From physical models to data intelligence: evolution of rail vehicle suspension fault diagnosis

Classical KF

The classical KF (see Table 1) is characterized by its computational efficiency and suitability for online fault diagnosis in linear systems. By fusing system model predictions with real-time sensor measurements, this method achieves precise estimation of internal system states and detects faults by monitoring residual deviations from the normal range.

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Table 1.

Classical KF algorithm. ⁸

Algorithm: classical KF
Input: State transition matrix F , control matrix G , observation matrix H , initial estimate x 0 and P 0 , system noise Q , measurement noise R , measurement value z k , system input u k :
for k = 1 : N do
Prediction step:
x ^ k − = F x ^ k − 1 + G u k
P k − = F P k − 1 F T + Q
Correction step:
K k = P k − H T ( H P k − H T + R ) − 1
x ^ k = x ^ k − + K k ( z k − H x ^ k − )
P k = ( I − K k H ) P k −
end for
Output: Optimal estimation x ^ k and P k .

KF: Kalman filter.

Wei et al. ¹³ established a light rail vehicle model consisting of two carbodies with two power bogies, one carbody with one trailer bogie. The KF was used to generate residuals, and the generalized likelihood ratio test was employed for analyzing residuals. This approach achieved online detection of secondary vertical damper and secondary spring faults. However, this study did not address the issue of fault isolation. Similar studies can be found in the studies by Wei et al.^14,15

To achieve suspension system fault isolation, Wei et al.^16–18 further introduced Dempster–Shafer (D-S) evidence theory to fuse information from KF-generated residuals. The core methodology involves first constructing a feature database containing multiple typical fault modes. Subsequently, the Eros similarity measure and norm distance measurement methods were employed to match new fault features against those in the database, generating basic belief assignments. Finally, these assignments were fused via the D-S evidence combination. A case study demonstrated that this framework effectively identifies and isolates faulty suspension components and their degrees of degradation.

Jesussek and Ellermann ¹⁹ employed multiple KFs for FDI in a full-scale rail vehicle suspension system. This approach involves establishing a set of KFs comprising a fault-free model and various fault models to perform parallel state estimation. By calculating residuals between the outputs of each KF and actual measurements to generate fault indicators, the method effectively detects single-component faults (including secondary vertical damper, yaw damper, and lateral damper) and distinguishes between multiple simultaneous faults. A similar study can be found in the study by Jesussek and Ellermann. ²⁰

Extended KF

Although the classical KF exhibits robust estimation performance in linear systems, it is inapplicable to nonlinear contexts. The EKF (see Table 2) overcomes this limitation by employing Taylor series expansion to linearize nonlinear functions, effectively extending the estimation capabilities of the classical KF to nonlinear systems.

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Table 2.

EKF algorithm. ⁸

Algorithm: EKF
Input: Initial estimate x 0 and P 0 , system noise Q , measurement noise R , measurement value z k , system input u k .
for k = 1 : N do
Prediction step:
x ^ k − = f ( x ^ k − 1 , u k , 0 )
A k = ∂ f ∂ x ( x ^ k − 1 , u k , 0 ) , W k = ∂ f ∂ w ( x ^ k − 1 , u k , 0 )
P k − = A k P k − 1 A k T + W k Q k − 1 W k T
Correction step:
V k = ∂ h ∂ v ( x ^ k − , 0 ) , H k = ∂ h ∂ x ( x ^ k − , 0 )
K k = P k − H k T ( H k P k − H k T + V k R V k T ) − 1
x ^ k = x ^ k − + K k ( z k − h ( x ^ k − , 0 ) )
P k = ( I − K k H k ) P k −
end for
Output: Optimal estimation x ^ k and P k .

EKF: extended Kalman filter.

Jesussek and Ellermann ²¹ proposed a fault diagnosis strategy based on a hybrid EKF and a nonlinear residual generator to capture the nonlinear characteristics of the damper. This method enables FDI for nonlinear rail vehicle dampers. Simulation results based on a half-train model demonstrated that, in most scenarios, the method reliably identifies lateral and yaw damper faults with high sensitivity. Jesussek and Ellermann ²² extended the hybrid EKF to a full-train multibody dynamic model, incorporating H 2 robust filter and weighted residual generation mechanism to enhance system robustness and fault identification capabilities. The method successfully achieved the detection and preliminary isolation of yaw damper faults, distinguishing between the front and rear bogies, though it remained unable to differentiate between the left and right sides.

Summary

In the context of rail vehicle suspension fault diagnosis, state estimation methods primarily comprise the classical KF and EKF, as summarized in Table 3.

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Table 3.

Comparison of various state estimation methods.

Methods	Faults	Advantages	Disadvantages
Classical KF	Primary and secondary vertical dampers, primary and secondary springs, lateral dampers, and yaw dampers.	Computationally efficient and suitable for online detection.	Inapplicable to nonlinear systems; limited fault isolation capability.
EKF	Lateral dampers, yaw dampers.	Effectively handles nonlinear systems.	Linearization errors under strong nonlinearity may lead to divergence and limited fault isolation capability.

KF: Kalman filter; EKF: extended Kalman filter.

In summary, while the classical KF offers algorithmic simplicity and computational efficiency, its restriction to linear systems severely limits its applicability to nonlinear suspension contexts. Although the EKF addresses this limitation via local linearization, making it a mainstream choice in early research, it suffers from linearization errors and divergence risks under conditions of strong nonlinearity. Moreover, the requirement for complex Jacobian matrix calculations renders its implementation cumbersome.

Classical KF

The classical KF based on the interacting multiple-model framework (IMM-KF) (see Figure 6) is widely applied in parameter estimation. This algorithm operates multiple KFs in parallel (each corresponding to a specific system mode) and fuses their outputs based on model matching probability, thereby achieving precise estimation of system states and parameters.

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Figure 6.

Fault diagnosis framework based on the IMM-KF algorithm in the study by Mori and Tsunashima. ²⁶ IMM-KF: Kalman filter based on the interacting multiple-model framework.

Hayashi et al.^23,24 proposed a solution based on the IMM-KF algorithm for the fault diagnosis of rail vehicle suspension systems and sensors. The core mechanism involves operating a bank of KFs in parallel, where each filter corresponds to a specific system mode (including the fault-free state, varying degrees of damper degradation, spring faults, and sensor faults). By updating mode probabilities based on the match between each model and current measurements, the method enables the identification of fault types and severities. Simulation results demonstrated that the method effectively detects performance degradation in secondary lateral dampers, accurately estimates damping coefficients, and successfully distinguishes between suspension and sensor faults. A similar study can be found in the study by Tsunashima et al. ²⁵

Mori and Tsunashima^26,27 integrated an updated estimation model into the IMM-KF framework. Simulation results indicate that this method effectively detects varying degrees of faults in secondary lateral dampers. Comparisons with the standard IMM-KF demonstrated that the IMM-KF algorithm equipped with the updated estimation model has superior parameter estimation performance.

Extended KF

When a single EKF simultaneously estimates multiple parameters, divergence or bias issues may arise. To address this, Alfi et al. ²⁸ proposed a three-stage procedure (see Figure 7). First, an EKF independently estimates the equivalent conicity. Then, a bank of parallel EKFs estimates specific suspension parameters, including lateral and yaw damper damping. Finally, a set of KFs identifies the most probable estimation, employing a Bayesian recursive algorithm to analyze residuals for fault isolation. The practical applicability of this condition monitoring system was validated on the ETR 500-Y1 high-speed train.

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Figure 7.

Fault diagnosis scheme based on multiple EKFs in the study by Alfi et al. ²⁸ EKF: extended Kalman filter.

Zhang et al. ²⁹ leveraged the computational efficiency and online implementation potential of the EKF to investigate the normal and faulty modes of the CRH380A vehicle operating at 360 km/h under realistic track irregularities. By estimating the parameters of suspension components for fault diagnosis, the method accurately localizes fault positions and identifies fault types of critical bogie components.

Unscented KF

While the EKF offers advantages in handling nonlinear systems, its reliance on first or second-order Taylor series expansions for linearization neglects higher-order terms. This approximation inevitably introduces linearization errors and may even lead to filter divergence. To address the limitations of the standard EKF, various improved variants, such as the UKF (see Table 4), have been developed.

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Table 4.

UKF algorithm. ⁸

Algorithm: UKF
Input: Initial estimate x 0 and P 0 , measurement value z k .
for k = 1 : N do
Prediction step:
x ^ k + 1 = ∑ i = 0 2 n χ k
P k − = ∑ i = 0 2 n ( χ k i − x ^ k − ) ( χ k i − x ^ k − ) T
Correction step:
K k = P k xz ( P k y ) − 1
x ^ k = x ^ k − + K k ( z k − z ^ k − )
P k = P k − − K k P k z K k T
end for
Output: Optimal estimation x ^ k and P k .

UKF: unscented Kalman filter.

Xu et al. ³⁰ applied both the UKF and EKF to secondary suspension parameter estimation, evaluating their performance via simulations using linear and nonlinear models subject to random track irregularities. The results demonstrated the superiority of the UKF. Specifically, under identical initial conditions, the UKF yielded lower relative errors in convergence values compared to the EKF.

Cubature KF

To circumvent the linearization errors and derivative calculation requirements of the EKF, the CKF (see Table 5) has been developed. In most scenarios, the CKF yields higher and more stable estimation accuracy and is particularly suitable for highly nonlinear systems.

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Table 5.

CKF algorithm. ³¹

Algorithm: CKF
Input: Initial estimate x 0 and P 0 , system noise Q , measurement noise R .
for k = 1 : N do
State prediction:
x ^ k | k − 1 = ∑ i = 1 L ω i F ( ξ i , k − 1 )
P k | k − 1 = ∑ i = 1 L ω i [ F ( ξ i , k − 1 ) − x ^ k | k − 1 ] 2 + Q k
Measurement prediction:
z ^ k | k − 1 = ∑ i = 1 L ω i H ( ξ i , k | k − 1 )
P zz , k | k − 1 = ∑ i = 1 L ω i [ H ( ξ i , k | k − 1 ) − z ^ k | k − 1 ] 2 + R k
P xz , k | k − 1 = ∑ i = 1 L ω i [ ξ i , k | k − 1 − x ^ k | k − 1 ] × [ H ( ξ i , k | k − 1 ) − z ^ k | k − 1 ] T
State estimation:
K k = P xz , k | k − 1 P zz , k | k − 1 − 1
x ^ k = x ^ k | k − 1 + K k ( z k − z ^ k | k − 1 )
P k = P k | k − 1 − K k P zz , k | k − 1 K k T
end for
Output: Optimal estimation x ^ k and P k .

CKF: cubature Kalman filter.

Zoljic-Beglerovic et al. ³¹ proposed and validated a CKF-based fault diagnosis method for rail vehicle suspension systems. The performance of the CKF was evaluated by introducing specific faults into the secondary vertical damper, including abrupt (± 50%) and drift-like (+ 25%) changes in the damping coefficient. Simulation results demonstrated that under both fault scenarios, CKF estimates rapidly converge to the true values with deviations of less than 3%. Moreover, a comparison with the discrete EKF highlights the superior parameter estimation performance of the CKF. A similar study can be found in the study by Zoljic-Beglerovic et al. ³²

Rao–Blackwellized PF

The PF is a representative nonlinear filtering technique that avoids the need for system model linearization, making it advantageous for handling complex systems. The RBPF is an enhanced variant of the standard PF, which partitions the state vector into linear and nonlinear components. By processing these components using the KF and PF, respectively, the RBPF achieves an effective balance between computational efficiency and estimation accuracy.

Li et al. ³³ applied the RBPF method to parameter estimation within rail vehicle dynamic models, specifically targeting suspension damping parameters. Simulation results demonstrated that, compared to the traditional EKF, RBPF estimates converge rapidly and stably to true values, effectively overcoming issues such as estimation bias and divergence often associated with the EKF. A similar study can be found in the study by Li et al. ³⁴ Weston et al. ³⁵ integrated RBPF-based parameter estimation with KF-based state estimation to develop a comprehensive integrated vehicle-track condition monitoring system. Within this framework, the RBPF was used to monitor vehicle component conditions, while the KF was used to rapidly respond to abrupt faults. Li et al. ³⁶ shifted their research focus toward the engineering practicality and robustness of the RBPF method. By evaluating the impact of various sensor configurations on parameter estimation, they validated the feasibility of the method using only bogie and carbody sensors, thereby demonstrating its engineering utility. Validation using field data from a Coradia Class 175 railway vehicle confirmed that the method successfully identifies damper damping coefficients and equivalent conicity from actual dynamic responses.

Building on the RBPF algorithm (see Figure 8), Zhang et al. ³⁷ proposed a repeat-uniform-sampling RBPF strategy to simultaneously address the diagnosis of suspension component parameter degradation and sudden faults. The method’s effectiveness was validated via numerical simulations on a full-vehicle lateral dynamic model. Results demonstrated that this method not only achieves high-precision estimation for up to six suspension parameters but also rapidly identifies abrupt component (including dampers) faults, through the repeat-uniform-sampling strategy.

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Figure 8.

Implementation of RBPF in the study by Zhang et al. ³⁷ RBPF: Rao–Blackwellized particle filter.

RLS method

The RLS possesses the memory property that enables parameter identification from the autocorrelation and cross-correlation of input and output variables in noisy systems, making it suitable for processing highly correlated signals.

Liu et al.^38,39 proposed a model-based condition monitoring strategy for rail vehicle suspensions using the RLS algorithm (see Table 6), focusing on fault identification for primary springs and dampers. Validated via numerical simulations and field tests on the E464 locomotive, the results demonstrated the method’s ability to accurately identify suspension component faults and monitor performance degradation.

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Table 6.

RLS algorithm. ³⁸

Algorithm: RLS
Input: Initial estimate θ 0 and P 0 , forgetting factor λ .
for k = 1 : N do
Estimation error:
e k = Y k − X k T θ ^ k − 1
Gain matrix:
G k − 1 = P k − 1 X k ( λ + X k T P k − 1 X k ) − 1
Correction step:
θ ^ k = θ ^ k − 1 + G k − 1 e k
P k = 1 λ ( I − G k − 1 X k T ) P k − 1
end for
Output: Optimal estimation θ ^ k and P k .

RLS: recursive least squares.

Liu and Bevan ⁴⁰ expanded the RLS method into an integrated, modular condition monitoring system. Targeting the more structurally complex Co-Co locomotive, this study innovatively designed three independent diagnostic modules, including vertical, lateral, and yaw motions, to achieve synchronous estimation and decoupling of multidimensional suspension parameters. The system’s engineering feasibility for multifault diagnosis and isolation was validated through simulations of various concurrent fault scenarios using the multibody software VAMPIRE.

SM-based method

The SM-based parameter identification method is grounded in SM control theory and nonlinear observer principles. It is suitable for rail vehicle suspension systems, which are engineering systems characterized by nonlinearity, time-varying dynamics, and susceptibility to external disturbances.

Zoljic-Beglerovic et al. ⁴¹ proposed an SM-based algorithm for FDI in rail vehicle suspension systems. The method was validated via simulations encompassing various scenarios, including fault-free conditions, abrupt parameter changes, and drift-like parameter changes. The results demonstrated that the algorithm not only identifies suspension parameters with high precision but also exhibits superior convergence speed and robustness compared to the traditional EKF. Zoljic-Beglerovic et al. ⁴² systematically presented a comprehensive framework for applying SM-based parameter identification to rail vehicle suspension fault diagnosis (see Figure 9). A key innovation of this study lies in applying the SM-based identifier to complex full and half vehicle models, enabling the simultaneous decoupling and identification of primary and secondary suspension parameters. Through a comparative study across four dimensions (including parameterization workload, computational efficiency, estimation accuracy, and convergence speed), the SM-based algorithm was proven to significantly outperform the hybrid EKF.

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Figure 9.

Framework for rail vehicle suspension system fault diagnosis in the study by Zoljic-Beglerovic et al. ⁴²

Summary

In rail vehicle suspension fault diagnosis, parameter estimation methods include the classical KF, EKF, UKF, CKF, RBPF, RLS, and SM-based methods, as summarized in Table 7.

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Table 7.

Comparison of various parameter estimation methods.

Methods	Faults	Advantages	Disadvantages
Classical KF	Secondary springs, lateral dampers.	Enables joint estimation of multiple parameters.	Complex parameter tuning.
EKF	Lateral dampers, yaw dampers.	Enables joint estimation of multiple parameters.	Subject to linearization errors, susceptible to bias in multiparameter estimation.
UKF	Secondary vertical dampers, secondary springs.	Sensitive to parameter variations, high accuracy.	Limited performance under simultaneous multiple faults.
CKF	Secondary vertical dampers.	Sensitive to slowly varying faults, rapid convergence and high accuracy.	Performance depends on process and measurement noise covariance matrix settings.
RBPF	Primary and secondary vertical dampers, primary and secondary springs, lateral dampers, and yaw dampers.	Handles high-dimensional state spaces with high accuracy.	Computationally intensive, high implementation complexity.
RLS	Primary and secondary vertical dampers, primary and secondary springs, lateral dampers, and yaw dampers.	Low computational cost; suitable for online real-time monitoring, possesses memory property.	Requires tuning of the forgetting factor.
SM-based	Primary and secondary vertical dampers, primary and secondary springs.	Simple parameter tuning, low computational effort.	Parameter tuning relies on experience and slow convergence speed.

KF: Kalman filter; EKF: extended Kalman filter; UKF: unscented Kalman filter; CKF: cubature Kalman filter; RBPF: Rao–Blackwellized particle filter; RLS: recursive least squares; SM: sliding mode.

In summary, parameter estimation methods facilitate precise fault localization and degradation assessment by monitoring deviations in the physical parameters of the suspension system. Compared to single-state observation, the IMM-KF framework effectively manages mode switching of the train between different operating conditions through parallel processing of multiple models. The UKF and CKF employ the unscented transform and cubature rules to directly capture the nonlinear characteristics of the system and circumvent complex Jacobian matrix calculations, thereby achieving superior stability in parameter identification compared to traditional linearization methods. Although the RBPF exhibits excellent estimation accuracy when dealing with high-dimensional nonlinear state spaces, its performance remains sensitive to the prior settings of system noise characteristics and the total count of particles. The RLS offers excellent real-time performance and low computational demand. However, it is restricted to linear or approximately linear systems and imposes high requirements on model accuracy and data preprocessing. Additionally, parameter identification algorithms based on SM theory offer significant advantages in robustness when facing model uncertainties and external disturbances. The primary focus of these methods is to directly map fault mechanisms through variations in physical parameters. However, their effectiveness is typically limited by the accuracy of the physical models and the quality of data preprocessing.

Correlation between modeling assumptions and failure modes

The technical logic of state estimation methods is founded upon the modeling assumption of analytic redundancy, which posits that the physical parameters of the system are precisely known and constant before the occurrence of a fault. Under this premise, the algorithm captures abnormal information within the system by monitoring abrupt changes in the observation residuals. This characteristic provides state estimation methods with a distinct advantage in identifying abrupt faults,^14,15 such as the sensitive detection of air bag ruptures, air spring deflations, or steel spring breakages that induce instantaneous step changes in system dynamic characteristics. However, the limitation of this assumption resides in its high sensitivity to model plant mismatch, as nonfault perturbations triggered by track irregularities or severe fluctuations in the operating environment are frequently misidentified as system state anomalies.

The modeling premise of parameter estimation methods is that faults manifest as drifts in physical parameters. Such methods^30,36 achieve diagnosis by tracking the evolution trajectories of key parameters such as system stiffness or damping coefficients in real time. This modeling logic aligns more closely with the evolutionary patterns of long-term performance degradation in suspension systems. For instance, it can effectively evaluate damping reduction caused by damper oil leakage or stiffness attenuation triggered by the long-term service of suspension springs.^31,41 However, the identifiability of parameters depends heavily on the intensity of external excitations. Under operating conditions with low excitations, the algorithms may fail or produce severe fluctuations due to insufficient input signal excitation. Additionally, when multiple physical parameters undergo coupled degradation simultaneously, a single algorithm often struggles to accurately isolate specific fault sources.

Evaluation metrics and engineering trade-off analysis

To systematically evaluate the practical utility of various model-based methods in engineering applications, five key performance indicators consisting of complexity, accuracy, detection delay, false alarm rate (FAR), and computational cost are introduced (see Table 8) to perform a comparative analysis of the model-based algorithms within a unified dimension.

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Table 8.

Comparison of various model-based methods based on unified evaluation metrics.

Methods	Complexity	Accuracy	Delay	FAR	Cost
Classical KF	Low	Medium	Very low	Medium	Very low
EKF	Medium	Medium	Low	Medium	Low
UKF/CKF	High	High	Low	Low	Medium
RBPF	Very high	Very high	Medium	Very low	High
RLS	Low	Medium	Very low	Medium	Very low
SM-based	Medium	High	Medium	Very low	Medium

FAR: false alarm rate; KF: Kalman filter; EKF: extended Kalman filter; UKF: unscented Kalman filter; CKF: cubature Kalman filter; RBPF: Rao–Blackwellized particle filter; RLS: recursive least squares; SM: sliding mode.

Analysis demonstrates that model-based methods exhibit significant trade-off relationships among these metrics. In state estimation methods, the classical KF and EKF possess extremely low computational costs and minimal delays, which make them highly suitable for the online real-time monitoring of linear or weakly nonlinear systems. However, when confronted with complex track excitations or strong nonlinear conditions, the estimation bias resulting from linearization errors significantly increases the risk of false alarms. Within the category of parameter estimation methods, UKF, CKF, and RBPF significantly enhance diagnostic accuracy through nonlinear filtering techniques. Nevertheless, this improvement in accuracy often comes at the expense of computational efficiency. For example, the computational cost of RBPF is typically several times higher than that of EKF due to its intensive particle sampling requirements, which limit its real-time application in large-scale sensor networks. In contrast, the RLS method provides an acceptable balance between accuracy and delay while maintaining low computational overhead due to its recursive storage characteristics, making it one of the mainstream engineering choices for balancing real-time performance and accuracy.

Correlation method

The diagnostic principle of correlation methods is that suspension faults disrupt structural symmetry, inducing changes in the dynamic interactions between carbody and bogie motion modes. These variations manifest as specific pattern alterations within signal cross-correlation functions.

Mei and Ding ⁴³ leveraged the structural symmetry of the bogie to achieve fault diagnosis by analyzing the dynamic coupling induced by suspension imbalance. Specifically, this method requires no precise system model, relying solely on basic parameters such as vehicle speed and distance between suspensions. It identifies performance degradation in suspension components (e.g., dampers) by calculating cross-correlation functions between the acceleration signals of the front and rear suspensions (or bounce and pitch accelerations) and monitoring feature variations at specific time shifts. A similar study can be found in the study by Guo et al. ⁴⁴ Also Ding et al. ⁴⁵ considered a full bogie model comprising three degrees of freedom (DOF), including bounce, pitch, and roll, to analyze the pairwise dynamic interactions among these motions. The introduction of cross-correlation coefficients enhanced the method’s robustness against variations in vehicle speed and track irregularities.

Mei and Ding ⁴⁶ proposed a fault detection scheme based on cross-correlation coefficients and augmented by a low-pass filter. This method maintains high sensitivity while mitigating the impact of increased bogie mode resonance caused by reduced damping associated with damper faults. Simulations using a nine-DOF vehicle model further validated the effectiveness of this method for suspension FDI. Kojima and Sugahara ⁴⁷ proposed a fault detection method for rail vehicle vertical dampers based on vibration phase difference. The principle of the method is that within a symmetric fault-free system, the phase difference between the bounce and pitch motions of the bogie or cabody remains at ± 90 °. However, damper faults disrupt this system symmetry, inducing abnormal phase differences. The effectiveness of this method for detecting faults in both primary and secondary dampers was validated through test rig experiments and on-track field tests. Similar studies can be found in the studies by Dumitriu.^48–50

Distinct from methods relying on the correlation analysis of on-board acceleration data, Teng and Wei ⁵¹ proposed a track-side signal detection method for diagnosing urban rail vehicle suspension faults. This method employs a rigid-flexible coupled wheel-rail contact model and track-side accelerometers to capture vertical vibration signals during train passage. The signals are analyzed using continuous wavelet packet analysis and short-time Fourier transform (STFT), followed by decomposition via local mean decomposition. Fault severity is then quantified by calculating the correlation coefficients between faulty and healthy signal components. Overcoming the limitations of traditional on-board monitoring, this noncontact method offers advantages such as ease of deployment and compatibility with existing lines, demonstrating robust performance in detecting and assessing the severity of spring and damper faults.

The aforementioned studies demonstrate the application of correlation-based diagnostic methods in passenger train suspensions. These techniques are equally applicable to freight wagons. Li et al. ⁵² used only two tri-axial accelerometers to analyze the cross-correlation between acceleration signals at the front-left and rear-right carbody positions. By constructing a specific fault index, the detection of ± 25% stiffness variation in bolster springs was achieved (see Figure 11). A similar study can be found in the study by Li et al. ⁵³ Alfi et al. ⁵⁴ employed the cross-correlation of bogie bounce, pitch, and roll vibrations to detect faults in Y25 freight wagon bogies (see Figure 12). Validated through numerical experiments, the results demonstrated that under full load conditions, the method effectively identified abnormal variations in suspension stiffness and friction characteristics, excelling particularly in spring fault detection. However, the diagnostic capability deteriorated significantly under tare load conditions, highlighting the significant influence of load status on freight wagon suspension fault detectability.

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Figure 11.

Fault detection framework based on carbody vibration correlation in the study by Li et al. ⁵²

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Figure 12.

Fault detection framework based on bogie vibration correlation in the study by Alfi et al. ⁵⁴

The studies above amply demonstrate that suspension faults can be effectively diagnosed by analyzing system dynamic interactions manifested in inertial sensor signals. Following this rationale, the system asymmetry induced by suspension faults also influences acoustic characteristics. Sorribes-Palmer et al. ⁵⁵ proposed a suspension fault diagnosis method using on-board acoustic sensors. By analyzing variations in acoustic emissions resulting from changes in structural mode coupling induced by suspension component faults, this method circumvents the placement constraints associated with inertial sensors. Experimental validation on a test ring confirmed the method’s superior classification performance for both complete fault and partial degradation of primary and secondary dampers.

Statistical characteristics method

The fundamental premise of statistical characteristics methods is that the operational status of equipment (normal or faulty) is manifested in generated signals such as vibration and acoustics, where state changes induce shifts in statistical characteristics. Consequently, extracting and analyzing these features enables both fault identification and severity assessment.

Melnik and Kostrzewski ³ evaluated the feasibility and limitations of acceleration-based statistical characteristics suspension fault monitoring (sensor placement shown in Figure 13) through field tests on passenger and freight vehicles. Results indicated that although parameters such as the root mean square (RMS), interquartile range (IQR), and crest factor reflect suspension state changes to a certain degree, their diagnostic effectiveness is sensitive to track excitation, measurement direction, and fault type, and damper fault detection is particularly challenging. Finally, the study proposed a potential diagnostic method based on geometric distances within a multidimensional space. A similar study can be found in the study by Chudzikiewicz et al. ⁵⁶

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Figure 13.

Accelerometer placement in the study by Melnik and Kostrzewski. ³

Melnik and Sowiński ⁵⁷ departed from simple threshold comparisons of standard statistical characteristics, instead employing a method that calculates the distance between current and normal states within a multidimensional space to achieve effective fault identification. Guided by the criterion of maximizing the spatial distance between normal and faulty states, the study screened specific parameter combinations sensitive to suspension faults (including signal energy, IQR, zero-peak, and peak-peak), thereby enabling the effective identification of reduced stiffness and damping faults. Hu ⁵⁸ developed a dynamic model of the CRH380B high-speed train to investigate the impact of three specific suspension faults (including primary vertical damper, air spring, and yaw damper) on vehicle dynamic responses. A fault detection and localization method based on frequency-domain filtering and RMS analysis was proposed. By explicitly identifying sensitive signals and characteristic frequency bands for each fault type and vehicle model, this method achieved precise diagnostic localization.

Oosterhof and Peters ⁵⁹ proposed a suspension fault diagnosis method based on dynamic wheel load difference. By leveraging the Gotcha measurement system to monitor load disparities between left and right wheels during operation, a dynamic suspension imbalance index framework was designed to differentiate between primary and secondary suspension faults. Kraemer et al. ⁴ investigated the impact of leaf spring faults on the vibration response of freight wagons, validating a diagnostic method based on vibration energy distribution and symmetry principles. Spring faults in the suspension system induce a loss of vibration energy in measurement signals and shifts in high-vibration modes. By employing symmetrically arranged sensors on the carbody and using RMS ratios as fault indicators, the method effectively translates suspension stiffness variations into observable feature deviations. Dumitriu ⁶⁰ proposed a primary damper fault detection method based on bogie vertical vibration, using only four accelerometers mounted on the frame and axle boxes (see Figure 14). By developing a vehicle-track system model and integrating field measurements with numerical simulations, the study characterized the RMS acceleration distribution of the bogie under both normal and faulty primary damper conditions. The results indicated that damper faults cause a significant increase in RMS acceleration at the frame, whereas changes at the axle box are not obvious.

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Figure 14.

(a) Bogie vibration acceleration acquisition system; (b and c) accelerometer mounting positions in the study by Dumitriu. ⁶⁰

Multivariate statistical method

Multivariate statistical methods do not require precise system models and are capable of processing high-dimensional data to detect abnormal states. However, the lack of diagnostic “labels” often limits their effectiveness in fault isolation. Common techniques include principal component analysis (PCA) (Table 9), partial least squares (PLS) (Table 10), independent component analysis, and canonical variate analysis (CVA). ⁶¹

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Table 9.

PCA algorithm. ⁶³

Algorithm: PCA
Step 1: Normalize the samples to zero mean and unit variance, denoted as follows:
X T = [ x 1 … x n ] ∈ R m × n
Step 2: Calculate the covariance matrix of the samples.
R = 1 n − 1 X ¯ T X ¯
Step 3: Calculate feature values and feature vectors of the sample covariance matrix.
R = P m S m P m T
S m = diag ( λ 1 , λ 2 , … , λ m ) , λ 1 ≥ λ 2 ≥ … ≥ λ m
P m = [ p 1 , p 2 , … , p m ]
Step 4: Calculate the cumulative variance contribution rate of the first k-row principal elements.
∑ j = 1 k λ j ∑ j = 1 m λ j ≥ η
Step 5: Set thresholds for the T 2 statistic and SPE statistic for a given significant level α .
J th , T 2 = k ( n 2 − 1 ) n ( n − k ) F α ( k , n − k )
J th , SPE = θ 1 [ c α h 0 2 θ 2 θ 1 + 1 + θ 2 h 0 ( h 0 − 1 ) θ 1 2 ] 1 / h 0
Step 6: Normalize the test samples using the mean and variance of the training samples.
Step 7: Calculate the T 2 statistic and SPE statistic.
T 2 = x T P k S k − 1 P k T x
SPE = x T ( I m − P k P k T ) x
Step 8: Determine if a malfunction has occurred based on the following logic.
When T 2 ≤ J th , T 2 and SPE ≤ J th , SPE , no fault has occurred. The rest of the cases are fault cases.

PCA: principal component analysis; SPE: squared prediction error.

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Table 10.

PLS algorithm. ⁶³

Algorithm: PLS
Step 1: Normalize the input matrix X and output matrix Y to zero mean and unit variance, denoted as X T = [ x 1 … x n ] ∈ R m × n and Y T = [ y 1 … y n ] ∈ R a × n .
Step 2: Perform the following iterative computations γ times ( k = 1 , … , γ ) .
( w k * , q k * ) = arg max ∥ w k ∥ = 1 , ∥ q k ∥ = 1 w k T X k T Y q k , X 1 = X
t k = X k w k * , p k = X k T t k ‖ t k ‖ 2 , X k + 1 = X k − t k p k T
r 1 = w 1 * , r k = Π j = 1 k − 1 ( I m × m − w j * p j T ) w k *
Step 3: Deposit p k , t k , q k , r k into P , T , Q , R . The correlation model given by the standard PLS algorithm is
X = T P T + E , Y = T Q T + F = XM + F , M = R Q T
Step 4: Set thresholds for T 2 and SPE statistics for a given significant level α :
J th , T 2 = γ ( n 2 − 1 ) n ( n − γ ) F α ( γ , n − γ )
J th , SPE = g χ α 2 ( h )
Step 5: Normalize the test samples using the mean and variance of the training samples.
Step 6: Calculate the T 2 and SPE statistics, where T 2 and SPE are defined as follows:
T 2 = x T R ( T T T n − 1 ) − 1 R T x
SPE = ‖ ( I m × m − P R T ) x ‖ 2
Step 7: Determine if a malfunction has occurred based on the following logic:
{ T 2 > J th , T 2 Faulty in x , which is related to y SPE > J th , SPE Faulty in x , which is unrelated to y T 2 ≤ J th , T 2 and SPE ≤ J th , SPE Fault - free in x .

PLS: partial least squares; SPE: squared prediction error.

Wei et al. ⁶² estimated a dynamic model of a rail vehicle suspension system to perform fault detection using two multivariate statistical methods, including PCA and CVA, relying solely on accelerometer data. Simulation results indicated that while both methods demonstrated high detection performance for large magnitude faults in springs and dampers, they failed to detect minor faults.

Wei et al. ⁶⁴ applied dynamic PCA (DPCA) and consensus PCA (CPCA) to suspension fault detection. A comparative analysis of the results revealed that CPCA was capable of detecting minor faults that elude DPCA, while also demonstrating a faster fault response speed. Wei et al. ⁶⁵ applied an extended PLS method, which is multiblock PLS (MBPLS), to rail vehicle suspension fault detection. Simulation results demonstrated that MBPLS was capable of detecting minor faults in suspension springs and dampers, exhibiting detection performance superior to that of DPCA. A similar study can be found in the study by Zhang. ⁶⁶

Building on DPCA, Wei Guo ⁶⁷ employed a distributed DPCA approach to diagnose faults in primary springs and secondary dampers. By partitioning the suspension system into multiple subsystems and establishing separate DPCA models for each, the method leverages the distributed relation of the subsystems to achieve fault detection and preliminary isolation. Wei et al. ⁶⁸ proposed an FDI method integrating PLS with D-S evidence theory. PLS was employed for rapid fault detection, demonstrating excellent performance in identifying moderate and severe faults. Moreover, D-S evidence theory was used to fuse the frequency-domain features of fault data with the standard feature database to successfully isolate both fault locations and severity levels. Wang et al. ⁶⁹ introduced a multilinear PCA (MPCA) framework for extracting features of minor faults by using tensor data. Comparisons with classical PCA and its extension, DPCA, demonstrated MPCA’s superior performance in the detection and isolation of minor faults. Fang et al. ⁷⁰ proposed a real-time monitoring method for high-speed train suspension systems based on probability-relevant PCA (PRPCA). This method exhibited high sensitivity to incipient suspension faults and outperforms traditional PCA in fault detection performance.

Subspace method

Subspace identification methods operate independently of a priori system models, avoiding parameterization and nonlinear optimization issues. They enable the direct extraction of system dynamics from input and output data.

Liu et al. ⁷¹ proposed a condition monitoring scheme for rail vehicle suspension systems based on the average correlation signals-based stochastic subspace identification (ACS-SSI) algorithm. The diagnostic logic relies on the premise that suspension faults directly induce variations in global modal parameters. Thus, identifying deviations in these parameters enables effective fault diagnosis. Validated via a SIMPACK dynamic model simulating normal conditions, spring faults, and damper faults, the results demonstrated that ACS-SSI accurately identifies modal frequencies and mode shapes, indicating potential for online condition monitoring. Liu et al. ⁷² validated the practical applicability of the ACS-SSI algorithm for operational modal analysis and condition monitoring of rail vehicle suspensions through experimental studies on a Y25 bogie. Liu et al. ⁷³ further proposed an online modal identification scheme using correlation subset-based SSI (CoS-SSI) for suspension condition monitoring. Validation results on a 1/5th scale roller rig (see Figure 15) demonstrated that CoS-SSI not only accurately identifies all critical suspension modes but also outperforms both covariance-based SSI (Cov-SSI) and ACS-SSI. Jung et al. ⁷⁴ combined SSI with an eigenfrequency density estimator to construct a suspension monitoring system capable of automatically distinguishing between healthy and faulty states. Validated through simulations involving a progressive reduction in primary spring stiffness (from 5 to 70%), the method demonstrated low classification error rates even under conditions of minor stiffness loss.

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Figure 15.

(a) The 1/5th scaled roller rig and (b) side view schematic of the roller rig in the study by Liu et al. ⁷³

Addressing the challenge of detecting incipient faults in high-speed train suspension springs and dampers, Wu et al. ⁷⁵ proposed a data-driven total measurable fault information residual (ToMFIR) detection method. By fusing output and controller residuals and using subspace techniques to extract fault features from historical data, the ToMFIR method achieves sensitive detection of slowly varying faults without reliance on precise system models. Simulation results demonstrated its effectiveness in identifying a 15% gradual reduction in spring and damper coefficients, exhibiting both high detection speed and accuracy. Addressing the challenges of FDI in nonlinear high-speed train suspension systems, Wu et al. ⁷⁶ proposed a framework incorporating the Takagi–Sugeno fuzzy dynamical model, building upon the ToMFIR method. Simulation results demonstrated that this scheme was effective not only in detecting slowly varying faults but also in identifying incipient faults with intermittent characteristics. A similar study can be found in the study by Wu et al. ⁷⁷ Vlachospyros et al. ⁷⁸ proposed a data-driven method using multiinput single-output transmittance within a multiple-model framework for the early detection and localization of rail vehicle suspension faults under varying operating conditions. This method employs the multiple-model structure to capture and compensate for uncertainties induced by load variations, while using PCA to reduce the dimensionality of the model parameter space for enhanced robustness (see Figure 16). Simulations and field tests on the Athens Metro demonstrated that, using only six sensors and limited training data, the method successfully detects incipient faults and achieves a precise component localization rate of 95.8%.

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Figure 16.

(a) Sensor placement and faulty components (red) and (b) schematic of the fault detection method in the study by Vlachospyros et al. ⁷⁸

Summary

Statistical methods offer various solutions based on signal and data analysis for rail vehicle suspension fault diagnosis. The characteristics of these methods are summarized in Table 11.

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Table 11.

Comparison of various statistical methods.

Methods	Complexity	Faults	Advantages	Disadvantages
Correlation method	Low	Primary and Secondary vertical dampers, primary springs, and freight wagon bolster springs.	Simple Implementation, low cost, supports real-time online detection.	Relies on system Symmetry, sensitive to sensor placement.
Statistical characteristics method	Medium	Primary and secondary vertical dampers, primary and secondary springs, yaw dampers, and leaf springs.	Simple implementation, low cost.	Variable sensitivity across different faults, dependent on historical data and calibration.
Multivariate statistical method	Medium	Primary and secondary vertical dampers, primary and secondary springs, and lateral dampers.	Handles multivariate and high-dimensional data.	Relies on extensive historical data, limited fault isolation capability, subjective threshold setting.
Subspace method	High	Primary and secondary vertical dampers, primary and secondary springs, and lateral dampers.	Good noise robustness, clear physical interpretation.	High computational complexity, parameter tuning relies on experience.

In summary, correlation methods offer excellent real-time performance and simplicity. However, they heavily rely on structural symmetry and exhibit limited capability in isolating concurrent faults. Statistical characteristics methods provide richer fault information than correlation methods and function without system models, yet their offline computation processes are often cumbersome. Multivariate statistical methods effectively handle high-dimensional multivariate data but involve complex implementation, depend on extensive, high-quality historical data for model construction, and exhibit weak fault isolation capabilities. While computationally intensive, subspace methods demonstrate strong adaptability to nonstationary and nonlinear systems, providing a reliable physical basis for fault localization.

K-nearest neighbor

The KNN algorithm is an intuitive, nonparametric supervised learning technique applicable to both classification and regression tasks. Its core principle involves identifying the KNNs in the training set that are most similar to a new data point and predicting its class via majority voting or weighted aggregation of the neighbors’ labels (see Figure 18).

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Figure 18.

Exemplification of the KNN classification method in the study by Gasparetto et al ⁷⁹ : the filled circle is the sample to be classified, whereas the void circles and crosses are the training samples representative of two different fault categories. In the example, it is assumed K = 5 , so the five nearest neighbors to the sample to be classified are considered, corresponding to distances d 1 to d 5 . KNN: K-nearest neighbor.

Gasparetto et al. ⁷⁹ employed the random decrement technique and Prony analysis to extract bogie stability parameters (including frequency, damping ratio, and amplitude ratio) from lateral frame acceleration. The KNN algorithm was used to classify wheel wear conditions and yaw damper fault states. Validated through the construction of a fault database and field tests on the ETR500 Y1 train, the results indicated that the method effectively distinguishes between new and worn wheel profiles and assesses the status of yaw dampers.

Support vector machine

The SVM is a robust supervised learning model renowned for its superior generalization capabilities, particularly in small-sample learning scenarios. Its primary objective is to construct an optimal separating hyperplane that maximizes the margin between data points of distinct classes, thereby facilitating efficient data classification (see Figure 19).

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Figure 19.

Schematic diagram of SVM for two data features, where X 1 and X 2 represent the features. ¹² SVM: support vector machine.

Qin et al. ⁸⁰ proposed a fault diagnosis method for high-speed train bogies based on wavelet entropy features and SVM. By acquiring bogie vibration signals, the study extracted six wavelet entropy features (such as energy entropy and time entropy) to construct a high-dimensional feature space, using SVM for the effective detection and classification of suspension component faults. Simulation experiments demonstrated that the method performed effectively in distinguishing among the healthy state, air spring faults, yaw damper faults, and lateral damper faults.

Wei et al.^81,82 investigated fault isolation in rail vehicle lateral suspension systems, proposing a framework based on multisensor feature fusion combined with D-S evidence theory, Fisher discrimination analysis (FDA), and SVM. By constructing a 17-DOF dynamic model and designing a low-cost accelerometer network, the study extracted seven time and frequency domain fault features and compared the performance of these three classification methods. Simulation results indicated that D-S evidence theory outperformed both FDA and SVM in terms of fault component isolation accuracy and faulty-type prediction accuracy, while exhibiting robust performance against fault magnitude changes. A similar study can be found in the study by Wei et al. ⁸³ In 2016, addressing the high DOF and strong correlations among monitoring data points in high-speed trains, Wu et al. ⁸⁴ proposed a fault feature extraction method based on multivariate multiscale sample entropy (MMSE). The study employed multivariate empirical mode decomposition to perform synchronous joint analysis of multichannel vibration signals under various operating conditions, thereby extracting common modes across data channels. The MMSE of the signals served as the fault feature, with an SVM used for fault state classification. Experimental results demonstrated that the classification recognition rate exceeds 90% across various speeds. Karlsson et al. ⁸⁵ generated a dataset encompassing diverse operating conditions and damper fault states via multibody dynamics simulation to evaluate the performance of various machine learning classifiers (including the 1-nearest neighbor classifier, linear SVM, Naïve Bayes, linear discriminant analysis, and Decision Trees) in suspension fault diagnosis. The study found that the 1-nearest-neighbor and linear SVM classifiers exhibited superior performance in damper fault classification, characterized by high accuracy, low false negative rate, and low misconfused damper rate. A similar study can be found in the study by Ye et al. ⁸⁶

Girstmair et al. ⁸⁷ compared the performance of standard simple criteria against statistical models for yaw damper fault diagnosis. Through multiscenario testing under actual operational conditions, the study demonstrated the significant advantages of statistical methods, such as SVM, in terms of sensitivity and robustness. Notably, statistical models exhibited superior adaptability and fault detection capabilities when confronting complex operational environments (such as various equivalent conicities and speeds). Girstmair and Moshammer ⁸⁸ integrated physical simulation, signal processing, SVM, and Bayesian inference to construct an efficient and reliable fault diagnosis framework for rail vehicle suspension systems (see Figure 20). Using a two-stage architecture comprising offline learning and online deployment, the method effectively detected and isolated faults in critical components such as dampers and springs, exhibiting superior performance even in noisy environments. Currently, this algorithm has been deployed on a Siemens commuter train.

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Figure 20.

Fault diagnosis framework for rail vehicle suspension systems in the study by Girstmair and Moshammer. ⁸⁸

Liu et al. ⁸⁹ proposed a machine learning approach integrating PCA and SVM for rail vehicle suspension fault diagnosis. Wavelet energy entropy extracted from axle box vibration signals served as the fault feature, with PCA employed to reduce feature dimensionality. Multiple SVM classifiers were used to diagnose seven operating conditions, including damper faults. Experimental validation on a 1/5th scaled roller rig demonstrated an overall diagnostic accuracy of 90%. However, the identification accuracy for minor damper faults was relatively low. Feng et al. ⁹⁰ proposed an incipient fault diagnosis method for suspension systems based on PRPCA and SVM. This method employed a Wasserstein distance-based nonlinear PRPCA for fault detection and data preprocessing. Then, SVM is used for fault identification, with diagnostic performance evaluated using the F1-Measure index. Comparative study against traditional PCA and SVM methods confirmed the superiority of this method in detecting and identifying incipient faults in dampers and springs.

Support vector regression

The SVR is the regression extension of SVM, which maps low-dimensional nonlinear problems into a high-dimensional space. By determining the optimal hyperplane that maximizes the margin relative to the training data, it effectively solves linear regression problems. This margin maximization strategy enhances the algorithm’s robustness and generalization capabilities, rendering SVR particularly suitable for fitting small-sample data compared to other machine learning methods.

Addressing the prediction of performance degradation in urban rail vehicle suspension systems, Wang et al. ⁹¹ proposed a predictive model combining least squares SVR (LSSVR) with the particle swarm optimization (PSO) algorithm. By constructing a fault sample set via a simulation platform and comparing prediction performance under varying input features, the results demonstrated that this model outperforms the traditional LSSVR model in both prediction accuracy and computational efficiency. Hong et al. ⁹² proposed a fault diagnosis framework for monitoring the status of high-speed rail vehicle suspension systems via train vibration measurements (see Figure 21). Based on multioutput SVR (MSVR), the on-board measured vibration signal was used to monitor suspension stiffness and damping coefficients in real time. Comparative study against multivariate Gaussian process regression and multivariate least squares linear regression demonstrated the significant accuracy advantage of MSVR.

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Figure 21.

Integral framework for suspension system health monitoring in the study by Hong et al. ⁹²

Summary

In the context of rail vehicle suspension fault diagnosis, TML methods primarily include KNN, SVM, and SVR, as summarized in Table 12.

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Table 12.

Comparison of various TML methods.

Methods	Complexity	Faults	Advantages	Disadvantages
KNN	Low	Yaw dampers.	Outputs multiclass probabilities, suitable for small-sample classification.	Requires appropriate selection of K, highly dependent on training set quality.
SVM	Medium	Primary and secondary vertical dampers, secondary springs, lateral dampers, and yaw dampers	Suitable for small-sample learning, strong generalization capability.	Requires multiple SVMs for multiclass tasks, performance is highly sensitive to parameter selection.
SVR	High	Primary and secondary vertical dampers, primary and secondary springs.	Robust against noise, supports multioutput regression.	High training complexity, cumbersome parameter tuning.

TML: traditional machine learning; KNN: K-nearest neighbor; SVM: support vector machine; SVR: support vector regression.

In summary, KNN offers a simple implementation without complex training, effectively handling small-sample classification tasks. However, it suffers from low prediction efficiency and sensitivity to data quality. SVM exhibits robust classification capabilities and superior generalization in small-sample, high-dimensional feature spaces, making it highly suitable for multifault pattern recognition. Nevertheless, its performance is heavily contingent upon the selection of kernel functions and parameters. SVR enables the direct output of degradation parameters with explicit physical significance (such as stiffness and damping), thereby achieving fine-grained monitoring and trend prediction of suspension status, though it entails high model complexity and significant training and tuning costs.

Multilayer perceptron

The MLP is a type of feedforward artificial neural network (ANN) typically employed in supervised learning tasks. It is composed of multiple layers of interconnected neurons that sequentially transform input data to generate the final output. Figure 23 illustrates the fundamental structure of the MLP, comprising an input layer, one or more hidden layers, and an output layer.

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Figure 23.

MLP with two hidden layers. ¹² MLP: multilayer perceptron.

Zhang et al. ⁹³ proposed a power spectral density (PSD) distance feature extraction method and developed a hybrid algorithm by integrating fuzzy possibilistic C-means clustering with a back propagation (BP) neural network to isolate faults across different suspension components. Simulation results demonstrated that the PSD distance feature extraction method improved sample quality, while the hybrid algorithm exhibited superior stability and accuracy in fault isolation compared to the standalone BP neural network. Xu and Yao ⁹⁴ used a genetic algorithm to optimize the BP neural network for rail vehicle suspension fault diagnosis. By extracting multidimensional fault features from a vertical vehicle dynamic model and employing the genetic algorithm for optimization, the method significantly enhanced diagnostic accuracy and stability. Experimental results demonstrated that the proposed method performed excellently in the multistate recognition of spring faults, outperforming the unimproved BP neural network. Melnik et al. ⁹⁵ employed an ANN to analyze the PSD of vertical and lateral acceleration signals from 36 measurement points distributed across the carbody, frame, and axle box. While the method achieved the detection of varying degrees of damper faults under complex vibration coupling and variable operating conditions, the maximum accuracy was below 63%.

Autoencoder

Autoencoders represent a class of self-supervised neural networks that play a pivotal role in unsupervised learning and dimensionality reduction tasks. As illustrated in Figure 24, the autoencoder architecture comprises an encoder, which compresses high-dimensional input data into a compact latent representation, and a decoder, tasked with reconstructing the original input from this compressed form. These networks are optimized to minimize reconstruction error, typically quantified by loss functions such as mean squared error or binary cross-entropy with parameters adjusted via the BP algorithm. In the context of fault diagnosis, autoencoders excel in dimensionality reduction, signal denoising, and efficient data compression, proving particularly effective for anomaly detection in complex, multivariate time-series sensor data.

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Figure 24.

Structure of autoencoder. ¹²

Hu et al. ⁹⁶ proposed a deep neural network (DNN)-based fault diagnosis method for high-speed train suspension systems. By constructing a deep architecture comprising autoencoders, the method enabled adaptive feature extraction from vibration signals, eliminating the reliance on traditional signal processing experience. Experimental results demonstrated that the method exhibited superior diagnostic accuracy and stability across various fault types, operating speeds, and small-sample conditions, significantly outperforming BP neural networks and their variants. Zhao et al. ⁹⁷ applied a DNN method based on the stacked denoising autoencoder (DAE) to suspension fault diagnosis (see Figure 25). Initial validation on a standard bearing fault dataset demonstrated that its diagnostic accuracy and stability significantly outperformed traditional neural networks, such as the firefly ANN and PSO neural network. The study used a multibody dynamic model to acquire vibration data representing the healthy state and seven single and compound fault conditions, extracting 16-dimensional time and frequency domain features. Experimental results indicated that the diagnostic model achieved an average accuracy of 98.3, with a standard deviation as low as 0.71, while demonstrating a significant advantage in training convergence speed.

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Figure 25.

(a) Architecture of the autoencoder-based DNN and (b) actual sensor mounting positions in the study by Zhao et al. ⁹⁷ DNN: deep neural network.

LSTM network

The LSTM network is a specialized variant of the recurrent neural network (RNN), designed to process sequential data characterized by long-term dependencies, such as speech, text, and time-series data. While traditional RNNs propagate hidden states to generate sequential outputs, they often suffer from vanishing or exploding gradient problems when processing extended sequences, which hinder the learning of long-term dependencies. The LSTM architecture alleviates this issue by incorporating “memory cells” that regulate the retention or forgetting of information through a selective gating mechanism. The structure of the LSTM network is illustrated in Figure 26.

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Figure 26.

The algorithm flow based on the LSTM network in the study by Chen et al. ¹⁰⁰ LSTM: long short-term memory.

Fu et al. ⁹⁸ developed a bogie model of the CRH-380A train using the SIMPACK simulation platform. Vibration signals from 58 channels were acquired, encompassing the healthy state and various typical faults (such as single and compound faults involving air springs, lateral dampers, and yaw dampers). The study demonstrated that the LSTM network can learn the spatiotemporal correlations of fault features within vibration signals without requiring data preprocessing or a priori knowledge, thereby validating the effectiveness of LSTM in bogie fault diagnosis. Similar studies can be found in the studies by Yang et al. ⁹⁹ and Huang et al. ¹⁰⁰ Chen et al. ¹⁰¹ proposed a modified bidirectional LSTM (BiLSTM) neural network architecture (see Figure 27) to address the limitation of the existing BiLSTM fault detection method, which requires condition monitoring data from fault states to determine additional noise levels. In this method, the specific output data point was excluded from the input when predicting this specific output data point. Validated using simulation data generated from a vehicle-track coupled dynamics model, the results demonstrated that the method exhibited superior fault detection accuracy and robustness across various fault types and severities compared to linear autoregression, LSTM, and BiLSTM-DAE models.

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Figure 27.

Fault detection framework based on the modified BiLSTM network in the study by Chen et al. ¹⁰¹ BiLSTM: bidirectional long short-term memory.

Chen et al. ¹⁰² further proposed a deep LSTM-based fault detection method for rail vehicle suspension systems. By employing the goodness-of-fit criterion as the fault detection index instead of the traditional LSTM residual mean square value, the method enhanced the sensitivity and accuracy of fault identification. Experiments using simulation data demonstrated that this method outperforms both the vanilla LSTM model and the linear autoregression model in detecting varying degrees of spring faults.

Convolutional neural network

A typical CNN consists of multiple layers, each playing a specific role in the network’s ability to learn and extract features from input images. The architecture of the CNN is illustrated in Figure 28.

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Figure 28.

Basic structure of the CNN. ¹² CNN: convolutional neural network.

Liang et al. ¹⁰³ combined CNN and RNN architectures to propose a convolutional RNN (CRNN) for diagnosing single and compound faults in rail vehicle suspension systems. This method leverages the strengths of both the one-dimensional CNN (1D CNN) and the simple recurrent unit (SRU). Features were first extracted from bogie vibration signals via multiple convolutional layers and subsequently passed to stacked SRU recurrent layers to capture hidden features with time-series correlations. Finally, these features were fed into the fully connected layer to calculate classification probabilities. Experimental results indicated that the CRNN outperforms both 1D CNN and LSTM models in terms of detection accuracy and training speed. A similar study can be found in the study by Liang et al. ¹⁰⁴ Peng and Jin ¹⁰⁵ proposed a fault detection method based on deep semisupervised feature extraction, validating it on rail vehicle suspension systems. This method first transforms multisensor vibration signals into time–frequency spectrograms using STFT, subsequently employs a convolutional autoencoder (CAE) for unsupervised pretraining on a dataset containing unlabeled faulty data, and finally fine-tunes a CNN using labeled healthy data to extract high-level features. Experimental results demonstrated that the method effectively detected vertical spring and damper faults even when using only labeled data from the normal state. Addressing the challenge of multichannel fault diagnosis in high-speed train suspension systems, Wu and Jin ¹⁰⁶ proposed a modular fault diagnosis method based on depthwise convolution. The core philosophy involves a structural design that separates feature extraction from channel fusion, thereby preventing the premature fusion of multichannel signals often encountered in traditional convolutions. Experimental results indicated that this method enhanced suspension fault diagnosis accuracy and demonstrated superior robustness under noisy and variable operating conditions.

Wu et al. ¹⁰⁷ analyzed the similarity among vibration signals using three synchronization measures (including instantaneous phase synchrony, amplitude envelope synchrony, and composite synchrony). By employing hierarchical clustering for intelligent channel grouping and incorporating a group convolution mechanism into the CNN, the method achieved the centralized processing of signals with similar patterns alongside differentiated feature extraction (see Figure 29). Experimental results demonstrated that this synchrony group convolutions method outperforms both normal convolutions and normal group convolutions in suspension fault classification tasks, exhibiting not only higher accuracy but also superior training stability and faster convergence.

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Figure 29.

The framework based on synchrony group convolutions for fault diagnosis of the high-speed train in the study by Wu et al. ¹⁰⁷

Wu et al. ¹⁰⁸ introduced a Bayesian DL framework for the fault diagnosis of high-speed train suspension systems. By interpreting Dropout as an approximation of Bayesian inference, a CNN model capable of quantifying prediction uncertainty was developed. This method not only accurately identifies known suspension fault types but also effectively detects unknown and concurrent faults, demonstrating strong generalization capabilities. Qin et al. ¹⁰⁹ and Chen et al., ¹¹⁰ respectively, investigated the applications of multiple CRNN and capsule network (CapsNet) (see Figure 30) in high-speed train suspension fault diagnosis. The former employed two parallel CRNN frameworks to achieve the synchronous diagnosis of fault types and performance degradation states. Conversely, the latter leveraged the vector output characteristics of capsules to achieve high-precision recognition of seven operating conditions, encompassing both single and compound faults, demonstrating superior performance, particularly in compound fault diagnosis.

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Figure 30.

The CapsNet architecture in the study by Chen et al. ¹¹⁰ CapsNet: capsule network.

Addressing the challenge of sample scarcity in high-speed train suspension fault diagnosis, Yang et al. ¹¹¹ proposed a few-shot diagnosis method combining model-agnostic meta-learning with the two-dimensional (2D) CNN. A sample reconstruction technique was employed to transform 1D suspension vibration signals into 2D feature matrices, thereby enhancing fault feature representation. This enabled the 2D CNN to achieve a diagnostic accuracy exceeding 90% even under small-sample conditions. Experimental results demonstrated that the method performed exceptionally well across various speed conditions, significantly outperforming traditional methods such as 1D CNN, gated recurrent units (GRUs), and CapsNet. A similar study can be found in the study by Yang et al. ¹¹² Zhang et al.^5,113 proposed two 1D CNN-based models for suspension fault diagnosis: the Fractional Brownian motion network and the Dense-Squeeze (DenseNet) network. The former integrated fractional Brownian motion into the 1D CNN architecture, endowing the model with the capability to perceive unknown faults and enabling the distinction between known and unknown suspension faults. The latter incorporated DenseNet and a feature channel weighting mechanism to enhance diagnostic precision, maintaining high accuracy under multi-speed conditions. Further studies on 1D CNNs can be found in studies.^114–117 Jia et al. ¹¹⁸ proposed a clustered blueprint separable CNN aimed at achieving lightweight and high-precision fault diagnosis for suspension systems. First, multisource sensor signals were clustered based on channel similarity. Then, a multibranch blueprint separable convolution structure was employed for lightweight feature extraction. This method exhibited high diagnostic accuracy while significantly reducing model complexity and training costs. Wu et al. ¹¹⁹ proposed a digital twin-based fault diagnosis framework for high-speed train suspension systems (see Figure 31). By constructing a seven-dimensional bogie digital twin system, the framework achieved deep fusion and real-time data interaction between physical and virtual models. An analytical-driven model was used for preliminary signal processing and feature extraction, while employing a multilayer CNN for deep feature learning and fault classification from vibration signals. This diagnostic mechanism, characterized by virtual-real linkage and model-data fusion, significantly enhanced the identification accuracy and real-time performance of suspension component faults.

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Figure 31.

Digital twin-based bogie fault diagnosis framework in the study by Wu et al. ¹¹⁹

Qin et al. ¹²⁰ focused on identifying unknown suspension fault types. By employing a residual network as the feature extractor and using a diffusion model to generate features for unknown faults, the method achieved the diagnosis of both known and unknown suspension faults. Addressing the challenges of data imbalance and privacy protection in high-speed train suspension fault diagnosis, Du et al. ¹²¹ proposed a multirank federated distillation framework (see Figure 32). By employing priority-ranked interclient knowledge distillation, decoupled distillation loss design, adaptive multitask weight adjustment, and a personalized model transfer mechanism, the framework significantly enhanced the diagnostic performance of small-sample clients while safeguarding data security. Experimental results demonstrated that the proposed method outperformed existing federated learning methods across multiple railway datasets, exhibiting strong generalization capabilities and practicality.

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Figure 32.

Basic process of the multirank federated distillation framework in the study by Du et al. ¹²¹

Addressing the challenge of fault diagnosis for high-speed train suspension systems under variable speed conditions, Yang et al. ¹²² proposed a dynamic transfer loss weight-deep subdomain adaptation network (DTLW-DSAN). This method optimized the single-sensor layout using wavelet packet energy and the coefficient of variation, thereby reducing system complexity. Using a single accelerometer and unsupervised training, DTLW-DSAN automatically updated transfer loss weights. Experiments on simulation and public datasets demonstrated that DTLW-DSAN achieved high diagnostic accuracy and stability under variable speed conditions, outperforming other existing mainstream methods. Gao et al. ¹²³ integrated the superior time–frequency localization properties of the Morlet wavelet (MW) into the CNN pooling design, facilitating a transition in feature selection from the spatial to the frequency domain. Building on this, a multiscale CNN incorporating MW pooling (MW-CNN) was developed. Multiscale feature extraction and residual learning were combined to establish a deep architecture for high-speed train bogie fault diagnosis. Experiments on a CRH380A simulation dataset demonstrated that MW-CNN achieved a diagnostic accuracy of 99.94% and maintains robust diagnostic performance across varying noise levels and operating conditions.

Graph neural network

The fundamental principle of GNN-based fault diagnosis (see Figure 33) lies in abstracting physical systems (e.g., mechanical equipment) into graph structures, where nodes represent components or sensors and edges denote their connections or correlations. By leveraging the message-passing mechanism, each node aggregates information from its neighbors, thereby capturing fault propagation paths and global impacts within the system to ultimately achieve high-precision classification and localization. Compared to DNNs, GNNs are particularly adept at processing data characterized by complex spatiotemporal dependencies. ¹²⁴

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Figure 33.

GNN-based fault diagnosis framework. ¹²⁴ GNN: graph neural network.

Man et al. ¹²⁵ proposed a novel suspension fault diagnosis scheme based on the graph convolutional network (GCN) (see Figure 34), GRU, and the attention mechanism. First, the bogie data network was established; then, temporal and spatial features were extracted and fused using the GCG unit. Moreover, an attention mechanism was incorporated to enhance the capture of critical fault information, with final fault classification performed via GCN. Experimental validation demonstrated that the model achieved high diagnostic accuracy for seven types of bogie faults using actual operational data, while exhibiting strong robustness on small-scale datasets. Man et al. ¹²⁶ further designed a deep network architecture integrating the graph attention network (GAT) with the residual-squeeze network (RS-Net). By employing RS-Net as the framework and using GAT for spatial information fusion and feature extraction, the model achieved the identification of six types of bogie faults.

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Figure 34.

GCN structure. ¹²⁴ GCN: graph convolutional network.

Leveraging deep transfer learning and GNN, Zhang et al. ¹²⁷ proposed a suspension fault diagnosis method based on a multisensor graph transfer network. A multisensor GNN (MSGNN) was constructed to extract features from vibration signals collected at three distinct train locations, and the graph-based fusion layer was used to achieve effective multisource information fusion. Experimental results on both simulated and measured data demonstrated that the MSGNN outperforms traditional data-driven methods in detecting spring and damper faults. Jia et al. ¹²⁸ integrated GNN with federated learning to construct a fault diagnosis and localization system for high-speed train suspension systems in multisensor environments (see Figure 35). The multisensor network was first mapped into a graph with identical node and edge features, which was then optimized via graph spectral filtering and node-level attention mechanisms. Then, graph-level topology adaptive technology and a postclassifier were employed to localize faulty suspension components within a single railway. Finally, personalized models were tailored for each railway through railway-specific optimization. Experimental results demonstrate that this method achieved high accuracy in both fault component localization and status identification.

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Figure 35.

Fault diagnosis and localization system for high-speed train suspension system in the study by Jia et al. ¹²⁸

Beyond the aforementioned modeling approaches focusing on spatial topological structures between sensors, recent research has introduced the time–frequency fully connected GNN, ¹²⁹ which offers a complementary perspective for capturing deep features in the vibration signals of rail vehicle suspension systems. This approach transforms multisource sensor signals into time–frequency representations and employs localized time–frequency patches as nodes to construct a fully connected graph, thereby overcoming the constraints of physical topology in traditional GNN and achieving profound feature coupling across spatiotemporal dimensions. Since vibration signals from suspension systems exhibit significant nonstationarity and time–variance, the model accurately captures transient time–frequency fluctuations triggered by subtle faults, which substantially improves the feature representation depth and robustness of diagnostic models in complex dynamic environments.

Summary

In rail vehicle suspension fault diagnosis, DL methods encompass MLP, autoencoder, LSTM network, CNN, and GNN, as summarized in Table 13.

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Table 13.

Comparison of various DL methods.

Methods	Complexity	Faults	Advantages	Disadvantages
MLP	Low	Primary vertical dampers, primary and secondary springs, lateral dampers, and yaw dampers.	Capable of multifault identification, handles high-dimensional, multisensor, and multifeature data.	Slow convergence, sensitive to initial weights.
Autoencoder	Medium	Secondary springs, lateral dampers, and yaw dampers.	Applicable to unlabeled data, strong feature dimensionality reduction capability.	Sensitive to hyperparameters, high training complexity.
LSTM	High	Secondary vertical dampers, secondary springs, lateral dampers, and yaw dampers.	Effective memory mechanism, high detection accuracy.	Challenging architecture selection, high computational resource demand, and high training complexity.
CNN	Medium	Primary and secondary vertical dampers, primary and secondary springs, lateral dampers, and yaw dampers.	Strong local feature capture capability, high parallel computing efficiency.	Requires extensive labeled data, architecture design relies on experience.
GNN	High	Primary and secondary vertical dampers, primary and secondary springs, lateral dampers, and yaw dampers.	Models complex spatial relationships, strong interpretability.	Graph structure construction relies on a priori knowledge, complex parameter tuning, and high computational complexity.

DL: deep learning; MLP: multilayer perceptron; LSTM: long short-term memory; CNN: convolutional neural network; GNN: graph neural network.

In summary, while the MLP offers structural simplicity and rapid training, its performance relies heavily on the quality of manual feature extraction, making it difficult to capture complex nonlinear patterns within vibration signals. Autoencoder facilitates unsupervised feature dimensionality reduction and anomaly detection with robustness to noisy data. However, its performance is constrained by its encoding capacity. LSTM network excels in processing time-series vibration signals, effectively capturing long-term fault dependencies and achieving high diagnostic accuracy. Nevertheless, it suffers from complex model structures, time-consuming training processes, and sensitivity to hyperparameters. CNN automatically extracts effective local spatial features from raw signals, reducing reliance on feature engineering, though its architectural design remains experience-dependent. Finally, GNN explicitly models the physical correlations among suspension sensors, providing a novel perspective for fault propagation analysis. However, it faces challenges regarding graph structure construction, high model complexity, and substantial computational costs.

Correlation between modeling assumptions and failure modes

The core logic of data-driven methods is founded on the principle that the health status of the suspension system is implicitly contained within vast operational data.

The statistical method is established upon the assumption of signal symmetry or statistical distribution consistency, providing the advantage of bypassing complex modeling processes to identify faults directly through signal cross-correlation or statistical components. However, these methods often fail in rail applications where intense background noise and stochastic vibrations from wheel–rail interactions mask subtle suspension defects. The TML methods typically assume that fault features are linearly separable in low-dimensional or kernel-transformed high-dimensional spaces. The primary advantage of these methods lies in their capability to use small sample sets. However, their reliance on manual feature engineering restricts the capture of the complex and time-varying dynamic characteristics inherent in vehicle systems. When encountering environmental uncertainties such as poor track quality, the predefined feature sets fail to effectively represent system variations, resulting in a decline in algorithmic robustness. The DL methods assume the automatic learning of hierarchical feature representations through multilayer nonlinear transformations, demonstrating significant advantages in mining implicit fault features from high-dimensional and nonlinear data. However, their heavy reliance on large-scale labeled datasets makes them struggle with practical deployment, as samples for low-probability but high-stakes suspension faults are scarce.

Evaluation metrics and engineering trade-off analysis

To systematically evaluate the practical utility of various data-driven methods in engineering applications, five key performance indicators consisting of complexity, accuracy, detection delay, FAR, and computational cost are introduced (see Table 14) to perform a comparative analysis of the data-driven algorithms within a unified dimension.

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Table 14.

Comparison of various data-driven methods based on unified evaluation metrics.

Methods	Complexity	Accuracy	Delay	FAR	Cost
Statistical methods	Low	Medium	Low	Medium	Low
TML methods	Medium	Medium	Low	Medium	Medium
DL methods	High	High	Medium	Low	High

FAR: false alarm rate; TML: traditional machine learning; DL: deep learning.

Analysis demonstrates that data-driven methods exhibit significant trade-off relationships among these performance metrics. Statistical methods perform excellently in terms of computational cost and detection delay because their relatively streamlined algorithmic logic makes them highly suitable for real-time deployment in computationally constrained on-board embedded environments. The TML methods demonstrate strong robustness in small sample scenarios; these methods offer a balance between diagnostic accuracy and resource consumption. While the DL methods possess absolute advantages in diagnostic accuracy and FAR suppression, the extremely high model complexity and dependence on high-performance computing resources represent barriers to large-scale engineering deployment. Furthermore, the substantial data demand and lengthy offline training processes associated with the DL methods significantly increase the initial development and subsequent maintenance costs of the system.

Technical essence and evolutionary drivers

Model-based and data-driven methods represent two fundamentally distinct diagnostic logics, and their evolutionary drivers differ significantly.

Model-based methods: The technical essence lies in leveraging analytical redundancy as a surrogate for hardware redundancy, with an evolutionary trajectory reflecting a transition from linear simplification toward addressing strong nonlinearity and system uncertainty. Tracing its application history in rail vehicle suspension fault diagnosis, these methods emerged around 2005 (see Figures 4 and 5), during which early research frequently employed RBPF for parameter identification alongside classical KF for state estimation in linear systems. With escalating requirements for the nonlinear modeling of rail vehicles, the EKF was introduced to the field around 2010 to manage local nonlinearities through Taylor series expansions. Post-2015, advanced variants such as the UKF and CKF were adopted to mitigate linearization errors and enhance filtering stability in high-dimensional spaces. In recent years, SM-based methods and RLS methods have received increasing attention to promote onboard online detection, primarily due to their low computational cost and simple parameter tuning. This evolutionary process reveals an intrinsic technological pattern whereby model-based algorithms continuously adapt to the strong nonlinear dynamic characteristics and complex environmental uncertainties of rail vehicle suspension through the iterative refinement of mathematical architectures to compensate for the limitations of physical modeling, thereby achieving precise perception and identification of fault states in complex suspension dynamical systems.

Data-driven methods: The technical essence lies in uncovering latent mapping patterns within massive multisource datasets to circumvent the complexities of physical modeling, with an evolutionary trajectory reflecting a transition from manual feature engineering toward automated and high-dimensional representation learning. Tracing its application history in rail vehicle suspension fault diagnosis, these methods gained momentum around 2010 (see Figures 10, 17, and 22), when initial research focused primarily on traditional multivariate statistical methods (e.g., PCA and CVA) as well as TML (e.g., SVM). Since 2015, the field has experienced a significant shift toward DL architectures (e.g., CNN), which effectively automate the feature extraction process and enable the construction of end-to-end diagnostic pipelines. Post-2020, the demand for modeling complex spatial-temporal correlations and addressing data scarcity has prompted researchers to adopt GNN for multi-sensor topological modeling. This evolutionary process reveals an intrinsic technological pattern where data-driven algorithms continuously evolve from shallow statistical inference toward deep hierarchical perception. By leveraging advanced sensing technologies, these methods effectively bridge the gap between high-dimensional raw data and precise fault identification in complex rail vehicle systems.

From physical models to data intelligence: The evolutionary trajectory from model-based methods to data intelligence reveals a fundamental shift in the management of uncertainty within complex systems. Initially, the model-based methods prioritized the rigor of physical logic. However, with the escalation of train speeds and system complexity, traditional simplified linear models struggled to capture nonlinear and nonstationary dynamic behaviors. As sensor technology advanced, the focus of research transitioned toward data-driven methods. Although data-driven approaches provided robust tools for feature representation, they introduced novel challenges concerning decision transparency and physical consistency. The contemporary shift toward data intelligence represents a fusion stage that effectively reconciles the disparity between theoretical abstraction and empirical data through the profound integration of mechanistic laws and DL architectures. This evolution is not a mere replacement of technologies but rather a synergistic advancement intended to achieve an optimal equilibrium between interpretability and adaptability in railway operations.

Cross-paradigm performance comparison

To provide a more intuitive illustration of the inherent trade-offs, Table 16 provides a comprehensive comparative analysis of model-based and data-driven methods within the specific context of rail vehicle suspension fault diagnosis.

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Table 16.

Cross-paradigm performance for suspension fault diagnosis.

Methods		Physical interpretability	Data dependency	Nonlinear capability	Real-time capability	Computation complexity
Model-based methods		High	Low	Low	High	Low
Data-driven methods	Statistical methods	Medium	Medium	Medium	High	Low
	TML methods	Medium	Medium	High	Medium	Medium
	DL methods	Low	High	High	Low	High

TML: traditional machine learning; DL: deep learning.

General characteristics and development trends of model-based methods

The core advantage of model-based methods lies in their strong theoretical foundation and inherent interpretability, as the diagnosis is rooted in the system’s physical mechanism model. This enables deep insight into system dynamic behavior and targeted analysis of specific faults. However, constructing high-fidelity mathematical models is typically a complex and high-cost process, and diagnostic performance is susceptible to degradation when the system exhibits strong nonlinearities or time-varying parameters. Future research should focus on developing simplified high-precision models that preserve mechanistic integrity while adapting to practical operational constraints to balance computational efficiency and diagnostic accuracy. Meanwhile, the active exploration of deep fusion approaches with data-driven methods, which use mechanistic knowledge to guide data learning and achieve complementary advantages, has emerged as a prevailing research trend. Furthermore, enhancing the online adaptive updating and parameter identification capabilities of models to track the progressive performance degradation of suspension components in real time constitutes another critical evolutionary direction.

General characteristics and development trends of data-driven methods

Data-driven methods facilitate fault diagnosis by extracting features directly from operational data, bypassing complex physical modeling. While they excel at handling nonlinear systems and discovering new fault modes, these methods remain constrained by their dependency on large-scale labeled datasets and the black-box nature of DL. This lack of interpretability limits their adoption in rail transit. Adhering to the technical evolution of DL is essential for constructing a comprehensive intelligent maintenance framework and overcoming the deficiencies of data-driven methods. An analysis of the recent trends in DL is presented below, including self-supervised learning, ¹³⁰ foundation models, ¹³¹ physics-informed learning, ¹³² and structured representation learning^133–136: