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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unreliable, while retaining prior information through convex combination. Robustness to outliers is ensured by requiring alignment of multiple reliability criteria before large updates are allowed. Computational overhead remains small because the procedure depends only on summary statistics and sampler diagnostics rather than full re-estimation

of expensive forward models. 3.3.4. Data fusion strategies

The framework considers two approaches for integrating offline historical datasets with streaming online measurements. The first is a conditional–progressive fusion scheme , in which the system begins with an offline bootstrap phase using A<),-' (0)= .##;-B% and then, for > 0 , the dataset expands as: A<),-' ( ) = .##;-B% ⋃ .B;-B% (1: ) (7) thus, retaining the full historical record while incrementally adding new measurements. Preprocessing includes duplicate elimination to avoid redundancy, ordering by crack length to reflect damage progression, and source-aware weighting to account for differences between offline and online data. The sequential replacement strategy uses the same bootstrap initialisation but subsequently replaces the offline dataset with online measurements, such that after the transition: A<),-' ( ) = .B;-B% (1: ) (8) The approach reduces computational cost by maintaining a bounded dataset size and emphasises recent observations when they are more representative of the current system state. Progressive fusion maximises total mutual information, whereas sequential replacement prioritises conditional information from the most recent data. Their comparative implications are examined in the results and discussion. 4. Results and Discussion The validation uses fatigue testing datasets to assess the adaptive Bayesian framework under different data integration schemes. The offline dataset comprises four historical fatigue records, while the online/observed dataset features real-time sensor inputs. Each dataset includes ~20 observations of cycle counts and corresponding crack lengths. Three schemes are tested. Scheme I updates parameters sequentially using only the online dataset. Scheme II applies the conditional–progressive fusion approach, combining offline and online data throughout the process. Scheme III follows the sequential replacement approach, transitioning from offline to online data. In all schemes, the same online data are processed row by row to emulate streaming acquisition, and the same prior distributions are used. The prior values are summarised in Table 1.

Table 1. Common prior values for all scenarios. Parameter Mean Std ! (mm) 1 1 " (mm) 1 1 ' ) √ . #$.& / 5 ´ 10 -10 5 ´ 10 -12 2.8 0.001

Performance is evaluated using three metrics: predicted crack growth trajectories with uncertainty bounds, probability distributions of cycles to failure ( # ) at the critical crack length, and the evolution of inferred material parameters ( and as fatigue properties, and as intrinsic flaw characteristics). The controlled conditions produce relatively predictable structural responses that do not fully stress the adaptive features. It should be noted that the purpose here is to demonstrate the fundamental capabilities of the methodology, which serve as a basis for later application to more complex cases.