PSI - Issue 80

Sadjad Naderi et al. / Procedia Structural Integrity 80 (2026) 77–92 Sadjad Naderi et al. / Structural Integrity Procedia 00 (2025) 000–000

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1. Introduction For digital twins (DTs), online monitoring and timely prediction of fatigue crack growth are critical to ensuring structural integrity, as cracks evolve irreversibly and can accelerate rapidly toward a critical threshold. Advances in sensing technologies have improved the ability to monitor crack progression in situ. However, the ability to detect damage alone is insufficient in scenarios where inspection or repair opportunities are constrained. For example, studies have shown that unmanned aerial vehicles in military and reconnaissance operations may operate for over 1,000 flight hours between depot-level maintenance cycles (Ray and Tangirala 2002), necessitating onboard systems capable of anticipating critical failures. In such settings, prognosis of Remaining Useful Life (RUL) becomes essential for maintaining operational safety and performance margins. The DT paradigm offers a pathway to this capability by integrating historical records, real-time sensor measurements, physics-based models, and machine learning methods to infer the evolving structural state. When properly calibrated and continuously updated, DTs can support predictive maintenance decisions and enable condition-based operation. Yet, their effectiveness ultimately hinges on the fidelity of their prognostic modules, which must contend with uncertainty from limited sensor coverage, measurement noise, material variability, and inherent limitations of physics-based models. Nomenclature crack length ( ) ! initial crack length/EIFS ( ) " critical crack length ! material constant in Paris’ law ∆ stress intensity factor range ( √ ) ∆ applied stress range ( ) stress intensity factor ( √ ) material exponent in Paris’ law Number of cycles # final number of cycles at failure (·) probability distribution ( | ) likelihood of data given parameters ( | ) prior distribution of parameters given hyperparameters ( ) hyperprior distribution ( | ) posterior distribution of parameters given data Σ covariance matrix of parameters standard deviation of parameter distribution mean of parameter distribution model parameter vector ₜ system state at time (parameters, covariances, hyperparameters) ₜ adaptive weight controlling information retention vs. adaptation geometry correction factor A well-formed DT in Structural Health Management (SHM) must go beyond passive condition monitoring to support proactive life prediction and adaptive operational control. In a modern twin system, this functionality rests on four foundational pillars: (i) data acquisition, which captures the in-service behaviour of the structure through distributed sensing systems; (ii) damage diagnosis, which interprets the incoming data to detect, localise, and classify structural anomalies; (iii) damage prognosis, which forecasts the future evolution of degradation under expected operational/environmental loading; and (iv) mission optimisation, which adapts control strategies or planning decisions to minimise damage accumulation and extend operational life. Importantly, a DT must support bidirectional and real-time interaction between the physical and digital realms. Sensor measurements (raw data) must be continuously transformed into higher levels of understanding – from raw signals to actionable information, up-to-date