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Computers & Chemical Engineering
Vol. 99, 2017, Pages: 96–105

Shape constrained splines as transparent black-box models for bioprocess modeling

Alma Mašic, Sriniketh Srinivasan, Julien Billeter, Dominique Bonvin, Kris Villez

 Eawag: Swiss Federal Institute of Aquatic Science and Technology, Überlandstrasse 133, CH-8600 Dübendorf, Switzerland.


Empirical model identification for biological systems is a challenging task due to the combined effects of complex interactions, nonlinear effects, and lack of specific measurements. In this context, several researchers have provided tools for experimental design, model structure selection, and optimal parameter estimation, often packaged together in iterative model identification schemes. Still, one often has to rely on a limited number of candidate rate laws such as Contois, Haldane, Monod, Moser, and Tessier. In this work, we propose to use shape-constrained spline functions as a way to reduce the number of candidate rate laws to be considered in a model identification study, while retaining or even expanding the explanatory power in comparison to conventional sets of candidate rate laws. The shape-constrained rate laws exhibit the flexibility of typical black-box models, while offering a transparent interpretation akin to conventionally applied rate laws such as Monod and Haldane. In addition, the shape-constrained spline models lead to limited extrapolation errors despite the large number of parameters.

Graphical abstract

Keywords: Mathematical models; Microbial growth-rate kinetics; Monod equation; Shape-constrained spline function; Wastewater treatment.

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