PSI - Issue 75

Mohamed El Yazrhi et al. / Procedia Structural Integrity 75 (2025) 262–275 Mohamed El Yazrhi , Jean-Yves Disson / Structural Integrity Procedia (2025)

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4. RUL Prognostics Framework In this study, we do not directly measure a time ‐ to ‐ failure but rather compute a “ virtual ” damage index — the cumulative Fatigue Damage Spectrum (FDS) — and predict RUL from its proximity to the qualification FDS level. Specifically: • We quantify fatigue damage using the FDS, either over narrow frequency bands [F] around known critical resonances of the equipment or, when none are pre ‐ identified, across the full operational bandwidth. • At each moment, we form the ratio for each frequency j R j (t) = FDS cjummulative (t) FDS tjhreshold , Where t h reshold is the spectrum level used during qualification testing for frequency j • Under the assumption that damage scales linearly with time (i.e.\ R ~ T/T lim ), the equipment remains within its qualified envelope as long as R (t)< 1 , ∀ ∈[ ] . • Projecting forward, we solve for the duration ∆T (sometimes denoted ) at which max j (R j (t)) would reach unity. In practice, although we describe this as a residual life estimate, our computations really produce a forecasted “virtual” damage value, which is then mapped to a notional RUL by identifying when that forecasted damage would equal the qualification SDF. In this context a wide range of analytical, statistical, and simulation-based techniques have been explored in the literature, each relying on different assumptions about how mechanical damage accumulates over time. As part of this work, we conducted an in-depth investigation of these existing approaches and selected three representative methods that offer a balance between accuracy, computational efficiency, and ease of implementation. These methods were not chosen arbitrarily — they reflect distinct paradigms of prediction: deterministic scaling, probabilistic modelling, and statistical inference based on confidence levels. We implemented all three approaches and carried out a comparative study to evaluate their suitability for integration into NOMAD, our embedded real-time monitoring system. This comparison focused not only on their theoretical robustness, but also on their practical feasibility for deployment in resource-constrained embedded environments. The following subsections present these methods in detail, from the simplest proportional extrapolation to more sophisticated probabilistic strategies. This comparative study aims to determine which method is best suited for integration into the NOMAD system, with the goal of enabling reliable and real-time RUL prediction in embedded applications. 4.1. Linear Extrapolation Method The most straightforward approach to RUL prediction is a proportional damage extrapolation method. It assumes that for a given usage condition the fatigue damage accumulates at a relatively constant rate over time. In essence, it performs a linear extrapolation of the observed (or monitored) damage to estimate when the component will reach the qualification level. Formally for the oscillator j related to frequency j, let be the cumulated FDS during the monitored period composed with N blocks and be the damage to be predicted. We have: ( ) = ∑ ( ) =1 ( ) = ∑ ( ) +1+ = +1 Using this method the predicted damage is ̂ ( ) = ( ) + × ( ) ℎ ℎ