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Accuracy of a lithium-ion battery model is pivotal in faithfully representing actual state of battery, thereby influencing safety of entire electric vehicles. Precise estimation of battery model parameters using key measured signals is essential. However, measured signals inevitably carry random noise due to complex real-world operating environments and sensor errors, potentially diminishing model estimation accuracy. Addressing the challenge of accuracy reduction caused by noise, this paper introduces a Bias-Compensated Forgetting Factor Recursive Least Squares (BCFFRLS) method. Initially, a variational error model is crafted to estimate the average weighted variance of random noise. Subsequently, an augmentation matrix is devised to calculate the bias term using augmented and extended parameter vectors, compensating for bias in the parameter estimates. To assess the proposed method's effectiveness in improving parameter identification accuracy, lithium-ion battery experiments were conducted in three test conditions—Urban Dynamometer Driving Schedule (UDDS), Dynamic Stress Test (DST), and Hybrid Pulse Power Characterization (HPPC). The proposed method, alongside two contrasting methods—the offline identification method and Forgetting Factor Recursive Least Squares (FFRLS)—was employed for battery model parameter identification. Comparative analysis reveals substantial improvements, with the mean absolute error reduced by 25%, 28%, and 15%, and the root mean square error reduced by 25.1%, 42.7%, and 15.9% in UDDS, HPPC, and DST operating conditions, respectively, when compared to the FFRLS method.

The increasing use of collaborative robots in smart manufacturing, owing to their flexibility and safety benefits, underscores a critical need for robust predictive maintenance strategies to prevent unexpected faults/failures of the machine. This paper focuses on fault detection and employs multivariate operational data from a universal robot to detect anomalies or early-stage faults using test data from designed anomalous conditions and artificial-intelligence-based anomaly detection techniques called autoencoders. The performance of three autoencoders, namely, a multi-layer-perceptron-based autoencoder, convolutional-neural-network-based autoencoder, and sparse autoencoder, was compared in detecting anomalies. The results indicate that the autoencoders effectively detected anomalies in the examined complex and noisy datasets with more than 93% overall accuracy and an F1 score exceeding 96% for the considered anomalous cases. Moreover, the integration of trajectory change detection and anomaly detection algorithms (i.e., the dynamic time warping algorithm and sparse autoencoder, respectively) was proposed for the local implementation of online condition monitoring. This integrated approach to anomaly detection and trajectory change provides a practical, adaptive, and economical solution for enhancing the reliability and safety of collaborative robots in smart manufacturing environments.

Maintaining exceptional product quality and boosting processing efficiency requires precise evaluation of various aspects of the turning process, including the cutting depth, feed rate, and size of the workpiece. This article presents a novel approach for observing the turning process state using modulation signal bispectrum (MSB) and motor current signals. A nonlinear model was established that clarifies the load torque oscillations during turning, which in turn affects the amplitude and phase modulation of the motor stator current. Random noise can be efficiently minimized using the MSB algorithm, allowing the extraction of the current-modulation characteristic sideband phase and amplitude from the collected current signal. This technique enables clear representation and enhanced monitoring of load torque changes throughout the turning process. The proposed method was validated via mathematical simulations and universal lathe tests, with the results indicating that the MSB phase and amplitude values effectively capture both dynamic and static torque alterations during the turning operation, making this approach a valuable tool for overseeing the turning process.

The chatter that occurs during the turning operation, especially when cutting a slender and flexible shaft, determines the surface quality of the workpiece and the stability of the machining system. However, when building a dynamic model of a slender workpiece with a chuck and tailstock, it is generally regarded as a cantilever or simply supported beam, without consideration of the axial force and supported stiffness effect. In this work, a dynamic model for thin and flexible workpieces with different clamping boundary conditions was first built. Then, a finite element analysis (FEA) was used to study the influence of the axial force and supporting stiffness on the mode frequencies of the workpiece. A further analysis found that the relationship between support stiffness, axial force, and the dynamic response of the workpiece is nonlinear and far more complex than that of the simply supported beam model. The clamping force directly influenced the magnitude of the vibration response with the decrease of shaft stiffness during the turning process. These results were verified experimentally by measuring the vibrational response of slender shafts with different clamping modes using an on-rotor sensing (ORS) system. It proved that the proposed model shows advantages for the identification of dynamic vibration and quality control when machining slender workpieces.

With electric vehicles (EVs) being widely accepted as a clean technology to solve carbon emissions in modern transportation, lithium-ion batteries (LIBs) have emerged as the dominant energy storage medium in EVs due to their superior properties, like high energy density, long lifespan, and low self-discharge. Performing real-time condition monitoring of LIBs, especially accurately estimating the state of charge (SOC) and state of health (SOH), is crucial to keep the LIBs work under safe state and maximize their performance. However, due to the non-linear dynamics caused by the electrochemical characteristics in LIBs, the accurate estimations of SOC and SOH are still challenging and many technologies have been developed to solve this challenge. This paper reviews and discusses the state-of-the-art online SOC and SOH evaluation technologies published within the recent five years in view of their advantages and limitations. As SOC and SOH are strongly correlated, the joint estimation methods are specifically reviewed and discussed. Based on the investigation, this study eventually summarizes the key issues and suggests future work in the real-time battery management technology. It is believed that this review will provide valuable support for future academic research and commercial applications.

Cost-effective technology for condition monitoring and fault diagnosis is of practical importance for equipment maintenance and accident prevention. Among many fault diagnosis methods, sound-based sensing technology has been highly regarded due to its rich information, non-contact and flexible installation advantages. However, noise from the environment and other machines can interfere with sound signals, decreasing the effectiveness of acoustic sensors. In this paper, a novel trumpet-shaped acoustic metamaterial (TSAM) with a high enhancement of sound wave selection is proposed to detect rotating machinery faults. Firstly, a numerical calculation was carried out to test the characteristics of the proposed metamaterials model. Secondly, a finite element simulation was implemented on the model to verify the properties of the designed metamaterials. Finally, an experiment was conducted based on an electrical fan to prove the effectiveness of the designed metamaterials. The results of the signal-to-noise ratio show more than 25% improvement, consistently demonstrating the potentiality of the designed acoustic metamaterials for enhancing the weak fault signal in acoustic sensing and the capabilities of contributing to a more cost-effective fault diagnosis technology.

The engine system is critical for a marine vehicle, and its performance significantly affects the efficiency and safety of the whole ship. Due to the harsh working environment and the complex system structure, a marine system is prone to have many kinds of novelties and faults. Timely detection of faults via effective condition monitoring is vital for such systems, avoiding serious damage and economic loss. However, it is difficult to realize online monitoring because of the limitations of measurement and health monitoring methods. In this paper, a marine engine system simulator is set up with enhanced sensory placement for static and dynamic data collection. The test rig and processing for static and dynamic data are described. Then, a physics-based multivariate modeling method is proposed for the health monitoring of the system. Case studies are carried out considering the misfire fault and the exhaust valve leakage fault. In the misfire fault test, the exhaust gas temperature of the misfired cylinder dropped from the confidence interval 100–150 °C to 70–80 °C and the head vibration features decreased from the confidence interval 900–1300 m/s2 to around 200–300 m/s2. For the exhaust valve leakage fault, the engine body vibration main bearing impact RMS increased nearly 10 times. Comparisons between the model-predicted confidence interval and measured data reveal that the proposed model based on the fault-related static and dynamic features successfully identified the two faults and their positions, proving the effectiveness of the proposed framework.

Abstract Gearbox condition monitoring (CM) plays a significant role in ensuring the operational reliability and efficiency of a wide range of critical industrial systems such as wind turbines and helicopters. Accurate and timely diagnosis of gear faults will improve the maintenance of gearboxes operating under sub-optimal conditions, avoid excessive energy consumption and prevent avoidable damages to systems. This study focuses on developing CM for a multi-stage helical gearbox using airborne sound. Based on signal phase alignments, Modulation Signal Bispectrum (MSB) analysis allows random noise and interrupting events in sound signals to be suppressed greatly and obtains nonlinear modulation features in association with gear dynamics. MSB coherence is evaluated for selecting the reliable bi-spectral peaks for indication of gear deterioration. A run-to-failure test of two industrial gearboxes was tested under various loading conditions. Two omnidirectional microphones were fixed near the gearboxes to sense acoustic information during operation. It has been shown that compared against vibration based CM, acoustics can perceive the responses of vibration in a larger areas and contains more comprehensive and stable information related to gear dynamics variation due to wear. Also, the MSB magnitude peaks at the first three harmonic components of gear mesh and rotation components are demonstrated to be sufficient in characterizing the gradual deterioration of gear transmission. Consequently, the combining of MSB peaks with baseline normalization yields more accurate monitoring trends and diagnostics, allowing the gradual deterioration process and gear wear location to be represented more consistently.

The marine engine is a complex-structured multidisciplinary system that operates in a harsh environment involving high temperatures and pressures and gas/fluid/solid interactions. Many malfunctions and faults can occur to the marine engine and efficient condition monitoring is critical to ensure the expected performance. In this paper, a marine engine test rig is established and its process data are recorded, including various temperatures and pressures. Two data-driven models, i.e., principal component analysis and the sparse autoencoder, and a physics-based model are applied to the marine engine for two classic faults, i.e., lubrication oil filter blocking and cylinder leakage. Comparative studies and discussions are conducted regarding their performance in terms of anomaly detection and fault isolation. The data points collected for the filter blocking fault are generally two times higher than the fault thresholds set by the data-driven models. In the physics-based model, it is observed that the lubrication oil pressure falls from the predicted 3.2–3.8 bar to around 2.3 bar. For the cylinder leakage fault, the fault test data are nearly four times higher than the thresholds in the data-driven models. The exhaust gas temperature of the leaked cylinder falls from an estimated 150–200 °C to about 100 °C. The transferability and interpretability of these models are finally discussed. The findings of the present study offer insights into the two types of models and can provide guidance for the effective condition monitoring of marine engines.

In order to improve the analytical result and robustness of modulation signal bispectrum based sideband estimator （MSB-SE）， a method for extracting wear characteristics combining wavelet packet energy （WPE） and MSB-SE is proposed. Firstly， the wavelet packet transform is used to decompose the signal into multiple frequency bands， and the WPE of each frequency band is calculated. The frequency band with higher energy is selected for reconstruction to optimize the analysis frequency band and reduce the calculation amount. Then， the MSB-SE is carried out to extract the characteristics of tooth surface wear， and the online monitoring of tooth surface wear damage state is realized by using a reasonable index. Simulation and experimental results show that the proposed method is more robust， and can more accurately monitor tooth surface wear and evaluate the degree of wear damage.

At present， the traditional Archard wear model is mostly used to study the influence of wear on the dynamic characteristics of gears， without considering the lubrication characteristics of gears, and the main research objects are mostly straight gears. In order to make up for the shortage of research on helical gear， the wear process under mixed elastohydrodynamic lubrication is numerically simulated. An eight-degree of freedom dynamics model of helical gear is established to investigate the influence of tooth surface wear on gear dynamic characteristic. The gear fatigue test is carried out on a helical gearbox test rig to validate the numerical results. The results show that the wear mainly occurs on the region close to the tooth root and tooth tip， and the maximum wear occurs at the tooth root due to the relative high sliding-to-roll ratio. The variation of the amplitudes of the gear meshing frequency and its harmonics demonstrates that the wear causes an increase in gear vibrations. The experimental results show a good agreement with the numerical results， which implies the study can provide a reliable theoretical basis for the prediction and fault diagnosis of helical gear wear.

Planetary Gearbox (PG) is widely used in many vital transmission systems with the advantages such as high power-weight ratio and high load capacity. To maintain the performance of these system, extensive attentions are paid in the vibration signal analysis for early fault detection and diagnosis of PGs. However, vibration signals are less accurate as they severely influenced by multi-interfaces energy dissipation and varying transmission paths. In contrast, Instantaneous Angular Speed (IAS) is directly related to the gear dynamics and free from the path varying effect. This paper evaluates the performance of an improved IAS measurement system to diagnose PG faults, in which a dual detector setup is adopted to suppress IAS errors caused by the setting parameters and encoder errors. Firstly, a PG dynamic model is established to simulate IAS responses from a PG with local faults on sun and planet gears. Secondly, the noise level of the demodulated IAS is studied under different system parameter configurations. Subsequently, a dual detector self-denoising method is developed to suppress the false IAS caused by encoder errors. Finally, the performance of proposed IAS measurement system is evaluated based on an industrial PG with sun and planet faults. Experimental results show PG faults can be effectively diagnosed from the simple IAS order spectra, indicating that the proposed IAS measurement system is a more promising and yet lower costing approach to monitor rotating machines.

Wear is one of the most common failures of hydrodynamic bearings. The main purpose of the present work was to investigate the effects of wear on lubrication performance and acquire efficient vibration signatures for fault diagnosis. In this paper, a finite element model (FEM) for a two-disk rotor supported on worn hydrodynamic bearings is presented in which the oil film force is evaluated by linear and nonlinear models. Numerical and experimental results indicate that the static and dynamic characteristics of the bearing are significantly changed by wear, leading to a drop in system critical speeds due to the deterioration of the constraint status provided by the bearings to the rotor. As the wear depth increases, the onset speed of oil whirl increases, while that of oil whip becomes lower, and large amplitudes of resonance and oil whip are more likely to be excited. More notably, all of the above vibration signatures in the y-direction are more sensitive to wear compared to those in the x-direction, which means that wear faults can be diagnosed by differences in vibration characteristics between the x- and y-directions. This research can provide a theoretical foundation and engineering guidance for the hydrodynamic bearing wear fault diagnosis.

Global orbits connect the saddle points in an infinite period through the homoclinic and heteroclinic types of manifolds. Different from the periodic movement analysis, it requires special strategies to obtain expression of the orbit and detect the associated profound dynamic behaviors, such as chaos. In this paper, a global dynamic frequency method is applied to detect the homoclinic and heteroclinic bifurcation of the complicated nonlinear systems. The so-called dynamic frequency refers to the newly introduced frequency that varies with time t , unlike the usual static variable. This new method obtains the critical bifurcation value as well as the analytic expression of the orbit by using a standard five-step hyperbolic function-balancing procedure, which represents the influence of the higher harmonic terms on the global orbit and leads to a significant reduction of calculation workload. Moreover, a new homoclinic manifold analysis maps the periodic excitation onto the target global manifold that transfers the chaos discussion of non-autonomous systems into the orbit computation of the general autonomous system. That strategy unifies the global bifurcation analysis into a standard orbit approximation procedure. The numerical simulation results are shown to compare with the predictions.

Belt transmission is one of the most common forms of transmission on CNC lathes. To assess the impact of belt performance on monitoring machining conditions using motor current signal analysis, we developed a dynamic model for belt-driven electromechanical spindle systems. This model enables the coupling of multi-physics variables including mechanical dynamics, particularly the dynamic axil and belt bending motions of belt transmissions and electromagnetic effects. Thus, various changes in belt transmission, including different degrees of belt tension and defects with inherent motor and spindle errors, can be investigated. The modulation characteristics of the current and speed signals revealed that belt transmission can cause a high degree of modulation, reflected by the rich harmonic sidebands at the belt-passing frequency in the motor current spectrum. The rate and extent of belt wear worsened with excessive wear and inadequate tension. It was confirmed that the sideband at the spindle rotating frequency was slightly impacted by changes in the belt conditions. This model was verified based on a CNC lathe induced with different degrees of belt looseness. These conclusions drawn from the numerical analyses can be used for motor current signal analysis, providing reliable and accurate results for machining monitoring.

With a strong legal basis and regulatory authority, cost-effective transient emission sensors that reflect real-driving emissions are key factors for accomplishing environmental requirements. It is difficult for the existing NOx emission monitoring techniques to achieve a balance between accuracy and timeliness. Fundamentally, in-cylinder combustion is the thermodynamic cause of NOx emissions and the main excitation source for engine vibration and noise emissions. A novel vibration-based virtual NOx sensor is developed based on these critical relationships for real-time NOx monitoring. First, the correlation between vibration and NOx emission was characterized in-depth. Then, a technique of constructing two-dimensional filters for vibration signals is proposed to extract combustion-related information. A principal component regression (PCR) model for NOx prediction was established based on the reconstructed in-cylinder pressure. Finally, the virtual NOx sensor is tested and validated on a single-cylinder diesel engine bench. The virtual NOx sensor is proven to meet the accuracy requirement of vehicle emission monitoring for both steady-state and transient conditions and has a better frequency response compared to the emission measurement system.

Rolling bearings are important parts of mechanical equipment. However, the early failures of the bearing are usually masked by heavy noise. This brings about difficulties to the extraction of its fault features. Therefore, there is a need to develop a reliable method for early fault detection of the bearing. Considering this issue, a novel fault diagnosis method using the improved wavelet threshold denoising and fast spectral correlation (Fast-SC) is proposed. First, to solve the discontinuity of the hard threshold function and avoid the constant deviation triggered by the soft threshold function, a piecewise continuous threshold function is proposed by using a new threshold selection rule to denoise the original signal. In the new threshold function, the adjuster α is introduced to improve the traditional wavelet denoising algorithm, so as to enhance the signal-to-noise ratio (SNR) of the original signal more effectively. Then, the denoised signal is analysed by Fast-SC to identify the rolling bearing fault features. Finally, simulation analysis and experimental data demonstrate that the proposed approach is effective for rolling bearing fault detection compared with Fast-SC and the combined method based on traditional wavelet threshold and Fast-SC.

In this paper, a novel model for fault detection of rolling bearing is proposed. It is based on a high-performance support vector machine (SVM) that is developed with a multifeature fusion and self-regulating particle swarm optimization (SRPSO). The fundamental of multikernel least square support vector machine (MK-LS-SVM) is overviewed to identify a classifier that allows multidimension features from empirical mode decomposition (EMD) to be fused with high generalization property. Then the multidimension parameters of the MK-LS-SVM are configured by the SRPSO for further performance improvement. Finally, the proposed model is evaluated through experiments and comparative studies. The results prove its effectiveness in detecting and classifying bearing faults.

A mechanical molecular spring isolator (MMSI) is proposed for the purpose of isolating the low-frequency vibration of a heavy payload. The MMSI is a passive vibration isolation technique mimicking molecular spring isolator characteristics of high-static-low-dynamic stiffness (HSLDS). An MMSI consists of a piston-cylinder container filled with the liquid and some hydraulic spring accumulators. The piston would support a lump of mass and be subjected to a specific external vibration excitation force. Those accumulators can get intercommunication by the liquid to produce the transformation from high static stiffness to low dynamic stiffness. The stiffness model of the MMSI with several identical accumulators is established based on the hydrostatic law. After that, some parameters that significantly influence the stiffness characteristics are studied. Results show that the stiffness property of this kind of MMSI demonstrates a piecewise linearity of three segments. It applies the averaging method to acquire amplitude-frequency and phase-frequency relationships of the piecewise linear vibration isolation system. An inevitable jump phenomenon may occur when the exciting force reaches the critical value. The vibration isolation performance is evaluated by energy transmissibility. Finally, an experimental prototype was designed to carry out quasi-static and dynamic experiments to verify the stiffness model and the dynamic properties as an HSLDS vibration isolator.

Planetary gearboxes are widely used in mechanical transmission systems due to their large transmission ratio and high transmission efficiency. In a planetary gearbox, the sun gear is usually set to float to balance the sharing of loads among planet gears. However, this floating set will result in the variation of pressure angle, overlap ratio, and meshing phase in the meshing progress and when gear faults occur, the variation will be enlarged. In the previous studies, these parameters were reduced to constant. To study the influence of the dynamic parameters on the vibration response of planetary gearboxes under different operating conditions, a new lumped-parameter model containing the time-varying pressure angle (TVPA), time-varying overlap ratio (TVOR), and time-varying meshing phase (TVMP) is established. Based on this model, the vibration response mechanism of the sun gear is analyzed. Moreover, the comparison with the previous model is made and the rule of phase modulation caused by these dynamic parameters is revealed. By comparing the dynamic responses under different loads and rotation speeds, the phase modulation is studied in detail. Finally, the sun gear fault is introduced, and the phase modulation is analyzed in different fault degrees. This study can provide theoretical reference for the condition monitoring and fault diagnosis of planetary gearbox based on vibration analysis.

Rotating machinery is part and parcel of modern industrial applications [...]

As a prime driver, induction motor is the most electric energy consuming component in industry. The exposure of the motor to stator winding asymmetry, combined with broken rotor bar fault significantly increases the temperature and reduces the efficiency and life of the motor. Accurate and timely diagnosis of these faults will help to maintain motors operating under optimal status and avoid excessive energy consumption and severe damages to systems. This paper examines the performance of diagnosing the effect of asymmetry stator winding on broken rotor bar (BRB) faults under closed loop operation modes. It examines the effectiveness of conventional diagnostic features in both motor current and voltage signals using spectrum and modulation signal bispectrum analysis (MSBA). Evaluation results show that the combined faults cause an additional increase in the sideband amplitude and this increase in sideband can be observed in both the current and voltage signals under the sensorless control mode. MSB analysis has a good noise reduction capability and produces a more accurate and reliable diagnosis in that it gives a more correct indication of the fault severity and its location for all operating conditions.

To understand the effects of vibration of cylinder liners on engine combustion performance, tribological behaviour and vibro-acoustic radiations, this study investigates the dynamic responses of cylinder liners by finite-element modelling and experimental validation. The finite-element model is established in this study to predict the dynamic responses of cylinder liners to two significant sources: combustion shock and piston side thrust. It takes into account both the characteristics of structural modes and nonlinearities of assembly constraints when selecting adequate elements for efficient computation of the responses under both the highly nonlinear combustion pressure excitations and subsequent piston slap impacts. The predictions are then evaluated against experimental results under different engine operating conditions. To suppressing noise in measured signals, continuous wavelet analysis is employed to process the complicated responses for characterizing key response events and their frequency ranges. The results show agreeable correspondences between the numerical predictions and measured vibration signals, paving the way for investigating its effect on the combustion and lubrication processes.

Operational modal analysis (OMA) is a powerful vibration analysis tool and widely used for structural health monitoring (SHM) of various system systems such as vehicles and civil structures. Most of the current OMA methods such as pick-picking, frequency domain decomposition, natural excitation technique, stochastic subspace identification (SSI), and so on are under the assumption of white noise excitation and system linearity. However, this assumption can be desecrated by inherent system nonlinearities and variable operating conditions, which often degrades the performance of these OMA methods in that the modal identification results show high fluctuations. To overcome this deficiency, an improved OMA method based on SSI has been proposed in this paper to make it suitable for systems with strong nonstationary vibration responses and nonlinearity. This novel method is denoted as correlation signal subset-based SSI (CoS-SSI) as it divides correlation signals from the system responses into several subsets based on their magnitudes; then, the average correlation signals with respective to each subset are taken into as the inputs of the SSI method. The performance of CoS-SSI was evaluated by a simulation case and was validated through an experimental study in a further step. The results indicate that CoS-SSI method is effective in handling nonstationary signals with low signal to noise ratio (SNR) to accurately identify modal parameters from a fairly complex system, which demonstrates the potential of this method to be employed for SHM.

The wide use of different alternative fuels (AL) has led to challenges to the internal combustion (IC) engine tribology. To avoid any unpredicted damages to lubrication joints by using AL fuels, this study aims to accurately evaluate the influences of alternative fuels on the tribological behavior of IC engines. Recent achievements of the acoustic emission (AE) mechanism in sliding friction provide an opportunity to explain the tribological AE responses on engines. The asperity–asperity–collision (AAC) and fluid–asperity–shearing (FAS) mechanisms were applied to explain the AE responses from the piston ring and cylinder liner system. A new adaptive threshold–wavelet packets transform (WPT) method was developed to extract tribological AE features. Experimental tests were conducted by fueling three fuels: pure diesel (PD), biodiesel (BD), and Fischer–Tropsch (F–T) diesel. The FAS–AE indicators of biodiesel and F–T diesel show a tiny difference compared to the baseline diesel using two types of lubricants. Biodiesel produces more AAC impacts with higher AAC–AE responses than F–T diesel, which occurs at high speeds due to high temperatures and more particles after combustion than diesel. This new algorithm demonstrated the high performance of using AE signals in monitoring the tribological impacts of alternative fuels on engines.

Gear wear is a common fault that occurs in a gear transmission system that degrades the operating efficiency and may cause other catastrophic failures such as tooth breakage and fatigue. The progressive wear of a helical gear and its influences on vibration responses are rarely investigated due to the combined effects of the complicated lubrication state and the time-varying characteristic. To fill this gap, a numerical study was put forward to investigate the interactions between gear wear and dynamic response. In this study, an Archard’s wear model with elastohydradynamic lubrication (EHL) effect is adopted to simulate the helical gear wear, which is incorporated with an eight-degree of freedom dynamic model for understanding the gear dynamic at different wear degrees. The wear model shows that the gear wear mainly happens at the gear root due to the relative high slide-to-roll ratio. The dynamic modelling results demonstrate that the wear causes a reduction in time-varying gear mesh stiffness further leads to more vibration. Besides, the simulated vibration responses and experimental validation show that the wear cause increases in the amplitudes of the gear mesh frequency and its harmonics, which can reflect the evolution of progressive gear wear and can be used as monitoring features of gear wear.

As the critical parts of wind turbines, rolling bearings are prone to faults due to the extreme operating conditions. To avoid the influence of the faults on wind turbine performance and asset damages, many methods have been developed to monitor the health of bearings by accurately analyzing their vibration signals. Stochastic resonance (SR)-based signal enhancement is one of effective methods to extract the characteristic frequencies of weak fault signals. This paper constructs a new SR model, which is established based on the joint properties of both Power Function Type Single-Well and Woods-Saxon (PWS), and used to make fault frequency easy to detect. However, the collected vibration signals usually contain strong noise interference, which leads to poor effect when using the SR analysis method alone. Therefore, this paper combines the Fourier Decomposition Method (FDM) and SR to improve the detection accuracy of bearing fault signals feature. Here, the FDM is an alternative method of empirical mode decomposition (EMD), which is widely used in nonlinear signal analysis to eliminate the interference of low-frequency coupled signals. In this paper, a new stochastic resonance model (PWS) is constructed and combined with FDM to enhance the vibration signals of the input and output shaft of the wind turbine gearbox bearing, make the bearing fault signals can be easily detected. The results show that the combination of the two methods can detect the frequency of a bearing failure, thereby reminding maintenance personnel to urgently develop a maintenance plan.

Rolling element bearing is a vital component in rotating machinery, such as a wind turbine (WT) system. By accurately monitoring its health condition, the faults can be detected at an early stage, providing sufficient lead time to perform maintenance and hence reducing accidents and economic losses. Bearing usually suffers from various wears and tears, which result in a gradual increase in clearance through its lifetime. Insufficient understanding of vibration characteristics under different clearances brings difficulties for bearing condition monitoring. Thus, this paper presents a nonlinear bearing vibration model with six degrees of freedom (DOF) to investigate the vibration characteristics under different radial clearances and load conditions. Then, a dedicated bearing test is established to verify the reasonability and effectiveness of the vibration model. Furthermore, a comprehensive simulation analysis is conducted to study the vibration characteristics over an extended range of the internal radial clearance and external load. Results show that the dynamic force on each ball presents an impulse whose magnitudes increases whereas the pulse width reduces with clearance increases. Ball pass frequency of outer race (BPFO) is the dominant modulation component and the frequency is in accordance with the number of dynamic force impulses. Two indicators, i.e., root mean square (RMS) value and spectral centroid, are proposed to indicate clearance changes. In general, they show an uptrend with the increase in clearance, which is in line with the dynamic force increasing with clearance, especially the spectral centroid of the low frequency band. However, it should be noted that the RMS value and spectral centroid exhibit a fluctuating behavior due to nonlinear vibration responses. For the first time, this study shows the details of vibration characteristics with clearance variations and provides a foundation for monitoring the bearing conditions before any obvious local defects on raceways.

As an essential mechanical device in many industrial applications, reciprocating compressors have a high demand for operating efficiency and availability. Because the temperature of each part of a reciprocating compressor depends considerably on operating conditions, faults in any parts will cause the variation of the temperature distribution, which provides the possibility to distinguish the fault type of reciprocating compressors by differentiating the distribution using infrared thermal imaging. In this paper, three types of common fault are laboratory experimented in an uncontrolled temperature environment. The temperature distribution signals of a reciprocating compressor are captured by a non-contact infrared camera remotely in the form of heat maps during the experimental process. Based on the temperature distribution under baseline condition, temperature fields of six main components were selected via Hue-Saturation-Value (HSV) image as diagnostic features. During the experiment, the average grayscale values of each component were calculated to form 6-dimension vectors to represent the variation of the temperature distribution. A computational efficient multiclass support vector machine (SVM) model is then used for classifying the differences of the distributions, and the classification results demonstrate that the average temperatures of six main components aided by SVM is a promising technique to diagnose the faults of reciprocating compressors under various operating conditions with a classification accuracy of more than 99%.

In this paper, the non-probabilistic steady-state dynamics of a dual-rotor system with parametric uncertainties under two-frequency excitations are investigated using the non-intrusive simplex form mathematical metamodel. The Lagrangian formulation is employed to derive the equations of motion (EOM) of the system. The simplex form metamodel without the distribution functions of the interval uncertainties is formulated in a non-intrusive way. In the multi-uncertain cases, strategies aimed at reducing the computational cost are incorporated. In numerical simulations for different interval parametric uncertainties, the special propagation mechanism is observed, which cannot be found in single rotor systems. Validations of the metamodel in terms of efficiency and accuracy are also carried out by comparisons with the scanning method. The results will be helpful to understand the dynamic behaviors of dual-rotor systems subject to uncertainties and provide guidance for robust design and analysis.

The vibration of a planetary gearbox (PG) is complex and mutually modulated, which makes the weak features of incipient fault difficult to detect. To target this problem, a novel method, based on an adaptive order bispectrum slice (AOBS) and the fault characteristics energy ratio (FCER), is proposed. The order bispectrum (OB) method has shown its effectiveness in the feature extraction of bearings and fixed-shaft gearboxes. However, the effectiveness of the PG still needs to be explored. The FCER is developed to sum up the fault information, which is scattered by mutual modulation. In this method, the raw vibration signal is firstly converted to that in the angle domain. Secondly, the characteristic slice of AOBS is extracted. Different from the conventional OB method, the AOBS is extracted by searching for a characteristic carrier frequency adaptively in the sensitive range of signal coupling. Finally, the FCER is summed up and calculated from the fault features that were dispersed in the characteristic slice. Experimental data was processed, using both the AOBS-FCER method, and the method that combines order spectrum analysis with sideband energy ratio (OSA-SER), respectively. Results indicated that the new method is effective in incipient fault feature extraction, compared with the methods of OB and OSA-SER.

Internal combustion (IC) engine based powertrains are one of the most commonly used transmission systems in various industries such as train, ship and power generation industries. The powertrains, acting as the cores of machinery, dominate the performance of the systems; however, the powertrain systems are inevitably degraded in service. Consequently, it is essential to monitor the health of the powertrains, which can secure the high efficiency and pronounced reliability of the machines. Conventional vibration based monitoring approaches often require a considerable number of transducers due to large layout of the systems, which results in a cost-intensive, difficultly-deployed and not-robust monitoring scheme. This study aims to develop an efficient and cost-effective approach for monitoring large engine powertrains. Our model based investigation showed that a single measurement at the position of coupling is optimal for monitoring deployment. By using the instantaneous angular speed (IAS) obtained at the coupling, a novel fault indicator and polar representation showed the effective and efficient fault diagnosis for the misfire faults in different cylinders under wide working conditions of engines; we also verified that by experimental studies. Based on the simulation and experimental investigation, it can be seen that single IAS channel is effective and efficient at monitoring the misfire faults in large powertrain systems.

Accurate diagnosis of incipient faults in wind turbine (WT) assets will provide sufficient lead time to apply an optimal maintenance for the expensive WT assets which often are located in a remote and harsh environment and their maintenance usually needs heavy equipment and highly skilled engineers. This paper presents an online bearing clearance monitoring approach to diagnose the change of bearing clearance, providing an early and interpretable indication of bearing health conditions. A novel dynamic load distribution method is developed to efficiently gain the general characteristics of vibration response of bearings without local defects but with small geometric errors. It shows that the ball pass frequency of outer race (BPFO) is the primary exciting source due to biased load distribution relating to bearing clearance. The geometric errors, including various orders of runouts on different bearing parts, can be the secondary excitation source. Both sources lead to compound modulation responses with very low amplitudes, being more than 20 dB lower than that of a small local defect on raceways and often buried by background noise. Then, Modulation Signal Bispectrum (MSB) is identified to purify the noisy signal and Gini index is introduced to represent the peakness of MSB results, thereby an interpretable indicator bounded between 0 and 1 is established to show bearing clearance status. Datasets from both a dedicated bearing test and a run-to-failure gearbox test are employed to verify the performance and reliability of the proposed approach. Results show that the proposed method is capable to indicate a change of about 20 µm in bearing clearance online, which provides a significantly long lead time compared to the diagnosis method that focuses only on local defects. Therefore, this method provides a big opportunity to implement more cost-effective maintenance works or carry out timely remedial actions to prolong the lifespan of bearings. Obviously, it is applicable to not only WT assets, but also most rotating machines.

The dynamic coefficients identification of journal bearings is essential for instability analysis of rotation machinery. Aiming at the measured displacement of a single location, an improvement method associated with the Kalman filter is proposed to estimate the bearing dynamic coefficients. Firstly, a finite element model of the flexible rotor-bearing system was established and then modified by the modal test. Secondly, the model-based identification procedure was derived, in which the displacements of the shaft at bearings locations were estimated by the Kalman filter algorithm to identify the dynamic coefficients. Finally, considering the effect of the different process noise covariance, the corresponding numerical simulations were carried out to validate the preliminary accuracy. Furthermore, experimental tests were conducted to confirm the practicality, where the real stiffness and damping were comprehensively identified under the different operating conditions. The results show that the proposed method is not only highly accurate, but also stable under different measured locations. Compared with the conventional method, this study presents a more than high practicality approach to identify dynamic coefficients, including under the resonance condition. With high efficiency, it can be extended to predict the dynamic behaviour of rotor-bearing systems.

In a multiobjective particle swarm optimization algorithm, selection of the global best particle for each particle of the population from a set of Pareto optimal solutions has a significant impact on the convergence and diversity of solutions, especially when optimizing problems with a large number of objectives. In this paper, a new method is introduced for selecting the global best particle, which is minimum distance of point to line multiobjective particle swarm optimization (MDPL-MOPSO). Using the basic concept of minimum distance of point to line and objective, the global best particle among archive members can be selected. Different test functions were used to test and compare MDPL-MOPSO with CD-MOPSO. The result shows that the convergence and diversity of MDPL-MOPSO are relatively better than CD-MOPSO. Finally, the proposed multiobjective particle swarm optimization algorithm is used for the Pareto optimal design of a five-degree-of-freedom vehicle vibration model, which resulted in numerous effective trade-offs among conflicting objectives, including seat acceleration, front tire velocity, rear tire velocity, relative displacement between sprung mass and front tire, and relative displacement between sprung mass and rear tire. The superiority of this work is demonstrated by comparing the obtained results with the literature.

In this paper a stochastic resonance (SR)-based method for recovering weak impulsive signals is developed for quantitative diagnosis of faults in rotating machinery. It was shown in theory that weak impulsive signals follow the mechanism of SR, but the SR produces a nonlinear distortion of the shape of the impulsive signal. To eliminate the distortion a moving least squares fitting method is introduced to reconstruct the signal from the output of the SR process. This proposed method is verified by comparing its detection results with that of a morphological filter based on both simulated and experimental signals. The experimental results show that the background noise is suppressed effectively and the key features of impulsive signals are reconstructed with a good degree of accuracy, which leads to an accurate diagnosis of faults in roller bearings in a run-to failure test.

Currently, alternative fuels are being investigated in detail for application in compression ignition (CI) engines resulting in exciting potential opportunities to increase energy security and reduce gas emissions. Biodiesel is one of the alternative fuels which is renewable and environmentally friendly and can be used in diesel engines with little or no modifications. The objective of this study is to investigate the effects of biodiesel types and biodiesel fraction on the emission characteristics of a CI engine. The experimental work was carried out on a four-cylinder, four-stroke, direct injection (DI) and turbocharged diesel engine by using biodiesel made from waste oil, rapeseed oil, corn oil and comparing them to normal diesel. The fuels used in the analyses are B10, B20, B50, B100 and neat diesel. The engine was operated over a range of engine speeds. Based on the measured parameters, detailed analyses were carried out on major regulated emissions such as NOx, CO, CO2, and THC. It has been seen that the biodiesel types (sources) do not result in any significant differences in emissions. The results also clearly indicate that the engine running with biodiesel and blends have higher NOx emission by up to 20%. However, the emissions of the CI engine running on neat biodiesel (B100) were reduced by up to 15%, 40% and 30% for CO, CO2 and THC emissions respectively, as compared to diesel fuel at various operating conditions.

This paper investigated the nonlinear vibrations of an uncertain overhung rotor system with rub-impact fault. As the clearance of the rotor and stator is getting smaller, contact between them often occurs at high rotation speeds. Meanwhile, inherent uncertainties in the rubbing can be introduced for a variety of reasons, and they are typically restricted to small-sample variables. It is important to gain a robust understanding of the dynamics of such a system under non-probabilistic uncertainties. A non-intrusive uncertainty quantification scheme, coupled with the Runge-Kutta method, was used to study the effects of the rub-impact related interval uncertainties on the dynamical response individually and simultaneously, including the uncertainties in the contact stiffness, clearance, and friction coefficient. Moreover, the numerical validation of the developed analysis method was verified through comparisons with the scanning approach. The results obtained provide some guidance for investigating the uncertain dynamics of rubbing rotors and diagnosing the rub-impact fault under non-random uncertainty.

Broken rotor bar (BRB) faults are one of the most common faults in induction motors (IM). One or more broken bars can reduce the performance and efficiency of the IM and hence waste the electrical power and decrease the reliability of the whole mechanical system. This paper proposes an effective fault diagnosis method using the Teager−Kaiser energy operator (TKEO) for BRB faults detection based on the motor current signal analysis (MCSA). The TKEO is investigated and applied to remove the main supply component of the motor current for accurate fault feature extraction, especially for an IM operating at low load with low slip. Through sensing the estimation of the instantaneous amplitude (IA) and instantaneous frequency (IF) of the motor current signal using TKEO, the fault characteristic frequencies can be enhanced and extracted for the accurate detection of BRB fault severities under different operating conditions. The proposed method has been validated by simulation and experimental studies that tested the IMs with different BRB fault severities to consider the effectiveness of the proposed method. The obtained results are compared with those obtained using the conventional envelope analysis methods and showed that the proposed method provides more accurate fault diagnosis results and can distinguish the BRB fault types and severities effectively, especially for operating conditions with low loads.

Induction motors (IMs) are widely used in many manufacturing processes and industrial applications. The harsh work environment, long-time enduring, and overloads mean that it is subjected to broken rotor bar (BRB) faults. The vibration signal of IMs with BRB faults consists of the reliable modulation information used for fault diagnosis. Cyclostationary analysis has been found to be effective in identifying and extracting fault feature. The estimators of cyclic modulation spectrum (CMS) and fast spectral correlation (FSC) based on the short-time fourier transform (STFT) have higher cyclic frequency resolution, which has proven efficient in demodulating second order cyclostationary (CS2) signals. However, these two estimators have limitations of processing the maximum cyclic frequency αmax that is smaller than Fs/2 (Fs is the sampling frequency) according to Nyquist’s Theorem. In addition, they have lower carrier frequency resolution due to the fixed window size used in STFT. In order to resolve the initial shortcomings of the CMS and FSC methods, in this paper, we extended the analysis of CMS algorithm based on the continuous wavelet transform (CWT), which enlarged the maximum cyclic frequency range to Fs/2 and provides higher carrier frequency resolution because the CWT has the advantage of multi-resolution analysis. The reliability and applicability of the proposed method for fault components localization were validated by CS2 simulation signals. Compared to CMS and FSC methods, the proposed approach shows better performance by analyzing vibration signals between healthy motor and faulty motor with one BRB fault under 0%, 20%, 40%, and 80% load conditions.

To realize the accurate fault detection of rolling element bearings, a novel fault detection method based on non-stationary vibration signal analysis using weighted average ensemble empirical mode decomposition (WAEEMD) and modulation signal bispectrum (MSB) is proposed in this paper. Bispectrum is a third-order statistic, which can not only effectively suppress Gaussian noise, but also help identify phase coupling. However, it cannot effectively decompose the modulation components which are inherent in vibration signals. To alleviate this issue, MSB based on the modulation characteristics of the signals is developed for demodulation and noise reduction. Still, the direct application of MSB has some interfering frequency components when extracting fault features from non-stationary signals. Ensemble empirical mode decomposition (EEMD) is an advanced nonlinear and non-stationary signal processing approach that can decompose the signal into a list of stationary intrinsic mode functions (IMFs). The proposed method takes advantage of WAEEMD and MSB for bearing fault diagnosis based on vibration signature analysis. Firstly, the vibration signal is decomposed into IMFs with a different frequency band using EEMD. Then, the IMFs are reconstructed into a new signal by the weighted average method, called WAEEMD, based on Teager energy kurtosis (TEK). Finally, MSB is applied to decompose the modulated components in the reconstructed signal and extract the fault characteristic frequencies for fault detection. Furthermore, the efficiency and performance of the proposed WAEEMD-MSB approach is demonstrated on the fault diagnosis for a motor bearing outer race fault and a gearbox bearing inner race fault. The experimental results verify that the WAEEMD-MSB has superior performance over conventional MSB and EEMD-MSB in extracting fault features and has precise and effective advantages for rolling element bearing fault detection.

Induction motors (IMs) play an essential role in the field of various industrial applications. Long-time service and tough working situations make IMs become prone to a broken rotor bar (BRB) that is one of the major causes of IMs faults. Hence, the continuous condition monitoring of BRB faults demands a computationally efficient and accurate signal diagnosis technique. The advantage of high reliability and wide applicability in condition monitoring and fault diagnosis based on vibration signature analysis results in an improved cyclic modulation spectrum (CMS), which is one of the cyclic spectral analysis algorithms. CMS is proposed in this paper for the detection and identification of BRB faults in IMs at a steady-state operation based on a vibration signature analysis. The application of CMS is based on the short-time Fourier transform (STFT) and the improved CMS approach is attributed to the optimization of STFT. The optimal window is selected to improve the accuracy for identifying the BRB fault types and severities. The appropriate window length and step size are optimized based on the selected window function to receive a better calculation benefit through simulation and experimental analysis. Compared to other estimators, the improved CMS method provides better fault detectability results by analyzing vertical vibration signatures of a healthy motor, and damaged motors with 1 BRB and 2 BRBs under 0%, 20%, 40%, 60%, and 80% load conditions. Both synthetic and experimental investigations demonstrate the proposed methodology can significantly reduce computational costs and identify the BRB fault types and severities effectively.

A novel bistable electromagnetic vibration energy harvester (BEMH) is constructed and optimized in this study, based on a nonlinear system consisting mainly of a flexible membrane and a magnetic spring. A large-amplitude transverse vibration equation of the system is established with the general nonlinear geometry and magnetic force. Firstly, the mathematical model, considering the higher-order nonlinearities given by nonlinear Galerkin method, is applied to a membrane with a co-axial magnet mass and magnetic spring. Secondly, the steady vibration response of the membrane subjected to a harmonic base motion is obtained, and then the output power considering electromagnetic effect is analytically derived. On this basis, a parametric study in a broad frequency domain has been achieved for the BEMH with different radius ratios and membrane thicknesses. It is demonstrated that model predictions are both in close agreement with results from the finite element simulation and experiment data. Finally, the proposed efficient solution method is used to obtain an optimizing strategy for the design of multi-stable energy harvesters with the similar flexible structure.

Fault identification for closed-loop control systems is a future trend in the field of fault diagnosis. Due to the inherent feedback adjustment mechanism, a closed-loop control system is generally very robust to external disturbances and internal noises. Closed-loop control systems often encourage faults to propagate inside the systems, which may lead to the consequence that faults amplitude becomes smaller and fault characteristics difference becomes more inapparent. Hence, it has been challenging to achieve fault identification for such systems. Traditional fault identification methods are not particularly designed for closed-loop control systems and thus cannot be applied directly. In this work, a new fault identification method is proposed, which is based on the deep neural network for closed-loop control systems. Firstly, the fault propagation mechanism in closed-loop control systems is theoretically derived, and the influence of fault propagation on system variables is analyzed. Then deep neural network is applied to find fault characteristics difference between different data modes, and a sliding window is used to amplify the fault-to-noise ratio and characteristics difference, with an aim to increase the identification performance. To verify this method, the simulations that are based on a numerical simulation model, the Tennessee industrial system and the satellite attitude control system are conducted. The results show that the proposed method is more feasible and more effective in fault identification for closed-loop control systems compared with traditional data-driven identification methods, including distance-based and angle-based identification methods.

This paper investigates the performance of the conventional bispectrum (CB) method and its new variant, the modulation signal bispectrum (MSB) method, in analysing the electrical current signals of induction machines for the condition monitoring of rotor systems driven by electrical motors. Current signal models which include the phases of the various electrical and magnetic quantities are explained first to show the theoretical relationships of spectral sidebands and their associated phases due to rotor faults. It then discusses the inefficiency of CB and the proficiency of MSB in characterising the sidebands based on simulated signals. Finally, these two methods are applied to analyse current signals measured from different rotor faults, including broken rotor bar (BRB), downstream gearbox wear progressions and various compressor faults, and the diagnostic results show that the MSB outperforms the CB method significantly in that it provides more accurate and sparse diagnostics, thanks to its unique capability of nonlinear modulation detection and random noise suppression.

Online monitoring of the lubrication and friction conditions in internal combustion engines can provide valuable information and thereby enables optimal maintenance actions to be undertaken to ensure safe and efficient operations. Acoustic emission (AE) has attracted significant attention in condition monitoring due to its high sensitivity to light defects on sliding surfaces. However, limited understanding of the AE mechanisms in fluid-lubricated conjunctions, such as piston rings and cylinder liners, confines the development of AE-based lubrication monitoring techniques. Therefore, this study focuses on developing new AE models and effective AE signal process methods in order to achieve accurate online lubrication monitoring. Based on the existing AE model for asperity⁻asperity collision (AAC), a new model for fluid⁻asperity shearing (FAS)-induced AE is proposed that will explain AE responses from the tribological conjunction of the piston ring and cylinder. These two AE models can then jointly demonstrate AE responses from the lubrication conjunction of engine ring⁻liner. In particular, FAS allows the observable AE responses in the middle of engine strokes to be characterised in association with engine speeds and lubricant viscosity. However, these AE components are relatively weak and noisy compared to others, with movements such as valve taring, fuel injection and combustions. To accurately extract these weaker AE’s for lubricant monitoring, an optimised wavelet packet transform (WPT) analysis is applied to the raw AE data from a running engine. This results in four distinctive narrow band indicators to describe the AE amplitude in the middle of an engine power stroke. Experimental evaluation shows the linear increasing trend of AE indicator with engine speeds allows a full separation of two baseline engine lubricants (CD-10W30 and CD-15W40), previously unused over a wide range of speeds. Moreover, the used oil can also be diagnosed by using the nonlinear and unstable behaviours of the indicator at various speeds. This model has demonstrated the high performance of using AE signals processed with the optimised WPT spectrum in monitoring the lubrication conditions between the ring and liner in IC engines.

Condition monitoring can reduce machine breakdown losses, increase productivity and operation safety, and therefore deliver significant benefits to many industries. The emergence of wireless sensor networks (WSNs) with smart processing ability play an ever-growing role in online condition monitoring of machines. WSNs are cost-effective networking systems for machine condition monitoring. It avoids cable usage and eases system deployment in industry, which leads to significant savings. Powering the nodes is one of the major challenges for a true WSN system, especially when positioned at inaccessible or dangerous locations and in harsh environments. Promising energy harvesting technologies have attracted the attention of engineers because they convert microwatt or milliwatt level power from the environment to implement maintenance-free machine condition monitoring systems with WSNs. The motivation of this review is to investigate the energy sources, stimulate the application of energy harvesting based WSNs, and evaluate the improvement of energy harvesting systems for mechanical condition monitoring. This paper overviews the principles of a number of energy harvesting technologies applicable to industrial machines by investigating the power consumption of WSNs and the potential energy sources in mechanical systems. Many models or prototypes with different features are reviewed, especially in the mechanical field. Energy harvesting technologies are evaluated for further development according to the comparison of their advantages and disadvantages. Finally, a discussion of the challenges and potential future research of energy harvesting systems powering WSNs for machine condition monitoring is made.

To ensure reliable and efficient operation of gas turbines, multiple model (MM) approaches have been extensively studied for online fault detection and isolation (FDI). However, current MM-FDI approaches are difficult to directly apply to gas path FDI, which is one of the common faults in gas turbines and is understood to mainly be due to the high complexity and computation in updating hypothetical gas path faults for online applications. In this paper, a fault contribution matrix (FCM) based MM-FDI approach is proposed to implement gas path FDI over a wide operating range. As the FCM is realized via an additive term of the healthy model set, the hypothetical models for various gas path faults can be easily established and updated online. In addition, a gap metric analysis method for operating points selection is also proposed, which yields the healthy model set from the equal intervals linearized models to approximate the nonlinearity of the gas turbine over a wide range of operating conditions with specified accuracy and computational efficiency. Simulation case studies conducted on a two-shaft marine gas turbine demonstrated the proposed approach is capable of adaptively updating hypothetical model sets to accurately differentiate both single and multiple faults of various gas path faults.

The planetary gearbox is at the heart of most rotating machinery. The premature failure and subsequent downtime of a planetary gearbox not only seriously affects the reliability and safety of the entire rotating machinery but also results in severe accidents and economic losses in industrial applications. It is an important and challenging task to accurately detect failures in a planetary gearbox at an early stage to ensure the safety and reliability of the mechanical transmission system. In this paper, a novel method based on wavelet packet energy (WPE) and modulation signal bispectrum (MSB) analysis is proposed for planetary gearbox early fault diagnostics. First, the vibration signal is decomposed into different time-frequency subspaces using wavelet packet decomposition (WPD). The WPE is calculated in each time-frequency subspace. Secondly, the relatively high energy vectors are selected from a WPE matrix to obtain a reconstructed signal. The reconstructed signal is then subjected to MSB analysis to obtain the fault characteristic frequency for fault diagnosis of the planetary gearbox. The validity of the proposed method is carried out through analyzing the vibration signals of the test planetary gearbox in two fault cases. One fault is a chipped sun gear tooth and the other is an inner-race fault in the planet gear bearing. The results show that the proposed method is feasible and effective for early fault diagnosis in planetary gearboxes.