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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1. Introduction Mechanical fatigue — progressive structural degradation under cyclic loading — remains a primary driver of in service failures across transportation, defense, energy, and consumer-electronics industries [3]. In roadway vehicles, rail cars, and aircraft, for instance, components endure complex vibration spectra punctuated by shocks whose cumulative effect may silently approach critical damage thresholds long before cracks become visible. Economically, fatigue-related downtime and unscheduled maintenance can account for upwards of 15 – 25 % of operational costs in heavy industry, not to mention the safety risks of catastrophic failure [4]. Historically, fatigue assessment has relied on off-line laboratory qualification tests using generic power-spectral density (PSD) or shock-response – spectrum profiles. While such tests provide reproducible conditions, they frequently misrepresent true field environments. Conservative spectra may lead to over-engineered designs and inflated test durations, whereas insufficiently severe tests can allow undetected damage accumulation and premature field failures [5]. The fundamental disconnect stems from two factors: (1) real-world loading is often non-stationary, non-Gaussian, and contains rare extreme events; and (2) time-domain fatigue metrics — like cycle counting and damage summation — cannot be fully captured by stationary spectral methods. Recent progress in micro-electro-mechanical (MEMS) sensing, low-power microcontrollers, and wireless communications has created an opportunity to overcome these limitations via real-time, in-situ fatigue monitoring. Compact modules integrating multi-axis accelerometers and edge computing can be permanently affixed to critical assets, continuously recording acceleration time histories and executing fatigue-damage algorithms on the fly. By filtering raw data through banks of single-degree-of-freedom (SDOF) models and applying rainflow cycle counting coupled with Miner’s rule, these embedded systems can quantify both instantaneous damage rates and cumulative fatigue consumption without data offload or manual post-processing [6]. Yet several technical challenges remain. Edge implementations must handle variable sampling rates, ensure numerical stability in convolution filters, and accommodate non-Gaussian load statistics — particularly when damaging shock events occur. Moreover, translating measured displacements into material stress requires careful calibration of modal constants and consistent treatment of damping. Finally, for applications spanning months or years of operation, damage extrapolation methods must account for mission length and acceptable risk levels, avoiding both undue conservatism and underestimated hazard. To address these needs, risk-based time-domain standards such as AFNOR XP X50-144 [9] have introduced extensions — XRS (eXtreme Response Spectrum) and XFS (eXtended Fatigue Spectrum) — that apply statistical extrapolation (e.g., Gumbel extreme-value theory and central-limit approximations) to extreme responses and damage accumulations, respectively. These spectra enable both (a) the design of tailored laboratory tests that replicate field fatigue damage profiles and shocks at specified confidence levels, and (b) real-time health tracking where running damage is compared against risk-adjusted thresholds to trigger maintenance before risk of failure. In this paper, we present NOMAD, an embedded and autonomous system for real-time vibration monitoring and fatigue analysis of dynamic structures. Our contributions include: • A continuous, on-board computation of key damage indicators (FDS and SRE) directly from raw acceleration time histories, eliminating the need for lengthy data offload and offline processing; • A classification framework that identifies distinct operating usages conditions, then extrapolates cumulative damage over a target mission to deliver reliable remaining useful life (RUL) estimates; • The implementation and comparison of predictive algorithms — including Monte Carlo simulation and a Central Limit Theorem – based method — validated on real-world accelerometer data from a highway vehicle setup. The remainder of the paper is organized as follows. Section 2 presents the theoretical background and mathematical foundations; Section 3 outlines the hardware and software architecture of the NOMAD platform; Section 4 details the damage-extrapolation and remaining useful life (RUL) prediction methodologies; Section 5 presents experimental validation results under realistic driving conditions; and Section 6 discusses practical applications, limitations, and directions for future work.