Transient extraction based on minimax concave regularized sparse representation for gear fault diagnosis

Abstract Extraction of fault-induced transients is one of the difficulties in gear fault diagnosis as the vibration signal is composed of multiple components. Sparse representation is one of the effective methods for extracting transients from such noisy and multicomponent vibration signals. However, conventional sparse representation approaches have the problems of amplitude underestimation, computational inefficiency and mono-component orientation. To address such problems, this paper first proposes to use minimax concave penalty function to construct the objective function as the minimax concave penalty function outperforms other penalty functions in preserving high-amplitude components based on the comparisons among different non-convex penalty functions. Then, the multiple over-complete dictionaries are established based on Fourier bases, where every two elements of each dictionary form a tight frame, enabling to simplify calculation and avoid computing high-dimensional inverse matrix when performing iterative optimization. Since multiple dictionaries are constructed, the multi-components of gear vibration signal can be extracted, respectively. With the constructed dictionaries, the sparse representation coefficients can be calculated using split augmented Lagrangian shrinkage algorithm and the repetitive transients can then be extracted. The simulation study and experimental analysis show that the fault transients and harmonic components can be accurately as well as computational-effectively extracted without underestimation of high amplitude components. Comparison results between minimax concave, arctan and L1 norm also prove the superior high-amplitude preserving ability of the proposed method.