On the ergodicity assumption in Performance-Based Engineering

TL;DR

This paper introduces a new formulation to accurately compute lifetime failure probabilities in Performance-Based Engineering by addressing non-ergodic uncertainties, reducing errors in failure rate calculations over time.

Contribution

The paper presents a novel product-of-lognormals formulation that avoids integration errors for non-ergodic variables in PBE, improving lifetime failure probability estimates.

Findings

Errors of 5-8% for 50-year lifetimes

Errors up to 14% for 100-year lifetimes

Compatible with existing fragility models

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.