An approach to fault diagnosis for gearbox based on reconstructed energy and support vector machine

2.1. Reconstructed FFT spectrum

FFT, a fast algorithm for discrete Fourier transforms, widely used in signal processing. Some signals are difficult to discover its characteristics in time domain. Fault information will be much more intuitive when convert raw signals to the frequency domain. As a powerful time-frequency conversion tool, FFT retains a higher efficiency and faster speed. In addition, FFT can extract the spectrum of a signal out of the spectrum. There are many other analysis tools have been developed in the literature, such as Hilbert-Huang Transform for time-frequency analysis, wavelet transform, Wigner-Ville distribution, power spectrum, spectrum for frequency domain analysis, autoregressive moving average, model for time domain analysis and time synchronous average [8].

The main purpose of reconstructed FFT spectrum analysis contains the following aspectes: (1) Remove noise or outside interference to reduce signal contamination; (2) Filter and assemble without loss of fault information and look closely at certain frequency components of interest; (3) Features can be extracted from reconstructed FFT spectrum directly. Fig. 2. and Fig. 3. are initial FFT spectrum and reconstructed FFT spectrum respectively.

Fig. 2Initial FFT spectrum

Fig. 3Reconstructed FFT spectrum

2.2. Support vector machine

Support vector machine (SVM) proposed by Vapnik in 1995, a small sample statistic learning method based on structural risk minimization, which famous for its unique advantages in solving small sample, nonlinear and high-dimensional pattern recognition. Through a nonlinear mapping p, SVM is capable of mapping the sample space to a feature space of high-dimensional so much as an infinite-dimension, which make the nonlinear separable problem in the original sample space is transformed into a linearly separable problem in the feature space [9].

3.1. Experimental facilities

The data sets used in this paper come from the 2009 PHM Conference Data Analysis Competition. three groups helical gears with different healthy states are selected for pattern recognition classification. The first group is on good condition, the second group and the third group have different failure parts, the detailed information listed in Table 1.

3.2. Reconstructed FFT spectrum and feature extraction

The failure of different parts of the gearbox will be reflected in different frequencies. In fault mode 1, the gear with 24 teeth is chipped, its gear meshing frequency and side band frequencies are the most remarkable frequencies. In fault mode 2, the bending of the input shaft produces harmonic frequency components of shaft rotating frequency. Therefore, the interest frequencies are GMFs and shaft rotating frequencies. The detailed interest information retained by filters in this article is shown in Table 2. 272 times FFT are carried out in each condition and the number of data points involved in each FFT is 131072.

3.3. Fault classification based on support vector machine

In the following, 816 samples with extracted features are divided into two parts and be sent to SVM classifier respectively, for one part that has 612 samples as training data set of SVM classifier and the other that has 204 samples as testing data set of SVM classifier.

As can be seen from Table 3, the approach based on reconstructed FFT spectrum and SVM has a stable diagnostic effect that all of the accuracies are higher than 0.89 and nearly three quarters are accurate to 100 percent, even though the gearbox under different loads and speeds.