deletions | additions       diff --git a/There_are_17_tagged.tex b/There_are_17_tagged.tex  index 40e9c11..3f75936 100644  --- a/There_are_17_tagged.tex  +++ b/There_are_17_tagged.tex 
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There are 17 tagged discord types containing anywhere from one to eight daily profiles. These discord candidate profiles are seen separated in Figure \ref{fig:sankeyheatmap1} and Figure \ref{fig:discords}a. They were filtered out of the dataset and investigated in more detail with the assistance of the facilities maintenance personnel on-site. The three days with patterns starting with the letter $c$ are most prominently divergent from the rest of the dataset. These patterns are $cccb$, $ccca$, and $ccba$ and can be seen in Figure \ref{fig:discords}b. They represent days in which a significant amount of consumption was measured in the very early morning hours; this is a situation which should never occur according to any schedule. These days corresponded to behavior experienced by the facilities team in which they noticed numerous air handling units (AHU) would turn on spontaneously in the middle of the night despite no signal from the BMS. The discord analysis was useful for the maintenance staff to observe as they were unsure of just how often the AHU's in the building had been "running wild" at night. This issue was remedied by replacement of certain power meters on the BMS network that were suspected of introducing significant signal noise that caused the AHU problems. The seven patterns starting with the letter $b$ are also suspected to have this root cause albeit with less AHU units malfunctioning in that way. An example of this type of pattern is the $bccb$, seen in Figure \ref{fig:discords}c, which also shows early evening consumption spikes that are correlated with planned extracurricular activities. The discord patterns starting with $a$ have normal early morning cooling energy use but have usage profiles slightly abnormal as compared to the common patterns. Most of these were determined to be scheduling-related with extracurricular activities that are not part of the conventional school schedule.  The next step in the process is to use k-means clustering to further aggregate the motif candidates. We chose in this case to group the day-types into five clusters based on the six motif candidates and the similarity between the $aaaa$ and $aaba$ patterns. The results of this clustering are seen in Figure~\ref{fig:clusters1}. Clusters 0 is strongly prevalent on the weekends, while clusters 2, 3, and 4 are weekday dominant. Cluster 1 correlates with days in which the facility is partially open due to a teacher working day without students or extracurricular activities.  The \emph{DayFilter} process is univariate in this analysis, however the clusters can be visualized as compared to distributions of potential influencing external variables using box plots. Figure \ref{fig:boxplots} illustrates this visualization. Figure \ref{fig:boxplots}a shows the distributions of daily cooling energy according to cluster, producing intuitive results of consecutively increasing, tight clusters due to utilization of this variable as the clustering target. The discord candidates span most of the cooling consumption range and include quite a few high consumption outliers as compared to the characteristic clusters. Figure \ref{fig:boxplots}b illustrates the chilled water plant efficiency distributions which vary slightly in mean but are quite different in variance and outliers. It is interesting to observe the difference in variance between the clusters, with some exhibiting very small ranges (Cluster 3) and others showing much larger ranges (Cluster 1). This insight could be further investigated with respect to cooling system control. The discord candidates actually exhibit a tight range of cooling system efficiency. Figure \ref{fig:boxplots}c shows the cluster distribution according to outside ambient dry bulb temperature. This result shows how consistent the chiller plant output is over the operating range with respect to weather conditions.   \subsection{Case Study 2: Whole building electricity from European temperate climate office building}