Sparsity-assisted signal decomposition via nonseparable and nonconvex penalty for bearing fault diagnosis

Monitoring vibration signals from a fault rotatory bearing is a commonly used technique for bearing fault diagnosis. Owing to harsh working conditions, observed signals are generally contaminated by strong background noise, which is a great challenge in extracting fault bearing signal. Sparsity-assisted signal decomposition offers an effective solution by transforming measured signals into sparse coefficients within specified domains, and reconstructing fault signals by multiplying these coefficients and overcomplete dictionaries representing the abovementioned domains. During the process, observed vibration signals tend to be decomposed, and fault components are extracted while noise is diminished. In this paper, a nonseparable and nonconvex log (NSNCL) penalty is proposed as a regularizer for sparse-decomposition model in bearing fault diagnosis. A convexity guarantee to the sparse model is presented, so globally optimal solutions can be calculated. During the process, tunable Q-factor wavelet transform with easily setting parameters, is applie din signifying multi-objective signals with a sparse manner. Numerical examples demonstrate advantages of the proposed method over other competitors.