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Inner product transform principle reveals that the basis functions most relevant or similar to the fault features are pivotal to the meaningful fault detection. Customized multiwavelet methods and practices have continued to improve over the recent years, focused on two-scale similarity transform (TST), lifting transform (LT), and lifting scheme (LS). Due to the respective advantages and disadvantages, a comparative study on the multiwavelet construction methods by TST, symmetric and dissymmetric LT, and LS is discussed in the paper, covering the differences of construction theories, the synthetic  analyses of construction strategies, and the comparison of waveform characteristics along with their applicable occasions. Comprehensively utilizing the capabilities of the construction methods, a novel customized multiwavelet library is established for the accurate fault detection. The proposed method is applied to incipient fault detection of rolling bearing for electric locomotive to verify the effectiveness and feasibility

A Comparative Study on Multiwavelet Construction Methods and Customized Multiwavelet Library for Mechanical Fault Detection