{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:39:21Z","timestamp":1760240361034,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T00:00:00Z","timestamp":1559001600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100006168","name":"National Nuclear Security Administration","doi-asserted-by":"publisher","award":["DE-NA0002576"],"award-info":[{"award-number":["DE-NA0002576"]}],"id":[{"id":"10.13039\/100006168","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>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 \u00d7 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.<\/jats:p>","DOI":"10.3390\/a12060113","type":"journal-article","created":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T11:18:09Z","timestamp":1559042289000},"page":"113","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Surrogate-Based Robust Design for a Non-Smooth Radiation Source Detection Problem"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4591-6891","authenticated-orcid":false,"given":"R\u0103zvan","family":"\u015etef\u0103nescu","sequence":"first","affiliation":[{"name":"Global Validation Model Department, Spire Global, Inc., Boulder, CO 80301, USA"},{"name":"Department of Computer Science, Virginia Tech, Blacksburg, VA 24060-0902, USA"}]},{"given":"Jason","family":"Hite","sequence":"additional","affiliation":[{"name":"Department of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695, USA"}]},{"given":"Jared","family":"Cook","sequence":"additional","affiliation":[{"name":"Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA"}]},{"given":"Ralph C.","family":"Smith","sequence":"additional","affiliation":[{"name":"Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA"}]},{"given":"John","family":"Mattingly","sequence":"additional","affiliation":[{"name":"Department of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695, USA"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1109\/87.880592","article-title":"Model-Based Solution Techniques for the Source Localization Problem","volume":"8","author":"Alpay","year":"2000","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1109\/TCST.2002.1014683","article-title":"Comments on \u201cModel-based solution techniques for the source localization problem\u201d","volume":"10","author":"Sivergina","year":"2002","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_3","unstructured":"Shultis, J.K., and Faw, R.E. (2000). Radiation Shielding, American Nuclear Society."},{"key":"ref_4","unstructured":"Briesmeister, J., Carlo, M.T.G.M., and Code, N.P.T. (2000). Report LA-13709-M."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"King, M.J., Harris, B., Toolin, M., DuBord, R.M., Skowronski, V.J., LuSoto, M.A., Estep, R.J., Brennan, S.M., Cosofret, B.R., and Shokhirev, K.N. (2010, January 8\u201310). An Urban Environment Simulation Framework for Evaluating Novel Distributed Radiation Detection Architectures. Proceedings of the 2010 IEEE International Conference on Technologies for Homeland Security (HST), Waltham, MA, USA.","DOI":"10.1109\/THS.2010.5654958"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1109\/MC.2004.103","article-title":"Radiation Detection with Distributed Sensor Networks","volume":"37","author":"Brennan","year":"2004","journal-title":"Computer"},{"key":"ref_7","unstructured":"Hensley, W., and Lepel, E. (1996). Synth: A Gamma-Ray Spectrum Synthesizer."},{"key":"ref_8","unstructured":"Morelande, M.R., and Skvortsov, A. (2009, January 6\u20139). Radiation field estimation using a Gaussian mixture. Proceedings of the 12th International Conference on Information Fusion, Seattle, WA, USA."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"955","DOI":"10.1002\/nme.5491","article-title":"Hybrid optimization and Bayesian inference techniques for a non-smooth radiation detection problem","volume":"111","author":"Schmidt","year":"2017","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_10","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle Swarm Optimization. Proceedings of the IEEE International Conference on Neural Networks, Perth, Australia."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1126\/science.220.4598.671","article-title":"Optimization by Simulated Annealing","volume":"220","author":"Kirkpatrick","year":"1983","journal-title":"Science"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Kelley, C.T. (2011). Implicit Filtering, SIAM.","DOI":"10.1137\/1.9781611971903"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/s11222-006-9438-0","article-title":"DRAM: Efficient adaptive MCMC","volume":"16","author":"Haario","year":"2006","journal-title":"Stat. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1515\/IJNSNS.2009.10.3.273","article-title":"Accelerating Markov Chain Monte Carlo Simulation by Differential Evolution with Self-Adaptive Randomized Subspace Sampling","volume":"10","author":"Vrugt","year":"2009","journal-title":"Int. J. Nonlinear Sci. Numer. Simul."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Ucinski, D. (2004). Optimal Measurement Methods for Distributed Parameter System Identification, CRC Press.","DOI":"10.1201\/9780203026786"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Sun, N.Z. (1999). Inverse Problems in Groundwater Modeling, Springer Science & Business Media.","DOI":"10.1007\/978-94-017-1970-4"},{"key":"ref_17","first-page":"235","article-title":"Near-optimal sensor placements in Gaussian processes: Theory, efficient algorithms and empirical studies","volume":"9","author":"Krause","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"ref_18","unstructured":"Michaud, I. (2019). Simulation-Based Bayesian Experimental Design Using Mutual Information. [Ph.D. Thesis, North Carolina State University]."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1214\/15-BA945","article-title":"Computational enhancements to Bayesian design of experiments using Gaussian processes","volume":"11","author":"Weaver","year":"2016","journal-title":"Bayesian Anal."},{"key":"ref_20","unstructured":"Schmidt, K. (2016). Uncertainty Quantification for Mixed-Effects Models with Applications in Nuclear Engineering. [Ph.D. Thesis, North Carolina State University]."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"066138","DOI":"10.1103\/PhysRevE.69.066138","article-title":"Estimating mutual information","volume":"69","author":"Kraskov","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.jcp.2016.08.001","article-title":"An information theoretic approach to use high-fidelity codes to calibrate low-fidelity codes","volume":"324","author":"Lewis","year":"2016","journal-title":"J. Comput. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.expthermflusci.2011.09.012","article-title":"Bayesian experimental design for the active nitridation of graphite by atomic nitrogen","volume":"36","author":"Terejanu","year":"2012","journal-title":"Exp. Therm. Fluid Sci."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Buhmann, M.D. (2003). Radial Basis Functions: Theory and Implementations, Cambridge University Press.","DOI":"10.1017\/CBO9780511543241"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Fedorov, V.V., and Leonov, S.L. (2013). Optimal Design for Nonlinear Response Models, CRC Press.","DOI":"10.1201\/b15054"},{"key":"ref_26","unstructured":"Spall, J.C. (2005). Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control, John Wiley & Sons."},{"key":"ref_27","unstructured":"Kennedy, J. (2010). Particle swarm optimization. Encyclopedia of Machine Learning, Springer."},{"key":"ref_28","unstructured":"Eberhart, R.C., and Kennedy, J. (1995, January 4\u20136). A New Optimizer Using Particle Swarm Theory. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan."},{"key":"ref_29","unstructured":"Marti, K. (2005). Stochastic Optimization Methods, Springer."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1574","DOI":"10.1137\/070704277","article-title":"Robust stochastic approximation approach to stochastic programming","volume":"19","author":"Nemirovski","year":"2009","journal-title":"SIAM J. Optim."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/6\/113\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:54:01Z","timestamp":1760187241000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/6\/113"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,28]]},"references-count":30,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2019,6]]}},"alternative-id":["a12060113"],"URL":"https:\/\/doi.org\/10.3390\/a12060113","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2019,5,28]]}}}