Due to the special working environments of axial piston pumps in engineering, fault features are disrupted by the natural periodic impulses. A finite element method (FEM) simulation-driven bandpass filter (BPF) is provided for detecting bearings. However, the bandwidth of the bandpass filter is designed empirically through human experience with uncertainty. To overcome the associated limitations, an bandwidth optimization strategy of FEM simulation-driven BPF is proposed by using an integrated kurtosis, i.e.,the combination of two kinds of kurtosis indices. The new index is used as a discrimination value for a success-failure algorithm to iteratively determine the optimal bandwidth of the BPF. Finally, compared to the original BPF and its improved version, experimental results of faulty bearings in an axial piston pump verify the fault feature extraction ability for the reciprocating motion machine under heavy impact-induced natural periodic impulses.