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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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Weibull based bridge deterioration models for iowa bridges

Weibull-Based Bridge Deterioration Models for Iowa Bridges

DimitriosBilionis

Basak Aldemir Bektas


Outline

outline

  • Introduction

  • Data

  • Methodology

  • Refinement

  • Results

  • Example

  • Implementation


Introduction

introduction

  • Purpose

    • Predict future condition


Introduction1

introduction

Deterioration models

Deterministic modelsStochastic models

state-based time-based

e.g. Markov chains e.g. Weibull


Methodology

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


Methodology1

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


Methodology2

methodology

  • Censoring

    • T=a, uncensored

    • T<b, right censored

    • c<T<d, interval censored


Weibull based bridge deterioration models for iowa bridges

data

  • NBI ratings

    • Deck

    • Superstructure

    • Substructure

  • 1983-2011 data

  • Process:

    • Eliminate increases

    • Gaps

    • Explanatory variables

    • Time-in-state


Results

results

Deck


Results1

results

Substructure


Results2

results

Superstructure


E xample

example

Deck NBI CR=8


Example

example


Refinement

refinement


Implementation

Implementation


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