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Rotating machinery fault diagnosis is of key significance for ensuring safe and efficient operation of various industrial equipment. However, under nonstationary operating conditions, the fault–induced characteristic frequencies are often time–varying. Conventional Fourier spectrum analysis is not suitable for revealing time–varying details, and nonstationary fault feature extraction methods are still in desperate need. Order spectrum can reveal the rotational–speed–related time–varying frequency components as spectral peaks in order domain, thus facilitating fault feature extraction under time–varying speed conditions. However, the speed–unrelated frequency components are still nonstationary after angular–domain resampling, thus causing wide–band features and interferences in the order spectrum. To overcome such a drawback, this work proposes a rotating machinery fault diagnosis method based on adaptive separation of time–varying components and order feature extraction. Firstly, the rotational speed is estimated by the multi–order probabilistic approach (MOPA), thus eliminating the inconvenience of installing measurement equipment. Secondly, adaptive separation of the time–varying frequency component is achieved through time–varying filtering and surrogate test. It effectively eliminates interference from irrelevant components and noise. Finally, a high–resolution order spectrum is constructed based on the average amplitude envelope of each mono–component. It does not involve Fourier transform or angular–domain resampling, thus avoiding spectral leakage and resampling errors. By identifying the fault–related spectral peaks in the constructed order spectrum, accurate fault diagnosis can be achieved. The Rényi entropy values of the proposed order spectrum are significantly lower than those of the traditional order spectrum. This result verifies the effective energy concentration and high resolution of the proposed order spectrum. The results of both numerical simulation and lab experiments confirm the effectiveness of the proposed method in accurately presenting the time–varying frequency components for rotating machinery diagnosing faults. [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]