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The key of bearing fault feature extraction is to select the optimal resonant frequency band (ORFB) containing fault information with an appropriate index. However, the background noise and cyclostationary impulsive noise will seriously affect the location of ORFB. Moreover, traditional indexes may be ineffective for compound faults. Thus, a novel fault feature method for rolling bearings is explored to solve these problems. First, by evaluating the potential fault types with the designed relative local threshold, an adaptive harmonic kurtosis (AHK) is first proposed to locate the ORFB for an arbitrary fault or compound fault. Then, according to the index of AHK, an improved bat algorithm (IBA) is proposed to find the ORFB unlike fast kurtogram (FK). The proposed rolling bearing fault diagnosis method based on an adaptive harmonic kurtosis and IBA has been applied to two single faults and a compound fault. The comparative results indicate that the proposed method can more accurately extract the fault feature compared with the FK method, the method based on the ratio of cyclic content, discrete wavelet transform based on kurtosis, and ensemble empirical mode decomposition based on kurtosis. [ABSTRACT FROM AUTHOR]