Biokinetic process model diagnosis with shape-constrained spline functions

Model-structure identification is important for the optimization and design of biokinetic processes. Standard Monod and Tessier functions are often used by default to describe bacterial growth with respect to a substrate, leading to significant optimization errors in case of inappropriate representation. This paper introduces shape-constrained spline (SCS) functions, which share the qualitative behavior of a number of conventional growth-rate functions expressing substrate affinity effects. A simulated case study demonstrates the capabilities in terms of model identification of SCS functions, which offer a high parametric flexibility and could replace incomplete libraries of functions by a single biokinetic model structure. Moreover, the diagnostic ability of the spline functions is illustrated for the case of Haldane kinetics, which exhibits a distinctively different shape. The major benefit of these spline functions lies in their model discrimination capabilities by indicating in a quick and conclusive way the presence of other effects than substrate affinity.