstick be about 12, and the kurtosis of wavelet coefficient is bigger.After above-mentioned adaptive approach processing, what show among Fig. 5 is the kurtosis of the wavelet coefficient after merging and the corresponding relation of yardstick, can find yardstick a _Opt=[7,8 ..., 16] the pairing 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 is as shown in Figure 6.As can be seen from Figure 6, this Optimal Signals has the obvious periodic impact, and the impact that produces with the bearing local damage is consistent, and has realized the extraction to the high-frequency resonance band.

Step 5: to the optimum analysis signal s that obtains in the step 4 _a(t) carry out envelope demodulation, obtain its envelope signal s _e(t); Its concrete computing method are following:

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

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

Wherein H [ ] expression Hilbert transform, τ is a transformation parameter.Envelope demodulation is a prior art, no longer details here.

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

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

Because FFT is transformed to prior art, no longer detail here.The envelope demodulation that has obtained the optimum analysis signal through step 6 is composed, and the envelope demodulation spectrum is analyzed, if it includes the fault characteristic frequency of bearing, gear, shows that then fault has taken place for bearing, gear; Otherwise then operation is normal.

In the present embodiment, we have provided respectively through direct demodulation preprocessed signal s ₁(n) envelope time domain figure and frequency domain figure are like Fig. 9 and shown in Figure 10.Though the envelope signal after the as can beappreciated from fig. 9 direct demodulation also has than obvious periodic property, can find this cycle T ₁The commentaries on classics of=0.0075s and bearing inner race 2 frequency multiplication 2f frequently _r=133.33Hz is consistent, from the frequency domain figure of Figure 10, can obtain checking, therefore can not reflect the fault signature of bearing.The right result (as shown in Figure 8) who from step 6, obtains can find out, the resulting result of the present invention obviously comprised bearing fault characteristic frequency BPFI=257Hz 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 to be understood 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 break away from essence of the present invention according to these teachings disclosed by the invention, and these distortion and combination are still in protection scope of the present invention.

Claims (3)

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

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

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

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

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

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

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

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

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

In the formula, wherein X (f), ψ (f) be respectively x (t),

Fourier transform, F ^-1The inverse transformation of [ ] expression Fourier transform, b is the time parameter after the inverse transformation, 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 analytic signal s with maximum kurtosis ku _a(n), the wavelet coefficient s after will merging here _aAs analytic signal, and its kurtosis ku compared.

3. according to the adaptive failure diagnostic method shown in the claim 2, it is characterized in that the idiographic flow of the adaptive algorithm in the step 4 is: select the i scale coefficient based on the rotary mechanical part of continuous wavelet transform

As a last coefficient WT _Pre(n) and the i scale coefficient

With the i+1 scale coefficient

Merge coefficient WT _Cur(n) compare (i is a natural number, and initial value is 1), i.e. WT _Pre(n) and WT _Cur(n) compare, if merge coefficient WT _Cur(n) ku _CurValue is greater than a last scale coefficient WT _Pre(n) ku _PreValue is so with current scale coefficient WT _Cur(n) as a last scale coefficient WT _Pre(n), with current scale coefficient WT _Cur(n) with the merge coefficient of i+2 scale coefficient as current scale coefficient WT _CurAnd compare (n); Otherwise, then reselect the i+1 scale coefficient as a last scale coefficient WT _Pre(n), and with the merge coefficient WT of i+1 scale coefficient and i+2 scale coefficient _Cur(n) compare.By that analogy, all merged up to all scale coefficients, the merge coefficient of selecting maximum ku value is as analytic signal, and the yardstick of respectively organizing coefficient that is merged is as optimal scale a _Opt=[a _m, a _M+1..., a _n].

Images