PSI - Issue 84

Vittorio Palma et al. / Procedia Structural Integrity 84 (2026) 1318–1325 1323 where , ( ) and , ( ) represent the direct and indirect consequences associated with system state , respectively. Since the management action modifies the post-action structural state through its effect on the effective tendon area and, consequently, on the resistance model, it is treated here as a system state action. In the absence of inspections, the prior decision risk associated with action is written as 0 ( )= ( )+∑ ( ∈ ) ( ( )) (10) and the corresponding optimal prior risk is 0 =min ∈ 0 ( ) (11) For a fixed inspection design ( , ) , the information outcome , updates the prior distribution of the system state to the posterior distribution ( ∣ , ) . The corresponding posterior decision risk is then written with the action performance ratio ( , ) for normal and extensive formulation equivalence (Thöns et al. 2025; Thöns 2024) as ( , )=min ∈ [ ( )+∑ ∈ ( ) ( ∣ , ) ( , )]with ( , )= ( ( )) ( ) (12) The informational contribution of an inspection campaign characterized by sample size and inspection method is quantified through the value of predicted information. Let ˉ ( , )=∑ ( , ∈ , , ) ( , ) (13) denote the pre-posterior expected decision risk, where ( , ) is the predictive distribution of the information outcome under design ( , ) . By including the direct inspection cost insp ( , ) , the expected pre-posterior strategy risk is written as PrePost ( , ) = ˉ ( , )+ insp ( , ) (14) The value of predicted information is then expressed as ( , )= 0 − PrePost ( , ) (15) Accordingly, the optimal inspection design is obtained by maximizing the value of predicted information: ( ∗ , ∗ )=arg max ∈{0,1,…, }, ∈ℳ ( , ) (16) 4. Case Study: Post-tensioned concrete beam with special inspections of tendons The proposed framework is applied to a simply supported post-tensioned concrete beam subjected to a uniformly distributed load and assessed in flexure. The load demand is evaluated in accordance with EN 1990 using the probabilistic combination factor =0.50 (Eq. 4). The reference configuration is obtained through a deterministic PT-only calibration under intact tendon conditions ( 0 ), by imposing equilibrium at the ultimate limit state, = (Section 3.3). A representative bridge girder with span =40 m and rectangular cross-section is considered, with a finite tendon population of size =40 . The probabilistic assessment is performed by keeping the geometry fixed and introducing aleatory variability in the actions ( , ) and model uncertainties on load effects and resistance ( , ), according to the distributions defined in Section 3 and Table 2. The dominant source of epistemic uncertainty is the tendon defectiveness state, represented by the discrete system state , modelled through a beta– binomial prior distribution with hyperparameters ( 0 , 0 ) = (2.0, 8.0) , reflecting historical information and previous inspections (Mazzatura et al. 2023). For defective tendons, defect severity is represented by an area-retention factor