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• 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]

• 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]