Weibull-Based Bridge Deterioration Models for Iowa Bridges

1. Weibull-Based Bridge Deterioration Models for Iowa Bridges DimitriosBilionis Basak Aldemir Bektas

2. outline • Introduction • Data • Methodology • Refinement • Results • Example • Implementation

3. introduction • Purpose • Predict future condition

4. introduction Deterioration models Deterministic models Stochastic models state-based time-based e.g. Markov chains e.g. Weibull

5. methodology • Survival analysis (failure time analysis) • Occurrence and timing of events • Hazard base models investigate the conditional probability that duration of time ends at a specific time t: Here F(t) is the c.d.f. of T • The conditional probability that an event will occur between time t and t+dt, is given by the hazard function: In other words, the hazard function gives the rate at which a duration terminates at time t

6. methodology • the probability that a duration is greater than or equal to a specific time t is given by the survivor function: • Weibull Survival function: Probability density function: where w=log(t), , µ is the location parameter and σ is the scale parameter

7. methodology • Censoring • T=a, uncensored • T<b, right censored • c<T<d, interval censored

8. data • NBI ratings • Deck • Superstructure • Substructure • 1983-2011 data • Process: • Eliminate increases • Gaps • Explanatory variables • Time-in-state

9. results Deck

10. results Substructure

11. results Superstructure

12. example Deck NBI CR=8

13. example

14. refinement

15. Implementation