- مبلغ: ۸۶,۰۰۰ تومان
- مبلغ: ۹۱,۰۰۰ تومان
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 effi- ciently. 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.
7. Summary and outlook
The experiments showed that the employed approaches can be successful in building cheaper yet quite accurate models of the concerned biogas plant optimization problem. Therefore, Question (Q-1) can be affirmed. In detail, Co-Kriging based on cheap evaluations from a basic biomethane potential model was shown to improve the model quality, compared to a standard Kriging model based on evaluations of an accurate ADM1 based simulation model only. Furthermore, model quality could be improved by using a Two-layer approach, thus avoiding discontinuities in the searched landscape. Besides these successes in improving surrogate model quality, their application in an optimization process proved to be more dif- ficult. In detail, time consumption of Co-Kriging proved to be too large in case of a 5-Dimensional optimization problem. On the other hand, Co-Kriging was still successful in the case of a 2-Dimensional problem formulation. The core issue here is the trade-off between 2 The variance in simulation time is mostly due to the substrate mixture. Repetition of a simulation usually yields very similar simulation times. Simulation time and function values (gain) are negatively correlated, although only weakly. computational effort of the objective function (ADM1) and the surrogate-model optimization procedure. Should the optimization be subjectto tighter time-constraints or a more expensive objective function, Co-Kriging based optimization may be profitable even in the higher-dimensional case. This depends on the kind of control problem to be solved in practice.