The performance of convolution sparse representation (CSR) in extracting impulses is sensitive to its improper penalty parameters. A novel fault detection method which is based on the combination of CSR, Hilbert transform (HT) and manifold learning is proposed. The impulses with different sparse characteristics are extracted by CSR at different penalty parameters. The impulse-envelope space is constructed with the Hilbert transform on the extracted impulses. The manifold based on Isomap is executed to learn the low-dimensionality intrinsic envelope of vibration signals for fault detection. The capability of the proposed fault detection method is verified by fault simulations as well as controlled experimental tests. The results show that the proposed fault detection method based on CSR-HT-Isomap can extract the fault characteristics of the inner and rolling fault. The method is also compared with two other envelope spaces spanned by the Hilbert transform on ensemble empirical mode decomposition and wavelet packet transform, respectively. The comparison shows that the CSR-Hilbert Transform-Isomap method is superior in extracting the intrinsic envelope, strengthening the amplitude of intrinsic envelope spectra and enlarging the harmonic number of fault-characteristic frequency.