Abstract
In this contribution we propose a systematic approach to field reconstruction of distributed process systems from a limited and usually reduced number of measurements. The method exploits the time scale separation property of dissipative processes and concepts derived from principal angles between subspaces, to optimally placing a given number of sensors in the spatial domain. Basic ingredients of the approach include the identification of a low-dimensional subspace capturing most of the relevant dynamic features of the distributed system, and the solution of a max-min optimization problem through a guided search technique. The low-dimensional subspace can be defined either through a spectral basis (eigenfunctions of a linear or linearized part of the operator) or through a semiempirical expansion known in the engineering literature as the Proper Orthogonal Decomposition (POD) or Karhunen-Loeve expansion. For both cases, the optimal sensor placement problem will be solved by taking advantage of the underlying algebraic structure of the low-dimensional subspace. The implications of this approach for dynamic observer design will be discussed together with examples illustrating the proposed methodology.
Original language | English (US) |
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Pages (from-to) | 1438-1452 |
Number of pages | 15 |
Journal | AIChE Journal |
Volume | 50 |
Issue number | 7 |
DOIs | |
State | Published - Jul 2004 |
All Science Journal Classification (ASJC) codes
- Biotechnology
- Environmental Engineering
- Chemical Engineering(all)
Keywords
- Distributed process systems
- Observer design
- Optimal sensor placement
- Proper orthogonal decomposition
- Spectral decomposition