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

Abstract

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.