Weibull-Based Bridge Deterioration Models for

Iowa BridgesDimitrios Bilionis

Basak Aldemir Bektas

outline Introduction Data Methodology Refinement Results Example Implementation

introduction Purpose

Predict future condition

introductionDeterioration models

Deterministic models Stochastic models

state-based time-basede.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:

• WeibullSurvival 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

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

8 7 7 7 7 7 7 7 7 7 6 6

data• NBI ratings• Deck• Superstructure• Substructure

• 1983-2011 data• Process:• Eliminate increases• Gaps• Explanatory variables• Time-in-state

Code Description

N NOT APPLICABLE

9 EXCELLENT CONDITION

8 VERY GOOD CONDITION ( No problems noted)

7 GOOD CONDITION (Some minor problems)

6 SATISFACTORY CONDITION (Minor deterioration in structural elements)

5 FAIR CONDITION (Sound structural elements with minor section loss)

4 POOR CONDITION (Advanced section loss)

3 SERIOUS CONDITION (Affected structural elements from section loss)

2 CRITICAL CONDITION (Advanced deterioration of structural elements)

1 “IMMINENT” FAILURE CONDITION (Obvious movement affecting structural stability)

0 FAILED CONDITION (Out of service)

results

Rating # observations Variables Median TISUncensored Right

CensoredUncensored sample

Right censored sample

Model

9 751* 138* ADT 4 3 4.68 280* 314 AGE, TR_ADT 8 6 7.37 145* 425 AGE 17 5 136 166* 239 AGE 10 4 9.15 63* 202 AGE 5 5.5 5.64 21* 145 - 4 6 4.8

Deck

resultsSubstructure

Rating # observations Variables Median TISUncensored Right

CensoredUncensored sample

Right censored sample

Model

9 882* 149 AGE, ADT 5 9 6.28 181* 603 AGE 8 6 7.67 83* 399 16 10 13.76 172* 265 8 8 7.65 67* 238 4 5 5.24 16 102 2.5 4 2.8

resultsSuperstructureRating # observations Variables Median TIS

Uncensored Right Censored

Uncensored sample

Right censored sample

Model

9 836* 236 AGE, ADT 5 7 5.78 133* 608 AGE, TR_ADT,

CNRCSL9 5 9

7 89 259 15 6 12.76 124 199 DLSLCNR 8 6 8.25 33 157 DMONCNR,

SSMG4 4 4.2

4 10 50 3.5 4.5 3.8

exampleDeck NBI CR=8

AGE TR_ADT Prob Survival Median Time2 636 0.5 11.082 100 0.5 12.152 9000 0.5 2.62

20 636 0.5 0.9820 100 0.5 1.0820 9000 0.5 0.23

2 636 0.5 11.082 100 0.5 12.152 9000 0.5 2.62

20 636 0.5 0.9820 100 0.5 1.0820 9000 0.5 0.23

example

refinement

Implementation

Yearly time-in-state update

Emphasis on models for ratings 4-7

Network level prioritization based on median time-in-state estimates

Thank you!

Questions?