**5. Results and discussion**

As above mentioned, some minor failures such as bearing failures are not distinguishable by exclusive use of ANFIS, figure 10. This is why the use of wavelets provides an effective tool for the identification of different types of failures in electric machines.

The results presented in the following are attained through simulations using real data, when the induction motor is under normal operating conditions and failure.

Phase I:

To exemplify the proposed strategy, the following results are obtained by using the x-axis measurement only. Firstly, the wavelet decomposition requires that n levels be selected, so that the inference process has sufficient information to identify the faulted condition. That is, the quantity of levels is proportional to the filtering quality. In this application, due to the good performance obtained when a correlation test to verify the data stability is carried out, n = 2 will be used.

That is, the number of levels affects the number of sets resulting from the wavelet decomposition, leading to four functions: two for high frequency, and two for low frequency. Figure 11 shows the wavelet decomposition corresponding to the motor in good condition.

In this study the Meyer wavelet family is used (which properties are symmetry, orthogonality, biortogonality) and the Shannon Entropy decomposition was used (Zadeh, 1965; Proakis, 2001; Anderson, 1984; Oppemheim & Schafer 2009)

Phase II:

Once the wavelet decomposition is evaluated, data must be structured and handled by the software, with the proper procedure.

*Training data*: the historical data set representing each particular state of the machine requires the corresponding wavelet decomposition.

*Checking data*: data used to test and infer. From a practical standpoint, they are the vibration measurements under the studied condition.

*Tags*: correspond to that feature that allows the user to differentiate one condition from another. For the studied case, numerical levels will be used for each engine's state.

Applying the proposed method to failures on bearings and broken bars, Figures 12-13 depict a typical result. It is noteworthy that the checking and training data are perfectly

In the case of bearing failure, there is a minimally invasive phenomenon in the machine's vibration, contrary to a broken bars failure, which gives rise to notorious vibration, Fig 9.

Likewise, at a first glance, the vibrations in the axial direction are more noticeable. Thus,

As above mentioned, some minor failures such as bearing failures are not distinguishable by exclusive use of ANFIS, figure 10. This is why the use of wavelets provides an effective tool

The results presented in the following are attained through simulations using real data,

To exemplify the proposed strategy, the following results are obtained by using the x-axis measurement only. Firstly, the wavelet decomposition requires that n levels be selected, so that the inference process has sufficient information to identify the faulted condition. That is, the quantity of levels is proportional to the filtering quality. In this application, due to the good performance obtained when a correlation test to verify the data stability is carried out,

That is, the number of levels affects the number of sets resulting from the wavelet decomposition, leading to four functions: two for high frequency, and two for low frequency. Figure 11 shows the wavelet decomposition corresponding to the motor in good condition.

In this study the Meyer wavelet family is used (which properties are symmetry, orthogonality, biortogonality) and the Shannon Entropy decomposition was used (Zadeh,

Once the wavelet decomposition is evaluated, data must be structured and handled by the

*Training data*: the historical data set representing each particular state of the machine

*Checking data*: data used to test and infer. From a practical standpoint, they are the vibration

*Tags*: correspond to that feature that allows the user to differentiate one condition from

Applying the proposed method to failures on bearings and broken bars, Figures 12-13 depict a typical result. It is noteworthy that the checking and training data are perfectly

another. For the studied case, numerical levels will be used for each engine's state.

The preliminary coarse filtering process is performed by the assembled sensor.

their measurements are employed in the following analysis.

for the identification of different types of failures in electric machines.

1965; Proakis, 2001; Anderson, 1984; Oppemheim & Schafer 2009)

when the induction motor is under normal operating conditions and failure.

1. A motor in good condition 2. A motor with bearing fault 3. A motor with broken bars

**5. Results and discussion** 

Phase I:

Phase II:

software, with the proper procedure.

requires the corresponding wavelet decomposition.

measurements under the studied condition.

n = 2 will be used.

differentiable through level changes observed in the data. Labels are selected by the user to have a reference, which is the state that the machine is undergoing.

Fig. 10. Bearing failure ANFIS without wavelet decomposition

Fig. 11. A machine in good condition: wavelet decomposition, n=2.

Additionally, Figures 14-15 display the Root Mean Squared Error (RMSE) between the checking and training curves, for both failures, where the RMSE is a quadratic scoring rule, which measures the average magnitude of the error. Expressing the expression in words, the difference between the forecasted and the corresponding observed values are each squared

Fuzzy Inference Systems Applied to the Analysis of Vibrations in Electrical Machines 149

Fig. 14. Error between checking and training curves for bearing failures

combination of the method by least squares and gradient descent.

Fig. 15. Error between checking and training curves for broken bars

It is important to clarify that, for the training-optimization process, ANFIS uses a

In Figures 16-17 the mean for both failures are exhibited, which have been calculated as an average data set for each level, where it is clear that inference process has been successful, because the labels are clearly differentiable, where positive and negative values are the

and then averaged over the sample. Finally, the square root of the average is calculated, since the errors are squared before they are averaged.

Fig. 12. Bearing failure

Fig. 13. Broken bars failure

and then averaged over the sample. Finally, the square root of the average is calculated,

since the errors are squared before they are averaged.

Fig. 12. Bearing failure

Fig. 13. Broken bars failure

Fig. 14. Error between checking and training curves for bearing failures

It is important to clarify that, for the training-optimization process, ANFIS uses a combination of the method by least squares and gradient descent.

Fig. 15. Error between checking and training curves for broken bars

In Figures 16-17 the mean for both failures are exhibited, which have been calculated as an average data set for each level, where it is clear that inference process has been successful, because the labels are clearly differentiable, where positive and negative values are the

Fuzzy Inference Systems Applied to the Analysis of Vibrations in Electrical Machines 151

The study of vibration in rotating electrical machines through ANFIS requires the use of signal conditioning tools, which are introduced through the training and test arrays. Special care should be taken with some overlapping modes, especially in those failures that, due to their nature, do not generate large perturbations in oscillations, but represent an imminent

The failures considered in the electrical machines studied, reflected changes in the three axes x, y and z. However, they are most noticeable in those that are axial to the axis of rotation, allowing the detection of failures through the analysis on a single axis, instead opening the

In the inference process it is quite attractive to use pragmatic strategies to handle large amount of measured information, and able to identify the machinery's operating condition. The errors between the check and learning curves for the two types of studied failures are satisfactory for identification purposes in both cases. Thus, ANFIS has been successfully

Anderson, T. (1984). *An introduction to Multivariate Statistical Analysis*, Wiley, ISBN 978-

Blodt, M.; Granjon, P.; Raison, B.; & Rostaing, G. (2008) Models for Bearing Damage

Bonissone, P.; Badami, V.; Chiang, K.; Khedkar, P.; Marcelle, K. & Schutten, M. (1995).

Cusido, J.; Romeral, L.; Ortega, J.; Rosro, J., & Espinosa, A. (2008). Fault Detection in

Jang, J. (1993). ANFIS: adaptive-network-based fuzzy inference system. *IEEE Transaction Systems, Man, Cybernetics*, Vol. 23, No. 3, pp. 665-685, ISSN 018-9472 Jang, J. & Sun, C. (1995). Neuro-fuzzy modeling and control. *Proceedings of the IEEE*, Vol. 83,

Jang, J. & Gulley, N. (1995). *The Fuzzy Logic Toolbox for use with MATLAB*, The MathWorks,

*on Industrial Electronics*, Vol. 55, No. 4, pp. 1813-1822. ISSN 0278-0046 Blodt, M.; Regnier, J.; & Faucher, J. (2009). Distinguishing Load Torque Oscillations and

Detection in Induction Motors Using Stator Current Monitoring. *IEEE Transactions* 

Eccentricity Faults in Induction Motors Using Stator Current Wigner Distributions. *IEEE Transactions on Industry Applications*, Vol. 45, No. 6. pp. 1991-2000, ISBN: 1-

Industrial applications of fuzzy logic at General Electric. *Proceedings of the IEEE*,

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way for the use of less sophisticated sensors, reducing the implementation costs.

Our gratitude to Universidad de Guanajuato for providing data for this research.

0471889878, Stanford, California, United States of America

Vol. 83, No.3, pp 450-465, ISSN 0018-9219

No. 3, pp 378-406. ISSN 0018-9219

Inc., Natick, Massachusetts

**6. Conclusions** 

risk to the engine's life.

**7. Acknowledgment** 

4244-0364-2

0046

**8. References** 

applied to distinguish between such failures.

result of a previous selection of tags formed by numerical extremes to differentiate the states where the motor is.

Fig. 16. Mean under bearing failure

Fig. 17. Mean under broken bars failure
