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For rotary machines, the measured vibration signals contain multiple frequency modulation components with much machine health information. Decomposing vibration signals of rotary machines into a series of sub-signal components with physical meaning is of great significance for a deep understanding of the machine properties in solving fault diagnosis problems. However, accurately detecting and decomposing frequency modulation components is a challenging problem. This article proposed a multiple frequency modulation components detection and decomposition approach for rotary machine fault diagnosis. Specifically, the amplitude and concentration at the orders (defined as multiple of the rotating frequency) of each signal to be analyzed are calculated, and thresholds are set to distinguish noise and non-noise signal components. Then the cross correlation between the non-noise signal components and an order ruler (constructed with normalized amplitude only on the orders of characteristic components of the faulty signal) is calculated to obtain the instantaneous frequencies (IFs) of these signal components. Finally, a variational algorithm framework defined only by the characteristic components of the faulty signal is used to achieve signal decomposition. The proposed method fully uses the inherent geometric relationship of the frequency modulation signal in the angular domain and is robust to strong environmental noise. Both the simulation example and the actual application cases demonstrated the effectiveness of the proposed method, which shows the potential in solving real industrial problems. [ABSTRACT FROM AUTHOR]

• A MWI approach is proposed for ill-conditioned inverse problem in dynamics. • The unbiasedness and convergence of the proposed MWI method are proved. • MWI is superior to TSVD and Tikhonov regularization in application cases. • MWI has high accuracy and anti-noise property. Many problems in dynamics can be formulated as inverse problems that require the determination of the unknown input from the known output. Limited by the measurement noise, the computational cost, the error in numerical computation, etc., solving ill-conditioned inverse problems in dynamics is a big challenge. In this paper, we propose Maximumly Weighted Iteration (MWI) approach to solve ill-conditioned inverse problems in dynamics generally. The ill-condition of the system coefficient matrix is controlled by iterative weighted decomposition and a weighted term, also avoiding matrix inversion of solving and reconstruction process. As an iterative method, MWI has been theoretically proven to have consistency, absolute convergence, and conditional unbiasedness. The numerical results demonstrate that MWI is superior to Truncated Singular Value Decomposition and Tikhonov regularization in terms of accuracy and anti-noise property. Two application cases are used to demonstrate the potential of MWI in engineering practice. The first is elastic vibrations identification combined with randomized resonant metamaterials, and the second is fault diagnosis of mechanical transmission systems. [Display omitted] [ABSTRACT FROM AUTHOR]

• Gearbox fault diagnosis using BFNCC is proposed for nonstationary condition. • The method can remove the effect of the structure transfer paths. • The proposed method is robust to the location of measuring points. • Method shows potential for a machinery with complicated structure transfer paths. The main challenges in gearbox condition monitoring and fault diagnosis are the heavy noises caused by harsh operating environments and the complicated nonstationary condition during the runtime. It is extremely difficult and even impossible to obtain sensitive fault characteristics through direct measurements. Thus, it is of great significance of fault characteristic inversion based on the structure vibration transfer paths for complicated mechanical systems fault diagnosis. This paper proposes a gearbox fault diagnosis method under nonstationary condition through using nonlinear chirp components extracted from bearing force (BFNCC). In the proposed method, the bearing dynamic forces are first identified based on the vibration transfer function matrix, and the intrinsic signal components are then decomposed through a nonlinear chirp mode decomposition method. The proposed method improved the quality of vibration signals by removing the effect of the structure vibration transfer paths. In comparison with order tracking, the BFNCC is capable of clearly reflecting the magnitude increase phenomenon under gear fault condition. Numerical simulation and experimental studies show that the proposed method is effective for gear fault diagnosis under nonstationary condition. The proposed method is demonstrated to be superior to the existing approaches and robust to the location of measuring points, and thus shows potential in machinery fault diagnosis under the interference of complicated structure transfer paths. [ABSTRACT FROM AUTHOR]

• A gearbox fault diagnosis method based on bearing force identification is proposed. • Identified bearing dynamic forces outperform vibration signals for fault diagnosis. • The proposed method avoids the dependence on the layout of measuring points. • The method can theoretically be combined with the feature extraction algorithms. In the area of gearbox fault diagnosis, to obtain sufficient and effective vibration information, traditional studies are usually conducted from the perspective of optimizing the layout of measuring points. This paper focuses on a gearbox fault diagnosis method based on bearing dynamic force identification. Gearbox bearing dynamic forces under the operating condition are modeled as excitation sources, and vibration signals measured at any position on the housing are modeled as receivers. Then mutual coupling effect of different structure transfer paths of housing on the excitation signals can be quantitatively modeled. The bearing dynamic forces are finally constructed with the transfer function matrix and vibration signals by solving the inverse problem. The identified bearing dynamic forces is capable of clearly reflecting the gear fault characteristics, which outperforms the original vibration signals measured on the gearbox housing due to poor signal quality and the effect of structure transfer paths. Numerical simulation and experimental studies show the effectiveness of the estimated bearing dynamic force signals for gear fault diagnosis. The proposed method is demonstrated to be insensitive to the location of measuring points, and shows a good potential in complicated mechanical system fault diagnosis. [ABSTRACT FROM AUTHOR]

• A mediator algorithm between simulation and experiment is proposed to identify the error excitation. • The proposed identification algorithm provides an indirect approach to estimate the error excitation of gears. • The pre-decomposition technique is proposed to accelerate the solution of the simulation dynamic model. • The proposed identification algorithm is robust to noise, damping and phase differences. • The performance of the proposed identification algorithm is verified by both simulation and experiment. There are three primary sources of internal excitation in gear systems: time-varying mesh stiffness, meshing damping and tooth error. Compared with the first two excitations, it is more difficult to evaluate or measure the error excitation. The error excitation is usually assumed empirically or even neglected in the majority of dynamic models. To address this issue, we desired to propose a mediator algorithm between the simulation and the experiment to identify the error excitation of gear systems. Based on the second-order cyclostationarity of gear signals, a signal processing procedure is proposed to acquire the mediator signal with a high signal-to-noise ratio. The mediator signal is served as the "media" between the simulation and experiment. The error parameter is updated repeatedly in the iterative optimization until the optimal matching is found between the simulation and the experiment. Simultaneously, the pre-decomposition technique is proposed to accelerate the solution of the simulation dynamic model. The performance of the proposed identification algorithm is verified both numerically and experimentally. Moreover, noise immunity analysis shows that the proposed identification algorithm is robust to noise, damping and phase differences between the experiment and simulation. The proposed identification algorithm provides an indirect approach to estimating the error excitation when the direct measurement is unavailable. [ABSTRACT FROM AUTHOR]

• An in-situ transfer path analysis method is proposed to avoid physical decoupling ;. • A virtual decoupling method is applied to estimate the decoupled frequency response function;. • The effectiveness of the proposed method is verified both numerically and experimentally ;. • The proposed method is capable of tracing the fault location by determining the dominant transfer path;. • A physically-interpretable signal decomposition method is proposed to enhance the fault feature. A transfer path analysis method based on the in-situ measurement is proposed for the fault tracing of parallel axis gear systems. A virtual decoupling technique is used to achieve the in-situ measurement of the decoupled frequency response function (FRF) between bearing positions and measuring points on housing, avoiding the tedious test procedure and non-representative assembly conditions caused by the physical decoupling. Based on the decoupled FRF and the responses of the gearbox housing, the bearing force is identified using the Tikhonov regularization theory. Then the frequency-dependent path contribution, which will be used to perform the transfer path analysis, is obtained by multiplying the decoupled FRF and the bearing force. Finally, the fault-specific path rank order is determined using the path contribution within the resonant frequency band. This band is located by the spectral kurtosis algorithm. Based on the proposed in-situ path analysis, fault tracing is conducted by determining the dominant transfer path. The effectiveness of the proposed path analysis method is verified both numerically and experimentally. A two-stage parallel axis gear test rig with localized defects is utilized to demonstrate the efficacy of the proposed fault tracing strategy. Moreover, based on the path analysis, a physically-interpretable signal decomposition method is proposed to enhance the fault feature. Through this decomposition method, the fault indicator of the weakest fault type (chipped tooth) can be magnified by 204%. The proposed transfer path analysis method provides a feasible strategy for fault tracing, feature enhancement and incipient fault diagnosis of parallel axis gear systems. [Display omitted] [ABSTRACT FROM AUTHOR]

• The proposed unsupervised method merges anomaly detection and fault tracing. • Signal decomposition-based energy features are extracted to make the diagnosis more robust. • The model training process only requires normal data. • The diagnostic process can be performed without labeled fault samples. The absence of detailed fault data presents a significant challenge in diagnosing faults of rotating machinery. This paper focuses on addressing abnormal detection and fault localization challenges in drivetrain components under the assumption that only normal data is available. Specifically, this paper proposes an unsupervised hypersphere description (UHD) framework by seamlessly integrating abnormal detection and localization. By constructing a one-class description hypersphere, this UHD method achieves fault detection without special fault samples. Abnormal samples can be detected based on their distance from the center of hypersphere, enabling accurate localization of the underlying abnormality. Validation of experimental data demonstrates that the UHD approach effectively detects anomalies and accurately localizes faults within specific locations. Remarkably, the UHD approach surpasses several mainstream unsupervised methods in terms of fault tracing accuracy. This shows the potential of the UHD approach in abnormal detection and localization in a drivetrain, particularly when only normal data is available. [ABSTRACT FROM AUTHOR]