## 1 Introduction
However, the aforementioned method is based on the fast Fourier transform (FFT), and the sampling frequency and the acquisition time have a significant impact on the analysis solution. Under the load, speed and voltage variations as well as the minor fault in the induction motor and the spectrum of the phase stator current using the FFT become distorted and may lead to inaccuracy detection of airgap eccentricity fault [8]. Compared to the frequency-domain analysis, other eccentricity fault signature processing methods are employed in order to handle the stationary signal as well as the non-stationary signal. Wavelet transform (WT) provides a time-frequency domain processing method that is known as  
Figure 1: Rotor–stator rub of an induction motor caused by eccentricity fault. its multi-resolution analysis application. The utilization of the discrete wavelet transform (DWT) in apparent power signals for diagnosis of airgap eccentricity fault under load torque variation is introduced by simulation as well as experiments [8]. The wavelet packet decomposition (WPD) has been used to detect the eccentricity fault and distinguished from each other in steady-state operation conditions [11]. Besides that, a time-domain modified Prony's method is proposed for diagnosis of the airgap eccentricity with high accuracy only using a 10-ms dataset [12]. However, the literature reveals that a few contributions have been previously provided to the method for diagnosis of the high levels of eccentricity fault. It is known that inherent airgap eccentricity exists in any electrical machine, even newly manufactured, so it is impossible to avoid it. For that, its level is estimated and accepted under 10% [13]. This produces a consistent amount of unbalanced magnetic pull (UMP) in one direction, which can gradually lead to bearing wear, bent rotor shaft and finally result in DE fault [14]. After a prolong operation under the DE, the fault severity may aggravate and even lead to the irretrievable loss. As for the motorized spindle, its rotation accuracy is influenced by undesired motion of rotor. Even low levels of eccentricity may have bad effect on the radial motions. Therefore, it is necessary to develop the study on fault diagnosis for induction motor under low levels of eccentricity fault. DWT and WPD are widely used for detecting fault in industrial applications. However, under the processing of bandpass filtering using these algorithms, the band overlap is inevitable for the DWT as well as WPD. This can be proved in [8]. Although the usage of DWT can help to extract the fault component for diagnosis of the airgap eccentricity, the problem of overlap can induce noisy component. As for the induction motor under low levels of eccentricity, the characteristic component is relatively weak, so that these noisy signals may lead to inaccurate diagnosis. Therefore, after using DWT or WPD, data post-processing is necessary in order to improve the SNR and overcome the overlap problem. In this paper, the combined use of WPD and empirical mode decomposition (EMD) for processing the apparent power signal is proposed. Simulation signals of apparent power under low levels of purely DE are produced using the finite element method. Precise determination of the DE levels and percentages of rated load are both discussed in this study.