PSI - Issue 84

1324 Vittorio Palma et al. / Procedia Structural Integrity 84 (2026) 1318–1325 , ∈ (0,1] , i.i.d. Beta distribution with [ ] =0.57 and [ ] =0.30 . This parameter provides a simplified representation of tendon cross-section loss (e.g. due to corrosion) and is assumed on the basis of plausible values in the absence of sufficiently extensive experimental data. Special inspections are modelled as sampling without replacement of tendons from the population and as observations affected by imperfect detection, characterised by non-unit sensitivity and specificity. Two representative diagnostic alternatives are considered: a high-performance method with ( , ) = (0.97, 0.90) and an intermediate-performance method with ( , ) = (0.92, 0.80) (Terzioglu et al. 2018), differing in diagnostic quality and operational costs. Inspection costs include a fixed mobilization cost, a unit cost per inspected tendon, and a duration-dependent cost reflecting daily productivity; intervention costs and collapse consequences are reported in Table 3. The pre-posterior analysis is carried out by varying the inspection sample size over a discrete set compatible with operational constraints. For each combination of and inspection method , the predictive distribution of information outcomes is used to evaluate the value of predicted information and the corresponding pre-posterior strategy risk PrePost . The optimal inspection design is then identified as the one maximizing , consistently with the decision model described in Section 3. Table 3 Inspection, intervention, and failure-consequence cost parameters adopted in the case study. Parameter Value ,ℎ ℎ Value 0 (fixed mobilisation cost per inspection campaign) 2 000 € 1 800 € (unit cost per inspected tendon) 800 €/tendon 500 €/tendon r (number of tendons inspected per day) 6 9 (daily operational cost of the inspection campaign) 2 500 €/day 1 000 €/day ℎ (cost of the rehabilitation action) 250 000 € (direct cost associated with structural failure) 30 000 000 € 4.1. Results The results indicate a strong dependence of structural reliability on tendon defectiveness. As the number of defective tendons increases, structural safety progressively deteriorates due to the loss of prestressing effectiveness and the associated reduction in flexural capacity. In the present model, tendon condition is represented by the system state , which accounts for a reduction in effective tendon area through the defect severity factor . For limited defectiveness levels, the structural response is mainly controlled by the variability of loads and model uncertainties, whereas for increasing defectiveness the uncertainty associated with tendon condition becomes dominant. The introduction of inspection information through Bayesian updating leads to a substantial reduction in epistemic uncertainty. Figure 1(a) shows the value of predicted information as a function of inspection sample size, whereas Figure 1(b) reports the corresponding pre-posterior strategy risk PrePost . Even limited inspection campaigns are sufficient to produce significant changes in the inferred tendon condition and, consequently, in the decision risk associated with alternative management actions. As inspection effort increases, posterior distributions progressively concentrate, while the marginal informational benefit decreases, leading to the identification of an optimal inspection sample size for each method.

Figure 1. (a) Value of predicted information versus inspection sample size . (b) Pre-posterior strategy risk versus inspection sample size . For the analysed case ( =40 ), the optimal strategy corresponds to inspecting 16 tendons (about 40%) with the high-