Fig. 1 Integrated probabilistic risk assessment (I-PRA) methodological framework [ 1 ] More

Fig. 2 Validation spectrum and associated validation approaches More

Fig. 3 Representation of uncertainties in the simulation prediction More

Fig. 4 Acceptability criteria concept for validity assessment in the probabilistic validation methodology ( a ) cases with acceptability criteria at the application output level and ( b ) cases with acceptability criteria at the simulation prediction level More

Fig. 5 Theoretical causal framework to guide the identification of uncertainty sources and their interrelationships that influence the simulation prediction and its uncertainty More

Fig. 6 Probabilistic validation methodological platform More

Fig. 7 Qualitative screening and categorizations of causal influencing factors in step 1 of the probabilistic validation methodological platform More

Fig. 8 Illustration of the total uncertainty p-box of M i , j , k model prediction obtained from using the probabilistic validation methodology (Figure adapted from Ref. [ 19 ]) More

Fig. 1 Stochastically excited tuned mass-damper-inerter (TMDI) nonlinear system with a fractional derivative element More

Fig. 2 Evolution in time of the response displacement PDF of the primary structure of a stochastically excited TMDI nonlinear system with a fractional derivative element: ( a ) WPI-based estimates and ( b ) MCS data—50,000 realizations More

Fig. 3 Wiener path integral (WPI)-based response displacement PDF of the primary structure of a stochastically excited TMDI nonlinear system with a fractional derivative element at various time instants; comparisons with MCS data—50,000 realizations More