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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
results
SubstructureRating # observations Variables Median TIS
Uncensored Right Censored
Uncensored 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
results
SuperstructureRating # 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?
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