CN104215905A - Motor fault diagnosis method based on Mahalanobis-Taguchi system and Box-Cox transformation - Google Patents

Abstract

The invention discloses a motor fault diagnosis method based on a Mahalanobis-Taguchi system and Box-Cox transformation. The motor fault diagnosis method includes the steps of firstly, acquiring vibration signals when a motor is in normal operation and in fault; secondly, computing time-domain and time-frequency-domain characteristic parameters of the vibration signals; thirdly, applying a robust design concept in the Mahalanobis-Taguchi system to the characteristic parameters and selecting useful characteristic parameters for computing Mahalanobis distances when the motor is operated in different health states; fourthly, transforming the Mahalanobis distances obtained by computation in the step three to Gaussian distribution data by means of Box-Cox transformation, and determining a Mahalanobis distance range when the motor is operated in different health states by the aid of the Gaussian distribution property and inverse Box-Cox transformation; fifthly, subjecting the motor in an unknown operation state to signal acquisition, useful characteristic parameter computation and Mahalanobis distance computation, comparing the Mahalanobis distance range determined in the step four and judging the health condition of the tested motor, so that motor fault diagnosis is achieved. The motor fault diagnosis method based on the Mahalanobis-Taguchi system and Box-Cox transformation is capable of achieving diagnosis for electrical faults of the motor effectively.

Description

A kind of Method of Motor Fault Diagnosis converted based on horse field system and Box-Cox

Technical field

The present invention relates to a kind of Method of Motor Fault Diagnosis.

Background technology

Along with the development of AC electric power systems, alternating current generator is used in commercial production widely.Because it uses frequent, load torque fluctuation, the reason such as overheated of transshipping, motor is easy to break down.Electrical fault not only can affect the production of industry, but also may cause the security incidents such as casualties.Therefore, for guaranteeing motor security of operation, reliable, the enforcement of Method of Motor Fault Diagnosis then seems particularly important.The fault type of motor can be divided into mechanical fault and electric fault two aspect.The diagnosis of motor electric fault under unbalanced input voltages that what the present invention was specifically related to is.Existing diagnostic method reasoning from logic is complicated, assesses the cost higher, is more difficultly actually applied.

Summary of the invention

In order to overcome the more difficult deficiency being applicable to motor electric fault diagnosis of existing method for diagnosing faults, the invention provides a kind of Method of Motor Fault Diagnosis converted based on horse field system and Box-Cox effectively realizing motor electric fault diagnosis.

The technical solution adopted for the present invention to solve the technical problems is:

Based on the Method of Motor Fault Diagnosis that horse field system and Box-Cox convert, it is characterized in that: said method comprising the steps of:

Step one, gather the vibration signal of motor when normally working and break down;

Step 2, the vibration signal obtained step one carry out the calculating of characteristic parameter, specifically: calculating vibration signal being carried out to time domain charactreristic parameter, simultaneously to vibration signal by wavelet package transforms, carry out the calculating of characteristic parameter on time-frequency domain;

Step 3, to the characteristic parameter calculated in step 2, characteristic parameter when normally working with motor is benchmark, uses the based Robust Design theory in the system of horse field to select useful characteristic parameter, and recalculates mahalanobis distance based on these characteristic parameters;

Step 4, to the non-negative that step 3 obtains, the mahalanobis distance of non-gaussian distribution, use Box-Cox conversion, convert the data of Gaussian distribution to, utilize the character of Gaussian distribution and inverse Box-Cox conversion, determine the mahalanobis distance scope of machine operation when different health status;

The one group of data x=[x be made up of mahalanobis distance ₁, x ₂..., x _n], N is the number of mahalanobis distance sample, i-th data x in x _ithe data y obtained after Box-Cox conversion _i(λ) calculate by following formula:

$y_i\left(\mathrm{\λ}\right)=\left\{\begin{array}{cc}\frac{x_i^{\mathrm{\λ}}-1}{\mathrm{\λ}},& \mathrm{\λ}\≠0\\ \ln \left(x_i\right),& \mathrm{\λ}=0\end{array}\right.$

Wherein convert parameter lambda to be estimated by the maximum likelihood function of following formula:

$f(y,\mathrm{\λ})=-\frac{N}{2}\ln \left[\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\frac{{(y_i\left(\mathrm{\λ}\right)-\stackrel{\‾}{y\left(\mathrm{\λ}\right)})}^2}{N}\right]+(\mathrm{\λ}-1)\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\ln \left(x_i\right)$

Wherein, y=[y ₁, y ₂..., y _n], before and after Box-Cox converts, the distribution situation of data can be undertaken judging or verifying by histogram or normal probability plot;

Then use the character of Gaussian distribution, obtain the upper and lower limit of the data of the rear Gaussian distributed of Box-Cox conversion, and determine the mahalanobis distance scope of machine operation under different health status by the inverse Box-Cox conversion of following formula:

$x=\left\{\begin{array}{cc}{(\mathrm{\λy}+1)}^{\frac{1}{\mathrm{\λ}}},& \mathrm{\λ}\≠0\\ e^y,& \mathrm{\λ}=0\end{array}\right.$

Step 5, to the motor of unknown duty through vibration signals collecting, useful feature parameter calculates and mahalanobis distance calculates, the mahalanobis distance scope determined in contrast step 4, judges the health status of testing of electric motors, thus realizes the fault diagnosis of motor.

Further, in described step 3, use the based Robust Design theory in the system of horse field to select useful characteristic parameter, comprise the following steps:

Step 3.1, to set after a stack features standard parameter characteristic of correspondence vector as z _i, its dimension is n, the mahalanobis distance MD that these group data are corresponding _ifor

$M{D}_i=\frac{1}{n}{z}_i{C}^{-1}{z}_i^T$

Wherein, C ^-1for the inverse matrix of correlation matrix, for character vector z _itransposition;

Step 3.2, use Taguchi's method are optimized characteristic parameter and choose;

Quantity n according to characteristic parameter in proper vector selects two-level orthogonal array L _p(t ^c), wherein p is test number (TN), and t=2 is number of levels, and definition level '+' is " using this characteristic parameter ", and level '-' is " not using this characteristic parameter ", and c is columns, represents and allows to arrange maximum characteristic parameter numbers; According to 13 characteristic parameter selection orthogonal arrage L that step 2 builds ₁₆(2 ¹⁵); To a jth characteristic parameter, if with be respectively the signal to noise ratio (S/N ratio) average of this characteristic parameter under level '+' and level '-'; represent and adopt this characteristic parameter on average to detect effect to fault, represent and do not adopt this characteristic parameter on average to detect effect to fault, therefore select satisfied useful feature parameter.

In described step 2, vibration signal is carried out to the calculating of time domain charactreristic parameter, include valid value, peak value, kurtosis, measure of skewness, crest factor, nargin coefficient, impulse ratio, form factor and root mean square; Use wavelet package transforms that vibration signal is decomposed 2 layers simultaneously, calculate 4 characteristic parameters about energy in wavelet packet coefficient.These 13 parameters use alphabetical A respectively ₁, A ₂..., A ₁₃represent.

Technical conceive of the present invention is: the diagnosis of motor electric fault under unbalanced input voltages that what the present invention was specifically related to is.Mahalanobis distance has been used to the health status of characterization device, but this parameter has the characteristic of non-negative and non-gaussian distribution, determines the mahalanobis distance scope of machine operation under different health status, usually more difficult.Converted by Box-Cox, and use the character of Gaussian distribution, in the training stage, construct the mahalanobis distance scope of machine operation under different health status; At test phase, calculate the mahalanobis distance of unknown health status testing of electric motors, by the contrast of mahalanobis distance scope built with the training stage, judge the health status of testing of electric motors, realize the fault diagnosis of motor.

Beneficial effect of the present invention is mainly manifested in: the diagnosis effectively realizing motor electric fault, reliability is good.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of Method of Motor Fault Diagnosis based on horse field system and Box-Cox conversion of the present invention.

Fig. 2 is motor when normally working, the histogram of mahalanobis distance.

Fig. 3 is the mahalanobis distance of motor when normally working when adopting Box-Cox conversion, the relation curve of maximum likelihood function f (y, λ) and conversion parameter lambda.

Fig. 4 be the mahalanobis distance of motor when normally working after Box-Cox conversion, the normal probability plot of sample data.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described.

With reference to Fig. 1 ~ Fig. 4, a kind of Method of Motor Fault Diagnosis converted based on horse field system and Box-Cox, comprises the following steps:

Step one, in the training stage, gather the vibration signal of motor faulty motor when normally working and under unbalanced input voltages respectively, wherein fault-signal includes three from small to large, the signal that fault level increases successively, represents respectively by fault 1, fault 2 and fault 3.

Step 2, to the vibration signal collected, carry out calculation of characteristic parameters, build the characteristic data set of a higher-dimension.Specifically vibration signal is carried out to the calculating of time domain charactreristic parameter, include valid value, peak value, kurtosis, measure of skewness, crest factor, nargin coefficient, impulse ratio, form factor and root mean square; Use wavelet package transforms that vibration signal is decomposed 2 layers simultaneously, calculate 4 characteristic parameters about energy in wavelet packet coefficient.These 13 parameters use alphabetical A respectively ₁, A ₂..., A ₁₃represent.

Step 3, calculate characteristic parameter in step 2, characteristic parameter when normally working with motor is benchmark, uses the based Robust Design theory in the system of horse field, and use two-level orthogonal array to test, result is as shown in table 1, extracts useful characteristic parameter A ₁, A ₂, A ₄, A ₅, A ₉, A ₁₀.The useful feature parameter extracted is used to recalculate mahalanobis distance.Mahalanobis distance when normally working for motor, its data are as shown in table 2, and the column distribution plan of data as shown in Figure 2, can see these data not Gaussian distributed.

Table 1

Table 2

Step 4, the mahalanobis distance that step 3 is obtained, use Box-Cox conversion, be the data of Gaussian distribution by the data transformation of non-gaussian distribution, then the character of Gaussian distribution is used, namely the Data distribution8 of 95.4% has in the scope within 2 standard deviations at distance average, and by inverse Box-Cox conversion, determine the mahalanobis distance scope of machine operation under different health status.When normally working for motor, find best conversion parameter lambda=0.39 by maximum likelihood function, as shown in Figure 3, it is-0.10 that the mahalanobis distance of non-gaussian distribution is transformed into a class mean, and variance is the data of 0.56 Gaussian distribution, as shown in Figure 4.Use the character of Gaussian distribution, namely about have the Data distribution8 of 95.4% in the scope of [-1.22,1.02], then by inverse Box-Cox conversion, $x=\left\{\begin{array}{cc}{(\mathrm{\λy}+1)}^{\frac{1}{\mathrm{\λ}}},& \mathrm{\λ}\≠0\\ e^y,& \mathrm{\λ}=0\end{array}\right.,$ The mahalanobis distance scope obtained when motor normally works is [0.19,2.36].

With reference to same method, can determine to break down 1 respectively when motor, when fault 2 and fault 3, corresponding mahalanobis distance scope is [5.59,19.70] respectively, [25.32,51.35] and [62.95,101.28].

Step 5, at test phase, to the motor of unknown duty through vibration signals collecting, useful feature parameter calculates and mahalanobis distance calculates, and by from set up in training process, corresponding to the contrast of the mahalanobis distance scope of the different health status of motor, the health status of testing of electric motors is judged, thus realizes the fault diagnosis of motor.

Claims (3)

1., based on the Method of Motor Fault Diagnosis that horse field system and Box-Cox convert, it is characterized in that: said method comprising the steps of:

Step one, gather the vibration signal of motor when normally working and break down;

Step 2, the vibration signal obtained step one carry out the calculating of characteristic parameter, specifically: calculating vibration signal being carried out to time domain charactreristic parameter, simultaneously to vibration signal by wavelet package transforms, carry out the calculating of characteristic parameter on time-frequency domain;

Step 3, the characteristic parameter that step 2 is obtained, the characteristic parameter obtained when normally working with motor is benchmark, uses the based Robust Design theory in the system of horse field to select useful characteristic parameter, and recalculates mahalanobis distance based on these characteristic parameters;

Step 4, to the non-negative that step 3 obtains, the mahalanobis distance of non-gaussian distribution, use Box-Cox conversion, convert the data of Gaussian distribution to, utilize the character of Gaussian distribution and inverse Box-Cox conversion, determine the mahalanobis distance scope of machine operation when different health status;

Sample data x=[the x be made up of mahalanobis distance ₁, x ₂..., x _n], N is the number of mahalanobis distance sample, i-th data x in x _ithe data y obtained after Box-Cox conversion _i(λ) calculate by following formula:

$y_i\left(\mathrm{\λ}\right)=\left\{\begin{array}{cc}\frac{x_i^{\mathrm{\λ}}-1}{\mathrm{\λ}},& \mathrm{\λ}\≠0\\ \ln \left(x_i\right),& \mathrm{\λ}=0\end{array}\right.$

Wherein convert parameter lambda to be estimated by the maximum likelihood function of following formula:

$f(y,\mathrm{\λ})=-\frac{N}{2}\ln \left[\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\frac{{(y_i\left(\mathrm{\λ}\right)-\stackrel{\‾}{y\left(\mathrm{\λ}\right)})}^2}{N}\right]+(\mathrm{\λ}-1)\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\ln \left(x_i\right)$

In formula, y=[y ₁, y ₂..., y _n], before and after Box-Cox converts, the distribution situation of data can be undertaken judging or verifying by histogram or normal probability plot;

Then use the character of Gaussian distribution, obtain the upper and lower limit of the data of the rear Gaussian distributed of Box-Cox conversion, and determine the mahalanobis distance scope of machine operation under different health status by the inverse Box-Cox conversion of following formula:

$x=\left\{\begin{array}{cc}{(\mathrm{\λy}+1)}^{\frac{1}{\mathrm{\λ}}},& \mathrm{\λ}\≠0\\ e^y,& \mathrm{\λ}=0\end{array}\right.$

Step 5, to the motor of unknown duty through vibration signals collecting, useful feature parameter calculates and mahalanobis distance calculates, the mahalanobis distance scope determined in contrast step 4, judges the carrying out of testing of electric motors health status, thus realizes the fault diagnosis of motor.

2. as claimed in claim 1 based on the Method of Motor Fault Diagnosis that horse field system and Box-Cox convert, it is characterized in that: in described step 3, use the based Robust Design theory in the system of horse field to select useful characteristic parameter, comprise the following steps:

Step 3.1, to set after a stack features standard parameter characteristic of correspondence vector as z _i, its dimension is n, the mahalanobis distance MD that these group data are corresponding _ifor

$M{D}_i=\frac{1}{n}{z}_i{C}^{-1}{z}_i^T$

Wherein, C ^-1for the inverse matrix of correlation matrix, for character vector z _itransposition;

Step 3.2, use Taguchi's method are optimized characteristic parameter and choose;

Quantity n according to characteristic parameter in proper vector selects two-level orthogonal array L _p(t ^c), wherein p is test number (TN), and t=2 is number of levels, and definition level '+' is " using this characteristic parameter ", and level '-' is " not using this characteristic parameter ", and c is columns, represents and allows to arrange maximum characteristic parameter numbers; According to 13 characteristic parameter selection orthogonal arrage L that step 2 builds ₁₆(2 ¹⁵); To a jth characteristic parameter, if with be respectively the signal to noise ratio (S/N ratio) average of this characteristic parameter under level '+' and level '-'; represent and adopt this characteristic parameter on average to detect effect to fault, represent and do not adopt this characteristic parameter on average to detect effect to fault, therefore select satisfied useful feature parameter.

3. as claimed in claim 1 or 2 based on the Method of Motor Fault Diagnosis that horse field system and Box-Cox convert, it is characterized in that: in described step 2, vibration signal is carried out to the calculating of time domain charactreristic parameter, include valid value, peak value, kurtosis, measure of skewness, crest factor, nargin coefficient, impulse ratio, form factor and root mean square; Use wavelet package transforms that vibration signal is decomposed 2 layers simultaneously, calculate 4 characteristic parameters about energy in wavelet packet coefficient.