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 11 The Paris’ law constant maintains logarithmic-scale stability with final values of 5.02×10⁻¹⁰ (Scheme I), 5.00×10⁻¹⁰ (Scheme II), and 5.05×10⁻¹⁰ (Scheme III). The exponent exhibits stability across all schemes, converging to 2.800±0.0001 with coefficient of variation below 0.1%. Minimal deviations from initial posterior distributions demonstrate preservation of material property knowledge from offline calibration while indicating that online measurements provide limited incremental information for this parameter under the current experimental configuration. Parameter uncertainty patterns reveal distinct behaviours: Paris’ law parameters maintain consistent uncertainty levels throughout sequential learning, reflecting their material-intrinsic nature and limited sensitivity to individual measurement variations. 4.2. Predicted capabilities Fig. 6 presents the crack growth trajectories with their associated uncertainty bounds, shown at several update stages (from 5 to 21 data points) for all three schemes. The confidence intervals consistently narrow as predictions approach the critical crack length of 15 mm, reflecting the asymptotic convergence behaviour near failure. Scheme I exhibits the most aggressive initial trajectory predictions with the widest uncertainty bounds due to its exclusive reliance on online data and strong weighting toward recent observations. The predicted mean fatigue life # converges toward 137k cycles after 12 iterations, with 90% credible intervals narrowing from ±2.4% of the mean prediction at iteration 5 (5 data points) to ±1.6% by iteration 22. The rapid convergence reflects the scheme’s responsiveness to incoming data but sacrifices early prediction stability. Scheme II produces more conservative trajectory predictions with narrower uncertainty bounds in early stages due to its fusion of offline and online data sources, which stabilises initial predictions. However, the conditional-progressive fusion strategy results in final mean cycle predictions of 129k cycles, ~6% lower than Scheme I. The 90% credible intervals remain wider at the final iteration (±2.1%), reflecting preserved uncertainty associated with incorporating historical data trends. This behaviour demonstrates the inherent trade-off between prediction confidence and information retention in conditional progressive fusion approaches. Scheme III reveals intermediate characteristics, transitioning rapidly from offline based predictions to online-dominated updates within the first 8 iterations, followed by targeted adaptation as data accumulates. Final predictions align closely with Scheme I at 136k cycles while retaining stabilising influence from the initial offline dataset. The credible intervals show faster convergence than Scheme II (±1.7% at final iteration) while maintaining better early-stage stability than Scheme I.

87