Low-dimensional Modeling of Linear Heat Transfer Systems Using the Incremental Proper Orthogonal Decomposition Method
C. Xu and E. Schuster
Asia-Pacific Journal of Chemical Engineering vol. 8, no. 4, p. 473-482, 2013
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Abstract
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In this work, we propose the incremental proper orthogonal decomposition (POD) method and the recursive Galerkin
projection to achieve model order reduction (MOR) for high-dimensional dynamical systems arising in the processes
of heat transfer for green buildings. For MOR of high-dimensional dynamical systems, we use a batch of historic data
to initially extract a sequence of POD modes and derive a low-dimensional system to approximate the high-dimensional
heat transfer system. Then, we check the prediction error at every subsequent sampling moment by using the obtained
POD modes. If the approximation error is larger than the pre-given threshold value, we then add the new snapshot
into the collected sampling ensemble. Instead of recalculating the POD-oriented eigenvalue decomposition problem at
each ensemble augmentation (which is time-consuming), the incremental POD method applies the updated singular value
decomposition approach to increase the number of POD modes and adjust the shape of POD modes, and also change
corresponding POD eigenvalues through a matrix rotation transformation.
