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Mathematical Problems in Engineering
Volume 2014, Article ID 353970, 17 pages
http://dx.doi.org/10.1155/2014/353970
Research Article

Data Driven Based Method for Field Information Sensing

1School of Energy, Power and Mechanical Engineering, North China Electric Power University, Changping District, Beijing 102206, China
2Key Laboratory of Efficient Utilization of Low and Medium Grade Energy (Tianjin University), Ministry of Education of China, Tianjin 300072, China

Received 15 July 2014; Accepted 16 October 2014; Published 9 November 2014

Academic Editor: Massimo Scalia

Copyright © 2014 Jing Lei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Acquiring the field information on temperature, pressure, concentration, or velocity is crucial for the monitoring of chemical reactors, multiphase flow systems, heat transfer units, atmospheric pollutants diffusion, and underground pollutant migration. In this paper, a dimensionality reduction matrix completion (DRMC) method is proposed for the field information sensing (FIS) of objects of interest from the scattered point measurement data. An objective functional that casts the FIS task as an optimization problem is proposed. An iteration scheme is developed for solving the proposed objective functional. Numerical simulations are implemented to validate the feasibility and effectiveness of the proposed algorithm. It is found that differing from common inverse problems, numerical simulation approaches, and tomography based field measurement methods, in the proposed method the field information can be reconstructed without the knowledge on governing equations of the measurement objects, initial conditions, boundary conditions, and physical properties of materials, except the limited number of the measurement data. As a result, an alternative insight is introduced for the FIS problems.