Constrained Regularization for Lagrangian Actinometry

Ultraviolet radiation (UV) is a broad-spectrum antimicrobial agent that is effective for disinfecting bacteria, viruses, and protozoa. During normal operation, UV disinfection systems deliver a distribution of UV doses. Therefore, the disinfection performance of UV systems is governed by a UV dose distribution. Lagrangian actinometry (LA) is an experimental method that allows for direct measurement of a UV dose distribution through the use of UV-sensitive dyed microspheres. The LA method estimates UV dose distributions by solving a constrained linear least-squares problem where both the coefficient matrix and the observation vector contain measurement errors. While this method has been successfully demonstrated to yield accurate estimates of dose distributions, the default numerical solver used provided unphysical results in certain settings. As a result, a more robust solver was desired. In order to develop this solver, the LA data were studied via the singular value decomposition (SVD). The SVD revealed that the LA data displayed characteristics typical of an ill-posed inverse problem. In this research a constrained truncated SVD (CTSVD) solver was developed in order to provide regularized solutions for the LA data. The method used to constrain the truncated SVD solution will be discussed, and improvements realized by the CTSVD algorithm will be shown using LA data from large-scale UV reactors.

Speaker Bio: Eric Cox is a post-doctoral research associate in the department of computer science at Purdue University. He received his doctorate in civil engineering in May 2010. He was selected to represent the Purdue student chapter of SIAM at the 2010 SIAM Annual Meeting Student Days session. His research interests include regularization methods for environmental engineering applications, algorithms for cloth simulation, parallel sparse matrix computations, and computational chemistry.

Presentation Slides: PDF

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