Source Term Estimation via SMC

SAMSI Undergraduate Workshop

31/10/08

Dr Nathan Green, UK MOD

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Contents

• Introduction

• Background

• Solutions…

• Technical details

• Application

• Toy model, R implementation

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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

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Me

• Brief history

• Skills and knowledge

• Current role and responsibilities

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Who are DSTL?

Part of the Ministry of Defence

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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

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Covert Hazardous Releases

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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

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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

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Release Modelled

• Release Mass– 60 kg

• Agent– GB

• Location of Release– 30UXC759083 (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

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Sensor Configuration

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Current solution

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Current Solution (with troops)

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Current Solution and source term estimation from SMC

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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!

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Bayes Theorem

Posterior

Likelihood

Prior

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Method of Solution

• How can we address this problem?

– MCMC?

– Kalman Filter?

– Particle Filter?

• Advantage/Drawbacks

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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

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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

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Unobserved Concentration

•Assume that the concentration at some point in time and space has a Clipped Gaussian distribution

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Clipped Gaussian Curve

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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

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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

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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

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Algorithm Description

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Algorithm Description

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Algorithm Description

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Algorithm Description

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Algorithm Description

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Algorithm Description

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Chemical Release Example Video

• Video

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R code

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R code

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R code

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Example Output

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Marginals

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Trace Plots

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Dispersion Model Output

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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

y coordinate

Close to sensors Further from

sensors

Co

nce

ntr

atio

n

Sensor y location