radu/Master-Thesis
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

Thesis update

Browse source
This commit is contained in:
Radu C. Martin 2021-06-25 06:22:43 +02:00
parent 3b1f852876
commit c213d3064e
14 changed files with 678 additions and 131 deletions
Download patch file Download diff file Expand all files Collapse all files

12
70_Implementation.tex
View file

@ -4,7 +4,7 @@ This section goes into the details of the implementation of the Simulink plant
and Python controller setup.
A high-level view of the setup is presented in Figure~\ref{fig:setup_diagram}.
The Simulink model's main responsability is running the CARNOT simulation. It
The Simulink model's main responsibility is running the CARNOT simulation. It
also has the task of providing the \acrshort{mpc} with information on the
weather forecast, since the weather information for the simulation comes from a
CARNOT \acrshort{wdb} object. A detailed view of all the information available
@ -62,7 +62,7 @@ starting and ending points, while retaining a simple implementation.
\subsection{Gaussian Processes}
As described in Section~\ref{sec:gaussian_processes}, both training and
evaluating a \acrshort{gp} has an algotirhmic complexity of $\mathcal{O}(n^3)$.
evaluating a \acrshort{gp} has an algorithmic complexity of $\mathcal{O}(n^3)$.
This means that naive implementations can get too expensive in terms of
computation time very quickly.
@ -70,7 +70,7 @@ In order to have as smallest of a bottleneck as possible when dealing with
\acrshort{gp}s, a very optimized implementation of \acrlong{gp} Models was
used, in the form of GPflow~\cite{matthewsGPflowGaussianProcess2017}. It is
based on TensorFlow~\cite{tensorflow2015-whitepaper}, which has very efficient
imeplentation of all the necessary Linear Algebra operations. Another benefit of
implementation of all the necessary Linear Algebra operations. Another benefit of
this implementation is the very simple use of any additional computational
resources, such as a GPU, TPU, etc.
@ -86,7 +86,7 @@ used for \acrshort{svgp} models.
\subsubsection{Sparse and Variational Gaussian Process training}
The \acrshort{svgp} models have a more involved oprimization procedure due to to
The \acrshort{svgp} models have a more involved optimization procedure due to to
several factors. First, when training an \acrshort{svgp} model, the optimization
objective is the value of the \acrshort{elbo} (cf. Section~\ref{sec:elbo}).
After several implementations, the more complex \textit{Adam} optimizer turned
@ -147,7 +147,7 @@ The optimization problem as presented in
Equation~\ref{eq:optimal_control_problem} becomes very nonlinear quite fast. In
fact, due to the autoregressive structure of the \acrshort{gp}, the predicted
temperature at time t is passed as an input to the model at time $t+1$. A simple
recursive implementation of the Optimization Problem becomes untractable after
recursive implementation of the Optimization Problem becomes intractable after
only 3 --- 4 prediction steps.
In order to solve this problem, a new OCP is introduced. It has a much sparser
@ -197,4 +197,6 @@ 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.
% TODO [Implementation] Add info on scaling
\clearpage