A Fractional-Derivative Multi-Kernel Adaptive Learning Approach for Remaining Useful Life Prediction of Rotating Machinery.

Robust Remaining Useful Life (RUL) forecasting is indispensable for condition-based maintenance in rotating machinery. Nevertheless, realizing high predictive precision constitutes an arduous endeavor, primarily complicated by the highly nonlinear and nonstationary nature of degradation processes. Existing prognostic approaches typically face critical bottlenecks: physical models require arduous parameter calibration, while data-driven deep learning methods suffer from "black-box" limitations and rely heavily on massive run-to-failure datasets. To overcome these challenges, this paper proposes a novel fractional-derivative multi-kernel adaptive learning approach for robust RUL prediction of rotating machinery. By integrating kernel adaptive learning with a multi-kernel mixture measure, the method provides a mathematically transparent "white-box" architecture that operates effectively in practical small-sample scenarios. Innovatively, the Hadamard fractional derivative is incorporated into the algorithm's weight-updating mechanism, mathematically encoding the "memory capacity" and "hereditary properties" of physical degradation to capture complex long-range temporal dependencies. Additionally, an adaptive 3σ confidence interval scheme featuring sequential delayed-triggering logic is designed for First Prediction Time (FPT) identification, effectively eliminating noise-induced false alarms. Extensive evaluations through multi-point sequential tracking on two practical datasets confirm that the proposed method surpasses established baselines. Notably, it achieves superior predictive accuracy and lower estimation errors while obtaining the lowest asymmetric penalty scores.