Data smoothing and resampling are often necessary in the handling of data obtained from laboratory and industrial experiments. This paper presents a new algorithm for incorporating prior knowledge into the spline smoothing of interrelated multivariate data. Prior knowledge based on 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 can then be simultaneously identified from the available data by solving one quadratic programming problem. To demonstrate the applicability of this method, two examples are given. In the first example, the proposed approach is applied to the identification of the kinetic parameters of a simulated reaction network, whereas in the second example, data taken from an industrial batch reactor are analyzed. The results show that, when the proposed constrained spline-smoothing algorithm is applied, one achieves not only better fitting to the data points, but also improved performance in the estimation of the kinetic parameters compared to the case in which no prior knowledge is involved.
ASJC Scopus subject areas
- Chemical Engineering(all)
- Industrial and Manufacturing Engineering