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 Deterministic models Stochastic models state-based e.g. Markov chains time-based 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: 𝐹 𝑡 = 𝑃(𝑇 < 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: 𝑓(𝑡) ℎ 𝑡 = 1 − 𝐹(𝑡) 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: 𝑆 𝑡 = 𝑃(𝑇 ≥ 𝑡) = 1 − 𝐹 𝑡 • Weibull Probability density function: 𝑓 𝑤 = 𝑤−𝜇 Survival function: 𝑆 𝑤 = exp − 𝑒𝑥𝑝 𝜎 1 𝜎 exp where w=log(t), 𝜇 = 𝑥 ′ 𝛽 parameter 𝑤−𝜇 𝜎 exp −𝑒𝑥𝑝 𝑤−𝜇 𝜎 , µ is the location parameter and σ is the scale

methodology

 Censoring  T=a, uncensored  T

data

• NBI ratings • Deck • Superstructure • Substructure • 1983-2011 data • Process: • Eliminate increases • Gaps • Explanatory variables • Time-in-state 6 5 4 3 2

Code

N 9 8 7 1 0

Description

NOT APPLICABLE EXCELLENT CONDITION VERY GOOD CONDITION ( No problems noted) GOOD CONDITION (Some minor problems) SATISFACTORY CONDITION (Minor deterioration in structural elements) FAIR CONDITION (Sound structural elements with minor section loss) POOR CONDITION (Advanced section loss) SERIOUS CONDITION (Affected structural elements from section loss) CRITICAL CONDITION (Advanced deterioration of structural elements) “IMMINENT” FAILURE CONDITION (Obvious movement affecting structural stability) FAILED CONDITION (Out of service)

9 8 7 6 5 4

results Deck

Rating # observations

Uncensored Right Censored 751* 280* 145* 166* 63* 21* 138* 314 425 239 202 145

Variables

ADT 4 AGE, TR_ADT 8 AGE 17 AGE AGE 10 5 4

Median TIS

Uncensored sample Right censored sample 3 6 5 4 5.5

6 Model 4.6

7.3

13 9.1

5.6

4.8

results

9 8 7 6 5 4

Substructure

Rating # observations

Uncensored Right Censored 882* 181* 83* 172* 67* 16 149 603 399 265 238 102

Variables

AGE, ADT AGE 5 8 16 8 4 2.5

Median TIS

Uncensored sample 8 5 4 Right censored sample 9 6 10 Model 6.2

7.6

13.7

7.6

5.2

2.8

results

7 6 5 4

Superstructure

Rating # observations

Uncensored Right

9 8

836* 133* Censored 236 608 89 124 33 10 259 199 157 50

Variables

AGE, ADT AGE, TR_ADT, CNRCSL

Median TIS

Uncensored sample 5 9 DLSLCNR DMONCNR, SSMG 15 8 4 3.5

6 6 4 Right censored sample 7 5 4.5

Model 5.7

9 12.7

8.2

4.2

3.8

example

Deck NBI CR=8 AGE

2 2 20 20 20 20 20 20 2 2 2 2

TR_ADT

636

Prob Survival Median Time

0.5

11.08

100 9000 0.5

0.5

12.15

2.62

636 100 9000 636 0.5

0.5

0.5

0.5

0.98

1.08

0.23

11.08

100 9000 636 100 9000 0.5

0.5

0.5

0.5

0.5

12.15

2.62

0.98

1.08

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?