Surrogate-Based Robust Design for a Non-Smooth Radiation Source Detection Problem

Abstract

In this paper, we develop and numerically illustrate a robust sensor network design to optimally detect a radiation source in an urban environment. This problem exhibits several challenges: penalty functionals are non-smooth due to the presence of buildings, radiation transport models are often computationally expensive, sensor locations are not limited to a discrete number of points, and source intensity and location responses, based on a fixed number of sensors, are not unique. We consider a radiation source located in a prototypical 250 m × 180 m urban setting. To address the non-smooth properties of the model and computationally expensive simulation codes, we employ a verified surrogate model based on radial basis functions. Using this surrogate, we formulate and solve a robust design problem that is optimal in an average sense for detecting source location and intensity with minimized uncertainty.

Logical Inference Framework for Experimental Design of Mechanical Characterization Procedures

“…Note that multiple dimensions of the problem can be coupled to try to solve problems such as robust parameter reconstruction [ 35 ], for instance, or others defined in future needs. The procedure for robust parameter reconstruction would imply a first step where the hypothesis plausibility is computed using Equation ( 13 ), followed by a second step where the model parameters plausibility is computed using an alternative derivation of Equation ( 5 ) without restricting to a particular hypothesis , but rather incorporating all of them, by, …”

Application and Evaluation of Surrogate Models for Radiation Source Search

“…Gradient free sensitivity analysis and optimization methods can be employed as done in prior work [2], which employs gradient free optimization methods for this problem, however another option is to develop differentiable surrogate models. To avoid similar difficulties in various non-differentiable models, studies have employed differentiable surrogate models for applications in reactor simulations [9], hydrology [10], and for use in general optimization strategies [11][12][13] and optimal design [14].Similarly, we address these difficulties by investigating various differentiable surrogate models that approximate model solutions, which quantify detector responses, with suitable accuracy at a fraction of the computational expense. We employ spectral expansions using Legendre polynomials and radial basis functions as bases to generate two surrogate models.…”

“…Gradient free sensitivity analysis and optimization methods can be employed as done in prior work [2], which employs gradient free optimization methods for this problem, however another option is to develop differentiable surrogate models. To avoid similar difficulties in various non-differentiable models, studies have employed differentiable surrogate models for applications in reactor simulations [9], hydrology [10], and for use in general optimization strategies [11][12][13] and optimal design [14].…”