UILLIS: Urban Infrastructures and Lifelines Interaction of Systems

Transcription

1 UILLIS: Urban Infrastructures and Lifelines Interaction of Systems Mohammad Javanbarg & Charles Scawthorn PEER Center October, 0

2 Agenda Summary of research System Multi-Hazard System Multistate System for Required Demand Interdependent System Urban Infrastructure and Lifeline Interactions of Systems (UILLIS) M. Javanbarg, 0

3 Summary of research Infrastructure risk should be modeled with accounting of interdependencies, cascading or common cause failures, collocation or other effects. Capture and quantify the complexities of large interdependent urban infrastructure. Such system of systems have applications far beyond urban infrastructure.

4 Failures: common-cause (CCF) and cascading failures (CF) CCF CF+CCF CF CCF CCF Inter-dependency CCF Dudenhoeffer et al, 007

5 Kobe: CF as a result of CCF Malfunction of traffic signals Loss of satellite emergency communications Hospital shutdowns Loss of water filtration plants and pump stations Loss of water and elevators in high-rises Fire ignitions (gas leaks and electricity sparks) Lack of heating at shelters Power outage due to the 995 Kobe EQ. (KEPCO, 997)

6 Katrina: lifeline interactions example Hurricane First order effect Electricity outages Transportation bottleneck Building collapse Both first & second order effects Water contamination Telecom outages Traffic light outages Impact City had no clean water City had no electricity High traffic volume preventing communications of response teams Hampered emergency response teams Refinery damage Gas pressure loss City had no gas for heating Gas price spiked nationwide as 40% of the US refinery is in this area

7 UILLIS

8 Algorithms for system reliability

9 Algorithm : multi-hazard system reliability Hazards - events Tsunami, 3, 5, 7, & 8 Earthquake, 8, 9,, & Hazards probability of occurrence Tsunami, Earthquake, 0.00 Earthquake Tsunami Pr( CCE) = ( P E )( P ) E Pr( CCE) = P E ( P ) E Pr( CCE ) ( 3 = P E PE Pr( CCE 4) = P E PE P F = ) m [ Pr( F CCEi ) Pr( CCEi )] i= Prob. no failure due to CCF Prob. of Tsunami, but no earthquake Prob. of earthquake, but no tsunami Prob. that both earthquake and tsunami happen Multi-hazard Prob. of system failure

10 Algorithm : MPM (minimal path method): system connectivity Run time-minpath Network Minpath (seconds)

11 Algorithm 3: Monte Carlo system reliability very large network binary x e e e 3 e 4 e 5 x x 0 0 x x multistate x e e e 3 e 4 e 5 x x 0 0 x x X s = ( x, x, x..., x E ) µ ( x) d e e Q( system success) s s e 3 3 t t R = Q N e 4 4 e 5 5

12 Algorithm 4: Multistate reliability - communication State vector of components: c 4 c 4 b={[0,3,4,8],[0,3,4,6],[0,3],[0,3,4],[0,3],[0,3,6],[0,3],[0,3,4,6],... c c 6 [0,3,4,8],[0,3],[0,3]} Probability vector of components: p = {[ ],[ ],[ ],... c 3 6 c 5 [ ],[ ],[ ],[ ],... [ ],[ ],[ ],[ ]} Demand node 4 node 5 node Demand (Flow level j) Comm.node (success probability) 4 5 6

13 Algorithm 5: Interdependent system reliability CCF & CF CCF & CF. System reliability Connectivity Error 3 4 CF Connectivity Error p p p 3 g w c t Multigraph dependency 5 6 g g Multistate system with multistate components Interdependent System reliability Theoretical probability model: CCF model S g

14 Types of interdependencies Probability of occurrence: s-independent P( E ) ( )( ) Prob. Of no failure due to e = P e P e P( E) = P e ( P ) e Prob. of e, but no e P ( E3 ) = ( P ) e P e Prob. of e, but no e P ( E4) = P e Pe Prob. that both e and e Mutual exclusive P E = P = P = P e P ( ) e ( E) Pe ( E 3 ) P e P( E4 ) = 0 s-dependent P( E) = ( Pe )( q) P( E) = Pe ( p) P E ) = ( Pe ). q ( 3 ( E4 ) = P p P e. P ( e / e ) = p P e / ~ e ) = q (

15 Example: transportation network t t t 3 State vector of components: b={[0,,,3,4],[0,,,3,4],[0,,,3,4],[0,,,3,4],[0,,,3,4],... [0,,,3,4],[0,,,3,4],[0,,,3,4],[0,,,3,4],[0,,,3,4],... [0,,,3,4],[0,,,3,4],[0,,,3,4],[0,,,3,4],[0,,,3,4], t 4 t 5 t t 7 t 8 t [0,,,3,4]} Probability vector of components: Demand node 9, R Probability of failure (P 9 =-R 9) 0.9 Transportation Network Demand (Flow at level j)

16 Reduced networks conditional probabilities transport power communication pow.+ comm. t t t 3 t t t t t t t 4 t 5 t t 4 t t 4 t t t 7 t 8 t t 8 t t 7 t 8 t t 8 t 9 6 N N N 3 N 4 Conditional probability P( F Ei ) = R( F Ei ) Demand (R 9 ) Demand (R 9 ) Demand (R 9 ) Demand (R 9 )

17 Interdependencies (s-independent) P P ( R )*6 + ( R )*5 p4 p5 e. = = ( R )*8 + ( R )*0 c4 c5 e. = = p Power network p p 3 p 5 p 4 p 6 Communication network c 4 c c 3 6 c 4 7 c c 6 P( E P( E P( E ) ( P e )( P = = e ) = P e ( P ) = e 3 ) = ( P e ) P = e P( E4 ) = P e Pe = ) t t t t 4 t 5 t 6 t 7 t 8 t Transportation network P F = m [ Pr( F E ) Pr( E )] i= i i

18 Multistate reliability and interdependent multistate reliability - transportation t t t 3 t t t t t t t 4 t 5 t t 4 t t 4 t t t 7 t 8 t t 8 t t 7 t 8 t t 8 t 9 6 N N N 3 N 4 Demand R 9 0 Interdependent R Transportation Network Interdependent reliability Demand (Flow at level j)

19 Thank you