Submitted version of thesis to prof

00_First_Page.tex

@@ -4,8 +4,13 @@
 \includegraphics[width=0.5\linewidth]{Logo-EPFL.png}\par
 \vspace{5cm}
 
-{\Huge \bf Multi-seasonal performance of Gaussian Processes for building control \par}
-\vspace{1cm}
+{\huge \bf 
+\setstretch{1.25}
+Inter-seasonal Performance of Gaussian Process-based
+Model Predictive Control of Buildings
+\par}
+
+\vspace{2cm}
 {\LARGE \bf Master Project\par}
 
 \vspace{6cm}

10_Introduction.tex

@@ -101,7 +101,8 @@ simulations for both \acrshort{gp} and \acrshort{svgp} models. A few variations
 on the initial \acrshort{svgp} model are further analyzed in order to identify
 the most important parameteres for long time operation.
 
-Finally, Section~\ref{sec:further_research} discusses the possible improvements
-to both the current \acrshort{gp} and \acrshort{svgp} implementations.
+Finally, Section~\ref{sec:conclusion} provides a review of all the different
+implementation and  discusses the possible improvements to both the current
+\acrshort{gp} and \acrshort{svgp} models.
 
 \clearpage

50_Choice_of_Hyperparameters.tex

@@ -351,7 +351,7 @@ computations. Other good choices for the combinations of lags are
 \model{2}{1}{3} and \model{1}{1}{3}, which have good performance on all four
 metrics, as well as being cheaper from a computational perspective. In order to
 make a more informed choice for the best hyperparameters, the simulation
-performance of all three combinations has been analysed.
+performance of all three combinations has been analyzed.
 
 \begin{table}[ht]
 %\vspace{-8pt}
@@ -403,7 +403,7 @@ the discrepancies.
 \subsubsection{Conventional Gaussian Process}
 
 The simulation performance of the three lag combinations chosen for the
-classical \acrlong{gp} models has been analysed, with the results presented in
+classical \acrlong{gp} models has been analyzed, with the results presented in
 Figures~\ref{fig:GP_113_multistep_validation},~\ref{fig:GP_213_multistep_validation}
 and~\ref{fig:GP_313_multistep_validation}. For reference, the one-step ahead
 predictions for the training and test datasets are presented in
@@ -449,8 +449,9 @@ this proves to be the best simulation model.
     \label{fig:GP_313_multistep_validation}
 \end{figure}
 
-Lastly, \model{3}{1}{3} has a much worse simulation performance than the other
-two models. This could hint at an over fitting of the model on the training data.
+Lastly, \model{3}{1}{3} (cf. Figure~\ref{fig:GP_313_multistep_validation}) has a
+much worse simulation performance than the other two models. This could hint at
+an over fitting of the model on the training data.
 
 \clearpage
 

80_Results.tex

@@ -3,10 +3,10 @@
 
 This section focuses on the presentation and interpretation of the year-long
 simulation of the control schemes presented previously. All the control schemes
-analysed in this Section have used a sampling time of 15 minutes and a control
+analyzed in this Section have used a sampling time of 15 minutes and a control
 horizon of 8 steps.
 
-Section~\ref{sec:GP_results} analyses the results of a conventional
+Section~\ref{sec:GP_results} analyzes the results of a conventional
 \acrlong{gp} Model trained on the first five days of gathered data. The model
 is then used for the rest of the year, with the goal of tracking the defined
 reference temperature.
@@ -57,9 +57,6 @@ exhibit similar performance. The spring months already make the controller less
 stable than at the start of the year, while the drastic temperature changes in
 the summer make the controller completely unstable.
 
-\clearpage
-
-
 Figure~\ref{fig:GP_fullyear_abserr} presents the absolute error measured at each
 step of the simulation over the course of the year. We can note a mean absolute
 error of 1.33 $\degree$C, with the largest deviations occurring in late summer
@@ -74,7 +71,7 @@ occurring during the winter months.
     \label{fig:GP_fullyear_abserr}
 \end{figure}
 
-Figure~\ref{fig:GP_first_model_performance} analyses the 20-step ahead
+Figure~\ref{fig:GP_first_model_performance} analyzes the 20-step ahead
 simulation performance of the identified model over the course of the year. At
 experimental step 250, the controller is still gathering data. It is therefore
 expected that the identified model will be capable of reproducing this data. At
@@ -334,6 +331,8 @@ This means that the model does not get much more complex as the data is
 gathered, but instead the same general structure is kept, with further
 refinements being done as data is added to the system.
 
+\clearpage
+
 \begin{figure}[ht]
     \centering
     \includegraphics[width =
@@ -382,6 +381,8 @@ cumbersome and potentially costly initial experiments for gathering data.
     \label{fig:SVGP_96pts_abserr}
 \end{figure}
 
+\clearpage
+
 \subsection{SVGP with a five days moving window}\label{sec:svgp_window}
 
 This section presents the result of running a different control scheme. Here, as
@@ -407,6 +408,8 @@ model, to again learn its behaviour. This cycle repeats every five days, when th
 controller becomes unstable. In the stable regions, however, the controller is
 able to track the reference temperature. 
 
+\clearpage
+
 \subsection{SVGP with Linear Kernel}\label{sec:svgp_linear}
 
 The last model to be investigated is the \acrshort{svgp} with Linear Kernel. As

90_Conclusion.tex

@@ -1,34 +1,55 @@
 \section{Conclusion}~\label{sec:conclusion}
 
-The aim of this project was to analyse the performance of \acrshort{gp} based
+The aim of this project was to analyze the performance of \acrshort{gp} based
 controllers for use in longer lasting implementations, where differences in
 building behaviour become important compared to the initially available data.
 
-{\color{red}
-First, the performance of a classical \acrshort{gp} model trained on 5 days
-worth of experimental data was analysed. This model turned out to be unable to
-correctly extrapolate building behaviour as the weather changed throughout the
-year.
-}
-
 First, the performance of a classical \acrshort{gp} model trained on five days
-worth of experimental data was analysed. Initially, this model performed very
+worth of experimental data was analyzed. Initially, this model performed very
 well both in one step ahead prediction and multi-step ahead simulation over new,
-unseen, data. With the change in weather, however, the model shifted  
+unseen, data. With the change in weather, however, the model shifted from
+operating in the interpolated regions to the extrapolated regions of the initial
+weather data. In this scenario the model was unable to properly predict the
+\pdome\ behaviour and, as a consequence, the \acrshort{mpc} controller became
+unstable.
 
-Several \acrshort{svgp} implementations were then analysed. They turned out to
-provide important benefits over the classical models, such as the ability to
-easily scale when new data is being added and the much reduced computational
-effort required. They do however present some downsides, namely increasing the
-number of hyperparameters by having to choose the number of inducing locations,
-as well as performing worse than then classical \acrshort{gp} implementation
-given the same amount of data.
+Following that, several \acrshort{svgp} implementations were analyzed. The
+initial behaviour exhibited during parameter identification (cf.
+Section~\ref{sec:hyperparameters}) showed that the \acrshort{svgp} model was
+less capable of capturing building dynamics only based on the initial
+experimental dataset, possibly due to the \acrshort{elbo} approximation of the
+true log likelihood. While the \acrshort{svgp} model remained stable over the
+course of the 20-step ahead simulation, in the later steps it drifted much
+further from the real values than the equivalent \acrshort{gp} model.
+However, during the full-year simulation, this downside of the \acrshort{svgp}
+model was compensated by adding new data to the model training dataset each
+night at midnight. The model performance continuously improved over the course
+of the simulation, providing much better results overall.
 
-%Finally, the possible improvements to the current implementations have been
-%addressed, noting that classical \acrshort{gp} implementations could also be
-%adapted to the \textit{learning control} paradigm, even if their implementation
-%could turn out to be much more involved and more computationally expensive than
-%the \acrshort{svgp} alternative.
+To better analyze the learning behaviour of the \acrshort{svgp} models, three
+variations of the initial \acrshort{svgp} were also simulated. The first
+variation consisted of training the initial model on only one day's worth of
+experimental data, as opposed to five days in the first case. This model was
+then regularly updated every night at midnight, just as the initial case. It
+turned out to provide very comparable results to the initial model, leading to
+the conclusion that the \acrshort{svgp} model can be initially deployed using
+much less training data, and it will still be able to correctly capture the
+building dynamics on subsequent updates.
+
+The second variation of the \acrshort{svgp} model was re-trained using a rolling
+window of five days' worth of data, in order to see the model's ability to learn 
+the proper building dynamics based only on closed-loop operation data. This
+model turned out to be unstable, and the full-year simulation showed that every
+time the model was trained using \textit{only} closed-loop operation data it
+turned unstable. This prompted a much higher excitation of the building for the
+following day, which in turn provided enough information to train a good model,
+that would last until this information was too old to be included in the
+training window, at which point the model would turn unstable again.
+
+In the last variation, the \acrshort{svgp} model was trained using a linear
+kernel. This model turned out to perform worse overall than the \acrshort{se}
+kernel model since it was unable to capture the more nuanced, non-linear
+behaviour of the building.
 
 
 \subsection{Further Research}~\label{sec:further_research}

main.tex

@@ -10,6 +10,7 @@
 \usepackage{array}
 \usepackage{makecell}
 \usepackage{comment}
+\usepackage{setspace}
 %\usepackage{fixltx2e}
 %% Language and font encodings
 
@@ -89,8 +90,9 @@
 }
 \renewcommand{\familydefault}{\sfdefault}
 
-\title{Multi-seasonal performance of Gaussian Process models for building
-temperature control}
+\title{Inter-seasonal Performance of Gaussian Process-based
+Model Predictive Control of Buildings}
+
 \author{Radu C. Martin}
 
 %header
@@ -99,7 +101,7 @@ temperature control}
 \pagestyle{fancy}
 \setlength\headheight{35pt}
 \setlength\footskip{13.6pt}
-\fancyhf{Multi-season GP performance for buildings}
+\fancyhf{Inter-seasonal GP MPC control for buildings}
 \rhead{\includegraphics[width=2cm]{Logo-EPFL.png}}
 \lhead{}
 \cfoot{\thepage}