Bearing Fault Diagnosis Based on Statistical Locally Linear Embedding

Abstract

Fault diagnosis is essentially a kind of pattern recognition. The measured signal samples usually distribute on nonlinear low-dimensional manifolds embedded in the high-dimensional signal space, so how to implement feature extraction, dimensionality reduction and improve recognition performance is a crucial task. In this paper a novel machinery fault diagnosis approach based on a statistical locally linear embedding (S-LLE) algorithm which is an extension of LLE by exploiting the fault class label information is proposed. The fault diagnosis approach first extracts the intrinsic manifold features from the high-dimensional feature vectors which are obtained from vibration signals that feature extraction by time-domain, frequency-domain and empirical mode decomposition (EMD), and then translates the complex mode space into a salient low-dimensional feature space by the manifold learning algorithm S-LLE, which outperforms other feature reduction methods such as PCA, LDA and LLE. Finally in the feature reduction space pattern classification and fault diagnosis by classifier are carried out easily and rapidly. Rolling bearing fault signals are used to validate the proposed fault diagnosis approach. The results indicate that the proposed approach obviously improves the classification performance of fault pattern recognition and outperforms the other traditional approaches.

Keywords: dimensionality reduction; fault diagnosis; feature extraction; high-dimensional data; manifold learning; statistical locally linear embedding.

Figure 1

Illustration of LLE algorithm: (a) Select neighbors; (b) Reconstruct with embedded linear weights; (c) Map to coordinates.

Figure 2

The implementation process and flow chart of the proposed approach.

Figure 3

The rolling bearing fault test-bed.

Figure 4

The vibration signal waveforms and power spectra from the different fault types: (a,b) Normal bearing vibration waveform/power spectrum; (c,d) Inner race fault vibration waveform/power spectrum; (e,f) Ball fault vibration waveform/power spectrum; (g,h) Outer race fault vibration waveform/power spectrum.

Figure 5

The six dimensional time-domain features value in the dataset: (a) Mean; (b) Root mean square; (c) Root; (d) Standard deviation; (e) Skewness; (f) Kurtosis (Note: sample data No.1–100, 101–200, 201–300, 301–400, represent normal, inner race fault, ball fault and outer race faults, respectively).

Figure 6

The six dimensionless time-domain features value in the dataset: (a) Shape factor. (b) Crest factor; (c) Impulse factor; (d) Clearance factor; (e) Skewness factor; (f) Kurtosis factor (Note: sample data No.1–100, 101–200, 201–300, 301–400 represent normal, inner race fault, ball fault and outer race faults, respectively).

Figure 7

The four frequency-domain features value in the dataset: (a) Mean frequency; (b) Frequency center; (c) Root mean square frequency. (d) Root variance frequency (Note: sample data No.1–100, 101–200, 201–300, 301–400 represent normal, inner race fault, ball fault and outer race faults, respectively).

Figure 8

The first six IMFs obtained by applying EMD method to a signal sample in the dataset: (a) Normal; (b) Inner race fault; (c) Ball fault; (d) Inner race fault (Note: sample data No. 1–4096, 4097–8192, 8193–12288, 12289–16384 represent normal, inner race fault, ball fault and outer race faults, respectively).

Figure 9

The normalized amplitude energy features value of the first six IMFs by EMD method (Note: sample data No. 1–100, 101–200, 201–300, 301–400 represent normal, inner race fault, ball fault and outer race faults, respectively).

Figure 10

Feature dimension reduction to rolling bearing multi-domain feature in the dataset: (a) Mapping with PCA; (b) Mapping with LDA; (c) Mapping with LLE; (d) Mapping with S-LLE.

Figure 11

The comparison of the average classification accuracy with different features dataset on classifiers using statistical LLE.

Figure 12

The comparison of the average classification accuracy with different features dataset on classifiers using supervised LLE.