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Fault Detection of Induction Motor Using Fast Fourier Transform with Feature Selection via Principal Component Analysis

  • Young-Jun YooEmail author
Regular Paper
  • 21 Downloads

Abstract

Fault detection and diagnosis of the induction motor is important to prevent the system downtime of industrial fields. Most of the fault detection and diagnosis is conducted in the frequency domain using fast Fourier transform (FFT). Although several studies have been done using FFT, this method has difficulties in finding the fault characteristic frequency component. To overcome these difficulties, this paper provides the algorithm using principal component analysis (PCA) to easily find the feature of the FFT signal and utilize the Hotelling’s \(T^{2}\) as an index for fault detection. After selecting the peak of top five frequencies and corresponding amplitude of the FFT as a feature and reducing the dimension through PCA, it is possible to detect a motor abnormality through Hotelling’s \(T^{2}\) value. The proposed method is verified for detecting abnormal states of three-phase squirrel-cage induction motor. It has been confirmed that using the fault characteristic frequency component of both frequency and corresponding amplitude is more accurate in determining the motor abnormality than the characteristic of only frequency.

Keywords

Fault detection and diagnosis Fast Fourier transforms Principal component analysis Induction motor 

List of Symbols

\(\alpha\)

The level of significance

\(\zeta\)

Frequency

\({\varLambda }\)

The loading vector directions and solving an eigenvalue decomposition of the sample covariance matrix

\(\Sigma\)

Covariance matrix

\(\Sigma _{a}\)

The non-negative real eigenvalues corresponding to the \(P\) principal components

\(a\)

The number of principal components

\({\text{c}}_{\alpha }\)

The value of the normal distribution

\(E\)

The residual term

\(k\)

The number of principal component loading vectors

\(n\)

Observations (samples)

\(p\)

Measurement variables

\(P\)

The loadings to be estimated

\(t\)

Time

\(t_{i}\)

A score vector of the PCA model

\(T\)

A principal component scores

\(v_{i}\)

A principal component loading vector

\(V\)

Loading matrix

\(x_{0}\), …, \(x_{N - 1}\)

Complex numbers

\(x\left( t \right)\)

Lebesgue integrable function

\(X\)

Measured data matrix

\(X\left( \zeta \right)\)

Fourier transform of \(x\left( t \right)\)

\(X_{k}\)

Discrete Fourier transforms of \(x_{0}\), …, \(x_{N - 1}\)

Abbreviations

DFT

Discrete Fourier transforms

FFT

Fast Fourier transforms

FCFC

Fault characteristic frequency component

PCA

Principal component analysis

PC

Principal component

SPE

Square prediction error

TSCFE-SS

Time-stepping coupled finite-element-state-space method

Notes

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Copyright information

© Korean Society for Precision Engineering 2019

Authors and Affiliations

  1. 1.Department of Electronic EngineeringPohang University of Science and Technology (POSTECH)PohangRepublic of Korea

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