WIP: Thesis update

50_Choice_of_Hyperparameters.tex

@@ -348,6 +348,8 @@ being cheaper from a computational perspective. In order to make a more informed
 choice for the best hyperparamerers, the performance of all three combinations
 has been analysed.
 
+\clearpage
+
 \begin{table}[ht]
 %\vspace{-8pt}
 \centering
@@ -384,25 +386,22 @@ therefore been chosen as the model for the full year simulations.
 
 % TODO: [Hyperparameters] Validation of hyperparameters
 
-The validation of model parameters has the dual purpose of 
+The validation step has the purpose of testing the fiability of the trained
+models. If choosing a model according to loss function values on a new dataset
+is a way of minimizing the possibility of overfitting the model to the training
+data, validating the model by analyzing its multi-step prediction performance
+ensures the model was able to learn the correct dynamics and is useful in
+simulation scenarios.
 
+The following subsections analyze the performance of the trained \arcshort{gp}
+and \acrshort{svgp} models over 20-step ahead predictions. For the \acrshort{gp}
+model the final choice of parameters is made according to the simulation
+performance. The simulation performance of the \acrshort{svgp} model is compared
+to that of the classical models while speculating on the possible reasons for
+the discrepancies.
 
 \subsubsection{Conventional Gaussian Process}
 
-\begin{figure}[ht]
-    \centering
-    \includegraphics[width = \textwidth]{Plots/GP_113_training_performance.pdf}
-    \caption{}
-    \label{fig:GP_train_validation}
-\end{figure}
-
-\begin{figure}[ht]
-    \centering
-    \includegraphics[width = \textwidth]{Plots/GP_113_test_performance.pdf}
-    \caption{}
-    \label{fig:GP_test_validation}
-\end{figure}
-
 
 \begin{figure}[ht]
     \centering
@@ -412,23 +411,39 @@ The validation of model parameters has the dual purpose of
     \label{fig:GP_multistep_validation}
 \end{figure}
 
+\begin{figure}[ht]
+    \centering
+    \includegraphics[width =
+    \textwidth]{Plots/GP_213_-1pts_test_prediction_20_steps.pdf}
+    \caption{}
+    \label{fig:GP_213_multistep_validation}
+\end{figure}
+
+\begin{figure}[ht]
+    \centering
+    \includegraphics[width =
+    \textwidth]{Plots/GP_313_-1pts_test_prediction_20_steps.pdf}
+    \caption{}
+    \label{fig:GP_313_multistep_validation}
+\end{figure}
+
 \clearpage
 
 \subsubsection{Sparse and Variational Gaussian Process}
 
-\begin{figure}[ht]
+%\begin{figure}[ht]
-    \centering
+%    \centering
-    \includegraphics[width = \textwidth]{Plots/SVGP_123_training_performance.pdf}
+%    \includegraphics[width = \textwidth]{Plots/SVGP_123_training_performance.pdf}
-    \caption{}
+%    \caption{}
-    \label{fig:SVGP_train_validation}
+%    \label{fig:SVGP_train_validation}
-\end{figure}
+%\end{figure}
-
+%
-\begin{figure}[ht]
+%\begin{figure}[ht]
-    \centering
+%    \centering
-    \includegraphics[width = \textwidth]{Plots/SVGP_123_test_performance.pdf}
+%    \includegraphics[width = \textwidth]{Plots/SVGP_123_test_performance.pdf}
-    \caption{}
+%    \caption{}
-    \label{fig:SVGP_test_validation}
+%    \label{fig:SVGP_test_validation}
-\end{figure}
+%\end{figure}
 
 \begin{figure}[ht]
     \centering

60_The_MPC_Problem.tex

@@ -30,7 +30,7 @@ the GP input vector at time t, composed of the exogenous autoregressive inputs
 $\mathbf{w}_{t}$, the autoregressive controlled inputs $\mathbf{u}_{t}$ and the
 autoregressive outputs $\mathbf{y}_{t}$.
 
-\subsection{Temperature reference}
+\subsection{Temperature reference}\label{sec:reference_temperature}
 
 The temperature reference for the controller has been taken as the mean value of
 the SIA~180:2014~\cite{sia180:2014ProtectionThermiqueProtection2014} temperature

70_Implementation.tex

@@ -20,21 +20,17 @@ in the \acrshort{wdb} object is given in Section~\ref{sec:CARNOT_WDB}.
 
 \subsection{Simulink Model}
 
-
+The secondary functions of the Simulink model is the weather prediction, as well
-% TODO: [Implementation] Move the simulink schema here, with explanations of tcp
+as communication with the Python controller. A complete schema of the Simulink
-
+setup is presented in Figure~\ref{fig:Simulink_complete}.
-The final Simulink schema is presented in Figure~\ref{fig:CARNOT_complete}:
 
 \begin{figure}[ht]
     \centering
-    \includegraphics[width = \textwidth]{Images/polydome_python.pdf}
+    \includegraphics[width = 0.75\textwidth]{Images/polydome_python.pdf}
     \caption{Simulink Schema of the Complete Simulation}
     \label{fig:Simulink_complete}
 \end{figure}
 
-The secondary functions of the Simulink model is the weather prediction, as well
-as communication with the Python controller.
-
 The communication between Simulink and the controller is done using three
 separate TCP/IP sockets: one for sending the control signal, one for reading the
 temperature measurement, and one for reading the weather forecast. This is
@@ -185,5 +181,20 @@ delegates which controller is active, is responsible for training and updating
 the \acrshort{gp} and \acrshort{svgp} models, as well as keeping track of all
 the intermediate results for analysis.
 
+In the beginning of the experiment there is no information available on the
+building's thermal behaviour. For this part of the simulation, the controller
+switches to a \acrshort{pi} controller until it gathers enough data to train a
+\acrshort{gp} model. The signal is then disturbed by a random signal before
+being applied to the CARNOT building. This ensured that the building is
+sufficiently excited to capture its dynamics, while maintaining the
+temperature within an acceptable range (~15 --- 25 $\degree$C).
+
+Once enough data has been captured, the Python controller trains the
+\acrshort{gp} model and switches to tracking the appropriate SIA 180:2014
+reference temperature (cf. Section~\ref{sec:reference_temperature}).
+
+For the case of the \acrshort{svgp}, a new model is trained once enough data is
+gathered. The implementations tested were updated once a day, either on the
+whole historical set of data, or on a window of the last five days of data.
 
 \clearpage

99A_GP_hyperparameters_validation.tex

@@ -2,6 +2,24 @@
 
 \section{Hyperparameters validation for classical GP}
 
+\subsection{113}
+
+\begin{figure}[ht]
+    \centering
+    \includegraphics[width = \textwidth]{Plots/GP_113_training_performance.pdf}
+    \caption{}
+    \label{fig:GP_train_validation}
+\end{figure}
+
+\begin{figure}[ht]
+    \centering
+    \includegraphics[width = \textwidth]{Plots/GP_113_test_performance.pdf}
+    \caption{}
+    \label{fig:GP_test_validation}
+\end{figure}
+
+\clearpage
+
 \subsection{213}
 
 \begin{figure}[ht]
@@ -18,21 +36,10 @@
     \label{fig:GP_213_test_validation}
 \end{figure}
 
-
-\begin{figure}[ht]
-    \centering
-    \includegraphics[width =
-    \textwidth]{Plots/GP_213_-1pts_test_prediction_20_steps.pdf}
-    \caption{}
-    \label{fig:GP_213_multistep_validation}
-\end{figure}
-
-
 \clearpage
 
 \subsection{313}
 
-
 \begin{figure}[ht]
     \centering
     \includegraphics[width = \textwidth]{Plots/GP_313_training_performance.pdf}
@@ -47,14 +54,4 @@
     \label{fig:GP_313_test_validation}
 \end{figure}
 
-
-\begin{figure}[ht]
-    \centering
-    \includegraphics[width =
-    \textwidth]{Plots/GP_313_-1pts_test_prediction_20_steps.pdf}
-    \caption{}
-    \label{fig:GP_313_multistep_validation}
-\end{figure}
-
-
 \clearpage

glossaries.tex

@@ -4,6 +4,8 @@
 
 % Acronyms
 
+\newacronym{pi}{PI}{Proportional Integral}
+
 \newacronym{ocp}{OCP}{Optimal Control Problem}
 \newacronym{mpc}{MPC}{Model Predictive Control}