Weak Fault Detection for Gearboxes Using Majorization–Minimization and Asymmetric Convex Penalty Regularization

Abstract

It is a primary challenge in the fault diagnosis community of the gearbox to extract the weak fault features under heavy background noise and nonstationary conditions. For this purpose, a novel weak fault detection approach based on majorization-minimization (MM) and asymmetric convex penalty regularization (ACPR) is proposed in this paper. The proposed objective cost function (OCF) consisting of a signal-fidelity term, and two parameterized penalty terms (i.e., one is an asymmetric nonconvex penalty regularization term, and another is a symmetric nonconvex penalty regularization term).To begin with, the asymmetric and symmetric penalty functions are established on the basis of an L1-norm model, then, according to the splitting idea, the majorizer of the symmetric function and the majorizer of the asymmetric function are respectively calculated via the MM algorithm. Finally, the MM is reintroduced to solve the proposed OCF. As examples, the effectiveness and reliability of the proposed method is verified through simulated data and gearbox experimental real data. Meanwhile, a comparison with the state of-the-art methods is illustrated, including nonconvex penalty regularization (NCPR) and L1-norm fused lasso optimization (LFLO) techniques, the results indicate that the gear chipping characteristic frequency 13.22 Hz and its harmonic (2f, 3f, 4f and 5f) can be identified clearly, which highlights the superiority of the proposed approach.

Weak Fault Detection of Tapered Rolling Bearing Based on Penalty Regularization Approach

“…The source of the problem lies in the establishment of penalty functions, because the symmetric and asymmetric penalty functions are contained and developed for the ACPR method, and as the establishment of the asymmetric function is random, those penalty functions may not be appropriate for such data. In previous research [35], another non-convex penalty regularization approach, namely the asymmetric convex penalty regularization (ACPR) method, was proposed for weak fault detection for gearboxes. To explore the advantage of the proposed approach over the ACPR method, the diagnosis results under same operation environments are compared, the ACPR method is introduced to process the same data that collected from the right side and left side of the input shaft, respectively, and the rules of parameter settings are based on the reference [35].…”

“…In previous research [35], another non-convex penalty regularization approach, namely the asymmetric convex penalty regularization (ACPR) method, was proposed for weak fault detection for gearboxes. To explore the advantage of the proposed approach over the ACPR method, the diagnosis results under same operation environments are compared, the ACPR method is introduced to process the same data that collected from the right side and left side of the input shaft, respectively, and the rules of parameter settings are based on the reference [35]. The sparse component of right-side of input shaft generated by the ACPR method is shown in Figure 14a, and its envelop spectrum is shown in Figure 14b.…”

Gearbox Incipient Fault Detection Based on Deep Recursive Dynamic Principal Component Analysis

“…Therefore, it is of great significance to identify the weak fault features at an incipient stage before the fault develops to a serious degree. Incipient fault detection is important to ensure the normal operation of equipment and avoid economic losses [6]- [8].…”

Fault Detection for Complex System under Multi-Operation Conditions Based on Correlation Analysis and Improved Similarity

“…The second problem is the fault detection method. At present, there are many works of literature about fault detection methods [10][11][12]. Among these, a majority are based on similarity.…”