# Weibull-Based Bridge Deterioration Models for Iowa Bridges - PowerPoint PPT Presentation

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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

DimitriosBilionis

Basak Aldemir Bektas

### outline

• Introduction

• Data

• Methodology

• Refinement

• Results

• Example

• Implementation

### introduction

• Purpose

• Predict future condition

### introduction

Deterioration models

Deterministic modelsStochastic models

state-based time-based

e.g. Markov chains e.g. Weibull

### 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

### 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

### methodology

• Censoring

• T=a, uncensored

• T<b, right censored

• c<T<d, interval censored

### data

• NBI ratings

• Deck

• Superstructure

• Substructure

• 1983-2011 data

• Process:

• Eliminate increases

• Gaps

• Explanatory variables

• Time-in-state

Deck

Substructure

Superstructure

Deck NBI CR=8