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

COMPUTERS & CHEMICAL ENGINEERING 2017年 99卷 96-105页

作者： Masic, Alma Srinivasan, Sriniketh Billeter, Julien Bonvin, Dominique Villez, Kris Eawag Swiss Fed Inst Aquat Sci & Technol Uberlandstr 133 CH-8600 Dubendorf Switzerland Ecole Polytech Fed Lausanne Lab Automat CH-1015 Lausanne 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. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Mathematical models Microbial growth-rate kinetics Monod equation shape-constrained spline function Wastewater treatment

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On the Use of shape-constrained splines for Biokinetic Process Modeling

On the Use of Shape-Constrained Splines for Biokinetic Proce...

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11th IFAC Symposium on Dynamics and Control of Process Systems including Biosystems

作者： Masic, Alma Srinivasan, Sriniketh Billeter, Julien Bonvin, Dominique Villez, Kris Swiss Fed Inst Aquat Sci & Technol Uberiandstr 133POB 611 CH-8600 Dubendorf Switzerland Ecole Polytech Fed Lausanne Lab Automat CH-1015 Lausanne Switzerland

Identification of mathematical models is an important task for the design and the optimization of biokinetic processes. Monod or Tessier growth-rate models are often chosen by default, although these models are not able to represent the dynamics of all bacterial growth processes. This imperfect representation then affects the quality of the model prediction. This paper introduces an alternative approach, which IS based on constraints such as monotonicity and concavity and the use of shape-constrained spline functions, to describe the substrate affinity with high parametric flexibility. This way, the difficult task of searching through potentially incomplete rate-model libraries can be circumvented. A simulated case study is used to illustrate the superiority of the proposed method to represent, non-ideal growth conditions, where neither Monod nor Tessier kinetics offer a good approximation. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Mathematical models microbial growth-rate kinetics Monod equation shape-constrained spline function wastewater treatment

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