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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3.1. Overview of system orchestration The robustness of prognosis depends on both the logical connectivity between core modules and their timing in relation to the evolving damage state. Fig. 3 outlines the sequence of prognosis and diagnosis events along the fatigue crack growth process. The crack measurement system operates continuously throughout the experiment. During the nucleation stage, signals are noisy, and detection confidence is low due to the small crack size. Once a crack is reliably detected, the detected cycle count and crack length ( $%&%"%' , $%&%"&%' ) are used to constrain the prior distribution of the at =0 , assuming 0 ≤ ≤ $%&%"&%' . This provides a physically bounded initial condition . From detection onward, the data acquisition module streams measurements in real time so that the prognosis module always has the latest inputs. From detection up to Point I , once sufficient observations ( ()* , ()* ) are available, an initial deterministic calibration (non-Bayesian) is performed to improve the mean values of Paris’ law parameters. Such prior refinements reduce uncertainty and thus, computational cost in Bayesian inference, ensuring that prognosis can be computed within operational time limits. From Point II onward, the updated priors ( +,-., , +,-., , +,-., ) , together with ( ()* , ()* ) , feed into the Bayesian update stage for parameter inference and RUL prediction. Prognosis targets the critical crack length " , reached at Point III , where the DT system can be validated against observed failure data. 14

Crack Measurement Acquisition Real-time crack monitoring/measurement

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Crack Initiation Phase (High Uncertainty Zone) Period before measurable crack growth begins; Early-stage measurements with high noise or low confidence due to small crack size. Crack Detection Threshold Point at which the crack becomes reliably detectable and measurable. on early data ( ≤ ) Baseline Model Calibration Estimation of material/model parameters (e.g., Paris law constants) using early data. Bayesian Update of EIFS Applying non-sequential updates to EIFS based on collected data, continuing until the onset of non-linear behaviour. Prior Model Adjustment Bayesian or statistical update of initial assumptions based

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Crack Growth Prediction Forward simulation of crack growth using updated model.

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Model Validation Comparison of predicted crack growth.

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Fig. 3. Temporal coordination of diagnosis and prognosis modules in the DT framework, illustrated alongside the fatigue crack growth process. In Bayesian terms, the forward model generates a full crack growth trajectory(an − curve) starting from ! = at =0 up to " at # . The trajectory is probabilistically calibrated against the observed data ( ()* , ()* ) , between detection and – i.e. from ( $%&%"&%' , $%&%"&%' ) to ( // , // ) . Calibration minimises the misfit between prediction and observation, leading to: back-calculation of +.*&%,-., , updated material parameters ( +.*&%,-., , +.*&%,-., ) , and a reconciled crack growth trajectory including # prediction (i.e. +,%'-"&%' ). In this way, the method integrates both latent ( pre-detection ) and observed ( post-detection ) phases of crack evolution into a unified prognosis.