# Enhanced Fault Detection in High-Speed Train Bearings Using Empirical Mode Decomposition (EMD) and Kurtosis-Based IMF Selection: A Test Bench Approach

Meryem Abtane, Khalid Dahi, Hervé Martinez, Mohamed Sedki, Hicham El Kimi, Luciano Fernandes Borges

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Meryem Abtane, Khalid Dahi, Hervé Martinez, Mohamed Sedki, Hicham El Kimi, et al.. Enhanced Fault Detection in High-Speed Train Bearings Using Empirical Mode Decomposition (EMD) and Kurtosis-Based IMF Selection: A Test Bench Approach. CISTEM 2024 (The 5th International Conference on Electrical Sciences and Technologies in the Maghreb), Oct 2024, Rabat, Morocco. 10.1051/epjconf/202533005002 . hal-05190468

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Submitted on 28 Jul 2025

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# Enhanced Fault Detection in High-Speed Train Bearings Using Empirical Mode Decomposition (EMD) and Kurtosis-Based IMF Selection: A Test Bench Approach

Meryem Abtane<fnref n="1" />,<fnref n="2" />,*, Khalid Dahi<fnref n="1" />, Hervé Martinez<fnref n="1" />,<fnref n="2" />, Mohamed Sedki<fnref n="3" />,<fnref n="4" />, Hicham El Kimi<fnref n="3" />, and Luciano Fernandes Borges<fnref n="3" />

**Abstract.** The critical operating conditions of high-speed trains (HSTs) increase the occurrence of mechanical faults, particularly in key components such as axle bearings. To enhance fault detection and prevention, our study begins with controlled experimental simulations performed on a dedicated test rig at the Complex Systems and Interactions (CSI) Laboratory of Ecole Centrale Casablanca. This setup enables a systematic investigation of various types of bearing faults under well-defined conditions. The proposed methodology utilizes Empirical Mode Decomposition (EMD) to decompose vibration signals into Intrinsic Mode Functions (IMFs). A kurtosis-based selection criterion is then applied to identify the IMF that best highlights fault-related features. This approach enhances the precision of fault detection and the characterization of bearing defects. It demonstrates strong potential for improving diagnostic capabilities in both conventional rolling-element bearings and future applications involving axle bearing fault detection in high-speed rail systems.

## 1 Introduction

The significant advantages of High-Speed Trains (HSTs) have led to their widespread adoption globally. However, prolonged operation under demanding conditions and exposure to unpredictable factors can result in component failures, making early and accurate fault detection essential. To prevent risks such as derailments and ensure passenger safety, advancing research on condition monitoring and fault diagnosis in HST systems is critical [1].

A key subsystem in HSTs is the bogie, which provides structural support, guidance, and motion stability. Composed of the axle, wheels, bearings, suspension system, and braking mechanisms, the bogie guarantees safe and efficient train operation. Axle bearings, as part of these components, play an important role by reducing friction between the axle and wheels, which enables smooth rotation and ensures reliable performance.

Fault detection in axle bearings employs various techniques, including vibration analysis, acoustic monitoring, and temperature measurement. While temperature monitoring presents limited sensitivity to incipient faults, acoustic methods face challenges such as Doppler distortion and contamination from ambient noise. In contrast, vibration-based approaches offer greater reliability for fault detection. However, conventional vibration analysis methods are often time-intensive and qualitative, fail-

ing to quantify fault severity effectively. Recent advances in machine learning-based intelligent diagnostics have enabled more automated and comprehensive bearing health assessment, overcoming the limitations of traditional techniques. Peng et al. [2] introduced a unique, deeper 1D convolutional neural network with residual learning, validated using vibration data from various operating conditions of HST wheelset bearings. This model achieves superior performance, even in challenging scenarios with significant noise and fluctuating loads. Additionally, Luo et al. [3] proposed a simplified shallow information fusion-convolutional neural network (SSIF-CNN) that extracts time-domain and frequency-domain features. These features are processed through global convolution operations, transforming feature maps into sequences, which are then concatenated for the fully connected layer to enable fault identification. Experimental results demonstrate that the SSIF-CNN reduces training time and improves fault diagnosis accuracy compared to standard CNNs.

This paper is structured as follows: Section 2 defines axle bearing faults in HSTs, emphasizing their fault characteristic frequencies. Section 3 develops the methodology of this research and highlights the EMD algorithm. Finally, Section 4 presents the results of the selected algorithm on collected vibration signals from our CSI test rig.

<footnote n="1">¹Complex Systems and Interactions, Ecole Centrale of Casablanca, Bouskoura, Morocco</footnote>

<footnote n="2">²Université de Pau et des Pays de l'Adour, E2S UPPA, CNRS UMR 5254, IPREM, Pau, France</footnote>

<footnote n="3">³Société Marocaine de Maintenance des Rames à Grande Vitesse (SIANA), Tanger, Morocco</footnote>

<footnote n="4">⁴Office National des Chemins de Fer (ONCF), Rabat-Salé, Morocco</footnote>

<footnote>*e-mail: meryem.abtane@centrale-casablanca.ma</footnote>
## 2 Axle bearing faults in high-speed trains

Axle bearings go through various stages of degradation during operation, with common failure types including surface pitting, fatigue cracks, and progressive wear. The vibrational characteristics vary significantly depending on the defect location, generating distinct frequency signatures for inner race defects, outer race defects, and rolling element faults. The analysis also considers the cage rotation frequency as an additional parameter of interest [4, 5]. The characteristic frequency components can be determined using the following fundamental equations:

$$ BPFI = \frac{N_b}{2} f_r \left( 1 + \frac{B_d}{P_d} \cos \beta \right) \quad (1) $$

$$ BPFO = \frac{N_b}{2} f_r \left( 1 - \frac{B_d}{P_d} \cos \beta \right) \quad (2) $$

$$ BSF = \frac{P_d}{B_d} f_r \left( 1 - \left( \frac{B_d}{P_d} \cos \beta \right)^2 \right) \quad (3) $$

$$ FTF = \frac{f_r}{2} \left( 1 - \frac{B_d}{P_d} \cos \beta \right) \quad (4) $$

These defect frequencies are determined by the bearing parameters as indicated in Fig. 1, specifically:

* $B_d$: Diameter of the ball.

* $P_d$: Mean diameter or diameter of the cage.

* $N_b$: Number of balls in the bearing.

* $\beta$: Contact angle.

<figure><img src="image_2.png" /><figcaption>Figure 1. Rolling element bearing parameters</figcaption></figure>

Distinctive fault-related frequencies can be identified in the frequency spectrum due to the deterioration of various components within a bearing system. These include the Ball Pass Frequency Outer (BPFO), which indicates how often a ball or roller passes a fixed point on the outer race per shaft revolution, and the Ball Pass Frequency Inner (BPFI), which reflects the same for the inner race. The Ball Spin Frequency (BSF) corresponds to the number of times a ball or roller rotates around its own axis per shaft revolution. Lastly, the Fundamental Train Frequency (FTF) represents the rotational frequency of the bearing cage relative to the shaft.

## 3 Methodology: Empirical Mode Decomposition for Bearing Fault Detection

### 3.1 Data Acquisition

The CSI laboratory test rig (see Fig. 2) is powered by a three-phase motor equipped with a variable frequency drive, enabling precise control of rotational speeds from 0 up to 6000 RPM. The motor includes a built-in tachometer with an LCD display for real-time speed readings and provides an analog output signal for data acquisition. Two sets of rolling bearings are mounted, representing both healthy and artificially induced defect cases.

The setup is instrumented with several types of sensors. A Frederiksen 248600 microphone, with a frequency response range of 100 to 20,000 Hz and a sensitivity of 8 mV/Pa, is used to capture acoustic signals. Vibration measurements are obtained from an ACOEM ASH205b sensor with a sensitivity of 100 mV/g, installed in a vertical orientation, along with two PCB 352A21 accelerometers, each with a sensitivity of 10 mV/g, one mounted vertically and the other horizontally.

<figure><img src="image_3.png" /><figcaption>Figure 2. CSI laboratory test rig</figcaption></figure>

In this study, only vibration signals are considered. These signals are acquired using a National Instruments DAQ card, while LabVIEW software is used for both real-time visualization and data storage.

### 3.2 Signal Processing

The acquired signals are analyzed using Empirical Mode Decomposition (EMD), which decomposes complex signals into a set of simpler oscillatory components called Intrinsic Mode Functions (IMFs). The overall structure of the EMD algorithm is presented in Figure 3.

The periodogram of the signal envelope is computed based on each IMF by estimating the power spectral density. The objective is to visualize the signal in the frequency domain and to identify dominant frequency components that may correspond to fault-related signatures.

To select the most informative IMF, a kurtosis-based criterion is employed. Kurtosis is a statistical measure that emphasizes the presence of impulsive or transient features within a signal [6]. The IMF with the highest kurtosis value is considered the most relevant for fault detection,
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Empirical Mode Decomposition (EMD) algorithm</figcaption></figure>

as it is likely to contain significant impulsive characteristics associated with bearing anomalies. Kurtosis is defined as follows:

$$ \text{Kurtosis} = \frac{1}{N} \sum_{i=1}^{N} \left( \frac{x(i) - \bar{x}}{\sigma} \right)^4 \quad (5) $$

where $\bar{x}$ is the mean and $\sigma$ is the standard deviation of the signal $x(i)$. A kurtosis value significantly greater than 3 suggests a deviation from normality, often linked to transient fault-related events.

Although kurtosis is highly effective in detecting fault-related impulsive characteristics, other statistical indicators such as skewness, variance, and root mean square (RMS) can also provide complementary insights. Amini et al. [7] examined how variations in defect size and rotational speed influence acoustic emission and vibration responses during the onboard monitoring of railway axle bearings. Other studies have also employed kurtosis as a key indicator. In this context, a multi-statistical indicator approach is under consideration, with upcoming field tests intended to guide the selection of the most effective combination of metrics for enhancing fault detection accuracy under real-world operating conditions.

# 4 Results and Discussion

Signals are acquired at a sampling rate of 25,600 Hz. During the experiments, three shaft rotational speeds are applied: 10 Hz, 15 Hz, and 20 Hz. The corresponding characteristic bearing fault frequencies for each rotational speed are summarized in Table 1.

## 4.1 Healthy Bearing Condition

The data acquisition process starts with measurements taken from bearings in a healthy state. These signals serve as a reference for comparison with those collected from defective bearings, reflecting stable performance and low mechanical noise.

The vibration signal acquired from a healthy bearing operating at a rotational frequency of 15 Hz is shown in Fig. 4. The waveform demonstrates a stable and periodic

<table><caption>**Table 1.** Bearing Fault Frequencies at Different Rotational Speeds</caption><thead><tr><th>Rotation Frequency (Hz)</th><th>FTF (Hz)</th><th>BPFO (Hz)</th><th>BPFI (Hz)</th><th>BSF (Hz)</th></tr></thead><tbody><tr><td>10</td><td>3.78</td><td>30.48</td><td>49.5</td><td>19.92</td></tr><tr><td>15</td><td>5.67</td><td>45.72</td><td>74.25</td><td>29.88</td></tr><tr><td>20</td><td>7.56</td><td>60.96</td><td>99.00</td><td>39.84</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Vibration waveform of healthy bearings</figcaption></figure>

pattern with low amplitude, indicating minimal internal friction and the absence of mechanical irregularities.

The signal was further decomposed using Empirical Mode Decomposition (EMD), as shown in Fig. 5. The resulting Intrinsic Mode Functions (IMFs) are smooth and regular, which is consistent with the expected behavior of a properly functioning bearing.

To determine the most informative IMF, kurtosis values were calculated for each component. As presented in Fig. 6, the 5th IMF showed the highest kurtosis value, suggesting it contains the most relevant information for further analysis.

The frequency analysis of the selected IMF (Fig. 7) reveals a dominant frequency of approximately 14.8438 Hz, which approximately matches the expected rotation speed. Minor deviations can be attributed to slight misalignments or inaccuracies in sensor placement.

## 4.2 Outer Race Bearing Defect

The vibration signal corresponding to an outer race defect, as shown in Fig. 8, demonstrates clear deviations from that of the healthy bearing. One of the most prominent features is the increased amplitude of the signal. The waveform also reveals irregular patterns and transient spikes, which are indicative of impact events occurring as the rolling elements pass over the damaged section of the outer race.

The resulting Intrinsic Mode Functions (IMFs) reveal increased irregularities. This observation aligns with the elevated signal amplitude and suggests that the IMFs capture more complex frequency components and harmonics, reflecting the mechanical instability introduced by the outer race defect.
<figure><img src="image_6.png" /><figcaption>**Figure 5.** Empirical Mode Decomposition results of the vibration signal from a healthy bearing</figcaption></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 6.** Kurtosis values of IMFs for a healthy bearing</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 8.** Waveform of the vibration signal for an outer race bearing defect</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 7.** Periodogram of the envelope of the selected IMF for a healthy bearing</figcaption></figure>

The highest kurtosis corresponds to the first IMF, as illustrated in Fig. 9, indicating that it carries the most significant fault-related features. This IMF is therefore selected for further frequency-domain analysis.

The periodogram of envelope analysis of the selected IMF, shown in Fig. 10, reveals a dominant frequency component at approximately 45.3125 Hz. This closely matches the theoretically calculated outer race fault frequency of 45.72 Hz, with only a minor discrepancy.

## 4.3 Inner Race Bearing Defect

The resulting vibration signal, shown in Fig. 11, displays pronounced irregularities and high-amplitude spikes. These characteristics suggest the presence of localized damage on the inner race. The periodic nature of the impacts caused by the defect introduces additional harmonic components and results in a more complex signal compared to the healthy case.

The decomposition of the signal using Empirical Mode Decomposition (EMD) reveals Intrinsic Mode Functions (IMFs) with significant irregularities and amplitude variations that are absent in the healthy condition. As shown
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Kurtosis values of IMFs for a bearing with an outer race defect</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 10.** Selected IMF for a bearing with an outer race defect</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 11.** Waveform of the vibration signal for an inner race bearing defect</figcaption></figure>

in Fig. 12, the kurtosis values for each IMF were calculated to identify the component containing the most fault-relevant information. The first IMF stands out with the highest kurtosis, signifying its impulsive characteristics and indicating it is strongly influenced by the inner race defect.

Frequency analysis of the selected IMF (Fig. 13) confirms the presence of the inner race defect frequency at approximately 72.6562 Hz and its harmonics, which is close to the theoretical value of 74.25 Hz.

<figure><img src="image_14.png" /><figcaption>**Figure 12.** Kurtosis values of IMFs for a bearing with an inner race defect</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Figure 13.** Selected IMF for a bearing with an inner race defect</figcaption></figure>

## 4.4 Rolling Element Defect

The rolling element defect represents the last fault type investigated in this study. As illustrated in Fig. 14, the corresponding vibration signal displays distinct irregularities, reflecting the effects of damaged rolling elements making contact with other bearing components. These interactions lead to interruptions in the signal's periodicity. In addition, the amplitude observed in this case is comparatively lower than that recorded for the other defect types.

<figure><img src="image_16.png" /><figcaption>**Figure 14.** Waveform of the vibration signal for a rolling element bearing defect</figcaption></figure>

The resulting IMFs capture patterns and frequency components that reflect the signal irregularities caused by
the defect. Analysis of kurtosis across the IMFs reveals that the first IMF exhibits the highest value, highlighting its relevance for fault frequency identification. The selected IMF (Fig.15) reveals a dominant frequency component near the ball spin frequency (BSF) of approximately 27.3438 Hz, along with its harmonics. Additionally, side-bands are present around these frequencies, corresponding to the fundamental train frequency (FTF) of about 5.67 Hz, indicating potential cage deterioration.

<figure><img src="image_17.png" /><figcaption>**Figure 15.** Selected IMF for Bearings with Rolling Element Fault</figcaption></figure>

Accurate fault detection depends strongly on proper setup configuration. Inadequate sensor placement, such as insufficient contact with the bearing, or mechanical issues like loose fittings, can lead to deviations between the actual and calculated fault frequencies. These anomalies may also distort vibration signals by introducing measurement errors and parasitic noise, which degrade overall signal quality.

This research contributes to the development of a sensor-based monitoring system that utilizes accelerometers mounted directly on axle bearings for real-time vibration analysis. The system architecture includes sensors connected to a data acquisition unit, which can transmit data either to an onboard processing system or via wireless networks for remote evaluation. After data collection, the signals are subjected to comprehensive preprocessing and feature extraction to reduce noise and reveal meaningful patterns. A diverse set of computed features is then used as input for machine learning algorithms such as Support Vector Machines (SVMs) and Random Forests, enabling automated fault classification in axle bearings. This integrated approach aims to establish a robust condition monitoring solution for predictive maintenance applications.

# 5 Conclusion

This study introduces an innovative test rig-based methodology for improving fault detection in high-speed train (HST) axle bearings through the use of Empirical Mode Decomposition (EMD) combined with kurtosis-driven selection of Intrinsic Mode Functions (IMFs). By breaking down vibration signals into IMFs and identifying those with the highest kurtosis values, the method effectively isolates features indicative of bearing faults, allowing for more precise diagnosis of defects within the CSI test rig. The ongoing project seeks to further enhance this detection process by exploring alternative variants of EMD techniques and evaluating different IMF selection strategies, together with the integration of machine learning methods to enable accurate, automated fault identification in real-world HST operating environments.

# 6 Acknowledgements

We gratefully acknowledge the support of the Société Marocaine de Maintenance des Rames à Grande Vitesse (SIANA), whose assistance greatly contributed to the success of this work.

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