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

Abstract

In this investigation, we propose several algorithms to recover the location and intensity of a radiation source located in a simulated 250 m × 180 m block in an urban center based on synthetic measurements. Radioactive decay and detection are Poisson random processes, so we employ likelihood functions based on this distribution. Due 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 comprised of mixed optimization techniques. For global optimization, we consider Simulated Annealing (SA), Particle Swarm (PS) and Genetic Algorithm (GA), which rely solely on objective function evaluations; i.e., 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 (IF), 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 alone. To quantify uncertainties associated with the source location and intensity, we employ the Delayed Rejection Adaptive Metropolis (DRAM) and DiffeRential Evolution Adaptive Metropolis (DREAM) algorithms. Marginal densities of the source properties are obtained, and the means of the chains' compare accurately with the estimates produced by the hybrid algorithms.

Sequential optimal positioning of mobile sensors using mutual information

“…A variety of radiation models and sensor strategies have been proposed, but we focus on those employed in ref. [26]. For the setup in ref.…”

“…For the setup in ref. [26], 10 stationary sensors are placed throughout a portion of downtown Washington, D.C., as shown in Figure 1. To model the gamma radiation arriving at these detectors, ref.…”

“…To model the gamma radiation arriving at these detectors, ref. [26] employs a solution of the Boltzmann transport equation (BTE). The changes made to the original transport equation are based on assumptions of the experimental design, and they allow for quick model evaluation, which is essential to many parameter estimation methods, including Bayesian Markov Chain Monte Carlo (MCMC) techniques.…”

“…In ref. [26], only radiation detection via stationary sensors was considered. Moreover, these stationary detectors were randomly positioned with no attention to the optimality of their placement aside from a cursory visual inspection that they were well-dispersed throughout the domain.…”

“…As a result, a significant body of literature focuses on ascertaining the location and intensity of a radiation source in an urban environment. This is generally approached as solving an inverse problem based on data from radiation sensors placed throughout the area of interest [11,20,21,23,26]. Similarly, there has been much attention in the literature to chemical plume source localization framed as an inverse problem [6,10,19,22,30].…”