A New Fractional-Order Augmented Quaternion-Valued Approach for Degradation Prognostics of Bearings Using Generalized Hamilton-Real Calculus

Accurate prediction of bearings degradation trajectories with multichannel or multidimensional 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 article, 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 multichannel 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 recent state-of-the-art benchmarks.