Stochastic source term estimation of HAZMAT releases: algorithms and uncertainty

公共安全研究院INSITITUTE OF PUBLIC SAFETY RESEARCH

Yan Wang1 , Hong Huang1, Wei Zhu2

Stochastic source term estimation of HAZMAT releases:

algorithms and uncertainty

wangyan14@mails.tsinghua.edu.cn

1Institute of Public Safety Research,

Department of Engineering Physics,

Tsinghua University2Beijing Research Center of Urban System Engineering,

Beijing Academy of Science and Technology

清华大学公共安全研究院Institute of Public Safety Research

Outline

Introduction

The Bayesian framework

Description of the three stochastic methods

Simulations and results

Conclusion

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Introduction (1)

The release of hazardous material is an

enormous threat to public safety.

Natural disaster, accidents, terrorist acts

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Introduction (2)

Information about the source parameters

plays an important role in decision making

and damage mitigation.

Gas type

Source location

Release rate

Release time

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Introduction (3)

Requirements for STE Approaches Effective

Quantitative and accurate

Efficient

Provide a solution within given time constraints

Flexible

Adaptable to a variety of classes of observations

Adaptable to problems of various scales

Robust

Can be used in operational or high consequence situations

Quantifies uncertainty

Probabilities are assigned to each possible state or outcome

This page is modified from National Center for Atmospheric Research (NCAR)

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Introduction (4)

Some popular methods for STE

Forward modelling

Optimization methods + Atmospheric transport and dispersion

(AT&D) model

Thomson et al. (2007), Zheng and Chen (2010)

Bayesian inference + AT&D model

Wade and Senocak (2013) , Hazart et al(2014)

Bayesian inference + Adjoint AT&D model

Keats et al.(2007), Guo et al.(2009)

Backward modelling

Reverse-time CFD (Eulerian)

Bady et al.(2009)

Backward Lagrangian stochastic (bLS) model

Wilson et al.(2012), Wang et al.(2013)

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Introduction (5)

Uncertainty in atmospheric dispersion

modelling, Rao (2005)

Initial and boundary conditions

Simplified treatment of complex physical or

chemical processes

Turbulent nature of the atmosphere

Approximate numerical solutions

Unpredictable human activities

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Basic idea

Features Take advantage of prior information

Incorporate model error and observation error

Quantify the uncertainty of estimation results

( ) ( ) 2

(t)2 (t)21 1 , ,

( | ) (X)( | )

(Y)

[ ( ) ]( | ) ( | ) (

| ( )

,

) exp2( )

,

t tm ki i

t i y i f i

denote the source paramet

p Y X pp X Y

p

F Yp Y X p Y T p T F X

ers

denote the observed concentration

concentra

dT

where

X

Y

T denote the true

X

( )

,

tion

concentration withF X denote the predict source parameed ters X

The Bayesian framework (1)

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The Bayesian framework (2)

The Posterior distribution is difficult to

calculate directly.

Approximate the Posterior distribution by

stochastic sampling

Markov chain Monte Carlo (MCMC)

Sequential Monte Carlo (SMC)

Ensemble Kalman filter (EnKF)

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Markov chain Monte Carlo

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Metropolis-Hasting algorithm

清华大学公共安全研究院Institute of Public Safety Research

Sequential Monte Carlo

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Sequential importance resampling (SIR)

1 1

1 1

1 1

( ) ( )( )

( )

j j j

j j j j

j j j

p pw w w p

q

Y X X X

Y XX X

清华大学公共安全研究院Institute of Public Safety Research

Ensemble Kalman filter

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Kalman filter

Ensemble Kalman filter

A Monte Carlo approximation of the Kalman Filter.

Applicable to high-dimensional nonlinear system.

All probability distributions involved are Gaussian.

清华大学公共安全研究院Institute of Public Safety Research

Simulations and results (1)

The synthetic experiment

• Observation: add a

maximum of 50% random

noise to the model output.

• Flat prior on the location and

strength of the source:

x ~ U[-10,60], x0=0

y ~ U[-20,30], y0=0

Q ~ U[500,20000],

Q0=10434

Gaussian plume model

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清华大学公共安全研究院Institute of Public Safety Research

Simulations and results (2)

Location estimation

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清华大学公共安全研究院Institute of Public Safety Research

Simulations and results (3)

Strength estimation

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清华大学公共安全研究院Institute of Public Safety Research

Simulations and results (4)

Efficiency comparison

MCMC SMC EnKF

Convergence step 17325 138 173

Number of running the forward

model per iteration1 100 101

Particle number or ensemble

size per iteration1 100 100

Total running of the forward

model until convergence17325 13800 17473

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Some further discussion

Simulations and results (5)

Requirements

for STE ApproachesMCMC SMC EnKF

Effective 1 1 1

Efficient Good Faster Faster

Flexible — — —

Robust — — —

Quantifies uncertainty Good Good Limited

Within the scenario in this work

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清华大学公共安全研究院Institute of Public Safety Research

Conclusion

Conclusion Three stochastic methods for STE are implemented under a unified

Bayesian framework, and are compared in accuracy, time

consumption as well as the quantification of uncertainty.

MCMC and SMC give similar results while EnKF tends to

overestimate the release rate and fails to capture the non-

Gaussian features of the posterior.

SMC and EnKF are inherently parallel and cost much less time to

convergence.

The flip ambiguity phenomenon is considered to be caused by the

axial symmetry of the experiment setup as well as the random

noise added to the synthetic concentration data.

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Thank you for your time and attention.

Any questions?

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