Risk assessment of bridges using Bayesian belief network: with consideration of seismic and aging

Transcription

1 Risk assessment of bridges using Bayesian belief network: with consideration of seismic and aging Dr. Solomon Tesfamariam, P.Eng. Associate Professor School of Engineering at Okanagan Campus Earthquake Engineering by the Beach II A Workshop on Seismic Risk of Civil Infrastructures Villa Orlandi, Anacapri, Italy June 8-10, 2013

2 Introduction

3 Introduction

4 Bridges in British Columbia (BC) N o. o f B rid g e s Year of Construction Total No. of Bridges 2743

5 Bridge Damage from 1994 Northridge Earthquake No. of Bridges Before After Minor Moderate Major Collapse Basöz, Kiremidjian, King and Law (1999)

6 BC Road Bridges s g e rid B f. o o N Before After 1980 Year of Construction

7 Problem Statement Existing bridges are vulnerable Comprehensive evaluation and retrofit is costly Prioritize retrofit based on criticality Use risk-based prioritization

8 Seismic risk

9 Seismic Risk Seismic risk may be defined the probability that a specified loss will exceed some quantifiable value during a given exposure time EERI Committee on Seismic Risk 1989

10 Why Risk Analysis? to quantify the potential for building damage (risk assessment) and evaluate the effectiveness of proposed retrofit (risk management)

11 Risk Index Risk = Likelihood of failure x Consequence of failure Seismic Risk Bridge damageability Consequence of failure Site seismic hazard Bridge vulnerability

12 Earthquake Hazard Assessment Earthquake Ground Shaking Landslide Liquefaction

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14 Bridge Consequence of Failure Consequence of failure Length, Height Road type SADT

15 Vulnerability Assessment QMT (Filiatrault et al. 1994): {structural type index, structural complexity index, deck discontinuity index, support redundancy index, bearing condition index, skew index} New Zealand (Transit New Zealand 1988): {year designed, superstructure hinges, superstructure overlap, superstructure length, pier type, bridge skew, abutment type}

16 BC MoTH Bridge Assessment System II Bridge Assessment System Index Adjusted bridge condition Index Urgency rating index Importance index Operation and safety index Live load capacity index

17 Bridge Vulnerability Superstructure Current condition Substructure Skewness Deck discontinuity Bearing condition Support redundancy Year of construction Bearing type Bearing seating condition

18 Aging and deterioration

19 Age of Infrastructure

20 Canada s Infrastructure Crisis There is a growing infrastructure investment deficit occurring in many sectors Financial costs to repair and replace deteriorating BC bridges exceeds $2 billion Need to prioritize based on riskinformed decision ( issues_infradeficit.asp#civil)

21 Markov Chains A stochastic process is considered Markov process if the probability of a future state in the process depends only on the current state and not on how it was attained (Parzen 1962) A Markov chain is a special case of the Markov process whose development can be treated as a series of transitions between certain states 21

22 Unit Jump Markov Chain Model

23 Prediction of Bridge Deterioration using Markovian Models

24 Advantage of Markov Chains Models Ability to capture the uncertainty from different sources, such as, Uncertainty in initial condition, Uncertainty in applied stresses, Presence of condition assessment errors, and Inherent uncertainty of the deterioration process (Morcous et al. 2003)

25 Incremental models that account for the current condition in predicting the future condition Applicability to both components and large size networks because of their computational efficiency and simplicity of use (Morcous et al. 2003)

26 Integration of Macro- and Micro-Deterioration Models for Multilevel Bridge Management (Lounis and Madanat 2002)

27 Future Condition State Given the initial condition vector P{S(0)} of the bridge element, the future condition vector P{S(t n )} at time n can be obtained as: P { S( t )} = P{ S(0)} P n n

28 Markov Deterioration Deterioration Type Severe environment Maintence Alternative Rehabilitate Performance Level 3

29 Uncertainty

30 Complex System As complexity rises, precise statements lose meaning and meaningful statements lose precision. Lotfi Zadeh

31 Uncertainty Vagueness The lack of definite or sharp distinctions Ambiguity One-to-many relationships Discord (conflict) Disagreement in choosing among several alternatives Non-specificity Two or more alternatives are left unspecified Klir and Yuan (1995)

32 Uncertainty Quantification Probabilistic methods Variance propagation Monte Carlo simulations (higher order MCS) First order reliability methods Fuzzy-based method Fuzzy arithmetic and possibility theory Fuzzy rule-based models Random sets (PBA, Dempster-Shafer)

33 Bayesian Belief Network

34 Bayesian Approach to Probability and Statistics Classical Probability: Physical property of the world (e.g., 50% flip of a fair coin). True probability. Bayesian Probability: A person s degree of belief in event X. Personal probability.

35 Bayesian Belief Network (BBN) Represented with Directed Acyclic Graph (DAG), nodes are variables and arrows are informational or causal dependencies Damage/Loss Consequence of Failure EDRI 35

36 DAG represents the dependencies between variables and specifies the joint probability distribution Random variables make up the nodes. Directed links represent causal direct influences. Each node has a conditional probability table quantifying the effects from the parents. No directed cycles.

37 BBN Variable A 1 Variable A 2 Variable A 1 L M H Probability P(A 1 =L) P(A 1 =M) P(A 1 =H) Unconditional probability (UP) Variable B 3 Variable A 2 L M H Probability P(A 2 =L) P(A 2 =M) P(A 2 =H) Unconditional probability (UP) Variable A 1 Variable A 2 Variable B 3 Probability L M H L L P(B 3 =L A 1 =L, A 2 =L) P(B 3 =M A 1 =L, A 2 =L) P(B 3 =H A 1 =L, A 2 =L) H M P(B 3 =L A 1 =H, A 2 =M) P(B 3 =M A 1 =H, A 2 =M) P(B 3 =H A 1 =H, A 2 =M) H H P(B 3 =L A 1 =H, A 2 =H) P(B 3 =M A 1 =H, A 2 =H) P(B 3 =H A 1 =H, A 2 =H) Conditional probability table (CPT)

38 Employs Bayes theorem: H is a hypothesis, E is evidence and P() are probabilities 38

39 BBN implementation of bridge seismic risk assessment

40 BBN seismic risk assessment of bridges Risk BridgeDamageability FailureConsequence BridgeVulnerability Length Height RoadType SADT PGA Liquefaction SuperStructure AgingDeterioration SubStructure Distance Soil_type Magnitude D50 sigma_vo sigma_vo_prime qc Skewness BearingCondition DeckDiscontinuity SupportRedundancy YearOfConstruction BearingType BearingSeatCondition

41 Site seismic hazard PGA Liquefaction Distance Soil_type Magnitude D50 sigma_vo sigma_vo_prime qc

42 Consequence of failure FailureConsequence Length Height RoadType SADT

43 Bridge vulnerability BridgeVulnerability SuperStructure AgingDeterioration SubStructure Skewness BearingCondition DeckDiscontinuity SupportRedundancy YearOfConstruction BearingType BearingSeatCondition

44 Risk index Risk BridgeDamageability FailureConsequence PGA Liquefaction BridgeVulnerability

45 Excel Interface

46 Scenario Site seismic hazard = high Environmental condition = Severe environment Scenario 1 Support redundancy = No pier Year of construction = 2010 Scenario 2 Support redundancy = Single column Year of construction = 1960

47 Probability of Risk Index = Very High

48 Thanks for listening You always got to be prepared, but you never know for what - Paradox of risk management