Weibull-Based Bridge Deterioration Models for Iowa Bridges Dimitrios Bilionis Basak Aldemir Bektas.
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Transcript of Weibull-Based Bridge Deterioration Models for Iowa Bridges Dimitrios Bilionis Basak Aldemir Bektas.
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Weibull-Based Bridge Deterioration Models for
Iowa BridgesDimitrios Bilionis
Basak Aldemir Bektas
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outline Introduction Data Methodology Refinement Results Example Implementation
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introduction
Purpose Predict future condition
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introductionDeterioration models
Deterministic models Stochastic models
state-based time-basede.g. Markov chains e.g. Weibull
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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
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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
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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
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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)
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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
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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
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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
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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
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example
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refinement
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Implementation
Yearly time-in-state update
Emphasis on models for ratings 4-7
Network level prioritization based on median time-in-state estimates
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Thank you!
Questions?