\subsubsection{Example -- Hot Zero Power Measurements}
This section will go through the process of filtering measured data for
\ac{HZP}. It should be noted that the algorithm developed to process \ac{HZP}
data was used for all detector data. Therefore, some of the detector maps may
show errors in processing. Current work is underway to develop an algorithm
that can be applied to all data. Under \ac{HZP} conditions, the core power for
these measurements is approximately 25 MWth. Raw data was processed by first
organizing it in Python objects. Each collection of measurements contain
detector information for multiple passes through the core in various assemblies.
Raw data for \ac{HZP} is shown in Figure \ref{fig:orig_all}. In order to show
all detector signals on one plot, each raw data signal was normalized to a sum
of unity.
\begin{figure}
\centering
\includegraphics{expdata/figs/original_all.pdf}
\caption{Initial Raw Detector Measurements (top to bottom). \label{fig:orig_all}}
\end{figure}
The first step in this process is to remove any detector background signal. This
information was supplied with the raw data and can be subtracted from each
detector measurement pass. The corrected data for background is shown in Figure
\ref{fig:back_all}.
\begin{figure}
\centering
\includegraphics{expdata/figs/background_all.pdf}
\caption{Detector Measurements Corrected for Background (top to bottom). \label{fig:back_all}}
\end{figure}
Depending on the strength of the signal being measured, the signal can be amplified
by adjusting the gain on the detectors. Gain factors are also reported with the raw data. When
processing, these gain factors are multiplied by the measured data. For \ac{HZP}, all
of the gain factors are unity. Figure \ref{fig:gain_all} shows the measured data
after gain factors are applied.
\begin{figure}
\centering
\includegraphics{expdata/figs/gain_all.pdf}
\caption{Detector Measurements Gain Factors Applied (top to bottom). \label{fig:gain_all}}
\end{figure}
In some of the detector signals, zero points exist where the detector failed. These zero points are removed by performing
a linear interpolation/extrapolation between/from the nearest two points. The corrected data is shown
in Figure \ref{fig:zero}.
\begin{figure}
\centering
\includegraphics{expdata/figs/zeros_all.pdf}
\caption{Detector Measurements with Zero Points Removed (top to bottom). \label{fig:zero}}
\end{figure}
As explained above, there is one common assembly where all detectors will pass. This is needed
for normalization of detector signals. In this plant, assembly J10 was chosen as the common
assembly. Figure \ref{fig:J10} shows the measurements taken in assembly J10.
\begin{figure}
\centering
\includegraphics{expdata/figs/zeros.pdf}
\caption{Detector Measurements with in J10 Assembly (top to bottom). \label{fig:J10}}
\end{figure}
Each detector measurement represents a different measurement pass. The core power
during one pass may not be the same as the others. There is typically a small fluctuation present in the core power. To account for this, each signal
is divided by the core power reported during that measurement pass. The resulting
detector signals are shown in Figure \ref{fig:dividepower} for assembly J10.
\begin{figure}[htbp]
\centering
\includegraphics{expdata/figs/divide_power.pdf}
\caption{J10 Detector Measurements Divided by Core Power (top to bottom). \label{fig:dividepower}}
\end{figure}
The next step in the process is to make sure that all detector signals line up with
one another. We can verify this by plotting all 58 detector signals on top of each
other. This is the same as plot as Figure \ref{fig:dividepower}, except all assemblies are plotted here with signals normalized for shape comparison. This is shown in Figure \ref{fig:beforerealign}.
\begin{figure}[htbp]
\centering
\includegraphics{expdata/figs/before_realign.pdf}
\caption{All Detector Signals Before Realignment. \label{fig:beforerealign}}
\end{figure}
It is observed that not all of the signals are aligned with each other. Luckily, signals can be
aligned to grid depressions. Here, we align to three grid depression positions, 25, 34, and 42, which are located in the centerline of grid 5, grid 4 and grid 3 respectively.
The first step in this process is to find the measurement indexes corresponding to the local minimum in three regions, 22 to 28, 31 to 37, and 39 to 45 respectively.
Then for each assembly, if the measurement indexes are inconsistent with correct indexes,
a shifting length is estimated to make all the measurement indexes best match the correct indexes.
All grids are then shifted either left or right. Depending on the
shift direction, one end will lose a point and the other will gain one. The data point
that is lost is just deleted from the data array, while the point that is gained is
determined by a simple linear extrapolation from the nearest two points. The resulting
realignment is shown in Figure \ref{fig:afterrealign}.
\begin{figure}[htbp]
\centering
\includegraphics{expdata/figs/after_realign.pdf}
\caption{All Detector Signals After Realignment. \label{fig:afterrealign}}
\end{figure}
Results show that all detector signals are more consistently aligned, however still not perfect. The span of these signals can also be attributed to measurement uncertainty as they should all have the same shape once normalized here. There
is one signal that is an outlier is observed between measurements
0 and 5. This assembly location corresponds to where control rod bank D
is slightly inserted. Therefore, we should expect this depression in the signal toward
the top of the core.
The next step in the process is to average detector signals that were measured from
the same detector. It is important to look at the raw signals before performing this
step since measurements may be poor. If this is observed, the poor measurement
is commented out in the data file. In Figure \ref{fig:dividepower} the two signals
from detector 4 are close to each other and should be averaged. The resulting signals
for assembly J10 are shown in Figure \ref{fig:averagemultiple}.
Table \ref{tbl:hzp_c1} lists the thermal power of the reactor during initial physics testing the first available detector maps. Also included are the rod bank positions and critical boron concentration. This data can be used to evaluate how far off reactor models are from critical at \ac{HZP} conditions.
\begin{table}[htp]
\centering
\caption{Cycle 1 hot zero power physics configuration.}
\label{tbl:hzp_c1}
\begin{tabular}{l r}
\toprule
Core Power & 25 MWth \\
Core Flow Rate &$61.5\times10^6$ kg/hr \\
Inlet Coolant Temperature & 560$^\circ$ F \\
Rod Bank A Position & Step 228 \\
Rod Bank B Position & Step 228 \\
Rod Bank C Position & Step 228 \\
Rod Bank D Position & Step 213 \\
Boron Concentration & 975 \acs{ppm}\\
\bottomrule
\end{tabular}
\end{table}
Radial maps were also created to view the average relative power produced per assembly.
These were obtained by renormalizing the signals in Figure \ref{fig:splineunnorm} such that their total
sum is the number of detector locations (in this case 58). Each measurement in an assembly was then
axially averaged to produce a relative radial peaking factor. In Figure \ref{fig:radial_meas}, this factor
is presented on each assembly where a measurement was taken.
\input{expdata/figs/radial_measurements_full}
Results show that measurement locations are consistent with the reported instrumentation
diagram shown in Figure \ref{fig_instr_pos}. Since the reactor is quarter-core symmetric (disregarding perturbations from instrument tubes),
measurements can be compared. For example, assemblies H13, C8, H3 and N8 are located in
symmetric positions. The measured values in these locations should be close. It is
observed that the measurements are on the same order, but not all that close. This can
happen at low powers and gives us an indication of measurement uncertainty.
Another way to look at the data is to collapse it to quarter core.
We can compare rotational quarter core positions. If more than one radial power is available, the mean and standard deviation are reported. Otherwise, the result from Figure \ref{fig:radial_meas} is listed without a standard deviation. This is shown in Figure \ref{fig:quarter_meas}.
In each assembly, three values are reported. From top to bottom they are:
average of radial (axially averaged) signals, standard deviation of average and
number of measurements that were averaged. The standard deviations give us some idea
on the uncertainty in these measured values. They can range all the way up to
5.4\%. A weighted average of the standard deviation was computed to get an idea
of the overall measurement uncertainty. This was determined by multiplying each uncertainty by the number of radial powers and then dividing by 58. For \ac{HZP}, this uncertainty is 3.7\%. This is
rather high since we really would like to see values below 1\%. However, when the power
is very low, power tilting can occur which contributes to this high uncertainty.
\input{expdata/figs/radial_measurements_quarter}
To compare simulation values to these measured data, axial edits of a tally such as U235 fission
rate must be applied to each instrumented assembly in the core. To be fully
consistent with the data a constant width 60 interval mesh (61 points) from
bottom of active fuel to top of active fuel should be applied. All signals
should be renormalized such that their average is 1.0 (or sum of all signals is
58).
Table \ref{tbl:meas_c1phys} presents measured data for control rod bank worths
and isothermal temperature coefficients for \ac{HZP} conditions. Also provided
are the critical boron concentrations for each configuration. Likewise, Table
\ref{tbl:meas_c2phys} presents the same data that is available for cycle 2. In
contrast to cycle 1, control rod bank worths in cycle 2 were reported per
individual bank.
\begin{table}[htp]
\centering
\caption[Cycle 1 hot zero power physics data.]{Cycle 1 hot zero power physics
data, including critical boron concentrations, control rod bank worths for the
full insertion sequence, and isothermal temperature coefficients.
