Dimension Embedded Basis Function for Spatiotemporal Modeling of Distributed Parameter System

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Original languageEnglish
Article number8936383
Pages (from-to)5846-5854
Number of pages9
Journal / PublicationIEEE Transactions on Industrial Informatics
Issue number9
Online published18 Dec 2019
Publication statusPublished - Sept 2020


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.

Research Area(s)

  • Dimension embedded, distributed parameter system (DPS), spatial basis function (BF), time/space separation