Constrained cubic spline approximation

Algorithm for incorporating prior knowledge into spline-smoothing of interrelated multivariate data

Data smoothening and re-sampling are often necessary to handle data obtained from laboratory and industrial experiments. This paper presents a new algorithm for incorporating prior knowledge into spline-smoothing of interrelated multivariate data. Prior knowledge based on the visual inspection of the variables and/or knowledge about the assumed balance equations can be transformed into linear equality and inequality constraints on the parameters of the splines. The splines than can be simultaneously identified from the available data by solving one quadratic programming problem. To demonstrate the applicability of the method two examples are given. In the first example, the proposed approach has been applied to the identification of kinetic parameters of a simulated reaction network, while in the second example data taken from an industrial batch reactor is analyzed. The results show that, when the proposed constrained spline-smoothing algorithm is applied, not only better fitting to the data points is achieved, but also the performance of the estimation of the kinetic parameters improves with regard to the case where no prior knowledge is involved.

The algorithm is also desribed in:
J. Madár, J. Abonyi, H. Roubos, F. Szeifert, Incorporating prior knowledge in cubic spline approximation - Application to the identification of reaction kinetic models, Industrial and Engineering Chemistry Research, 1-6, 2003

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