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address sf comments, add sections to write

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Arthur Grisel-Davy 2023-06-14 13:42:45 -04:00
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PhD/research_proposal/futurwork.tex
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@ -73,37 +73,27 @@ Figure \ref{fig:notation} illustrate the $ts$ and $P$ objects.
\end{figure}
\subsection{Applications}
The goal of the multi-measure setup is dual.
First, correlated information allows for a more robust detection mechanism.
If all components of a machine display behaviours associated with the same global activity, the detection confidence is greater than with the global consumption only.
Second, multiple measures enable a more granular activity detection.
The multi-measure setup present two potential benefits that will be investigated in this thesis.
First, correlated information could allows for a more robust detection mechanism.
If all components of a machine display behaviours associated with the same global activity, the detection confidence could improve compared with the global consumption only.
Second, multiple measures could enable a more granular activity detection.
With the power consumption measurement of multiple components available, every combination of component's activity can be associated with a different global activity.
These changes allow for detecting potentially anomalous combinations of states and for a better understanding of the machine's behaviour.
These changes would allow for detecting potentially anomalous combinations of states and for a better understanding of the machine's behaviour.
\sfm{Because we address embedded stsrems, somewhere discuss the problem of actuators distorting the power trace (e.g., fans, motors, etc). You can link that to the MSSM problem.}
The typical application of this technology would concern general-purpose computers or medium-complexity systems with multiple internal components.
These machines are typically difficult to profile with global consumption as each component influences the measure in a different way.
The detection of the activity can be restricted to general states like \textit{ON}, \textit{OFF}, \textit{SLEEP} or \textit{HIGH LOAD}.
While this information is still valuable, it does not enable in-depth monitoring of the machine.
\section{Multi-Source Single-Measure}
If the Single-Source Multi-Measure was looking \textit{in} a machine to get more insight, the Multi-Source Single-Measure is looking \textit{out} and considering multiple devices at once.
In a context where measuring the consumption of individual machines is not possible, the problem of disambiguation arises.
Signal disambiguation is the ability to identify the source of each component signal from a single aggregated signal.
This is a complicated problem as the different sources can affect each other, sometimes in a non-linear way.
\subsection{Problem Statement}
\begin{problem-statement}[Multi-Source Single-Measure]
Given a discretized aggregated time series $t_a = t_1 \oplus t_2 \oplus \dots \oplus t_k$ and a set of patterns $P=\{(P_1\times\dots\times P_n)\}$, identify an injective mapping $m_{MSSM}:\mathbb{N}\longrightarrow P$ such that every sample $t_a[i]$ maps to a pattern set in $P$ with the condition that the sample matches an occurrence of the pattern in $t_a$.
\end{problem-statement}
The time series $t_a$ is a discretized, mono-variate, real-valued time series.
The set of patterns $P$ is the cartesian product of the sets of patterns for each source $P_i$.
Thus, each element of $P$ is a set of $n$ patterns, each associated with one source.
Each set $P_i$ contain any number of pattern and the unknown $\chi$ pattern.
The unknown pattern is not added to the set $P$ as the set of all $\chi$ is already present and bears the same meaning.
The operator $\oplus$ is the aggregation function, generally the summation or caped summation.
In some applications, the associativity of the $\oplus$ operator can be discarded as the aggregation is performed at the physical level, instantly across all sources $t_i$.
This is a difficult problem as the different sources can affect each other, sometimes in a non-linear way.
Figure \ref{fig:mssm_illustration} illustrate the aggregation of multiple consumption sources in a single measurement.
\begin{figure}
\centering
@ -111,14 +101,34 @@ In some applications, the associativity of the $\oplus$ operator can be discarde
\caption{Illustration of the MSSM setup.}
\label{fig:mssm_illustration}
\end{figure}
\agd{add a map of the problems and what is planned. Some visual representation of the SSSM, SSMM, MSSM and MSMM problems}
\subsection{Problem Statement}
\begin{problem-statement}[Multi-Source Single-Measure]
Given a discretized aggregated time series $ts_a = ts_1 \oplus ts_2 \oplus \dots \oplus ts_k$ and a set of patterns $P=\{(P_1\times\dots\times P_k)\}$, identify an injective mapping $m_{MSSM}:\mathbb{N}\longrightarrow P$ such that every sample $ts_a[i]$ maps to a pattern set in $P$ with the condition that the sample matches an occurrence of the pattern in $ts_a$.
\end{problem-statement}
The time series $ts_a$ is a discretized, mono-variate, real-valued time series.
The set of patterns $P$ is the cartesian product of the sets of patterns for each source $P_i$.
Thus, each element of $P$ is a set of $n$ patterns, each associated with one source.
Each set $P_i$ contain any number of pattern and the unknown $\chi$ pattern.
The unknown pattern is not added to the set $P$ as the set of all $\chi$ is already present and bears the same meaning.
The operator $\oplus$ is the aggregation function, generally the summation or caped summation.
%In some applications, the associativity of the $\oplus$ operator can be discarded as the aggregation is performed at the physical level, instantly across all sources $ts_i$.
The MSSM problem can be expressed as a combination of $k$ SSSM problems with a different input time series.
Because the input is an aggregated time series, the patterns describing an activity may not appear similarly in the input.
These patterns may be distorded by the aggregation with another pattern from another source.
The main hurdle when developping a solution for the MSSM problem will be to correctly identify the distorded patterns when having access to all possible distortion sources (the other patterns).
\subsection{Applications}
The successful design of a Multi-source Single-Measure monitoring system finds its best application in an industrial setting.
The successful design of a Multi-source Single-Measure monitoring system would finds its best application in an industrial setting.
Any industry that relies on many simple embedded systems to reliably perform a task can benefit from a monitoring system that is minimally disruptive to install.
For example, an assembly line can leverage hundreds of conveyor belt drivers, robotic arms, or quality assessment points.
Each type of system is simple in its design and task.
However, adding a designated power monitoring measurement device to each individual system is costly, maintenance-heavy, and it multiplies the potential points of failure.
Capturing the power consumption of these machines at a single point is an efficient way to minimize the implementation footprint while maintaining a reliable physics-based monitoring solution.
However, adding a designated power monitoring measurement device to each individual system can significantly increase cost, maintenance, and points of failure.
Capturing the power consumption of these machines at a single point could minimize the implementation footprint while maintaining a reliable physics-based monitoring solution.
\section{Conclusion}
\agd{to be filled}