KR20090078075A - Fault diagnosis of inductirn motors by dft and wavelet - Google Patents

Abstract

A method for diagnosing fault of an induction motor is provided to finally diagnose fault of induction motor using fusion algorithm. A characteristic vector is calculated using fourier transform, linear discriminant analysis and wavelet transform from current signal value. Similarity value is calculated through distance comparison between standard model and characteristic vector calculated. Similarity value is calculated according to each fault classification. The diagnosis is performed by selecting a model having high similarity with conventional model.

Description

Fault Diagnosis of Inductirn Motors by DFT and Wavelet}

In the present invention, a failure diagnosis algorithm using a Discrete Fourier Transform (DFT) and a wavelet is proposed. The proposed method extracts the feature points using the method of extracting the fault pattern by frequency based DFT and the method of extracting the fault pattern using time-frequency based wavelet. The final diagnosis of the induction motor is extracted by DFT and wavelet. Performed by a fusion algorithm that can effectively fuse feature values. The developed algorithm is applied to various measured data and shows its validity.

Unexpected failures of induction motors widely used in industrial sites can lead to paralysis of all or part of the process, which can result in fatal accidents and economic losses. In recent years, troubleshooting techniques that can prevent accidents caused by these failures have emerged as an important part along with maintenance. In general, online failure diagnosis of an induction motor is performed by a motor current signal analysis (MCSA). In the past, many researches based on vibration monitoring have been conducted, but the construction of such a diagnostic system in small and medium-sized induction motors used throughout the industry is costly to increase the performance specifications of the sensor and the diagnostic system. It is difficult to ignore the problem of induction of structural vibration due to the performance change depending on the position of the motor and the support environment of the motor.

On the other hand, when using the MCSA detection method, it is possible to diagnose the static dynamic eccentricity of the stator and the rotor and the bearing failure state except the insulation state. In addition, since the fault diagnosis can be performed online, researches on these have been actively conducted in recent years.

A feature extraction technique is needed to effectively represent the fault condition of an induction motor used for diagnosis after acquiring a current signal by the MCSA detection method. As the feature vector extraction method, a d-q pattern is extracted by Park transform, and a specific frequency is extracted by using a frequency spectrum (FFT) of a current signal.

However, in the case of the d-q pattern, it is difficult to obtain a unique pattern for each fault condition, and it is difficult to classify the fault pattern under the noise. In addition, in the case of the frequency spectrum, the frequency component is changed by the load variation or the high frequency component of the input power source, and there is a limit in extracting a specific specific frequency spectrum for each fault condition.

In order to solve this problem, a method of extracting features using wavelets that can be interpreted in the time axis and the frequency space has been proposed. In addition, a method of extracting a feature using Principal Component Analysis (PCA) is used. However, this method also does not completely overcome the existing limitations, and according to the present invention, the existing classification algorithms extract complementary elements according to the application field, and solve the failure diagnosis algorithm using the Discrete Fourier Transform (DFT) and the wavelet. It is proposed to implement the above-mentioned problem overcoming.

SUMMARY OF THE INVENTION The present invention has been made to solve the above problems, and an object of the present invention is to use a method of extracting a fault pattern by a frequency-based DFT and a method of extracting a fault pattern using a time-frequency based wavelet for feature point extraction. In addition, the present invention provides a failure diagnosis method performed by a fusion algorithm capable of effectively fusing the extracted feature values of the final failure diagnosis of the induction motor to provide a failure diagnosis method of excellent performance.

According to the present invention, a method of calculating a feature vector using discrete discrete Fourier transform (DFT), linear discriminant analysis (LDA), and wavelet transform is performed on the current signal value obtained from an induction motor, and the calculation is performed. Calculating a similarity value by comparing each of the feature vectors with a reference model; Calculating the calculated similarity value as the similarity for each failure classification state by a weight agreement method; The above-described problem is solved by providing a method for diagnosing a failure of an induction motor using a DFT and a wavelet, which comprises performing a diagnosis by selecting a model having a high similarity with the reference model.

According to the present invention, a method of extracting a fault pattern by a frequency-based DFT and a method of extracting a fault pattern using a wavelet based on a time-frequency for extracting feature points, and extracting a final fault diagnosis of an induction motor There is an effect of providing a high performance fault diagnosis method by providing a fault diagnosis method performed by a fusion algorithm that can effectively fuse the values.

(1) calculating a characteristic vector by a discrete Fourier transform (DFT), a linear discriminant analysis (LDA), and a wavelet transform, respectively, of current signals obtained from an induction motor;

(2) calculating a similarity value by comparing the calculated feature vectors with a reference model;

(3) calculating the calculated similarity value as the similarity for each failure classification state by a weight agreement method;

(4) performing a diagnosis by selecting a model having high similarity with the reference model;

It provides a failure diagnosis method of the induction motor using a DFT and wavelets, characterized in that made.

In addition, the present invention is to extract the feature by the discrete Fourier transform (DFT) using the DFT and wavelet, characterized in that to extract the feature vector by converting the current signal of the induction motor into the frequency space using the following equation (11) To provide a method for diagnosing failure of induction motors.

(식 11)

(Eq. 11)

(Where X (k) is the discrete Fourier transform coefficient and N is the number of samples)

In addition, the present invention is to extract the feature vector by the linear discrimination analysis (LDA), after obtaining the current signal of the induction motor is converted to the frequency space by the DFT, the dimension of the failure pattern is reduced by the linear discrimination analysis It is desirable to provide a failure diagnosis method for an induction motor using a DFT and a wavelet.

In addition, the present invention to extract the failure pattern by the linear discrimination analysis,

a) converting the measured learning current signal into a one-dimensional column vector, _and obtaining the BCS matrix S _B and the WCS matrix S _W by Equation 1 and Equation 2 below;

b) obtaining by Equation 9 an optimal projective matrix W having a normal orthogonal matrix that maximizes the ratio of the BCS matrix to the WSC matrix, such as Equations 8 and 9 below; And

c) learning signal x _i Obtaining a feature vector T _i for the call;

It provides a failure diagnosis method of an induction motor using a DFT and wavelets, characterized in that consisting of.

Also, in the present invention, acquiring a feature vector of the flow motor using the wavelet may be performed by dividing the obtained current signal into frequency bands by using the wavelet multi-resolution technique, and then by band as shown in Equation 14 below. It provides a fault diagnosis method of an induction motor using a DFT and a wavelet, characterized by calculating the sum of the existing coefficients.

Hereinafter, with reference to the accompanying drawings will be described the configuration and operation of the present invention.

(The signs of the formulas given in the detailed description of the invention and in the claims are the same.)

1. Extraction of features by PCA

The PCA algorithm is widely used as a technique for obtaining eigenvectors of covariance matrices that best represent the characteristics of the data, and reducing them to low-order vectors. The current signal of the time series is processed by obtaining the eigenvectors by obtaining the covariance matrix, converting them into low-order feature vectors by arranging them in order of magnitude of the eigenvalues. The detailed algorithm for this is as follows.

{Step 1} After converting the measured p learning current signals into a one-dimensional column vector, the average of all signals is obtained by Equation 1.

{Step 2} Find the covariance matrix for the current signal for learning.

N eigenvalues and n eigenvectors for the covariance calculated by {step 3} (Equation 2) are obtained.

를 구한 후에 학습신호에 x_i대한 특징벡터

를 (식 4)에 의해 산출한다. (식 4)에서 알 수 있는 바와 같이 입력신호에 대한 특징벡터는 공분산에 대한 고유벡터를 이용하여 PCA변환된 공간으로 투영함으로써 얻을 수 있다.Step 4 {} eigenvector v number of dimensions to be considered a _j (k) unique as rearranged in order of size of the eigenvalues vector

Find the feature vector for x _{i in} the learning signal

Is calculated by (Equation 4). As can be seen from Equation 4, the feature vector for the input signal can be obtained by projecting onto the PCA transformed space using the eigenvector for covariance.

{} Step 5 calculates a "feature vector z of the _{i, i} i-th input for verification by the current x PCA techniques.

2. Feature Extraction by LDA

After acquiring the current signal of the induction motor and converting it into the frequency space by DFT, the fault pattern whose dimension is reduced by linear discriminant analysis (LDA) is extracted.

Linear discriminant analysis finds a matrix in which the ratio of the WCS (within-class scatter) matrix S _W representing the variance in the class and the BCS (between-class scatter) matrix S _B representing the variance between the classes is maximized. Linear transformation. In other words, rather than finding a projection that maximizes the variance projected like the principal component analysis technique, the optimal projection matrix is obtained to maximize the difference between classes, and then the input signal is linearly transformed using the projection matrix. The process of feature extraction and comparison by linear discrimination analysis method is as follows.

{Step 1} After converting the measured training current signal into a one-dimensional column vector, Equation 6 and Equation 7 obtain S _B , a BCS matrix, and S _W , a WCS matrix.

Here, n _i is the number of data in the i th class C _i , and m _i represents the average value in the i th class C _i . In Equation 7, m is an average value of all classes.

{Step 2} An optimal projection matrix having a normal orthogonal matrix that maximizes the ratio of the BCS matrix to the WCS matrix as shown in Equation (8) is obtained by Equation (9).

{Step 3} The feature vector T _i for the learning signal x _i is obtained.

As can be seen from Equation 10, in order to perform linear discriminant analysis, first, the input signal is reduced to low dimension by principal component analysis, and then the calculated feature vector z _i is transformed into the LDA space by the optimal projection matrix W. Project it. In general, when the number P of learning signals is smaller than the length N of the signals, the WCS matrix S _W is always irregular. This means that the projected WCS matrix can be zero if the projective matrix is not properly selected. Therefore, to solve this problem, linear discrimination analysis is performed after the input signal is reduced to low dimensional space using principal component analysis.

3. Feature Extraction by DFT

The DFT can be applied to process digital signals in the time domain and transform them into representations in the digital frequency domain. The final Fourier transform, which can be numerically computed for any finite sequence, is called the discrete Fourier transform coefficient. The coefficient is also an N-point sequence.

The DFT of the digital signal of N points is defined as follows.

(식 11)

(Eq. 11)

Conversely, to obtain the discrete sequence in the discrete signal spectrum, it is represented by the following inverse discrete Fourier transform.

(식 12)

(Eq. 12)

4. Feature Extraction by Wavelet

을 정의하고, 이 원형 웨이블렛을 시간축으로 b만큼 이동(translation)시키고, a만큼 스케일링(scaling)하여 다양한 웨이블렛을 구성하여 신호를 분해한다.The wavelet transform is a prototype wavelet called a basis function such as Daubechies, Coiflet, Haar, Symmlet, etc., capable of aperiodic signal separation as shown in equation (13).

The circular wavelet is translated by b on the time axis and scaled by a to form various wavelets to decompose the signal.

(식 13)

(Eq. 13)

In the wavelet transform, the term scale is used instead of frequency, and a signal passing through one wavelet is called a detail signal of one scale. Because wavelet base functions consist of a set of functions with different resolutions, the wavelet transform has multiresolution resolution. That is, the high frequency band has low frequency resolution and the low frequency band has multiresolution resolution with high frequency resolution. By using these characteristics, multiresolution filter banks can be implemented.

The discrete wavelet transform consists of a wavelet having a high-pass section as a filter bank, an octave-band structure that extends the low-pass section into a continuous filter bank, and a high-band section as a filter bank. It may be implemented in a packet structure (wavelet packet).

은 저역 통과 필터를,

은 고역 통과 필터를 각각 나타내며, 원형 웨이블렛으로부터 구성됨을 알 수 있다. 또한

는 샘플의 개수를 1/2로 줄이는 데시메이션(decimation)을 나타낸다.Figure 1 shows the octave band structure used in this paper, where

Low pass filter,

Denotes a high pass filter, respectively, and can be seen constructed from circular wavelets. Also

Denotes a decimation that reduces the number of samples by half.

The feature vector of the induction motor using wavelet transform is obtained by dividing the obtained current signal into frequency bands using the wavelet multi-resolution technique, and then calculating the sum of coefficients existing for each band as shown in Equation (14). .

를 이용하여 산출된 웨이블렛 특징값을 나타낸다.In Equation (7), W (j, k) is a signal obtained by wavelet transform at jth depth and kth node.

Represents a wavelet feature value calculated using.

5. Failure Diagnosis by Convergence Algorithm

FIG. 2 shows a configuration diagram performed by fusion of a feature vector calculated by DFT + LDA and a feature vector calculated by wavelet transform. As shown in FIG. 2, the characteristics of the current signal obtained from the induction motor to be diagnosed are calculated by DFT + LDA and wavelet (S1), and then similarity is calculated through distance comparison with a previously constructed reference model. (S2). The similarity value for each failure classification state is finally calculated by the weighted sum method of the calculated similarity values (S3), and a diagnosis is performed by selecting a model having a high similarity level with the reference model (S4). In the final fusion step, since the spatial distance data of the feature vectors extracted by DFT + LDA and DWT are in different ranges, each average value is obtained and automatically set to the same size by a weighting technique.

6. Application method and diagnosis result of fault condition

3 and Table 1 show the diagnostic results of the application method and the failure state.

{Table 1}

As shown in Table 1, which shows the diagnosis result by fault condition, in the case of steady state (H1), the diagnostic method by LDA showed the highest performance by 97%, while the diagnostic method by wavelet showed 85%. Poor performance was shown. Voltage unbalance (F1) showed the best performance with wavelet and LDA method at 100%, while diagnostic method with DFT + PCA showed the lowest performance with 95%. The bearing failure (F2) showed the best performance with PCA and DFT + LDA method showing 100%, while the diagnostic method with PCA showed the lowest performance with 95%. Rotor failure (F3) showed the best performance with DFT + LDA method showing 99%, while the wavelet diagnosis method showed the lowest performance with 78%. In the case of stator failure (F4), 99% of DFT + LDA method showed the best performance, while 74A of PCA diagnosis showed the lowest performance. The rotor unbalance (F5) showed the best performance with 99% of DFT + LDA method, while the lowest with 83% of wavelet diagnostic method.

Taken together, the LDA applied in the time domain shows excellent performances in the normal (H1) and voltage imbalance (F1), while the rotor failure (F3), stator failure (F4) and rotor imbalance (F5). The diagnostic performance was low for. On the other hand, after converting the current signal with time information into the frequency domain by DTF, DFT + LDA with LDA shows poor performance for normal (H1) and voltage imbalance (F1), while rotor failure (F3), The diagnostic performance was excellent for stator failure (F4) and rotor imbalance (F5).

In the present invention, as a method of improving the fault diagnosis performance by the fusion method, the LDA method showing excellent performance in the time domain and the DFT + LDA fusion method showing excellent performance in the frequency space (fusion method-A) are poorly performed. Although a wavelet with time-frequency information and a DFT + LDA are fused (fusion method-B).

{Table 2}

As a result, the fusion method-A was 99.7%, and the fusion method-B was 100%, and the fusion method applying the wavelet and DFT + LDA showed the best performance. In order to analyze the contribution of the low wavelet-based scheme to the convergence, Table 2 and the Euclidean distance comparison with the standard feature values for each failure state for the stator failure (F4) data in FIGS. 4A and 4B The calculated distance scale value is shown.

As shown in Table 2 and FIG. 4A and FIG. 4B, stator failure (F4) data was diagnosed as rotor failure (F3) as a result of applying LDA and DFT + LDA, and as a result, stator failure (F4) data was recovered even after fusion. Diagnosis was made by electronic failure (F3). On the other hand, even though the result of applying DFT + LDA diagnosed stator failure (F4) data as rotor failure (F3), the wavelet method diagnosed stator failure (F4) data as stator failure (F4) and finally fused it. In this case, stator failure (F4) data was diagnosed as stator failure (F4). These results were analyzed to be due to the superior diagnostic performance of the wavelet method than the LDA method in the case of stator failure (F4).

Table 3 and FIG. 5 below show distance scale values for each fault condition for normal (H1) data. As a result of applying the wavelet, normal (H1) data was diagnosed as stator failure (F4). Also, as a result of applying DFT + LDA, the normal (H1) data was diagnosed as voltage imbalance (F1). However, as a result of applying the wavelet and DFT + LDA, it is confirmed that the performance is improved by diagnosing the normal (H1) data as the normal (H1) and fusion. In other words, it can be analyzed that the recognition rate is improved because the wavelet technique has a low diagnosis rate but a region classified by the wavelet well and a region classified by the DFT + LDA method complementarily.

{Table 3}

According to the present invention, after the real-time current signal is converted into the frequency space by the DFT, the fault condition is extracted by the linear discrimination analysis technique. In addition, a feature having time-frequency information of the current signal is extracted by the wavelet multi-resolution technique. In the final classification stage, the diagnosis is effectively carried out by fusing two characteristics. In order to show the feasibility of the proposed method, after designing and fabricating a failure diagnosis device for induction motor, and using the measured data by the data acquisition device, the proposed fusion method is 11.2%, which is DFT + LDA. It was found that the performance was improved by 2.3% compared to the case of applying only Bay. Therefore, the proposed method shows better performance than other classification methods.

In the detailed description of the invention as described above, specific embodiments have been described. However, many modifications are possible without departing from the scope of the invention. The technical spirit of the present invention should not be limited to the described embodiments of the present invention, but should be determined not only by the claims, but also by those equivalent to the claims.

1 shows the structure of an octave band

2 is a flowchart illustrating a fault diagnosis process by a fusion algorithm.

Figure 3 shows the diagnostic rate according to the application method and the failure state of the present invention.

4A and 4B are graphs showing distance scales according to a failure state and a fusion method.

5 is a graph showing the distance scale according to the failure state and the fusion method.

Claims (5)

(1) calculating a characteristic vector by a discrete Fourier transform (DFT), a linear discriminant analysis (LDA), and a wavelet transform, respectively, of current signals obtained from an induction motor; (2) calculating a similarity value by comparing the calculated feature vectors with a reference model; (3) calculating the calculated similarity value as the similarity for each failure classification state by a weight agreement method; (4) performing a diagnosis by selecting a model having high similarity with the reference model; Failure diagnosis method of the induction motor using the DFT and wavelets, characterized in that comprises a. The method according to claim 1, In the extraction of the feature by the discrete Fourier transform (DFT), the fault diagnosis of the induction motor using the DFT and wavelet is characterized by extracting the feature vector by converting the current signal of the induction motor into the frequency space using Equation 11 below. Way.

(Eq. 11) (Where X (k) is the discrete Fourier transform coefficient and N is the number of samples) The method according to claim 1, The feature vector extraction by the linear discrimination analysis (LDA) is characterized in that after the current signal of the induction motor is acquired and converted into a frequency space by the DFT, the fault pattern whose dimension is reduced by the linear discrimination analysis is extracted. Fault diagnosis method of induction motor using DFT and wavelet. The method of claim 3, wherein the extraction of the failure pattern by the linear discrimination analysis, a) converting the measured learning current signal into a one-dimensional column vector, _and obtaining the BCS matrix S _B and the WCS matrix S _W by Equation 1 and Equation 2 below;

b) obtaining by Equation 9 an optimal projective matrix W having a normal orthogonal matrix that maximizes the ratio of the BCS matrix to the WSC matrix, such as Equations 8 and 9 below; And

c) learning signal x _i Obtaining a feature vector T _i for the call;

Failure diagnosis method of induction motor using DFT and wavelet, characterized in that consisting of. The method according to claim 1, Acquiring the feature vector of the flow motor using the wavelet is, by dividing the acquired one-phase current signal by the frequency band by using the wavelet multi-resolution technique, and then sum the coefficients existing for each band as shown in Equation 14 below. The fault diagnosis method of the induction motor using the DFT and wavelets, characterized in that to obtain and calculate.

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