Adaptive sparsest narrow-band decomposition method and its applications to rotor fault diagnosis

• A signal decomposition method for analyzing non-stationary signals is proposed.
• The method is inspired by matching pursuit and empirical mode decomposition.
• Signal is decomposed into narrow-band signals when applying the proposed method.
• The method is applied to analyze a vibration signal of rotor with fault.

Enlightened by empirical mode decomposition (EMD) and matching pursuit (MP), adaptive sparsest narrow-band decomposition (ASNBD) method is proposed in this paper. The main idea of the method is to obtain the sparsest representation of a signal by constraining the components to be local narrow-band signals. In ASNBD, an optimized filter must be established at first. The parameters of the filter are determined by solving a nonlinear optimization problem. A regulated differential operator is used as the objective function so that each component is constrained to be a local narrow-band signal. Afterwards, the signal is filtered by the optimized filter to generate a single component. ASNBD is superior to matching pursuit in both the adaptivity and the physical meaning of the components. And problems such as mode mixing and end effect in EMD are alleviated in ASNBD as the computing of extremas is avoided. As it is robust and adaptive to non-stationary signals, artificial chemical reaction optimization algorithm (ACROA) is chosen to solve the optimization problems in ASNBD. Compared with GA, ACROA can reach a global optimum in a shorter time while the classification result is the same. Comparisons are made between ASNBD optimized by ACROA, ASNBD optimized by genetic algorithm and empirical mode decomposition (EMD) by analyzing simulation and experimental signals. The results indicate that ASNBD–ACROA is superior to the other two methods at least in restraining boundary effect, gaining more accurate components in the presence of noise and showing better orthogonality; moreover, it performs better in the analysis of experimental data.