Low-speed rotating machines are extensively used in heavy industry. Among those, the planetary gearbox is a pivotal component with a high power–weight ratio and large loadbearing capacity, which inevitably fail due to the tough working conditions. The fault signature in such conditions is rather weak due to the complex planetary structure and the low rotating speed. Hence, the diagnosis of planetary gearbox problems in low-speed working conditions is considered as a bottleneck issue. In view of this, a rotary encoder signal, instead of conventional vibration, is initially applied to capture the fault-related information from the low-speed planetary gearbox. Then, a periodic group sparse-robust principal component analysis (PGS-RPCA) model with adaptive parameter programming, called adaptive PGS-RPCA (APGS-RPCA) is presented to extract the weak fault transient immersed in harmonic interferences and heavy noise. Finally, the effectiveness of the presented APGS-RPCA approach is verified via an experimental encoder signal at a very low input frequency. The diagnostic results show that the presented approach is superior to the conventional approach, and it may provide a promising solution for health monitoring of low-speed rotating machinery.

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Due to inaccurate period knowledge or incomplete information, there are limitations in extracting all potential complex faults of rolling bearings and enhancing weak faults. To address this problem, this article introduces a novel deconvolution method, named multi-period synchronous deconvolution (MPSD). In this method, decomposing matrix-matrix in solving the filter coefficients are used to replace designing objective function to avoid only obtaining the filter signal of the optimal objective function. Based on eliminating the effects of subspace noise, a novel evaluation index, called characteristic information ratio, is proposed to evaluate fault significance by fault information levels instead of energy. In addition, an informative subspace selection strategy is proposed to control the weighting coefficients of each subspace in reconstructed signal. Without the predetermined fault periods, the proposed MPSD can simultaneously extract latent multiple faults and enhance weak fault features. Finally, simulations and experimental cases substantiate the efficacy and eminence of MPSD.