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Helical gearboxes play a critical role in power transmission of industrial applications. They are vulnerable to various faults due to long-term and heavy-duty operating conditions. To improve the safety and reliability of helical gearboxes, it is necessary to monitor their health conditions and diagnose various types of faults. The conventional measurements for gearbox fault diagnosis mainly include lubricant analysis, vibration, airborne acoustics, thermal images, electrical signals, etc. However, a single domain measurement may lead to unreliable fault diagnosis and the contact installation of transducers is not always accessible, especially in harsh and dangerous environments. In this article, a Compressive Sensing (CS)-based Dual-Channel Convolutional Neural Network (CNN) method was proposed to accurately and intelligently diagnose common gearbox faults based on two complementary non-contact measurements (thermal images and acoustic signals) from a mobile phone. The raw acoustic signals were analysed by the Modulation Signal Bispectrum (MSB) to highlight the coupled modulation components relating to gear faults and suppress the irrelevant components and random noise, which generates a series of two-dimensional matrices as sparse MSB magnitude images. Then, CS was used to reduce the image redundancy but retain key information owing to the high sparsity of thermal images and acoustic MSB images, which significantly accelerates the CNN training speed. The experimental results convincingly demonstrate that the proposed CS-based Dual-Channel CNN method significantly improves the diagnostic accuracy (99.39% on average) of industrial helical gearbox faults compared to the single-channel ones. • Using two complementary non-contact measurements to overcome the instability and inaccuracy of a single domain signal. • Reducing the image redundancy and capacity to significantly accelerate the training speed through Compressive Sensing. • The proposed Compressive Sensing-based Dual-Channel CNN method achieves accurate and efficient gearbox fault diagnosis. [ABSTRACT FROM AUTHOR]

Cyclostationary analysis has been strongly recognized as an effective demodulation tool in identifying fault features of rotating machinery based on vibration signature analysis. This study improves two current mature cyclostationary approaches, cyclic modulation spectrum (CMS) and fast spectral correlation (Fast-SC), combined with the novel frequency-domain application of Teager Kaiser energy operator (TKEO). They can enhance fault feature identification with the lower computational burden. Firstly, the raw vibration signal is transformed into the time–frequency domain through the short-time Fourier transform (STFT) to realize the conversion of the multi-carrier signal to a multiple signal-carrier signal. Secondly, the TKEO is utilized to enhance the fault feature by taking full advantage of demodulating the mono-component. Finally, the spectral coherence and enhanced envelope spectrum (EES) are calculated to effectively exhibit fault features. The superiority of the proposed methods is successfully validated by the simulation study and diagnosing the broken rotor bar (BRB) and bearing outer race faults of induction motors (IMs) under various operating conditions. • The frequency domain TKEO is proposed for processing the single carrier signal. • The fault extraction capabilities of CMS and Fast-SC are enhanced using TKEO. • The optimized methods have high computational efficiency. • The results validate the effectiveness of the proposed methods for IM fault diagnosis. [ABSTRACT FROM AUTHOR]

Identifying a spectral frequency band with abundant fault information from spectral coherence is essential for improved envelope spectrum-based bearing diagnosis. Both blind features and targeted features have been employed to distinguish informative spectral frequency band of spectral coherence. However, how to select appropriate feature to correctly discriminate the optimal frequency band of spectral coherence in different scenarios is problematic. In this study, a new targeted feature is presented to quantify the signal-to-noise ratio in narrow frequency bands of spectral coherence, and further a method based on the proposed feature is developed to distinguish an optimal spectral frequency band of spectral coherence for bearing diagnostics. The efficiency of the developed method, typical blind feature-based methods and typical targeted feature-based methods in identifying the defect-sensitive frequency band of spectral coherence and bearing fault diagnosis is validated and compared using simulated signals with different interference noises and bearing experimental signals. The advantages and limitations of typical blind and targeted feature-based methods in different scenarios are summarized to guide the application. The results demonstrate that the developed targeted feature can efficiently evaluate bearing failure information in the cyclic frequency domain, and the presented approach can accurately discriminate the failure-related spectral frequency band of spectral coherence and detect different bearing faults compared with the methods based on the state-of-the-art features. • FDSNR is proposed to evaluate the fault information in the frequency domain. • Performance of typical blind and targeted features-based IESFOgram is investigated. • Characteristics of typical feature metrics in selecting ISFB of SCoh are provided. • The IESFOgram based on DFSNR exhibit excellent bearing diagnostic performance. [ABSTRACT FROM AUTHOR]

Transient impulses caused by local defects are critical for the fault detection of rotating machines. However, they are extremely weak and overwhelmed in the strong noise and harmonic components, making the transient features are very difficult to be extracted. This paper proposes an adaptive multi-scale improved differential filter (AMIDIF) to enhance the identification of transient impulses for rotating machine fault diagnosis. In this scheme, firstly, the AMIDIF is performed to decompose the measured signal of rotating machine into a series of multi-scale improved differential filter (MIDIF) filtered signals. Subsequently, in view of the MIDIF filtered signals exhibit varying extents of validity in revealing fault features, a weighted reconstruction method using correlation analysis is proposed in which the weighted coefficients are counted and distributed to the corresponding MIDIF filtered signals to highlight the effective MIDIF filtered signals and weaken the invalid ones. Finally, the transient impulse components of rotating machinery are obtained by multiplying the weighted coefficients and the MIDIF filtered signals under different scales. Furthermore, the fault types of rotating machines are inferred from the fault defect frequencies in the envelope spectrum of the transient impulses. Simulation analysis and experimental studies are implemented to verify the performance of the AMIDIF compared with the state-of-the-art methods including spectral kurtosis (SK), multi-scale average combination different morphological filter (ACDIF) and multi-scale morphology gradient product operation (MGPO). The results prove that the AMIDIF has excellent performance in extracting transient features for rotating machines fault diagnosis. • An AMIDIF is developed for transient impulse enhancement. • AMIDIF can extract the bidirectional impulses in the signal at the same time. • Correlation coefficient is used to optimize the weighted coefficient in AMIDIF. • Performance of the AMIDIF is validated by simulation and experimental cases. [ABSTRACT FROM AUTHOR]

Blade cracks pose deadly threats to aviation safety and have caused serious aviation accidents in recent years. In order to diagnose blade cracks at the early stage, the harmonic vibration of cracked blade was analyzed theoretically and experimentally. Firstly, a recursive form solution was deduced for the complex the nonlinear dynamic equation of blade vibration, revealing the close relationship between harmonic component power and crack parameters. Furthermore, the upper bound of the adjacent harmonic component power ratio was obtained by theoretical derivations. The results show that the harmonic power decreases as the harmonic component order increases, and the degree of attenuation is decided by the crack parameters. Therefore, a crack detection approach was proposed according to the power ratio of harmonic components. The advantage of this method is that the blades do not need to be in a resonant state and can process vibration data at all rotational frequencies. This improves data utilization and diagnostic robustness. The recommended method was validated by the simulation analysis of stainless-steel and titanium blades. Finally, a test bench for blade vibration was set up whose highlight was the use of optical sensors for non-contact measurements of blade vibration. The results of both simulation and testbed experiment were much consistent with the theoretical inference. • Although a closed-form solution to the nonlinear kinetic equation of blade vibration is theoretically not available, we obtain a solution in a recursive form. • Further, the energy attenuation function of adjacent harmonic components is defined, and it is theoretically derived that there is an upper bound of the energy attenuation function. Moreover, the upper bound of the energy attenuation function is determined by the harmonic order, crack location, and crack depth. • The results of simulation and test bench experiments are consistent with theoretical inferences. [ABSTRACT FROM AUTHOR]

Skidding is an inevitable phenomenon in rolling element bearing but accelerates the bearing wear and shortens the bearing life. Recognizing skidding behavior under different clearances will benefit to bearing health monitoring. In this study, an improved bearing dynamic model is developed to investigate its vibration characteristics and skidding behavior taking into all bearing structure components, time-varying oil film characteristics and bearing clearances. A novel method is proposed to include time-varying oil film stiffness and thickness under different clearances into the bearing dynamic model. A fast algorithm is adopted through interpolation during the model solving process. Furthermore, vibration responses and skidding behavior under different clearances are analyzed. Finally, a designed synchronous differential encoder (SDE) system tests the skidding behavior of bearings and verifies the proposed model through measuring the angular velocity of cage transformed by distance test. Numerical result shows that both RMS and ball pass frequency of outer race (BPFO) increase with bearing clearances. The slip ratio represents growth with the increase of bearing clearances, which is verified by the designed experiment with good consistency with the simulation. It can be foreseen that this novel dynamic model with SDE system can be well performed for bearing skidding detection and fault detection. [ABSTRACT FROM AUTHOR]

Bearing waviness is a kind of geometric unevenness on the surface of bearing components, which has vital influence on lifetime, vibration and noise. In order to accurately evaluate the impact of waviness on bearing operating performance and diagnostic features, it is necessary to reveal the mapping relationship between waviness excitation and vibration characteristics. However, current simulated waviness when modeling bearing vibrations is usually simplified by a uniform or non-uniform sinusoidal function, which cannot characterize the real topography of bearing waviness and lead to inaccuracy of diagnostics and prognostics. To address this issue, a novel waviness characterizing method based on Gaussian filter is developed in this study. Based on the proposed waviness characterizing method, a bearing waviness dynamic model is developed and vibration responses under various amplitude and order of waviness are investigated by simulation and experiment. Results show that the established waviness characterizing method can generate waviness curves closer to the actual shape. The bearing waviness dynamic model and the based vibration responses reveals unusual random phenomenon due to different waviness effects. These findings provide theoretical support for accurate identification of waviness on vibration characteristics, which has great significance on condition monitoring and fault diagnosis of bearing. [ABSTRACT FROM AUTHOR]

• A novel method for pressure prediction and cavitation evaluation of water jacket in engines is proposed. • The pressure amplification factor for a thin liquid layer under modal vibration is derived. • The nonlinear relationship between liner vibration and coolant pressure is investigated to reveal the mechanism of vibration-induced cavitation. • Effects of acoustic parameters and liner modal parameters on cavitation are discussed. • The correctness and rationality of the method is verified by experiment. Vibrations of the cylinder liner in internal combustion engines cause coolant cavitation, inducing cavitation erosion. Owing to the lack of a comprehensive understanding of vibration-induced cavitation, the cavitation erosion has been long an unresolved problem influencing engine lifetime and reliability and concerned more in recent years due to lightweight designs. This study proposes a novel pressure prediction method that considers the dynamic properties of a cylinder liner and the pressure amplification effect of a thin water jacket. A pressure amplification factor for a thin water jacket, defined as the ratio of the acoustic pressure to the plane progressive wave pressure generated by the same liner vibration, was derived for the first time. The pressure amplification mechanism in the thin water jackets was revealed. The cavitation risk area on the cylinder liner was predicted, and the effects of acoustic parameters and liner modal properties on cavitation were analysed. The theoretical analyses agreed with the experimental results, proving the accuracy of the proposed method. Moreover, it has found that the thin-layer configuration of the water jacket significantly reduced the vibration threshold for triggering cavitation. Vibration-induced cavitation in cylinder liners is closely related to the liner constraint modes and acoustic properties of the water jackets. The research results enrich the theoretical understanding of vibration-induced cavitation and provide theoretical support for the prediction and mitigation of cavitation erosion in internal combustion engines. [Display omitted] [ABSTRACT FROM AUTHOR]

Intelligent transportation necessitates advanced perception and cognitive systems that can provide continuous feedback from the vehicle. However, sensors relying on batteries face challenges such as high maintenance costs and environmental issues due to the limited lifespan of the power source. To overcome these challenges, this paper reports an efficient battery-free solution for transportation monitoring. The solution utilizes a speed-amplified rotary energy harvester (SAREH) to power various wireless Bluetooth sensors, enabling continuous monitoring of the vehicle's motion state. The SAREH combines a contra-rotating mechanism with a friction pendulum, resulting in excellent power output in a compact design. Experimental results demonstrate the ability of SAREH to extract power from vehicles operating at speeds ranging from 180 to 1260 rpm. The maximum power output and corresponding power density are measured as 712 mW and 34 mW cm−3, respectively. The prototype successfully powers portable electronics and supports battery-free navigation, triaxial acceleration, and temperature multi-sensors during real road and railway simulation tests. Additionally, the SAREH operates as a highly sensitive speed sensor and an early-warning system for detecting the vehicle's motion state. These results represent a significant advancement in intelligent transportation systems by showcasing the practicality of self-powered wireless monitoring capabilities on vehicles. [Display omitted] • A novel speed-amplified energy harvesting technique is proposed. • The proposed system incorporates contra-rotating and friction pendulum mechanisms. • The prototype enables installation in confined spaces while achieving a high power density of up to 34 mW cm−3. • The prototype simultaneously powers daily electronics and supports battery-free wireless sensors. • The prototype operates as a speed sensor and an early-warning system for detecting the motion state of the vehicle. [ABSTRACT FROM AUTHOR]

[Display omitted] • The counterweight acts as the friction pendulum to form the all-in-one prototype. • The power density can reach 1982 W m−3. • The prototype can drive the daily used electric appliance and wireless sensor. • The prototype can serve as a speed sensor to detect the motion state of vehicles. • The prototype supports self-powered and real-time bogie frames monitoring. To maintain desirable service quality and operational safety, a wireless monitoring unit integrated with the vibration energy harvesting technology becomes an available choice to achieve self-powered, maintenance-free, and real-time monitoring of the train. However, owing to the bulky size and split design, to collect the mechanical energy from the bogie frame movement is still a considerable challenge for conventional harvesters. Here, we proposed a compact all-in-one on-rotor electromagnetic energy harvester. The key novelty is that a counterweight acts as the friction pendulum to produce the desired relative motion between the coils and magnet and make the device more easily install on the wheelset. Besides, the layout of the magnetic materials and coils is optimized to improve the conversion efficiency. The output performance under broad train speeds of 420–820 rpm is systematically studied to verify the improvements of the power density (up to 1982 W m−3), and the converted electricity successfully powers the daily electric appliance and the commercial wireless Bluetooth sensors. Additionally, the harvester serves as a speed sensor to detect the motion state of the vehicle. This work makes significant progress towards potential applications in the embedded self-powered wireless condition monitoring units. [ABSTRACT FROM AUTHOR]

• ORS is developed to be installed on the rotating shaft for vibration measurements. • The developed ORS largely improves the SNR of vibration collections than OHS. • The FFT-based fault diagnosis theory for the rolling bearing is presented. • ORS can achieve easier and more robust Hilbert envelope analysis for diagnosis. • Results validate the performance of ORS for early rolling bearing fault diagnosis. The traditional on-house sensing (OHS) accelerometer for vibration measurements causes poor signal-to-noise ratio (SNR) and complicated fault modulations, which increases the difficulty and complexity for early bearing fault diagnosis. To overcome these challenges, this paper develops a wireless triaxial on-rotor sensing (ORS) system to largely improve the SNR and deduces fast Fourier transform (FFT) and Hilbert envelope analysis for accurate early rolling bearing fault diagnosis, which largely improves accuracy and efficiency for early fault diagnosis. First, the development of the ORS system for wireless vibration measurements is given. Second, the theoretical diagnostic relationships between dynamic ORS signals and rolling bearing faults are derived for FFT and Hilbert envelope analysis for the first time. Finally, the induction motor tests with outer and inner race faults successfully validate that both simple FFT and Hilbert envelope analysis can achieve more robust early rolling bearing fault diagnosis compared to OHS measurements. [ABSTRACT FROM AUTHOR]

• The proposed method extends the cyclic frequency range to Fs /2. • The designed scale factor in CWT can help locate important frequency bands. • TKEO is improved to process the single-carrier signal in the frequency domain. • The developed method can enhance the fault features effectively. • Induction motor tests validate the superiority of the method for early fault detection. The cyclostationary analysis techniques have been extensively explored for the purpose of fault detection in rotating machinery. However, there are still huge challenges because of both limited detection frequency range and low fault identification accuracy. This paper proposes an improved cyclostationary method to enhance incipient fault features. Firstly, the continuous wavelet transform is used to accurately locate important frequency bands, and the fault modulation mechanism or fast kurtogram can be adopted to design the optimal wavelet transform scale factor. Secondly, the Teager-Kaiser energy operator is improved to be used in the frequency domain for the weak fault feature enhancement. Finally, fault features are presented in the cyclic frequency domain through spectral coherence and enhanced envelope spectrum. The proposed method is verified through both numerical simulation and experiments, including incipient half-broken rotor bar, and rolling bearing outer race faults in induction motors. [ABSTRACT FROM AUTHOR]

• A multiscale denoising branch is developed to extract multi-level information and reduce noise interference. • An improved flow direction strategy-based adaptive resonance branch is introduced to learn fault-related periodic impulsive features. • Case studies are conducted to validate the efficacy of the developed IFD-MDCN. Rolling bearings are the core components of rotating machinery, and their normal operation is crucial to the entire industrial production. Most existing condition monitoring methods have been devoted to extracting discriminative features from vibration signals that reflect bearing health status information. However, the complex working conditions of rolling bearings often make the periodic impulsive characteristics related to fault information easily buried in noise interferences. Therefore, it is challenging for existing approaches to learning discriminative fault-related features in these scenarios. To address this issue, a novel multibranch CNN named IFD-MDCN is developed in this paper, which represents multibranch denoising convolutional networks (MDCN) with an improved flow direction (IFD) strategy. The main contributions of this work include: (1) designing a multiscale denoising branch to extract multi-level information and reduce noise impact. More specifically, the multiscale denoising branch adopts a Gaussian multi-level noise reduction procedure to represent vibration signals at multiple levels and filter out the noise components, and then it uses a multiscale convolutional module to extract abundant features from these denoised signal representations; (2) establishing an improved flow direction strategy-based adaptive resonance branch to learn periodic impulsive features associated with fault information from vibration signals. Extensive experimental results reveal that the IFD-MDCN outperforms five state-of-the-art approaches, especially in strong noise scenarios. [ABSTRACT FROM AUTHOR]

• A method to accurately calculate the blade characteristic frequency is proposed. • It relies on the physical relationship between the BPF and fundamental frequency. • Blade vibrations are separated using VKF with parameters optimization. • A framework for blade early diagnosis based on unsupervised learning is verified. Blade fault is a catastrophic failure of gas turbines. In order to improve the reliability of blade during operation, condition monitoring is one of the effective methods. However, there always exist two problems with blade monitoring: 1) challenges in warning of the occurrence of blade failure in advance and 2) difficulties finding the location after blade failure. In this article, we solve these problems by excavating the characteristics of blade-related signals in broadband casing vibration with advanced signal processing methods and machine learning technology. First, a novel method--Sparse Harmonic Product Spectrum (SHPS)--is proposed to accurately calculate blade passing frequency from gas turbine broadband casing vibration. The SPHS relies on Fourier transform, and its calculation utilizes the physical relationship between fundamental frequency and blade passing frequencies. Combining Vold-Kalman filter with adaptive parameter optimization process (AVKF), the blade-related vibration can be separated from casing vibration even in strong noise. Analysis of simulated casing vibration signal is used to verify the effectiveness and superiority of proposed method. Based on blade-related vibration, we build a gas turbine blade condition model in an unsupervised learning manner. The model can excavate potential blade failures earlier and more accurately than conventional threshold methods. Then, three coefficients are constructed according to the blade-related vibration characteristics to identify the blade fault location in multi-stage system. Moreover, the effectiveness of the proposed blade diagnosis framework is verified using actual industrial gas turbine blade fracturing failure data. [ABSTRACT FROM AUTHOR]

Fault diagnosis of rolling bearings has attracted extensive attention in industrial fields, which plays a vital role in guaranteeing the reliability, safety, and economical efficiency of mechanical systems. Traditional data-driven fault diagnosis methods require obtaining a dataset of full failure modes in advance as the training data. However, this kind of dataset is not always available in some critical industrial scenarios, which impairs the practicability of the data-driven fault diagnosis methods for various applications. A digital twin, which establishes a virtual representation of a physical entity to mirror its operating conditions, would make fault diagnosis of rolling bearings feasible when the fault data are insufficient. In this paper, we propose a novel digital twin-driven approach for implementing fault diagnosis of rolling bearings with insufficient training data. First, a dynamics-based virtual representation of rolling bearings is built to generate simulated data. Then, a Transformer-based network is developed to learn the knowledge of the simulated data for diagnostics. Meanwhile, a selective adversarial strategy is introduced to achieve cross-domain feature alignments in scenarios where the health conditions of the measured data are unknown. To this end, this study proposes a digital twin-driven fault diagnosis framework by using labeled simulated data and unlabeled measured data. The experimental results show that the proposed method can obtain high diagnostic performance when the real-world data is unlabeled and has unknown health conditions, proving that the proposed method has significant benefits for the health management of critical rolling bearings. • A digital twin-driven intelligent diagnosis method is developed. • A high-fidelity digital twin model is built for the rolling bearing. • A partial domain adaptation algorithm is introduced for bearing condition assessment. • One test is conducted to validate the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

• Improved cyclic spectral covariance matrix (ICSCM) is presented for multi-sensor data fusion. • An efficient demodulation algorithm ICS is proposed to discriminative features from different rotating machinery fault types. • ICSCM fully preserve the interaction relationship between different sensors. • The merits of ICSCM are demonstrated by using two sets of experimental case. When an abnormal situation occurs in rotating machinery, fault feature information may be scattered on multiple sensors, and fault feature extraction through a single sensor is not enough for fault detection. Moreover, fault detection techniques based on vibration signals are commonly applied to monitor the health of rotating machinery. However, the installation of vibration sensor is inconvenient, which will greatly affect collected signal and thus influence detection effect. This paper proposes a novel method with improved cyclic spectral covariance matrix (ICSCM) and motor current signal analysis, which achieves multi-sensor data fusion for rotating machinery fault detection. Firstly, an improved cyclic spectral is proposed to process multi-sensor signals collected from rotating machinery, which adaptively acquires multi-sensor mode components. Subsequently, sample entropy of acquired mode components is utilized to construct the ICSCM, which can fully preserve the interaction relationship between different sensors. Finally, ICSCM is incorporated into extreme learning machine classifier to identify different fault types for rotating machinery. The merits of the proposed method are validated using two datasets. Analysis results demonstrate that the proposed method has achieved satisfactory results and more reliable diagnosis accuracy than other state-of-the-art algorithms in rotating machinery fault detection. [ABSTRACT FROM AUTHOR]

• Time-varying dynamic coefficients of journal bearing are estimated without the tachometers. • Instantaneous angular speed of the journal bearing-rotor system is extracted. • An iteration strategy based on the square-root cubature Kalman filter is formulated. Accurate estimation of time-varying dynamic coefficients (TVDCs) of the journal bearing is important for the dynamic characteristic analysis of rotating machinery. This paper proposes a novel estimation method to identify TVDCs of journal bearings without the tachometers. Firstly, a phase-based method is introduced to extract the instantaneous angular speed (IAS) from the shaft displacement. Secondly, an iteration strategy based on the square-root cubature Kalman filter (SRCKF) is developed to estimate the TVDCs in the time domain. The state-space model and the measured shaft displacements of the journal bearing-rotor system have been applied in the estimation process. The proposed method can estimate TVDCs of journal bearing under speed-variable conditions without a tachometer by combining the phase-based and SRCKF methods. Finally, the simulation and experiments studies are conducted to demonstrate the effectiveness of the proposed methods. The results show that the proposed method can efficiently estimate TVDCs of the journal bearing under speed-variable conditions and at varied measurement noise levels. [ABSTRACT FROM AUTHOR]

[Display omitted] • Mesh stiffness model of opening-crack tooth with elastoplastic deflection is built. • The model can accurately estimate the mesh stiffness of gears with crack failure. • Impacts of failure severity on the mesh stiffness and load sharing are analyzed. • Tooth deflection affects mesh stiffness, load sharing and meshing zone ratio. In the gear transmission system, tooth root crack often occurs due to the impact of machining technology and cyclic load. The appearance of tooth root cracks will affect its mesh stiffness and change the vibration characteristics of the system, thereby reducing system reliability and service life. In previous studies on the modeling of the mesh stiffness of cracked gears, the cracks were often supposed to be in a closed state, and the elastoplastic deflection of the fault gear teeth was also neglected, resulting in significant errors in the estimation of the mesh stiffness. When a tooth root crack occurs, the engaged gear teeth will deviate from the theoretical meshing position due to the elastoplastic deflection of the fault tooth. Therefore, an accurate mesh stiffness estimation model in view of the opening crack and elastoplastic deflection of the cracked tooth is put forward in this study. Firstly, the actual meshing position of the tooth pairs is derived considering the elastoplastic deformation in the crack opening state; Then, the improved potential energy method is adopted to calculate the mesh stiffness, and the finite element method (FEM) is applied to verify it. At last, the influence of failure severity and elastoplastic deflection degree on mesh stiffness and load sharing is analyzed. The results show that the severity of the crack failure and elastoplastic deflection has a significant impact on the mesh stiffness and load-bearing. This research can provide stiffness input for the study of fault dynamics of the gear transmission system. [ABSTRACT FROM AUTHOR]

• A NFE is proposed to quantify the fault information distribution in the SCoh. • A WCES from the SCoh with normalized weight is proposed as fault detector. • WCES can effectively extract fault information distributed in multiple bands. • WCES delivers superior bearing diagnostic performance than SES, EES and IES. Enhanced envelope spectrum (EES) and improved envelope spectrum (IES) generated from spectral coherence (SCoh) are proven to be more robust fault detection tools than squared envelope spectrum (SES). However, EES cannot effectively detect the fault-induced components under strong interference noise and IES can only capture the information of a fault-sensitive resonance spectral frequency band. To overcome these problems, weighted combined envelope spectrum (WCES) from SCoh is proposed as a novel fault detector. WCES integrates the fault components distributed in multiple resonance frequency bands using normalized feature energy and removes the envelope spectrum slices with less fault information to exclude disturbance noises. The performance of WCES is validated using simulations and experiments and compared with the advanced envelope spectra. The results demonstrate that WCES can effectively detect bearing faults under strong interference noise and multiple resonances compared with the SES, EES and IES, and has potential application value in bearing diagnostics. [ABSTRACT FROM AUTHOR]