Wayside Condition Monitoring of Metro Wheelsets Using Vibration and Acoustic Sensors

In recent advancements in railway vehicle condition monitoring methods, researchers are focusing extensively on wayside condition monitoring. This involves real-time assessment of sensor data to identify potential mechanical issues with the railway vehicles. The aim is to achieve cost-effective maintenance strategies, which offer greater advantages than periodic servicing or repairs based on condition [1]. Monitoring the condition of the wheelset in railway vehicles is particularly critical for ensuring operational safety. Traditional stationary techniques often require complex static or dynamic laboratory tests and the installation of onboard sensors at specific points on vehicle components. However, wayside condition monitoring offers a more convenient approach for detecting faults in dynamic systems with minimal effort compared to stationary methods. Employing an appropriate evaluation process enables cost-effective maintenance. Additionally, it allows for detecting faults that may gradually or suddenly appear due to significant changes in system parameters, such as the dynamic response of a wheelset, during real-world operations. The scarcity of wheelset fault detection schemes for metro trains in literature, coupled with the limited accuracy observed in existing research compared to our proposed framework, highlights the need for comprehensive understanding and unique approaches to address the metro train and operating company-specific details, underscoring the significance of this research for specialists, especially those in PPTC- Prague Public Transport Company and similar regions across Europe.

Proposed approaches utilizing sensor data from onboard systems have emerged for enhancing running safety monitoring. These techniques require multiple sensor arrays and assessment protocols, along with comprehensive vehicle specifications, to ensure precise condition monitoring [2]. Successful application of these methods demands robust dynamic modelling, effective signal filtration, and addressing calibration challenges.

Fundamental methods for detecting anomalies in railway vehicle operation include utilizing strain, acoustic, accelerometer, or gyroscope sensors [3, 4].

References to wayside condition monitoring systems in Europe are available in the literature [5]. In Czechia, a wayside condition monitoring system called ASDEK enables the measurement of physical parameters such as weight and temperature. This is achieved through sensors installed on or near the railway tracks, catering to train speeds of up to 160km/h at over 40 locations. Real-time detection of wheelset eccentricity, wheel defects, and hot axle-box/brake disk issues is also feasible, facilitating the implementation of decision-making systems, including railway vehicle stoppage. However, there is currently no available application for metros in the Czechia area.

In the Netherlands, GOTCHA can detect wheel anomalies and offer load measurements with a tolerance of 3% within the operational speed range of 30-70km/h. AVI tags are utilized for vehicle identification. LASCA, on the other hand, utilizes laser beam deflection to detect Q-forces with a 2-3% tolerance at speeds of up to 350km/h, identifying railway vehicles through ZLV bus technology. MULTIRAIL, on the other hand, monitors safety parameters such as wheelset loads and vertical wheel forces, employing RFID for vehicle identification. ARGOS, developed in Austria, employs strain-gauge sensors to monitor axle loads with precision up to 99.5%, offering insights into wheel irregularities at speeds ranging from 10-40km/h. It also assesses wheel roundness with a precision of 0.01mm, utilizing RFID for vehicle recognition. Various other company-specific systems are mentioned in existing literature [6].

The initial adoption of wayside methodologies [7] for identifying wheel anomalies through impact load measurement occurred in New York in 1983. Subsequently, Sweden devised a technique employing strain gauges to detect wheel problems, establishing wayside condition monitoring systems in over 190 locations.

With new advancements, various devices are employed to identify wheel irregularities such as out-of-roundness, shelling, and wheel flats. Strain gauge measurement techniques commonly utilize vertical force and maximum quantities for detecting wheel defects [7]. Utilizing a total of 128 strain gauges enables the identification of such defects for wheels of varying sizes [8].

Observing variations in the refractive index of ultraviolet rays, fiber-optic sensors offer diagnostic capabilities that outperform strain gauge measurements. They exhibit superior resistance to electromagnetic interference and allow fewer challenges in fabrication, recalibration, and installation. Additionally, they are immune to temperature fluctuations, give faster response times, and ensure reliability [9]. Employing fiber-optic sensors enables the detection of rail shear strain, facilitating the identification of vertical impact force. Reports indicate that in addition to axle counting, weight monitoring, and wheel imperfection detection [10] are possible. Literature already presents various other wayside implementations of fiber-optic technologies [11-13].

Utilizing lasers and high-speed cameras offers an alternative method for monitoring wheelset condition and capturing images of wheel profiles. By comparing these images with standard profiles, prognostic wear monitoring is attained [14-16].

The literature also discusses the use of ultrasonic sensors [17-19], employing pulse-echo transmission for detecting wheel defects such as wheel cracks [20]. However, these sensors typically require complex infrastructures and operate at consistent, slow speeds.

Acoustic sensor technology offers a viable approach for monitoring conditions under varying speeds [21-24], particularly focusing on the wheelset. This is because abnormal structures on the wheelset generate a periodic acoustic impulse corresponding to train velocity. Various methods have been explored, including time-domain and frequency energy statistics [25], implementing low-pass filtering and root mean square analysis within suitable time frames, followed by Fourier transform [26]. However, these methods are less effective than vibration signals [27]. Nonetheless, the effectiveness of acoustic wayside applications is reportedly compromised when employing Doppler correction before STFT-Short Time Fourier Transform variants [28].

Vibration sensors provide another efficient means for diagnosing wheel defects. They can effectively detect wheel flats and corrugation, even in noisy signals, through analyzing power cepstrum and comparing energy levels [29]. However, a notable limitation of this approach is the necessity for a constant speed. Additionally, fuzzy logic methods can be employed to monitor the severity of failure on the wheel [30]. In this approach, sensors for detecting vibrations are positioned at the base of the rail, where they assess the centre frequency, train speed, and vibration magnitude. Accordingly, findings suggest that the central frequency and train velocity are the most critical factors affecting output signals. An additional study [31] discusses the efficiency of wavelet-based techniques and direct thresholding in effectively determining the extent of wheel damage when utilizing piezoelectric accelerometer sensors. While employing shear bridges, which include multiple strain gauges, is said to yield superior results compared to accelerometers [32], establishing such trackside systems is challenging due to calibration complexity and cost considerations.

It is essential to select the most appropriate approach for vibration-based condition monitoring of a railway vehicle within its unique wayside setting. Vibration signals typically exhibit non-stationary random characteristics [33]. An efficient method for processing non-stationary signals is STFT, which employs overlapping time windows. However, it requires repeating experiments for consistent performance. Similarly, CWT-Continuous Wavelet Transform) offers fast and convenient non-stationary signal processing. [34], PCA-Principal Component Analysis is utilized to identify frequency differences in the faulty signal despite its unreliability [35].

In contrast to traditional methods, alternative techniques such as AR-Auto-Regressive model [35, 36], ARMA-Auto-regressive Moving Average [37], and EMD-Empirical Mode Decomposition [38] have demonstrated their effectiveness in diagnosing mechanical faults, particularly in conditions with varying speeds, as documented in the literature. Various methods have been proposed, including time-domain statistical features like kurtosis, crest factor [39], variance, skewness, kurtosis, higher-order moments [40], impulse and clearance factors [41], DWT-Discrete Wavelet Transform for denoising, TSA-Time-synchronous Averaging, [42], Kurtograms and wavelets [43, 44], MCKD-Maximum Correlated Kurtosis Deconvolution [45], Gabor wavelets and, wavelet transform [46], HHT-Hilbert Huang Transform and SVMs-Support Vector Machines [47], time domain analysis combined with fuzzy C-means [48], envelope analysis from the Kurtogram [49] as well as various statistical features [50], have been proposed in the literature for detecting rotating component faults. Moreover, recent advancements in deep learning techniques such as LSTM (Long Short Time Memory), RNN (Recurrent Neural Networks), DBN (Deep Belief Network) [51], Multi-Layer Perceptron (MLP) [52], and CNN-Convolutional Neural Networks [53] are also examined in vibration based condition monitoring.

Various techniques discussed in the introduction part require complex mathematical models or sensor calibrations, which gradually can decrease performance, and specialized personal periodic checks, which make it much more costly (on device measurements) or suffer from low performance in detection (other data-driven methods) and lack of availability to train networks (deep neural networks) and none of them provide a straightforward speed adaptive and short length features via both vibration and acoustic signals with reliability in boosting as ADASYN offers.

This study introduces advanced model-based techniques combined with cutting-edge feature extraction and classification methods to develop an effective framework for monitoring wheelset-related faults. The proposed methods combine one-period signal segmentation, which ensures one rotation of the wheelset under speed-varying conditions, with feature extraction algorithms (TDF, WPE, and LCP-K). These algorithms provide representative features with a fixed output size, and they also benefit from classifier combination techniques. According to the obtained results and validation from metro maintenance specialists, the efficiency of various feature extraction techniques, as compared across different scenarios, is demonstrated.

The paper is structured as follows: Firstly, it outlines the wayside measurement system and details the preparation of the acoustic and vibration databases. Secondly, it presents the methods utilized for signal processing, feature extraction, and classification of wheelset-related faults. Thirdly, it provides the experimental study and analysis of results. Finally, the conclusion is given, followed by a distinct highlights section emphasizing our methodology highlights.

Effective fault characterization is essential for achieving a precise diagnostic mechanism. Whether conducted offline or in real-time, the process of sensor data can indicate potential mechanical faults within the structure, provided that suitable signal processing techniques are applied. This section presents the methodologies dealing with signal processing, feature extraction, and classification employed in this study.

3.1 Fault characteristics of a wheelset

Various potential fault modes for the wheelsets can be characterized based on the mechanical model of the wheelset and its components. Leveraging model-based methodologies facilitates the estimation of expected fault frequencies associated with the wheelsets of the railway vehicle. Subsequently, these characteristic frequencies can be examined upon using a filtering mechanism prior to subsequent diagnostic procedures.

Two predominant types of faults that can noticeably impact ride quality are wheelset eccentricity (see Figure 2 (a)) and wheel defects (see Figure 2 (b)). Wheel defects, especially those that affect both the rail and vehicle structures, should urgently be identified due to their potential propagation. The characteristic frequency associated with this type of fault is harmonically related to the rotational frequency of the wheelset, and its calculation is shown in Eq. (1).

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Figure 2. Wheelset-related faults; wheelset eccentricity (a), flat-wheel defect (b)

Eccentric faults in the wheelset imbalance contribute to the wheel rotational frequency in the spectrum. Eq. (1) demonstrates the calculation of this fault frequency, where v represents the translational velocity of the train, and D_k refers to the wheel diameter. Having the possibility to measure the maximum and minimum speed of the train in Dejvická passage, the expected faulty frequency interval can be calculated as in Table 1.

${{f}_{ws}}=\frac{v}{\pi {{D}_{k}}}$                          (1)

Table 1. Wheelset eccentricity (imbalance) fault frequency range for the train set 81-71M

3.2 One-period signal segmentation

This method assumes that vehicle vibrations transmit to the rail on the contact points with the wheel. The wheelset serves as the fundamental unit for diagnosis within the train running gear. By referencing the train identification and maintenance database, one can link the measured wheelset to its identification and maintenance history, as well as that of related components like traction motors, gearboxes, and bearings. The initial step involves segmenting the recorded signals into blocks, each representing a single wheelset rotation, with the block length determined by the wheel diameters and train speed obtained from the maintenance database and optical gate signals, respectively. Eq. (2) shows the calculation of the signal block length:

${{n}_{i}}=\text{2}\cdot \text{round}\left( \frac{\pi \cdot {{d}_{i}}\cdot {{f}_{s}}}{\text{2}\cdot {{v}_{i}}} \right)$                          (2)

Assuming that $i$ as the index of wheelset, $n_i$ as the sample count in the block, $d_i$ as the mean diameter of left and right wheels, $v_i$ is the velocity of wheelset, $f_s$ as the sampling frequency. Train speed is calculated by Eq. (3) with a tolerance of 0.5km/h validated through hundreds of passes:

${{v}_{i}}=\frac{L\cdot {{f}_{s}}}{{{s}_{Bi}}-{{s}_{Ai}}}$                          (3)

Given $L$ as the distance between optical gate sensors, $s_{A i}$ as the sample number for detecting the centre of the wheelset number $i$ by optical gate OGA, similarly $s_{B i}$ is the sample number from optical gate OGB. Centre of the block should be positioned at sample $s_{A i}$ for segmenting signals from $Z 1$ and Z2 sensors or at sample $s_{B i}$ in case of segmenting signals from Z3 and Z4 sensors.

Wheelset velocities are retrieved from the train and are fitted by a linear function. A histogram of speed values is given in Figure 3, while Figure 4 shows an example of one period block signal with the following parameters: $v_i=22 \mathrm{~m} \cdot \mathrm{s}^{-1}; d_i=0.745 \mathrm{~m}$; train ID: 108, wheelset No: 13, passing ID: 20160713_070409.

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Figure 3. Histogram of train velocity measurement in one day

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Figure 4. One-period segmented vibration signal

3.3 Wavelet packet analysis

Fault transients can appear randomly, their exact location can be dominated by significant environmental noise, even with a full understanding of the dynamic system model. However, in mechanical fault diagnosis, these transients exhibit periodicity, making frequency domain methods feasible. To investigate such periodic transients, WPT-Wavelet Packet Analysis offers a solution, as in STFT [57], but provides variable frequency resolution, as highlighted in academic literature for time-frequency analysis. Through wavelet packet analysis, the Fourier spectrum can be partitioned into numerous frequency bands, allowing for the desired frequency resolution. WPT shares a structure similar to DWT-Discrete Wavelet Transform, which enables a multi-scale time-frequency representation of signal data [58]. Various wavelet functions such as Haar, Daubechies, and Symlets [59] can be utilized in the calculation of DWT. The mathematical representation of the DWT for a discrete signal $x[n]$ is shown in equations Eq. (4) and Eq. (5) with the wavelet basis function $\psi_{a, b}$ while a is the dilation and b is the location parameter.

${{\psi }_{a,b}}[n]=\frac{1}{\sqrt{a}}\psi \left[ \frac{n-b}{a} \right]$                          (4)

$X[a,b]=\sum\limits_{n=-\infty }^{\infty }{x[n]}\,{{\psi }_{a,b}}[n]$                          (5)

Utilizing filter banks known as QMF-Quadrature Mirror Filters, DWT operates as a multiresolution analysis tool [60], employing both low-pass and high-pass filtering operations. The low-pass filter generates approximation coefficients (A), while the high-pass filter produces detail coefficients (D). This method outperforms STFT in offering improved time resolution at high frequencies while maintaining adequate frequency resolution at lower frequencies. However, DWT suffers from reduced frequency resolution at higher frequencies compared to WPT, which employs linear combinations of wavelet functions and retains the advantages of orthonormality and time-frequency domain localization. If we assume the number of levels $n_w ; k_w=2^{n_w}$ refers to the number of wavelet packets in WPT. The signal is then filtered to capture low and high-frequency components, followed by downsampling for the subsequent level. Figure 5 illustrates a two-level decomposition of the wavelet packet tree for a discrete signal $x[n]$, where $h[n]$, is a low-pass (L) and $g[n]$ is a high-pass (H) QMF results yielding approximation (A) and detail (D) coefficients, respectively.

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Figure 5. Two-level wavelet packet decomposition

However, the components of WPT remain non-translation invariant, and addressing this issue can be accomplished by computing the energy levels of each wavelet packet $k_w$ as given in Eq. (6) where $c_{j, n}$ denotes the wavelet coefficients at index $j-t h$ on $n_w-t h$ level. Utilizing these energy measures directly as a feature vector is feasible due to the reduction of feature dimension enabled by WPE [61], ensuring that periodic transients propagate effectively in WPE coefficients [61].

${{E}_{{{n}_{w}},{{k}_{w}}}}=\sum\limits_{j}^{{}}{c_{j,\,{{n}_{w}},{{k}_{w}}}^{2}}$                          (6)

3.4 Linear configuration pattern Kurtograms

Methods based on spectral kurtosis are widely used in monitoring the condition of rotating machinery to detect signal non-stationarities. Recently, a more efficient approach called Kurtogram has been introduced as a fourth-order analysis tool [62]. In the Kurtogram method, signals are transformed into frequency-delta frequency spectra, allowing for the investigation of transients associated with faulty conditions, which exhibit high kurtosis in a dyad view $(f, \Delta f)$. However, the main drawback of Kurtogram is its computational inefficiency. To address this, a faster algorithm called FK-Fast Kurtogram has been developed, which has a similar complexity to FFT-Fast Fourier Transform [49]. FK divides frequency bands finely and presents the magnitude of each spectral kurtosis in a grid view, represented as a dynamic intensity image [49]. Additionally, LBP-Local Binary Patterns is a popular method in two-dimensional pattern recognition that focuses on texture recognition and bioinformatics [63]. LBP aims to maximize mutual information by comparing pixel intensities in the surrounding area while labelling discriminative features of a two-dimensional signal. For a given circular window radius, it calculates binary patterns for each neighbourhood using a specific formulation as described in the study [64] in Eq. (7):

$LBP\left( P,R \right)=\underset{i=0}{\overset{P-1}{\mathop \sum }}\,u({{g}_{i}}-{{g}_{c}}){{2}^{i}}$                          (7)

where, $g_i$ denotes the intensity for $i_{t h}$ pixel while $g_c$ refers to the centre pixel intensity, $P$ is the number of pixels at radius $R$.

Therefore, the LBP method can function effectively across varying colour maps. A recent study [65] introduces an enhanced variant of LBP known as LCP-Local Configuration Pattern, which is capable of identifying similar patterns with differing orientations. This algorithm integrates LBP features with microstructural details of the image, ensuring a consistent output. By combining LCP with the FK method, a novel approach, LCP-K-Linear Configuration Pattern-Kurtograms, is developed, offering robust dimension reduction and accurate representation of fault signatures in any one-dimensional signal.

Initially, the five-level Fast Kurtogram (FK) is computed. Subsequently, the Kurtogram image is resized to 128x128 pixels using bi-cubic interpolation [66] and converted to grayscale.

Lastly, the LCP is applied to the grayscale image, which is partitioned into 16×16 blocks, extracting 81×1 feature vectors of double precision.

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Figure 6. LCP-K Feature extraction scheme for a one-period segmented healthy signal

In conclusion, our LCP-K algorithm (Figure 6) [67] applies a location invariant textural descriptor to Kurtogram images of the signal to discard fluctuation effects in Kurtogram images ensuring the representative output feature vectors with the same size addressing signal sample size issues.

3.5 Time-domain features

In vibration-based analysis, anomaly signals exhibit similar temporal characteristics statistically. Utilizing statistical features in time domain is a fundamental and effective way in feature extraction, in machinery condition monitoring. In this investigation, mean $(\mu)$, standard deviation ( $\sigma$ ), maximum $(\max )$, minimum ( $\min$ ), kurtosis, skewness and crest factor; a measure of RMS-Root Mean Square and energy, are computed, as inspired by studies [48, 50] for mechanical fault detection. The proposed TDF-Time Domain Features are computed via Eqs. (8)-(11) for a given discrete signal $x_n$ with length $N$, and then concatenated in a matrix of double precision.

$\,Energy:\sum\limits_{n=1}^{N}{{{\left| {{x}_{n}} \right|}^{2}}}\,,\,\,\,Skewness:\sum\limits_{n=1}^{N}{\frac{{{({{x}_{n}}-\mu )}^{3}}}{(N-1){{\sigma }^{3}}}}\,$                          (8)

$Kurtosis:\sum\limits_{n=1}^{N}{\frac{{{({{x}_{n}}-\mu )}^{4}}}{N{{\sigma }^{4}}}}-3\,\,\,\,\,$                          (9)

$Crest\,Factor:\text{20}\left[ \text{lo}{{\text{g}}_{\text{10}}}\left( \frac{\text{max(}{{x}_{n}}\text{)}}{\text{RMS(}{{x}_{n}}\text{)}} \right) \right]\,\,$                          (10)

$TDF={{\left[ \begin{align}  & energy,\,\,mean,\,\,std.\,deviation,\,\,max,\,\, \\ & \,min,\,kurtosis,\,\,skewness,\,\,crest\,factor \\\end{align} \right]}_{\,\text{8}\,\text{x}\,\text{1}}}$                          (11)

3.6 Adaptive synthetic sampling

The most common data encountered in wayside railway vehicle fault detection is healthy, leading to the observation of a significantly greater number of normal signal samples than abnormal ones. Moreover, obtaining abnormal samples for vehicles of the same type is costly unless a real-time measurement system is consistently maintained.

Typically, the number of observations $\left(m_o\right)$ within each class should exceed the length of each feature vector $\left(n_o\right)$, or an insufficient case scenario $\left(n_o \geq m_o\right)$ arises [68]. This insufficient case is often encountered in applications such as signature and voice recognition due to limited observed samples. Misclassifying faulty samples as healthy (false negatives) can be highly challenging to recover from. In such cases, the minority class, comprising less frequent feature vectors, requires oversampling. A straightforward approach to tackle this issue is to accurately interpolate the minority class samples to generate new samples.

To address imbalanced datasets, the literature suggests using SMOTE-Synthetic Over Sampling Method [69]. This approach involves linearly interpolating existing feature vectors from the minority class to create new vectors. However, SMOTE solely targets the minority class vectors, disregarding the majority class samples, which may not always be a practical method for generating additional data. This issue is addressed by an extension of the SMOTE technique known as ADASYN-Adaptive Synthetic Sampling [70]; ADASYN considers samples across each class boundary and dynamically generates samples for the minority class.

The application of ADASYN for feature generation is illustrated in Figure 7 using our wayside measurement database. Specifically, we demonstrate its utilization for the minority class, which comprises 16 observations associated with wheel faults $\left(m_0^{Faulty}=16\right)$ and the majority healthy class with 128 normal observations $\left(m_0^{Normal}=128\right)$. The parameters k-ADASYN and k-SMOTE, which are required for density estimation in the k-Nearest Neighbour (kNN) utilizing Euclidean distance, are both set to a default value of 5. ADASYN boosts each specific feature within the minority class by considering both classes, resulting in the creation of a total of $m_0^{Normal}-m_0^{Faulty}=112$ number of feature vectors that contribute to reinforcing the minority class. It is important to highlight that the synthesized feature vectors gather near the boundaries between classes, and the outlier sample on the right top was not used to generate a new sample by algorithm automatically. This enhances the reliability and complexity of the database, minimizing the impact of outliers rather than solely relying on in-class interpolation.

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Figure 7. Utilizing ADASYN to generate synthetic samples in the minority class to achieve a balance with the majority class [71]

Wayside systems for monitoring rail vehicle conditions offer more benefits compared to scheduled maintenance or condition-based repairs (when a fault inevitably appears), particularly in terms of safety and cost-effectiveness. This study focuses on collecting vibration and acoustic signals from the Prague metro tunnel during regular metro operations to establish an effective framework for monitoring the metro wheelset condition. By employing the proposed methods, a precise procedure for detecting wheelset faults is developed.

Initially, vibration sensor data is utilized to identify wheel defects known to exist on the ID-108 metro train set. This is achieved through the application of TDF, WPE, and LCP-K algorithms, coupled with advanced classifiers like SVM-I, Dec. Tree, and PERLC, following speed-adaptive segmentation. Subsequently, ADASYN is employed to ensure the reliability and alignment of measured faulty signals with healthy ones. The results reveal that the two-class problem is addressed with 100% accuracy for both the A1 and SA1 datasets using TDF features and the Dec. Tree classifier.

In addition, the vibration signal dataset is split into two parts, and a two-class classification is conducted using classifier combination techniques. The results indicate that WPE performs exceptionally well when combined with Med-C, Mean-C, and Vote-C, achieving a 100% success rate in classifying the A1 dataset. However, TDF continues to perform remarkably in classifying the SA1 dataset, achieving an accuracy of 96.1% while LCP-K outperforms WPE in this scenario.

In conclusion, the acoustic signal database is used to assess faulty wheelsets compared to the vibration-based system. While LCP-K shows superior classification accuracy in both measured (A2) and synthesized (SA2) databases (87.5% and 93% respectively), overall accuracy is notably lower in acoustic-based monitoring.

Hence, the methodologies proposed in this study offer the potential to develop suitable frameworks for both acoustic and vibration-based condition monitoring systems, offering simplicity and cost-effectiveness.

The efficiency and applicability of the proposed framework are limited to the complexity of the number of interactions of the rotating device and speed (e.g.: high speed-trains) which can require increased number of wavelet scales or levels in the Kurtogram calculation to prevent low resolution. As a future work, after having adjusted the parameters of the proposed methods to the model-based natural behaviour of the problem in railways, this framework has the potential to assist maintenance specialists and can be adapted for the use of various railway vehicles.

This study was supported by the Competence Centre of Railway Vehicles (TAČR TE01020038), and we are grateful to the Prague Public Transport Company, a.s. for facilitating the measurements.