K.-L. Wen, Y.-F. Huang, and C.-C. Tong (Taiwan)

Interpolation, Data Reconstruction, Equal Space, Class Ratio, Grey Theory.

Generally speaking, it is apparent and convenient to analyze and predict a set of sequence that is equally spaced in the field of engineering applications. However, the data sequence under study is often messed-up and sometimes has missing points. Data pre-conditioning is required to reconstruct the original sequence with equal space on the horizontal axis. This step is so crucial to the outcome and has to be taken into careful consideration. As a result, analysis, prediction, or estimation based on the sequence therefore becomes smooth, useful and accurate. In this paper, a new method based on the class ratio theorem in Grey Theory is proposed to provide a new approach to this problem. There are three major contributions throughout this research. First, the class ratio theorem in Grey Theory can be reduced from three to two equations. This is the main academic contribution of this paper. Second, another major contribution is that the reconstruction of the third missing point is better than that of the second point in a sequence of four points. The reconstruction of the third missing point method is highly recommended instead of the second point method in the case of four points interpolation. Finally, a convenient toolbox is developed along with the research to pass through the tedious process of calculation and derive the result.

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