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Dietrich Brunn, Felix Sawo, Uwe D. Hanebeck
Model-based Reconstruction of Distributed Phenomena and Optimal Sensor Placement
Keywords: information fusion, distributed system, sensor scheduling, PDE, Kalman filter
This article addresses the model-based reconstruction and prediction of distributed phenomena characterized by partial differential equations. The novelty of the proposed reconstruction method is the systematic approach and the consideration of uncertainties, which occur in the physical model and arise naturally from noisy measurements. By these means, it is possible to reconstruct the complete density function of the state characterizing the distributed phenomenon. It is shown how the partial differential equation, i. e., distributed-parameter system, is spatially and temporally decomposed leading to a lumped-parameter finite-dimensional state space form. Based on the state space form, classical estimators, e. g. the Kalman filter, can directly be applied for the estimation of the solution of the underlying partial differential equation. Furthermore, a method for the optimal sensor placement is introduced. This method makes it possible to derive an optimal sequence of measurements in order to minimize the costs of measurements for a given uncertainty of the estimation result. The performance of the proposed methods is demonstrated by means of two scenarios, i. e., a temperature distribution and a deformation of a bearing. Finally, challenges of the treatment of nonlinear systems and problems of a decentralized information fusion, necessary for large sensor networks, are stated.
tm – Technisches Messen, Oldenbourg Wissenschaftsverlag
Print ISSN: 0171-8096
Volume: 74, 03/2007
Pages: 147 - 156