The data-driven methods extract the feature information from data to build system models, which enable estimation and identification of the systems and can be utilized for prognosis and health management (PHM). However, most data-driven models are still black-box models that cannot be interpreted. In this study, we use the neural ordinary differential equations (ODEs), especially the inherent computational relationships of a system added to the loss function calculation, to approximate the governing equations. In addition, a new strategy for identifying the local parameters of the system is investigated, which can be utilized for system parameter identification and damage detection. The numerical and experimental examples presented in the paper demonstrate that the strategy has high accuracy and good local parameter identification. Moreover, the proposed method has the advantage of being interpretable. It can directly approximate the underlying governing dynamics and be a worthwhile strategy for system identification and PHM.

Blind deconvolution (BD) has proven to be an effective approach to detecting repetitive transients caused by bearing faults. However, BD suffers from instability issues including excessive sensitivity of kurtosis-guided BD methods to the single impulse and high computational time cost of the eigenvector algorithm-aided BD methods. To address these critical issues, this paper proposed a novel BD method maximizing negative entropy (NE), shortened as maximum negative entropy deconvolution (MNED). MNED utilizes NE instead of kurtosis as the optimization metric and optimizes the filter coefficients through the objective function method. The effectiveness of MNED in enhancing repetitive transients is illustrated through a simulation case and two experimental cases. A quantitative comparison with three existing BD methods demonstrates the advantages of MNED in fault detection and computational efficiency. In addition, the performance of the four methods under different filter lengths and external shocks is compared. MNED exhibits lower sensitivity to random impulse noise than the kurtosis-guided BD methods and higher computational efficiency than the BD methods based on the eigenvalue algorithm. The simulation and experimental results demonstrate that MNED is a robust and cost-effective method for bearing fault diagnosis and condition monitoring.

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