Adaptive sparsest narrow-band decomposition (ASNBD) method is proposed based on matching pursuit (MP) and empirical mode decomposition (EMD). ASNBD obtains the local narrow-band (LNB) components during the optimization process. Firstly, an optimal filter is designed. The parameter vector in the filter is obtained during optimization. The optimized objective function is a regulated singular local linear operator so that each obtained component is limited to be a LNB signal. Afterward, a component is generated by filtering the original signal with the optimized filter. Compared with MP, ASNBD is superior in both the physical meaning and the adaptivity. Drawbacks in EMD such as end effect and mode mixing are reduced in the proposed method because the application of interpolation function is not required. To achieve the fault diagnosis of roller bearings, raw signals are decomposed by ASNBD at first. Then, appropriate features of the decomposed results are chosen by applying distance evaluation technique (DET). Afterward, different faults are recognized by utilizing maximum margin classification based on flexible convex hulls (MMC-FCH). Comparisons between EMD and ASNBD show that the proposed method performs better in the antinoise performance, accuracy, orthogonality, and extracting the fault features of roller bearings.

Adaptive sparsest narrow-band decomposition is the most sparse solution to search for signals in the over-complete dictionary library containing intrinsic mode functions, which transform the signal decomposition into an optimization problem, but the calculation accuracy must be improved in the case of strong noise interference. Therefore, in combination with the algorithm of the complementary ensemble empirical mode decomposition, a new method of the complementary ensemble adaptive sparsest narrow-band decomposition is obtained. In the complementary ensemble adaptive sparsest narrow-band decomposition, the white noise opposite to the paired symbol is added to the target signal to reduce the reconstruction error and realize the adaptive decomposition of the signal in the process of optimizing the filter parameters. The analysis results of the simulation and experimental data show this method is superior to complementary ensemble empirical mode decomposition and adaptive sparsest narrow-band decomposition in inhibiting the mode confusion, endpoint effect, improving the component orthogonality and accuracy, and effectively identifying the gears fault types.