Publish articles presenting new and important events in all areas of mathematics

Publish articles presenting new and important events in all areas of mathematics

Prognostic health management of rolling element bearings requires feature representations that reliably track degradation while remaining tractable for real-time deployment. This paper investigates whether uniform time-delay embedding can serve as a near-optimal substitute for computationally expensive non-uniform embedding in recurrence-based vibration analysis. We show empirically that optimally chosen uniform delay vectors yield phase-space reconstructions of bearing vibration signals not significantly inferior to those produced by globally optimized non-uniform delay vectors, compressing the parameter search from a combinatorial optimization to a single scalar selection. Building on this near-optimality result, we construct color recurrence plots from uniformly embedded phase spaces and apply them to remaining useful life (RUL) prediction on the Intelligent Maintenance Systems (IMS) bearing dataset. We further demonstrate that standard binary recurrence plots are poorly suited for RUL estimation: their dense and erratically varying local patterns obscure the degradation trends required for reliable prognostics. Color recurrence plots, by contrast, suppress these local instabilities by averaging recurrence structures across multiple phase-space projections, exposing a globally evolving intensity that tracks bearing health throughout its degradation trajectory. This work establishes uniform delay embedding combined with color recurrence representation as an efficient, principled, and practically deployable approach to recurrence-based condition monitoring in industrial predictive maintenance.