Advanced methods for data reconstruction: interpolation methods applied to a set of radiation data

One of the main step in data analysis is represented by the data reconstruction. The relatively easiest approach to solve that problem is interpolation. In our work, different interpolation methods has been analyzed and applied to radiation measurements collected by sensors. Numerical quality of the reconstruction and complexity has been evaluated using the O-notation. The methods analyzed are: 1. Interpolation by polynomials: Lagrange and Newton interpolation algorithm. 2. Rational interpolation: Thiele’s formula. 3. Spline interpolation: Bézier, cubic and Catmull-Rom. 4. Least squares method: linear and quadratic (statistical interpolation). 5. Ordinary Kriging method (geostatistical interpolation). For each method we have written an algorithm in pseudo-code used to evaluate the complexity expressed in terms of O-notation, then the Java code has been written using the framework Eclipse and executed on a MacBook Pro armed with a 2.4GHz Intel Core Duo. The input dataset used for each interpolation method (except for the Kriging’s method) has 96 samples and corresponds to the day 15-07-2011 (from the midnight to the midnight) of the photovoltaic field located in Moie (An). We first cancelled both singular samples and subset of data from the original dataset, and then performed the reconstruction. Using the mean square difference index Ism we evaluated the quality of the reconstruction. For the Kriging’s method we used the radiation value recorded at the 15-07-2011 01.15pm in four PV systems. Polynomial and rational interpolation algorithms can be designed with a dynamic programming approach: each partial solutions can be stored in a properly data structure that allows us to optimize computation time and resources management. In terms of complexity, our results suggest to use the algorithms of Newton and Thiele, in particular, for the reconstruction of m points with n=96 samples we obtain . In terms of Ism , the algorithms that we suggest to use are the Newton or Thiele for a single missing data, Spline Catmull-Rom for an entire subset. We validated the Kriging ordinary method using a physical model developed for the the software R called r.sun