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Weibull-Based Bridge Deterioration Models for Iowa Bridges

Weibull-Based Bridge Deterioration Models for Iowa Bridges. Dimitrios Bilionis Basak Aldemir Bektas. outline. Introduction Data Methodology Refinement Results Example Implementation. introduction. Purpose Predict future condition. introduction. Deterioration models

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Weibull-Based Bridge Deterioration Models for Iowa Bridges

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  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

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