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Two methods of selecting smoothing splines applied to fermentation process data
Author(s) -
Thornhill Nina F.,
Manela Mauro,
Campbell John A.,
Stone Karl M.
Publication year - 1994
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690400414
Subject(s) - smoothing spline , smoothing , goodness of fit , spline (mechanical) , mathematics , genetic algorithm , thin plate spline , cross validation , computer science , algorithm , statistics , mathematical optimization , engineering , spline interpolation , structural engineering , bilinear interpolation
Two methods for generating smoothing splines are compared and applied to data from a fed‐batch fermentation process. One method chose both the degree of the spline and its parameters by minimizing the generalized cross validation (GCV) function using a genetic algorithm (GA). The other method adjusted the smoothing spline to a specified chi‐square goodness‐of‐fit, requiring prior knowledge of the measurement variability. The GCV/GA method led to excellent results with all the fermentation data records. The goodness‐of‐fit method gave a family of spline fits; splines with a low percentage fit extracted trends from the data, while for general use a 50% fit appeared satisfactory. The goodness‐of‐fit method executed more quickly than the GCV/GA method, but the GCV/GA method was more generally applicable as it chose both the degree of the spline and the amount of smoothing automatically.