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Arthur Grisel-Davy 2023-06-14 11:34:01 -04:00
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PhD/research_proposal/futurwork.tex
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@ -37,28 +37,40 @@ The work on \gls{dsd} is the fundation for the planned development of more speci
\end{figure}
\section{Single-Source, Multi-Measure}
The global power consumption of a machine does not always tell the full story about its activity.
The global power consumption of a machine does not fully describe its activity.
In an embedded system, the power consumption can be attributed to different components, each with its specific activity.
For the simplest systems performing one specific task --- such as \gls{rtu} ---, the activity of each component is often correlated.
If the system is in a mode \textit{A} then each component is in mode \textit{A}, and the global power consumption will display the \textit{mode A} pattern.
For the simplest systems performing one specific task, the activity of each component is often correlate with each other.
If the system is in a Mode \textit{A} then each component is in Mode \textit{A}, and the global power consumption will display the Mode \textit{A} pattern.
For more complex systems, different components can be in different modes to accommodate the multi-tasking nature of the global activity.
In this case, if the first component is in mode \textit{A} but the second is in mode \textit{B}, this indicates a different global activity than if both are in the same mode.
For example, if the bootup sequence of a general-purpose computer shows a high \gls{cpu} activity but a low storage activity, it could indicate a failure to boot or an attacker booting the system from external storage.
In this case, if the first component is in Mode \textit{A} but the second is in Mode \textit{B}, this indicates a different global activity than if both are in the same mode.
For example, if the bootup sequence of a general-purpose computer shows a significant \gls{cpu} activity but no \gls{hdd} activity, it could indicate a failure to boot or an attacker booting the system from external storage.
Access to each component's individual power consumption opens the way to a more granular understanding of the machine's activity.
However, the new nature of the captured data requires an evolution of the techniques developed before.
However, the multivariate aspect of the captured data requires an evolution of the detection techniques.
\subsection{Problem Statement}
Differentiating between the different components to better understand the activity of a machine is a valuable capability associated with a new problem.
\begin{problem-statement}[Single-Source Multi-Measure]
Given a discretized time series $t$ and a set of $n$ components for each of $m$ patterns $P=\{\{\chi\},\{P_{11},\dots, P_{1n}\},\dots, \{P_{m1},\dots, P_{mn}\}\}$, identify an injective mapping $m_{SSMM}:\mathbb{N}\longrightarrow P$ such that every sample $t[i]$\agd{fix equation overflow}
Given a discretized, multivariate time series $ts$ and a set of $n$ components for each of $m$ patterns $P=\{\{\chi\},P_1=\{P_{1,1},\dots, P_{1,n}\},\dots,$
$P_m=\{P_{m,1},\dots, P_{m,n}\}\}$, identify an injective mapping $m_{SSMM}:\mathbb{N}\longrightarrow P$ such that every sample $ts[i]$
maps to exactly one set of pattern components in $P$ with the condition that the sample matches an occurrence of the set of patterns in $t$.
\end{problem-statement}
The time series $t$ is a discretized, multivariate, real-valued time series.
Each sample $t[i]$ is a vector or $n$ component representing the value of each dimension of $t$ at a point in time.
Each pattern in $P$ contain multiple pattern components and represent a global pattern across all dimension of $t$.
Thus, the number of components of each pattern must be equal to the dimensions of $t$.
The time series $ts$ is a discretized, multivariate, real-valued time series.
$ts$ is composed of $n$ dimensions with the $j^{th}$ dimension referred to as $ts_j$.
Each sample $ts[i]$ is a vector or $n$ component representing the value of each dimension of $t$ at a point in time.
The items of the set $P$ are sets of patterns $P_j$ with $j\in[1,m]$.
Each set of patterns $P_j$ is associated with one component of a global pattern.
In other words, each component $P_{j,k}$ represent a the pattern $j$ along the $k^{th}$ dimension of $ts$.
Thus, the number of components of each pattern must be equal to the dimensions of $ts$.
Figure \ref{fig:notation} illustrate the $ts$ and $P$ objects.
\begin{figure}
\centering
\includegraphics[width=0.9\textwidth]{images/ssmm_illustration.pdf}
\caption{Notations for the multivariate time series and the patterns set.}
\label{fig:notation}
\end{figure}
\subsection{Applications}
The goal of the multi-measure setup is dual.