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This paper offers a new perspective on the vibrations of discrete bearing faults by focusing on the micro-motion states of rolling elements in spall fault bearings and proposes an improved matching pursuit algorithm for quantitative diagnosis with a high accuracy of atom selection and calculation efficiency. The generation mechanism of the vibration response signal is explained by analyzing the micro-motion status when rolling elements passing through the spall. A concatenation dictionary composed of an impact dictionary as the higher level and step dictionary as the lower level is constructed based on the acceleration variation analysis of the rolling elements. The information output by the higher-level dictionary is used as the input information for the lower-level dictionary to extract the fault features. Only one iteration on the higher-level dictionary is necessary to extract the correct impact atoms, with all subsequent iterative steps assigned to the lower-level dictionary. The advantage is that the influence of high-energy impact components on the extraction of step atoms can be removed. Thereafter, the optimized algorithm based on the concatenation dictionary is applied to the analysis of simulation and experimental signals. The comparative analysis demonstrates that the effective quantitative diagnosis is obtained, while the diagnostic precision and calculation efficiency are improved.

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In array signal processing systems, the direction of arrival (DOA) and polarization of signals based on uniform linear or rectangular sensor arrays are generally obtained by rotational invariance techniques (ESPRIT). However, since the ESPRIT algorithm relies on the rotational invariant structure of the received data, it cannot be applied to electromagnetic vector sensor arrays (EVSAs) featuring uniform circular patterns. To overcome this limitation, a fourth-order cumulant-based ESPRIT algorithm is proposed in this paper, for joint estimation of DOA and polarization based on a uniform circular EVSA. The proposed algorithm utilizes the fourth-order cumulant to obtain a virtual extended array of a uniform circular EVSA, from which the pairs of rotation invariant sub-arrays are obtained. The ESPRIT algorithm and parameter pair matching are then utilized to estimate the DOA and polarization of the incident signals. The closed-form parameter estimation algorithm can effectively reduce the computational complexity of the joint estimation, which has been demonstrated by numerical simulations.