A New Fractional-Order Augmented Quaternion-Valued Approach for Degradation Prognostics of Bearings Using Generalized Hamilton-Real Calculus
Qing Li, Zhida Ren
Abstract
Accurate prediction of bearings degradation trajectories with multi-channel or multi-dimensional data is critical for collaborative prognostics and health management (PHM) of rotating machines to guarantee the safety and reliability of operation, thereby reducing maintenance costs. In this paper, a new fractional-order augmented quaternion-valued approach named augmented quaternion-valued least mean p-power (AQLMP) for degradation prognostics of rolling bearings based on multi-channel run-to-failure signals is proposed under the framework of hypercomplex data, for the first time. The augmented fractional-order order quaternion statistics and smoothing logarithmic penalty (SLP) term are designed elaborately to capture complete fractional-order statistical information of hypercomplex data and time-variant model uncertainty in widely linear quaternion-domain. Meanwhile, the generalized Hamilton-real calculus (GHRC) is employed for solving the weight update problem of the proposed AQLMP algorithm. The effectiveness and availability of the proposed approach are validated using two run-to-failure datasets of rolling bearings, and promising prognostics performance is achieved when compared with recently state-of-the-art benchmarks.