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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Wheel-bearings easily acquire defects due to their high-speed operating conditions and constant metal-metal contact, so defect detection is of great importance for railroad safety. The conventional spectral kurtosis (SK) technique provides an optimal bandwidth for envelope demodulation. However, this technique may cause false detections when processing real vibration signals for wheel-bearings, because of sparse interference impulses. In this paper, a novel defect detection method with entropy, time-spectral kurtosis (TSK) and support vector machine (SVM) is proposed. In this method, the possible outliers in the short time Fourier transform (STFT) amplitude series are first estimated and preprocessed with information entropy. Then the method extends the SK technique to the time-domain, and extracts defective frequencies from reconstructed vibration signals by TSK filtering. Finally, the multi-class SVM was applied to classify bearing defects. The effectiveness of the proposed method is illustrated using real wheel-bearing vibration signals. Experimental results show that the proposed method provides a better performance in defect frequency detection and classification than the conventional SK-based envelope demodulation.

Wheel-bearings are an essential mechanical component of railway vehicles. The high-speed operating conditions and constant metal-metal contact easily leads to defects, such as axle burn-off, metal losses and cage fragmentation. They can affect the normal operation of railway traffic systems, and ultimately lead to train derailments. Therefore, the detection of bearing defects is of great importance, especially with the great improvements of train speed in recent years.

Vibration or sound signals generated by bearings usually contain rich information. Their corresponding analysis is an effective way to detection defects, and has received wide attention in recent years [

In addition, in recent years some detection systems have been developed with different inspection techniques to identify defective bearings prior to failure. The Hot Bearing Detector (HBD) was developed first. It uses wayside rail-mounted infrared transducers to monitor bearings’ temperatures as a train passes the detector. The system issues an alarm if the bearing operating temperature exceeds a certain threshold. The catastrophic failure of roller bearings happens very quickly and results in axle burn-off, even derailment. Unfortunately, current HBD systems may miss overheated roller bearings.

In order to prevent catastrophic bearing failure, acoustic methods have been employed to identify defective bearings. Among the well-known systems are Railway Bearing Acoustic Monitoring System (RailBAM) and Trackside Acoustic Detection System (TADS). They are developed by VIPAC, Inc. [

Recently, ENSCO, Inc. has investigated a novel technology, which used accelerometers mounted on the rail, designed to detect bearing defects early. They investigated the transmissibility of the vibration signals from defective bearings to rails, a transient mechanical path formed by the bearing, axle, wheel, rail, and accelerometers. The rolling wheel-rail contact patch was considered a challenge for the technology. The data analysis appeared to indicate defective bearing signals could transmit from the bearing down to the accelerometers on the rail. However, the field test was conducted under less than ideal conditions. A credible signal-to-noise ratio (SNR) to allow meaningful detection of bearing defects was not established.

The above systems have an important role in detecting defects, but they cannot discover all potential defects. To fullfil the strict safty regulations of railroads, wheel-bearings require regularly servicing at maintenance workshops. As far as we know, the detection is conducted manually in China. More reliable and automatic detection methods are needed. To realize defect detection and classification accurately, a major challenge is how to find characteristic frequencies of roller bearings. Conventional envelope analysis technique gives an effective extraction method from low SNR vibration signals with a band-pass filter. In practical applications, the resonance frequency band (RFB) for a band-pass filter may vary as the locomotive wheel sets, axles or bearings change. The key problem is how to accurately find the optimal RFB. Antoni

Based on an in-depth study of SK abnormity, a defect detection method with entropy, time-spectral kurtosis (TSK) and SVM is proposed in this paper. In the method, entropy is introduced to estimate and preprocess possible outliers in STFT amplitude series (STFTAS) of raw vibration signals. Then the SK is extended to the time-domain, and the vibration signal is reconstructed with TSK filtering. The TSK technique can indicate not only the transients in frequency domain, but also their locations in the time domain. Finally, extracted features are used as an input eigenvector of the SVM model to classify bearing defects. Experimental results show that the proposed method could effectively identify defects from real vibration signals collected from wheel-bearings.

Dwyer [

For a given non-stationary signal

Let _{4}_{Y}_{2}_{nY}

Given a non-stationary signal _{k}

When roller bearings have defects, they will generate a series of impacts and excite the resonance of the structure. The measured vibration signal _{k}_{k}

If _{2}_{N}_{2}_{Y}_{2}_{N}_{2}_{Y}

If

From _{Z}_{Y}

SK could detect the transients in non-stationary signals, and indicate the locations in the frequency domain by calculating the kurtosis of each spectral line. However, when processing the real vibration signals collected from wheel-bearings, we found that RFBs selected by the SK technique cannot always detect defective frequencies. This may be caused by sparse interference impulses, which are usually caused by the impurities in the lubricant oil, striking of wheel-sets, and surrounding constructions at the wheel maintenance workshop.

To study the effect of interference impulses on the SK technique, we first simulated a synthesized signal as shown in

The results of SK and envelope demodulation analysis of the synthesized signal are shown in

To study in depth the amplitude and intensity of interference impulses influenced on the SK technique, a new series

In 1948, Shannon proposed entropy to characterize information hidden in data [

The advantage of entropy is introduced to estimate possible outliers in STFTAS. Let |_{i},f_{j}_{i}_{j}

The entropy is thus formulated as:

The corresponding normalization with different frequencies is defined as:

According to

On the basis of above principles, this paper gives a realization method by replacing those large value points with near one. Among them, the ratio _{outlier}_{outlier}

At 2 kHz, the statistical distribution has no change after preprocessing the outliers in signals, which mainly contains the pink noise. Its shape is similar to the white Gaussian signal as shown in

As the signal mainly contains defect information at 4 kHz, the statistical distribution has also no obvious change after preprocessing.

In contrast, the statistical distribution changes notably after preprocessing at 10 kHz, which mainly contains a single interference impulse. It can be concluded that it mainly changes the distribution of random interference impulse.

The SK estimator depends only on statistical distribution of amplitude series, but has nothing to do with time information. In fact, the appearance of defective impulses in vibration signal is regular and periodic. However, SK has no reflection on time-domain information. In this section, motivated by previous SK efforts, we extend SK further to time-domain with entropy analysis, and propose a time-spectral kurtosis filtering method.

The definition of time-spectral kurtosis is:
_{G}

Detailed TSK-based filtering can be summarized as follows.

If roller bearings have defects on the inner race, outer race or balls, it generates a series of periodic vibrations as a running roller passes over the surfaces of the defects. These vibrations occur at certain characteristic frequencies, which are determined by the rotational speed, locations of defects, and geometric parameters [

Defective frequency of the outer race _{OR}

Defective frequency of the inner race (DFIR) _{IR}

Defective frequency of the roller element (DFRE) _{RE}

Defective frequency of the cage (DFC) _{C}_{s}_{b}

In order to reduce the influence caused by the slight change of motor speed, the maximum values are chosen in intervals [_{OR}_{OR}_{IR}_{IR}_{RE}_{RE}_{C}_{C}

In this section, the effectiveness of proposed method is illustrated by the vibration signals collected from real wheel-bearings at the Xuzhou Wheel Maintenance Workshop, Jiangsu Province, China.

The SNR of the defective signals is low, except for two strong impulses in the time-domain. According to

Band-pass filtering is firstly implemented to extract the envelope signal according to the maximum value of SK. After demodulation, the corresponding spectrum zoomed in 0–100 Hz is illustrated in

In addition, vibration signals collected from an outer race fault bearing, shown in

In this section, a dataset collected from the test-rig is used to illustrate the effectiveness of the proposed method. It consists of four conditions, namely normal state, inner race fault, outer race fault and roller fault. For each condition, 30 samples were used, and the dataset contains 120 samples. Each sample is a section of vibration signal containing 65,536 sampling points. In addition, cage defecta are rare because of the improvement in materials, and we don’t have this type of samples.

Considering a frequency resolution of 0.5 Hz (32768/65536), variation range of speed and the defective frequencies in

We choose the multi-class SVM technique (one-versus-one) to classify different conditions, and adopt LIBSVM software [

From

However, there are still a small percentage (about 1.96%) of false positives. Furthermore, it has the highest false classification accuracies (3.5%) for the normal state. That is to say, about 3.5% normal samples are misclassified as faults. In previous experiments, we found that impurities in the lubricant oil for normal wheel-bearings may also produce defective frequencies, especially outer race ones, which will lead to the errors in classification. In our future work, we will study how to distinguish impurities from defects.

Based on an in-depth study of the SK abnormity for real wheel-bearings, a defect detection method with entropy, time-spectral kurtosis and SVM has been investigated. Through entropy, it can effectively estimate and preprocess outliers in STFTAS, and reduce the influence of interference impulses on characteristic frequency extraction greatly. The TSK filtering technique extends SK to the time-domain, and is sensitive to the relatively slight variations caused by the positive value under low-SNR conditions. Real vibration signals collected from wheel-bearings at a maintenance workshop are measured for validating the effectiveness of the proposed method. Experimental results show that the method provides a higher accuracy for the defective frequency detection, and classifies four conditions of roller bearings more accurately than the conventional SK-based envelope demodulation. In addition, the proposed method has better generalization and robustness for interference impulses in railway applications.

This work is supported by the National Natural Science Foundation of China (Grant No. 11304019).

The authors declare no conflict of interest.

The synthesized signal.

Analysis results of simulated signal. (

Analysis results of signal. (

The SK amplitude varying with different intensive impulses.

The entropy of STFTAS.

Statistical distribution at different frequencies. (

The test-rig for wheel-bearing.

The defect on the inner race.

The analysis results of inner race fault bearing. (

The defect on the outer race.

The analysis results of outer race fault bearing. (

The distribution of defective features. (

Roller diameter and experimental parameters.

Type of wheel-bearing | 197726 |

Contact angle | 10° |

Diameter of roller | 23.776 mm |

Pitch diameter | 180 mm |

Number of rollers | 20 |

Sampling frequency | 32,768 Hz |

Rotational speed | 245 rpm |

Type of accelerometer | Lance2052 |

Threshold of TSK value | 0.3 |

Proportion _{outlier} |
0.8% |

Data length | 65,536 |

The defective frequencies at speed of 245rpm.

DFOR | 35.5216 Hz |

DFIR | 46.1450 Hz |

DFRE | 15.1952 Hz |

DFC | 1.7761 Hz |

The accuracy of prediction.

SK-based method | 81.67% | 76.33% | 83.17% | 86.50% | 80.67% |

Proposed method | 98.04% | 96.50% | 98.17% | 99.67% | 97.83% |