Prognosticating RULs while exploiting the future characteristics of operating profiles

Amit Kumar Jain*, Bhupesh Kumar Lad

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


We put forward a generic tool condition monitoring system capable of embracing the critical problem of prognosticating remaining useful life (RUL) under time-variant operating profiles witnessed in real-world production environments. First, we mathematically model the tool degradation progression via a new, adaptive, and hybrid stochastic degradation model, unifying (1) the real-time degradation signal characteristics from the sensor; (2) the rate of degradation characteristics from historical data; (3) the evolution of the future operating profile; (4) jerks owing to dynamic transitions. Next, for the account of reality, we formulated new mappings, i.e., degradation rate function, and jerk function. Successively, for the first time, we modeled the physics of the evolution of dynamic operating profiles for various scenarios. In the first scenario, the dynamic operating profile evolves in a deterministic way. Here, we approximate the evolution of future profiles as a piecewise constant function. Next, we embrace the accompanying scenario by aiding the future profile to be uncertain. This uncertainty in the evolution of the future profile is modeled via a discrete-time Markov chain. This is further extended to handle a more complex scenario where the prior understanding of the expected future profile is known. Though, the dynamic transitions of distinct profiles in the future are yet again subjected to uncertainty. We inventively capitalize on the total number of transitions in respective profiles and accordingly update the transition distribution. The updated distribution better characterizes the expected profile and eventually reduces the uncertainty. The resulting generalized system approximates the first passage time of the degradation process to a threshold and provides a precise life estimate in real-time. The system is extensively assessed via real-life vibration-based signals to substantiate the claim.
Original languageEnglish
Article number107031
JournalReliability Engineering and System Safety
Early online date19 May 2020
Publication statusPublished - Oct 2020


  • intelligent machining process
  • remaining useful life
  • sensor
  • tool condition monitoring


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