Source Term Estimation via SMC SAMSI Undergraduate Workshop 31/10/08 Dr Nathan Green, UK MOD

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Contents Introduction Background Solutions… Technical details Application Toy model, R implementation

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Introduction I’m going to concentrate on one particular application of SMC methodology This is a –real-life –important problem Hopefully, highlight the practicality of using an SMC approach and demonstrate its use in the real world

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Me Brief history Skills and knowledge Current role and responsibilities

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Who are DSTL? Part of the Ministry of Defence

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Who are we? Not in the Army, Navy or Air Force Civil servants – civilians who work for the government Our job is to: –Carry out research for the Ministry of Defence –Help the MoD to buy our forces the best equipment –Keep our forces safe

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Covert Hazardous Releases

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED The Problem: Source Term Estimation In order to protect UK forces in the event of a CBRN event it will be necessary to make a hazard prediction Accurate hazard prediction requires knowledge of a source term Source term estimation provides the ability to take sensor readings and provide a source term and therefore a hazard prediction This allows commanders to protects their forces and plan counter measures

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Aim Develop a Real-time Source-Term Estimation capability –To make best estimates of the parameters of the release –From low resolution alarms or high resolution time series data –Produce results in a timely fashion, i.e. Under 5 minutes

Example Problem

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Release Modelled Release Mass –60 kg Agent –GB Location of Release –30UXC (MGRS) –51°29’54.4”N 0°27’26.8”W (Lat Lon) Time of Release –011200ZNOV2007 Basic Met –Wind speed 18kmh –Easterly Wind Direction –Neutral Conditions

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Sensor Configuration

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Current solution

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Current Solution (with troops)

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Current Solution and source term estimation from SMC

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED The Model We want to estimate the (static) source term parameters The only information we have about a release is through sensor measurements downwind, y So we want to estimate on-line the source term parameters as more data arrives Use a Bayesian approach!

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Bayes Theorem Posterior Likelihood Prior

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Method of Solution How can we address this problem? –MCMC? –Kalman Filter? –Particle Filter? Advantage/Drawbacks

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Prior Knowledge We know that given a positive sensor measurement the release time will have been in the past! We can have an idea of where is likely to be attacked/protected Previous scenario information can be used, perhaps through an MCMC approach

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Likelihood Function The likelihood is a way in which the data can be incorporated into our analysis It can be thought of as supplying the evidence in support of a given model In our case, the data (sensor measurements) tell use about the source term via an unobserved concentration

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Unobserved Concentration Assume that the concentration at some point in time and space has a Clipped Gaussian distribution

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Clipped Gaussian Curve

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Sensors Many different sensors to model: –Chemical Releases Bar sensor Threshold sensor Concentration realisation sensor –Biological Releases Particle Detector / Resonant Mirror –Radiological Releases Long Range Gamma Sensor

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Key Elements Generate a ‘cloud’ of source term hypotheses (particles) A dispersion model produces concentration probability distributions at each sensor location and time point for every hypothesis Sensor models use these probabilities to create likelihood values for these hypotheses The hypotheses are updated in light of in-coming sensor measurement

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Particle Diversity Unfortunately, the initial source term estimates may not prove to be very good guesses In this case, we may be left with just a single decent particle To remedy this problem a ‘diversifying’ step is included –New particles are probabilistically generated and accepted –A Metropolis-Hastings MCMC step

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Algorithm Description

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Algorithm Description

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Algorithm Description

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Algorithm Description

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Algorithm Description

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Algorithm Description

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Chemical Release Example Video Video

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED R code

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED R code

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED R code

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Example Output

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Marginals

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Trace Plots

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Dispersion Model Output

© Dstl October 2008 Dstl is part of the Ministry of Defence UNCLASSIFIED Note on Estimation Bias A small release mass close to the sensor array and a large release mass further away from the sensors produce comparable concentration measurements at the sensors –The release location estimate is likely to be over-predicted (i.e. further away) –In terms of warning and reporting, will err on the side of safety and predict a larger affected hazard area Close to sensors Further from sensors Concentration Sensor y location