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On the ergodicity assumption in Performance-Based engineering
Highlights Error in handling system parameter uncertainties in Performance-Based Engineering (PBE) is addressed. Error is not proportional to annual failure rates, as usually thought. Practical product-of-lognormals approach proposed for ergodic × non-ergodic fragility decomposition. Approach completely avoids non-ergodicity error, allowing computation of accurate lifetime failure probabilities.
Abstract In the Performance-Based Engineering (PBE) framework, uncertainties in system parameters, or modelling uncertainties, have been shown to have significant effects on capacity fragilities and annual collapse rates of buildings. Yet, since modelling uncertainties are non-ergodic variables, their consideration in failure rate calculations offends the Poisson assumption of independent crossings. This problem has been addressed in the literature, and errors found negligible for small annual collapse failure rates. However, the errors could be significant for serviceability limit states, and when failure rates are integrated in time, to provide lifetime failure probabilities. Herein, we present a novel formulation to fully avoid the error in integration of non-ergodic variables. The proposed product-of-lognormals formulation is fully compatible with popular fragility modelling approaches in PBE context. Moreover, we address collapse limit states of realistic reinforced concrete buildings, and find errors of the order of 5 to 8% for 50-year lifetimes, up to 14% for 100 years. Computation of accurate lifetime failure probabilities in a PBE context is clearly important, as it allows comparison with lifetime target reliability values for other structural analysis formulations.
On the ergodicity assumption in Performance-Based engineering
Highlights Error in handling system parameter uncertainties in Performance-Based Engineering (PBE) is addressed. Error is not proportional to annual failure rates, as usually thought. Practical product-of-lognormals approach proposed for ergodic × non-ergodic fragility decomposition. Approach completely avoids non-ergodicity error, allowing computation of accurate lifetime failure probabilities.
Abstract In the Performance-Based Engineering (PBE) framework, uncertainties in system parameters, or modelling uncertainties, have been shown to have significant effects on capacity fragilities and annual collapse rates of buildings. Yet, since modelling uncertainties are non-ergodic variables, their consideration in failure rate calculations offends the Poisson assumption of independent crossings. This problem has been addressed in the literature, and errors found negligible for small annual collapse failure rates. However, the errors could be significant for serviceability limit states, and when failure rates are integrated in time, to provide lifetime failure probabilities. Herein, we present a novel formulation to fully avoid the error in integration of non-ergodic variables. The proposed product-of-lognormals formulation is fully compatible with popular fragility modelling approaches in PBE context. Moreover, we address collapse limit states of realistic reinforced concrete buildings, and find errors of the order of 5 to 8% for 50-year lifetimes, up to 14% for 100 years. Computation of accurate lifetime failure probabilities in a PBE context is clearly important, as it allows comparison with lifetime target reliability values for other structural analysis formulations.
On the ergodicity assumption in Performance-Based engineering
Beck, André T. (author) / Mara Bosse, Rubia (author) / Durci Rodrigues, Isabela (author)
Structural Safety ; 97
2022-03-21
Article (Journal)
Electronic Resource
English
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