Bayesian Networks for Modeling and Managing Risks of Natural Hazards

Transcription

1 [National Telford Institute and Scottish Informatics and Comuter Science Alliance, Glasgow University, Set 8, 200 ] Bayesian Networks for Modeling and Managing Risks of Natural Hazards Daniel Straub Engineering Risk Analysis Grou TU München Decisions in comle systems under conditions of uncertainty Aging of the infrastructure system: Monitoring & Insection Maintenance R l t/ d i Natural hazards in the system built environment Prevention Emergency resonse R h bilit ti Relacement / redesign Rehabilitation Safety in the system society Target reliability Prescritive limits Service life duration 2

2 Vision Decision suort systems which: Provide accurate assessments of system state at all times Include state-of-the-art models Account for ast observations Use near-real-time observation Suggest otimal decisions Bensi M.T PhD thesis, UC Berkeley. 3 What to eect Part A: Bayesian network in a nutshell Eemlified with EQ risk management eamles Part B: Alications of Bayesian networks ongoing Avalanche risk assessment Wildfire risk Flood detection Deterioration Earthquake Part C: Discussion 4 2

3 Bayesian network in a nutshell Probabilistic models based on directed acyclic grahs Models the joint robability distribution of a set of variables 5 Bayesian network in a nutshell 6 3

4 4 Bayesian network in a nutshell Efficient factoring of the joint robability distribution into robability distribution into conditional local distributions given the arents,,, Here: ] [ n i i i a General: Bayesian network in a nutshell Facilitates Bayesian udating when additional information evidence additional information evidence is available, e e e E.g.: X X e e e

5 Bayesian network is a owerful modeling tool Tsunami warning eamle: Comutational benefits through conditional indeendence assumtions Straub D., 200. Lecture notes. TU München 9 Modelling with BN: System deendence through common factors Performance of an electrical substation during an EQ Frag gility PGA [g] 0 5

6 System fragility Redundant system: arallel system with 5 comonents 0 0 Parallel system TR 0 System fragility Including deendence Neglecting deendence PGA [g] Straub D., Der Kiureghian A Structural Safety, 304, Modelling comle systems using BN: Object-oriented BN Princiles of object-oriented rogramming can be alied. Straub D., Der Kiureghian A., 200. Journal of Engineering Mechanics, in rint 4 6

7 Bayesian networks can be etended to decision grahs as a tool for otimizing decisions Eamle: EQ emergency resonse: Seismic demand Observable condition Bridge condition Bensi M.T PhD thesis, UC Berkeley. 5 How do we use information udating? Two tyes of information: Data obtained from revious rojects and investigations Observations made during the actual alication Model Y = gx,a A: Model arameters X: Observables 6 7

8 How do we use information udating? Two tyes of information: Data obtained from revious rojects and investigations Observations made during the actual alication Model Y = gx,a A: Model arameters X: Observables Data 7 How do we use information udating? Two tyes of information: Data obtained from revious rojects and investigations Observations made during the actual alication Model Y = gx,a A: Model arameters X: Observables Present/future Past 8 8

9 How do we use information udating? Two tyes of information: Data obtained from revious rojects and investigations Observations made during the actual alication Model Y = gx,a A: Model arameters X: Observables Otimize decisions: Decision Consequences 9 What to eect Part A: Bayesian network in a nutshell Eemlified with EQ risk management eamles Part B: Alications of Bayesian networks ongoing Avalanche risk assessment Wildfire risk Flood detection Deterioration Earthquake Part C: Discussion 2 9

10 Avalanche risk assessment Where is it safe to build? Where should rotection measures be imlemented? When should roads be closed / buildings be evacuated? Source: Kt. St. Gallen, Switzerland 22 Bayesian networks for avalanche risk assessment Grêt Regamey A., Straub D Natural Hazards and Earth System Sciences, 66,

11 Avalanche risk assessment Observations available here 50 years 24 Avalanche risk analysis Information udating 25

12 Avalanche risk analysis Straub D., Grêt Regamey A Cold Regions Science and Technology, 463, Bayesian networks for avalanche risk assessment Grêt Regamey A., Straub D Natural Hazards and Earth System Sciences, 66,

13 Imlementation of the BN models in software is straightforward Imlementation in a GIS environment Regional risk analysis Grêt Regamey A., Straub D Natural Hazards and Earth System Sciences, 66, BN for wildfire risk management 29 3

14 Case study: Rhodes Weather Station Municiality 30 BN model Geograhy 3 4

15 Land Cover Human Poulation density 32 BN inut is obtained from GIS E.g. elevation 33 5

16 Automatic flood detection from satelite images Flooded Possibly Trafficable Trafficable Flooded Trafficable with Daniel Frey, Chair of Remote Sensing, TUM 34 Automatic flood detection from satelite images BN: Combining the flood model elevation with satelite data Clouds Flooded Elelvation e Visible object e with Daniel Frey, Chair of Remote Sensing, TUM Grey channels 35 6

17 Detection of flooded objects using GIS and remote sensing data θ θ θ 2 θ 3 θ T d 0 d d 2 d 3 d T W 3 U V 2 X T U,V,W,X: observations from different sensors θ: Altitude from DEM d: damage inde flooded or not flooded with Daniel Frey, Chair of Remote Sensing, TUM 36 Detection of flooded objects using GIS and remote sensing data including damage models States: θ k : altitude of object θ [θ, θ k ] object n: number of bands i: number of iels in object c: classes i.e. water, forest, road m: number of classes g: grayvalues d [flooded, not flooded] c [c, c, c m ] iel g c c c [c, c, c m ] g 2 g n g g 2 g n g g 2 g n [0 255] iel iel 2 iel i with Daniel Frey, Chair of Remote Sensing, TUM 37 7

18 Automatic flood detection from satelite images Flooded Possibly Trafficable Trafficable Flooded Trafficable with Daniel Frey, Chair of Remote Sensing, TUM 38 Managing deterioration through insection and monitoring 39 8

19 DBN model for deterioration modeling C m m m 2 m 3 m T S q q q 2 q 3 q T a 0 a a 2 a 3 a T Insection Z Z 2 Z 3 Z T Failure/survival E E 2 E 3 E T Straub D Journal of Engineering Mechanics, 350, Calculations are robust AND efficient Straub D Journal of Engineering Mechanics, 350,

20 Performance of buildings subject to hazards: Combining continuous and discrete random variables Measurements Structural model: V H R 2 R 3 R 4 5m R R 5 Performance 5m 5m Straub D., Der Kiureghian A., 200. Journal of Engineering Mechanics, in rint 42 Combining eact BN inference algorithms with structural reliability methods Eliminate continuous RV nodes: Y reverse X,Y 5 Y reverse X,Y 6 Y remove X Y Y 2 Y 3 Y 2 Y 3 Y 2 Y 3 Y 2 Y 3 Y 4 X Y 4 X Y 4 X Y 4 Y 5 Y 6 Y 5 Y 6 Y 5 Y 6 Y 5 Y 6 Y 7 Y 7 Y 7 Y 7 Comute new conditional PMF using FORM Straub D., Der Kiureghian A., 200. Journal of Engineering Mechanics, in rint 43 20

21 Enhanced BN: Structural model: H V R 2 R 3 R 4 Eliminate continuous RV nodes: R R 5 5m Comute new conditional PMF using FORM Straub D., Der Kiureghian A., 200. Journal of Engineering Mechanics, in rint 44 Reliability of an infrastructure system Determine the reliability connectivity under evolving information on hazards, system erformances, measurement Straub D., Der Kiureghian A., 200. Journal of Engineering Mechanics, in rint 45 2

22 Temoral model Straub D., Der Kiureghian A., 200. Journal of Engineering Mechanics, in rint 46 Satial model Straub D., Der Kiureghian A., 200. Journal of Engineering Mechanics, in rint 47 22

23 EQ: Modeling systems and ortfolio of structures M 4 M 5 U R R 4a R 5a R R 2 R 3 R 4 R 5 V R 4b R 5b Q Q Q 2 Q 20 E E2 E20 H H 2 H 20 H H2 H20 U H U H2 U H20 U H Straub D., Der Kiureghian A., 200. Journal of Engineering Mechanics, in rint 48 Reliability of the infrastructure system is udated in near-real-time as information becomes available Small earthquake event roof loading effect One year later Detailed insection of structures Prior model First observations after EQ Immediately after EQ event Straub D., Der Kiureghian A., 200. Journal of Engineering Mechanics, in rint 49 23

24 Do we now have the Deus E Machina? Limitations of the analysis: Comleity of the BN Number of SRM comutations required In articular, satial correlation can be handled only aroimately Certain deendence must be simlified Markov assumtion 50 Satial modelling of the EQ hazard Straub D., Bensi M., Der Kiureghian A Proc. EM

25 Aroimate satial models Bensi M. et al Submitted to Structural Safety 52 Conditional distribution of PGA Distribution of PGA conditional on observations: Observation: PGA at site 4 equal to 0.75g Straub D., Bensi M., Der Kiureghian A Proc. EM

26 System erformance models are also not straightforward But a formalism for establishing them has been develoed: Bensi M., 200. PhD thesis, UC Berkeley 54 Discussion Bayesian network models enable the robabilistic modeling of comle systems Particularily efficient when he roblem can be comartialized conditional statistical indeendences They are ideal for roblems with evolving information as they allow model udating ad learning Comutational limitations eist, which make a careful modeling necessary BNs are a modelling tool: The models must still be develoed and data must be collected 55 26

27 Outlook