Multi-fidelity modeling and optimization of biogas plants

Graphical abstractDisplay Omitted HighlightsAccurate and fast simulation models mandatory for the optimization of biogas plants.Improve precision of simulation models without increasing the number of evaluations.Combining results: complex simulator, simple estimation-based model and surrogate model.Advantages and limitations of multi-fidelity modeling approaches are discussed. An essential task for operation and planning of biogas plants is the optimization of substrate feed mixtures. Optimizing the monetary gain requires the determination of the exact amounts of maize, manure, grass silage, and other substrates. For this purpose, accurate simulation models are mandatory, because the underlying biochemical processes are very slow. The simulation models may be time-consuming to evaluate, hence we show how to use surrogate-model-based approaches to optimize biogas plants efficiently. In detail, a Kriging surrogate is employed. To improve model quality of this surrogate, we integrate cheaply available data into the optimization process. To this end, multi-fidelity modeling methods like Co-Kriging are applied. Furthermore, a two-layered modeling approach is used to avoid deterioration of model quality due to discontinuities in the search space. At the same time, the cheaply available data is shown to be very useful for initialization of the employed optimization algorithms. Overall, we show how biogas plants can be efficiently modeled using data-driven methods, avoiding discontinuities as well as including cheaply available data. The application of the derived surrogate models to an optimization process is only partly successful. Given the same budget of function evaluations, the multi-fidelity approach outperforms the alternatives. However, due to considerable computational requirements, this advantage may not translate into a success with regards to overall computation time.