Dimension Embedded Basis Function for Spatiotemporal Modeling of Distributed Parameter System

The construction of spatial basis functions (BFs) is critical to the time/space separation of the distributed parameter system (DPS). The spatial BFs constructed by traditional Karhunen-Loéve may not work satisfactorily for two spatial-dimensional (2-D) DPS, because of a distorted mapping of the original sensor array in the row-wise vectorization process. In this article, a novel time/space separation based method is proposed to construct dimension embedded BFs (DE-BFs) for modeling 2-D DPS. The DE-BFs are first formulated according to the spatial sensor array structure, and sequentially optimized with alternating least squares by minimizing the reconstruction error. The mapping relationship between the DE-BFs and the spatial sensor array is well preserved. In addition, the coupling across temporal and different spatial dimensions is sufficiently captured. A satisfactory model accuracy can be achieved by the DE-BFs, even with limited training data. Experiments of a 2-D curing thermal process are used to verify the effectiveness of the proposed method.