PSI - Issue 84

1322 Vittorio Palma et al. / Procedia Structural Integrity 84 (2026) 1318–1325 variables describing loads, material properties and model uncertainties. Let ∈ denote the management action (e.g. do-nothing vs rehabilitation), which modifies the post-action structural state through its effect on the effective tendon area. For a given system state , the probabilistic flexural resistance is expressed as = ( | , ) , explicitly accounting for the variability of the basic random variables and for the dependence on the defectiveness state. Structural safety in flexure is evaluated through the limit-state function , = − , where and are model uncertainty factors acting on resistance and load effects, respectively (Table 2). Structural reliability is quantified by Monte Carlo simulation with sim realizations, performing the analysis conditionally on and on the management action . The conditional probability of failure is estimated as ( ∣ ) = ( ( | , )<0)≈ 1 ∑ =1 [ ( ( ) | , )<0] (7) and the corresponding reliability index as ( ∣ )=−Φ −1 ( ( ∣ )) . When an unconditional measure of safety is required, the probability of failure is obtained by marginalization with respect to the system-state probabilities, either prior or posterior to inspection: ( )=∑ ∈ ( ∣ ) ( ), ( ∣ , )=∑ ∈ ( ∣ ) ( ∣ , ) (8) These quantities provide the input to the decision model and to the evaluation of the value of predicted information as a function of the inspection sample size and the inspection method . Table 2 Model uncertainty variables and defect severity parameters Parameter Distribution Mean Standard Deviation (European Commission 2024) Log-normal 1,20 0,15 (European Commission 2024) Log-normal 1,00 0,10 3.4. Dependence modelling The dependence between the quantities governing flexural demand and resistance is modelled by evaluating the limit state function using the same realizations of the physically shared basic variables. In particular, the permanent and variable actions ( , ) and the variables describing tendon condition, represented by the system state and, when applicable, by defect severity factors such as , are shared by flexural demand and resistance and are therefore represented by the same realisations of the random vector in the evaluation of the limit state function ( , | ) . In this way, the statistical dependence between demand and resistance induced by shared underlying variables is captured without introducing an explicit correlation model between marginal distributions. Resistance and load effect model uncertainty variables are modelled mutually independent and independent of the actions variables. Epistemic uncertainty associated with tendon condition is treated separately through Bayesian updating of the system-state probabilities based on the information outcomes , , as described in Section 3.1. 3.5. Decision model and predicted value of information Let denote the discrete system state associated with defective tendons, with support = { 0 , 1 ,…, } , where = . Let ( , ) define the inspection design, where is the number of inspected tendons and ∈ℳ is the selected inspection method from the set of available methods ℳ . For a given inspection design ( , ) , the information outcome is represented by the discrete random variable , , taking values in the set of admissible information outcomes , . The admissible management actions are collected in the set = { 0 , 1 ,…, −1 } , where 0 denotes continued operation without intervention and 1 denotes intervention or rehabilitation. Additional actions may be included without loss of generality. The state-dependent loss is denoted by ( ) and is expressed as ( )= ( )= , ( )+ , ( ) (9)