Matthias Schubert. Jochen Köhler. Michael H. Faber
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1 [ 1 International Probabilistic Symposium 2006, Ghent, November 2007 Analysis of Tunnel accidents by using Bayesian Networks Matthias Schubert ETH Zürich, Institute for Structural Engineering, Group Risk & Safety Jochen Köhler ETH Zürich, Institute for Structural Engineering, Group Risk & Safety Michael H. Faber ETH Zürich, Institute for Structural Engineering, Group Risk & Safety
2 [ 2 International Probabilistic Symposium 2006, Ghent, November 2007 Overview Introduction Modeling tunnel accidents Analysis and results Hierarchical approach for roadway networks Conclusions
3 [ 3 Introduction & Motivation Accidents in tunnel often lead to severe direct consequences (fire and explosions). Temporary closure of life lines generates large societal consequences. Societal perception p of tunnel risks. Careful consideration and modeling of the accidents in tunnels is necessary to provide a certain level of safety and to develop a rational decision criterion.
4 [ 4 Modeling tunnel accidents Which indicators are meaningful to predict tunnel accidents? Length Number of tubes Longitudinal gradient Width of the banquet HGV AADT
5 [ 5 Modeling tunnel accidents Which indicators are meaningful to predict tunnel accidents? For this study a data set of 126 tunnels in Switzerland (bfu *) was used. Not for all tunnels all the data is available (missing data) * Schweizerische Beratungsstelle für Unfallverhütung bfu / Swiss Council for Accident Prevention bfu
6 [ 6 Bayesian network
7 [ 7 Quantification of the conditional probability tables (CPT) Impossible to observe every possible combination (here ) in the node Accidents because The number of tunnels is limited The time to observe is limited The quantification of the CPT s is performed in 2 steps: 1) Using a crude linear regression model 2) Update the model using observed data
8 [ 8 Quantification of the conditional probability tables (CPT) A linear regression model is established using the available data (First step): ( Y) = X + X ( A) + X ( B) X ( C) X ( D) + X ( E) X ( F) ln ln ln ln ln ln ln ( Y) = + ( A) + ( B) ( C) ( D) + ( E) ( F) ln ln 0.40ln 0.54ln 0.06ln 0.66ln 0.96ln Y: Number of accidents [yr -1 ] A: AADT [Veh./d] B: Fraction HGV [%] C: Tubes (one or two) D: Length [km] E: Width of the banquet [m] F: Longitudinal gradient [%] Result: Conditional distribution of the number of accidents for every combination of the describing parameters. P( Y = y A, B, C, D, E, F)
9 [ 9 Quantification of the conditional probability tables (CPT) The model is then updated d using the E-M learning algorithm (second step) and the available data set. The E-M learning algorithm consists of: 1. Calculation of the expected value of a (missing) realization 2. Calculate the Maximum-Likelihood-Estimator (MLE) 3. Perform step 1. using the MLE and iterate until the MLE is converging.
10 [ 10 Quantification of the conditional probability tables (CPT) Discussion of this approach The introduction of experience in the model facilitates to weight the information in the network. The experience (equivalent sample size) of the regression model is assigned with a small number (here 0.2 is used). If one observation is made, the linear regression model has almost no influence on the CPT. The regression model is used to interpolate between not observed states. It will vanish if the number of observations increases.
11 [ 11 Quantification of the conditional probability tables (CPT) Updated marginal posterior distribution of the node HGV
12 [ 12 Quantification of the conditional probability tables (CPT) Updated marginal posterior distribution of the node HGV e AADT= [Veh day -1 ]
13 [ 13 Results for a specific tunnel The results for a specific tunnel can be evaluated by introducing evidence in the Nodes of the Bayesian network
14 [ 14 Hierarchical modeling using Bayesian networks
15 [ 15 Hierarchical modeling using Bayesian networks Result: Marginal distribution of the number of accidents; all dependencies are modeled explicitly.
16 [ 16 Hierarchical modeling using Bayesian networks Configuration 1 Configuration 2
17 [ 17 Hierarchical modeling using Bayesian networks Joint distribution of the number of accidents for configuration 1 and configuration 2
18 [ 18 Conclusion and outlook A general way is shown how to quantify large CPT in Bayesian networks. A generic model for the assessment of tunnel accidents is developed The model can be updated if new data is available; more information could be used to improve the model prediction The model facilitates to take consistently dependencies between random variables into account. Further work is necessary to develop networks which facilitates the risk assessment and risk management in tunnel.
19 [ 19 International Probabilistic Symposium 2006, Ghent, November 2007 Thank you for your attention! Matthias Schubert ETH Zürich, Institute for Structural Engineering, Group Risk & Safety Jochen Köhler ETH Zürich, Institute for Structural Engineering, Group Risk & Safety Michael H. Faber ETH Zürich, Institute for Structural Engineering, Group Risk & Safety
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