PAMM · Proc. Appl. Math. Mech. 17, 837 – 838 (2017) / DOI 10.1002/pamm.201710386
Real-time model adaptation
and Christof Büskens
University of Bremen, Bibliothekstraße 5, 28359 Bremen
Solving an engineering problem starts with the description of the problem in mathematical formulas and the identiﬁcation of
parameters. The generated model is then used to simulate the behavior of the underlying system. However, most systems are
not static. They change over time. Thus, the model needs to be adapted to these activities otherwise the predictions are wrong.
A data driven modeling method has been developed. The resulting models are adaptable in real time, which will also been
shown. The approach is tested on a real application of a gas engine, which has been changed signiﬁcantly by a renovation.
Therefore, the old model cannot be used anymore and model updates are generated with different forgetting rates. They are
compared to each other and to a new model. Using this comparison a recommendation is given which method is to be favored.
2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
In decreasing the production of CO2, cogeneration is a very important factor due to its high efﬁciency in transforming a
primary energy in two usable secondary energies. In a cogeneration plant, also known as a combined heat and power plant,
fossil fuel is burnt so that mechanical energy and heat is produced. The mechanical energy is transformed to electrical power
by a generator. Both forms of energy are generally used locally to prevent losses due to transportation.
In  Panno et al. show that the energy demand in the production of pasta can be decreased to 9 % by using a cogeneration
plant. The energy demand can be reduced even more if an optimization is used to improve the operational strategy. This is
demonstrated in . Chen et al. show that the energy demand and the production of CO
can be reduced to 14 %. However,
the result of the optimization algorithm depends on the models that describes the behavior of the plant. Therefore, they have
to be accurate. In this case, they also need to be computed fast because WORHP, a SQP based algorithm (cf. ), is used.
In  a data based modeling method is applied to create the precise models. However, due to aging, soiling and wears
the plants are not static and change over time. These changes also have to be mirrored by the models as well. Otherwise
the forecast of the models will be wrong. In  Chen et al. showed an example of a gas turbine where small changes in the
component make a model failing. That illustrates how important an adaptation is. To update the models Chen et al. use a
method that has been introduced by Blume in .
So far only small changes have been considered. Thus, the next question that arises is if the model adaptation can also be
used after more severe changes. To answer this question the adaptation method is used on a gas engine that was renovated for
several months. Different forgetting rates are chosen to give a weight between the old and new data. These various created
models are compared with each other and with the newly generated model.
Another aspect that has not been considered yet is the computational time for an update. It is analyzed to ﬁnd out if the
model adaptation is real-time compatible. Hence, several time measurements for different degrees of freedom are taken and
compared to the frequency of logging.
2 Comparison of the model adaptation to a newly generated model after a renovation
Usually, a new model is created after a renovation because the changes are too big to be adapted. However, to create a reliable
data based model a huge range of data is needed. This data situation is often not given after a renovation. Thus, it has to be
analyzed whether a data adaption is capable of solving this problem.
To discuss this possibility a gas engine that has been recently renovated is considered. In Figure 1 the electrical power
after and before the renovation is shown. In the identiﬁcation part, which corresponds to the time before the renovation, the
model of the electrical power mirrors the data very well. This behavior changes after the renovation. In the simulation part,
the course of the model looks similar to the data but the values are about 500 kW lower than the data. It shows that this model
cannot be applied anymore. Therefore, either a new model or an adaptation is necessary.
To decide which method is to prefer Figure 2 is regarded. The new model has problems in the simulation if there is not
enough data available. However, after 3000 data points the error gets more stable and is comparable with the errors of the
models with adaptations. This result shows that a model adaptation should be done right after a renovation and a new model
is not much better than adapting, even if enough data is available. But the adaptation with a too small forgetting rate can also
cause problems as seen in Figure 2.
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2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim