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Title: Hybrid optimization and Bayesian inference techniques for a non-smooth radiation detection problem

Abstract

In this paper, we propose several algorithms to recover the location and intensity of a radiation source located in a simulated 250 × 180 m block of an urban center based on synthetic measurements. Radioactive decay and detection are Poisson random processes, so we employ likelihood functions based on this distribution. Owing to the domain geometry and the proposed response model, the negative logarithm of the likelihood is only piecewise continuous differentiable, and it has multiple local minima. To address these difficulties, we investigate three hybrid algorithms composed of mixed optimization techniques. For global optimization, we consider simulated annealing, particle swarm, and genetic algorithm, which rely solely on objective function evaluations; that is, they do not evaluate the gradient in the objective function. By employing early stopping criteria for the global optimization methods, a pseudo-optimum point is obtained. This is subsequently utilized as the initial value by the deterministic implicit filtering method, which is able to find local extrema in non-smooth functions, to finish the search in a narrow domain. These new hybrid techniques, combining global optimization and implicit filtering address, difficulties associated with the non-smooth response, and their performances, are shown to significantly decrease the computational time over themore » global optimization methods. To quantify uncertainties associated with the source location and intensity, we employ the delayed rejection adaptive Metropolis and DiffeRential Evolution Adaptive Metropolis algorithms. Finally, marginal densities of the source properties are obtained, and the means of the chains compare accurately with the estimates produced by the hybrid algorithms.« less

Authors:
 [1];  [1];  [2];  [1];  [2]
  1. North Carolina State Univ., Raleigh, NC (United States). Dept. of Mathematics
  2. North Carolina State Univ., Raleigh, NC (United States). Dept. of Nuclear Engineering
Publication Date:
Research Org.:
North Carolina State Univ., Raleigh, NC (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA), Office of Defense Nuclear Nonproliferation
OSTI Identifier:
1438214
Grant/Contract Number:  
NA0002576
Resource Type:
Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Engineering
Additional Journal Information:
Journal Volume: 111; Journal Issue: 10; Journal ID: ISSN 0029-5981
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; inverse problems; simulated annealing; particle swarm; genetic algorithm; implicit filtering; DiffeRential Evolution Adaptive Metropolis; delayed rejection adaptive Metropolis

Citation Formats

Stefanescu, Razvan, Schmidt, Kathleen, Hite, Jason, Smith, Ralph C., and Mattingly, John. Hybrid optimization and Bayesian inference techniques for a non-smooth radiation detection problem. United States: N. p., 2016. Web. doi:10.1002/nme.5491.
Stefanescu, Razvan, Schmidt, Kathleen, Hite, Jason, Smith, Ralph C., & Mattingly, John. Hybrid optimization and Bayesian inference techniques for a non-smooth radiation detection problem. United States. doi:10.1002/nme.5491.
Stefanescu, Razvan, Schmidt, Kathleen, Hite, Jason, Smith, Ralph C., and Mattingly, John. Mon . "Hybrid optimization and Bayesian inference techniques for a non-smooth radiation detection problem". United States. doi:10.1002/nme.5491. https://www.osti.gov/servlets/purl/1438214.
@article{osti_1438214,
title = {Hybrid optimization and Bayesian inference techniques for a non-smooth radiation detection problem},
author = {Stefanescu, Razvan and Schmidt, Kathleen and Hite, Jason and Smith, Ralph C. and Mattingly, John},
abstractNote = {In this paper, we propose several algorithms to recover the location and intensity of a radiation source located in a simulated 250 × 180 m block of an urban center based on synthetic measurements. Radioactive decay and detection are Poisson random processes, so we employ likelihood functions based on this distribution. Owing to the domain geometry and the proposed response model, the negative logarithm of the likelihood is only piecewise continuous differentiable, and it has multiple local minima. To address these difficulties, we investigate three hybrid algorithms composed of mixed optimization techniques. For global optimization, we consider simulated annealing, particle swarm, and genetic algorithm, which rely solely on objective function evaluations; that is, they do not evaluate the gradient in the objective function. By employing early stopping criteria for the global optimization methods, a pseudo-optimum point is obtained. This is subsequently utilized as the initial value by the deterministic implicit filtering method, which is able to find local extrema in non-smooth functions, to finish the search in a narrow domain. These new hybrid techniques, combining global optimization and implicit filtering address, difficulties associated with the non-smooth response, and their performances, are shown to significantly decrease the computational time over the global optimization methods. To quantify uncertainties associated with the source location and intensity, we employ the delayed rejection adaptive Metropolis and DiffeRential Evolution Adaptive Metropolis algorithms. Finally, marginal densities of the source properties are obtained, and the means of the chains compare accurately with the estimates produced by the hybrid algorithms.},
doi = {10.1002/nme.5491},
journal = {International Journal for Numerical Methods in Engineering},
number = 10,
volume = 111,
place = {United States},
year = {2016},
month = {12}
}

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