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Sections/90_Conclusion.tex
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\section{Conclusion}~\label{sec:conclusion}
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The aim of this project was to analyze the performance of \acrshort{gp} based
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controllers for use in longer lasting implementations, where differences in
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building behaviour become important compared to the initially available data.
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First, the performance of a classical \acrshort{gp} model trained on five days
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worth of experimental data was analyzed. Initially, this model performed very
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well both in one step ahead prediction and multi-step ahead simulation over new,
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unseen, data. With the change in weather, however, the model shifted from
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operating in the interpolated regions to the extrapolated regions of the initial
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weather data. In this scenario the model was unable to properly predict the
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\pdome\ behaviour and, as a consequence, the \acrshort{mpc} controller became
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unstable.
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Following that, several \acrshort{svgp} implementations were analyzed. The
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initial behaviour exhibited during parameter identification (cf.
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Section~\ref{sec:hyperparameters}) showed that the \acrshort{svgp} model was
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less capable of capturing building dynamics only based on the initial
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experimental dataset, possibly due to the \acrshort{elbo} approximation of the
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true log likelihood. While the \acrshort{svgp} model remained stable over the
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course of the 20-step ahead simulation, in the later steps it drifted much
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further from the real values than the equivalent \acrshort{gp} model.
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However, during the full-year simulation, this downside of the \acrshort{svgp}
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model was compensated by adding new data to the model training dataset each
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night at midnight. The model performance continuously improved over the course
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of the simulation, providing much better results overall.
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To better analyze the learning behaviour of the \acrshort{svgp} models, three
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variations of the initial \acrshort{svgp} were also simulated. The first
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variation consisted of training the initial model on only one day's worth of
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experimental data, as opposed to five days in the first case. This model was
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then regularly updated every night at midnight, just as the initial case. It
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turned out to provide very comparable results to the initial model, leading to
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the conclusion that the \acrshort{svgp} model can be initially deployed using
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much less training data, and it will still be able to correctly capture the
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building dynamics on subsequent updates.
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The second variation of the \acrshort{svgp} model was re-trained using a rolling
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window of five days' worth of data, in order to see the model's ability to learn
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the proper building dynamics based only on closed-loop operation data. This
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model turned out to be unstable, and the full-year simulation showed that every
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time the model was trained using \textit{only} closed-loop operation data it
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turned unstable. This prompted a much higher excitation of the building for the
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following day, which in turn provided enough information to train a good model,
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that would last until this information was too old to be included in the
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training window, at which point the model would turn unstable again.
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In the last variation, the \acrshort{svgp} model was trained using a linear
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kernel. This model turned out to perform worse overall than the \acrshort{se}
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kernel model since it was unable to capture the more nuanced, non-linear
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behaviour of the building.
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\subsection{Further Research}~\label{sec:further_research}
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Section~\ref{sec:results} has presented and compared the results of a full-year
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simulation for a classical \acrshort{gp} model, as well as a few incarnations of
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\acrshort{svgp} models. The results show that the \acrshort{svgp} have much
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better performance, mainly due to the possibility of updating the model
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throughout the year. The \acrshort{svgp} models also present a computational
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cost advantage both in training and in evaluation, due to several approximations
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shown in Section~\ref{sec:gaussian_processes}.
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Focusing on the \acrlong{gp} models, there could be several ways of improving
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its performance, as noted previously: a more varied identification dataset and
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smart update of a fixed-size data dictionary according to information gain,
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could mitigate the present problems.
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Using a Sparse \acrshort{gp} without replacing the maximum log likelihood
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with the \acrshort{elbo} could improve performance of the \acrshort{gp} model at
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the expense of training time.
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An additional change that could be made is inclusion of the most amount of prior
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information possible through setting a more refined kernel, as well as adding
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prior information on all the model hyperparameters when available. This approach
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however goes against the `spirit' of black-box approaches, since significant
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insight into the physics of the plant is required in order to properly model and
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implement this information.
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On the \acrshort{svgp} side, several changes could also be proposed, which were
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not properly addressed in this work. First, the size of the inducing dataset was
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chosen experimentally until it was found to accurately reproduce the manually
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collected experimental data. In order to better use the available computational
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resources, this value could be found programmatically in a way to minimize
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evaluation time, while still providing good performance. Another possibility is
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the periodic re-evaluation of this value when new data comes in, since as more
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and more data is collected the model becomes more complex, and in general more
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inducing locations could be necessary to properly reproduce the training data.
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Finally, none of the presented controllers take into account occupancy rates or
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adapt to possible changes in the real building, such as adding or removing
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furniture, deteriorating insulation and so on. The presented update methods only
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deals with adding information on behaviour in different state space regions, i.e
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\textit{learning}. Additionally, their ability to \textit{adapt} to changes in
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the actual plant's behaviour should be further addressed.
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\section*{Acknowledgements}
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I would like to thank Manuel Koch for the great help provided during the course
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of the project starting from the basics on CARNOT modelling, to helping me
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better compare the performance of different controllers, as well as Prof.\ Colin
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Jones, whose insights were always very guiding, while still allowing me to
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discover everything on my own.
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\clearpage
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