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:

Stefanescu, Razvan ^[1]; Schmidt, Kathleen ^[1]; Hite, Jason ^[2]; Smith, Ralph C. ^[1]; Mattingly, John ^[2]

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+ Show Author Affiliations

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:

2016-12-12

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:

Journal Article: 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