Noise Analysis Techniques Of In-core Modulation Experiments
For The European Project CORTEX
Klemen Ambrožič 1 , Vincent Lamirand 1,2a , Sebastian Hübner 3 , Mathieu Hursin 1,2a ,
Adolfo Rais 1 , Oskari Pakari1 , Axel Laureau1 , Pavel Frajtag1 , Carlo Fiorina1 , Andreas
Pautz 1,2b
1
Laboratory for Reactor Physics and Systems Behaviour
École Polytechnique Fédérale de Lausanne
Route Cantonale
1015 Lausanne, Switzerland
2a
Laboratory for Reactor Physics and Thermal-Hydraulics
2b
Nuclear Energy and Safety Division
Paul Scherrer Institut
Forschungsstrasse 111
5232 Villigen PSI, Switzerland
3
Institute of Power Engineering
Technische Universität Dresden
01062 Dresden, Germany
klemen.ambrozic@epfl.ch, vincent.lamirand@epfl.ch, sebastian.huebner@tu-dresden.de,
mathieu.hursin@epfl.ch, adolfo.rais@epfl.ch, oskari.pakari@epfl.ch, axel.laureau@epfl.ch,
pavel.frajtag@epfl.ch, carlo.fiorina@epfl.ch andreas.pautz@epfl.ch
ABSTRACT
This paper deals with the analysis of reactor modulation experiments for code validation
in the framework of the Horizon 2020 European project CORTEX. The analysis is based on
a statistical based approach on spectral powers and their phase shift angles calculations. The
treatment of individual oscillations as independent aids in elimination of possible biases and
correlations of consecutive oscillations. Results from one of the experimental campaign performed at the AKR-2 and CROCUS reactors are also presented.
1
INTRODUCTION
The European project CORTEX project [1] aims to develop core monitoring techniques
for identifying reactor noise sources and their location inside the reactor core, coming from
oscillating fuel rods, boiling and numerous other oscillatory perturbations, which effect the
neutron field. More specifically the tasks of the Work package 2 (WP2) validation of computational codes for predicting the modulations by experiments. The experiments were performed at
212.1
212.2
two reactors, equipped with neutron field modulators and numerous distributed detectors. The
quantities of interest (QOI) for code validation are spectral power (PS) and phase shift angle
between detector pairs. For normalization purposes, PS ratios to a reference detector set and
phase shifts in relation to a reference detector are calculated.
In order to extract high quality QOI from the experimental data, a set of analysis scripts were
developed. These are based on statistical resampling of detector and oscillator position datasets using Bootstrapping with replacement with individual oscillations as representative subsamples. This methodology is able to identify possible biases and eliminates any possible temporal correlations between individual oscillations [2, 3].
Experiments at the Techniche Universität Dresden (TUD) Ausbildungskernreaktor 2 (AKR2) reactor and the experimental campaign at the École Polytechnique Fédérale de Lausanne
(EPFL) CROCUS reactor are briefly presented. A detailed description of the analysis techniques is presented, followed by a presentation of final results for a selected experiment in
CROCUS reactor. The paper is concluded by a discussion and future outlooks.
2
EXPERIMENTS AT TUD AKR-2 AND EPFL CROCUS REACTORS
Experimental campaigns were performed at zero power research reactors which are capable of inducing neutron field modulation by various oscillators. A detailed description of the
experimental campaigns is provided in [4, 5, 6]. In both cases, measurements were performed
by numerous detectors in and around the reactor core. Three separate data acquisition (DAQ)
systems were used namely ISTec , EPFL and TUD.
• The TUD AKR-2 reactor core consists of uranium loaded polyethylene discs, which are
joined together during operation. The reactivity is controlled via neutron absorber control
rods. The reactor is also equipped with two different types of neutron oscillators in the
form of moving absorbers: a variable strength absorber with rotating movement (Figure
5a) and a vibrating absorber (linear actuation) (Figure 5b). The detector and oscillating
absorber positions during are schematically displayed in Figure 2.
(a) Absorber of
variable strengths.
(b) Vibrating absorber.
Figure 1: Oscillator assemblies mounted on the TUD AKR-2 reactor casing.
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 7–10, 2020
212.3
Detector 5
Detector 7 (9)
Wide-range monitor 1
(fission chamber)
Position: 246°
7
Power range detector
(comp. ion chamber)
Position: 282°
Baryte heavy
concrete (58 cm)
Control and safety
rods
Detector 2
He-3 proportional counter,
Position: 334°
(Channel 6)
4
Linear absorber
6
Detector 4
Paraffin (15 cm)
Fission chamber,
Position: 189°
Steel vessel walls
2
1
Φ
Detector 3
He-3 proportional
Reactor tank
with core
counter, Position: 0°
(Channel 2)
Graphite
reflector
(32 cm)
Rotating
absorber
Horizontal experimental
channels:
1-2 central channel
3-4 tangential channel
5-6 tangential channel
7 radial channel
Air gap (7 cm)
3
5
Detector 6 (8)
Detector 1
He-3 proportional counter,
Position: 116°
Wide-range monitor 1
(fission chamber)
Position: 84°
(Channel 5)
Figure 2: TUD AKR-2 schematic during the experimental campaign. Detector numbers in
violet denote an additional measurement chain from the same detector.
• The EPFL CROCUS reactor (Figure 3a) is a pool-type zero power nuclear reactor, where
the reactivity is controlled by adjusting the pool water level or by two boron carbide
control rods. The reactor has two interlocking fuel zones: inner and outer fuel zone, each
comprising of a different fuel type and different pitch. The fuel oscillation experiment
called COLIBRI (Figure 3b) is located at the edge of the reactor. It has the capability to
oscillate up to 18 fuel elements with a frequency of up to 2 Hz and amplitude of up to
±2.5 mm.
The detector positions during the first experimental campaign are schematically displayed
in Figure 4.
3
NOVEL ANALYSIS TECHNIQUES
When dealing with spectral analysis of noise or induced oscillations, the intermediate
quantities of interest are power spectral density (PSD) and the PSD derived phase angle of two
signals, showing their spectral density relation and phase shift between them. The PSD between
signals i and j is defined as the average of periodograms (PER) between same respective signals,
which is defined by Equation 1:
P ERi,j (υ) = Xi (υ)∗ · Xj (υ) = F F T (xi (t))∗ · F F T (xj (t))
(1)
where Xi (υ) and Xj (υ) are frequency domain Fourier transforms of temporal signals xi and xj
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 7–10, 2020
212.4
(a) Reactor with COLIBRI experiment in (b) CAD drawing of the COLIBRI exfront.
periment
Figure 3: Pictures of EPFL CROCUS reactor and the COLIBRI experiment.
det 3
NORTH
det 9
det 11
det 7
det 6
det 2
COLIBRI
det 1
det 5
det 8
det 10
det 4
Figure 4: CROCUS schematic and detector positions during the first CORTEX experimental
campaign. Inner fuel zone in green, outer fuel zone in orange and a single control rod in black.
from detectors i and j respectively. The PSD derivation is described by Equation 2:
PN
P ERk,i,j (υ)
(2)
N
The established way of calculating a P SD is by selecting signal sections of equal size without
or with overlap (and appropriately weighted) for P ER calculations.
Calculation of the phase angle φi,j between signals i and j is described in Equation 3.
P SDi,j (υ) =
k=1
φi,j (υ) = arg(P SDi,j (υ))
(3)
Another useful quantity describing the relation i.e. the power transfer between signal i and
signal j is known as coherence COHi,j , defined by Equation 4.
COHi,j (υ) =
abs(P SDi,j (υ))2
real(P SDi,i (υ)) · real(P SDj,j (υ))
(4)
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 7–10, 2020
212.5
In practice, this acts as an indicator of the data quality: one aims for the COH > 0.8.
Most commonly the Welch windowing method is used [7] for P SD calculations, which induces
spectral effects similar to band-pass filters [8]. Due to using shorter original signals, the frequency resolution of the resulting Fourier transform drops as well. The correlations between
consecutive oscillations and biases present in sections of the signal also affect the analysis.
The analysis results will be used for code validation using simulating stationary oscillations. It
is therefore of utmost importance to eliminate any additional changes to the spectral response,
and to treat measurement data as a collection of individual oscillations, without making any assumptions. The methodology discussed in [2, 3] proposes resampling of the original data from
a pool of representative sub-samples, reconstructing a new data series with ≈ M M different
possibilities (where M is a number of subsections). Fourier transform of the resampled data is
used to obtain the modified P ER. Using a large number of resampled data, the mean value and
the standard deviation converge and can be easily calculated. This resampling methodology is
used in this work to obtain P SD, phase angle φ and COH with detector signals during individual oscillations as representative subsamples. The aim of this analysis is to identify the PSD
spectral peaks at the base or higher harmonic frequencies of the induced perturbation frequency
i.e. calculating the spectral power P Si,j,l which is the area under the P SDi,j peak l. In case
of arbitrary normalization and detector signal standardization P S to a reference detector’s (R)
P Si,j,k
P Si,j,k
and a harmonic of the same order P Si,R,k
are calculated. Same goes for
base frequency P Si,R,0
the phase angles φi,j,l , except instead of the ratios ratio, differences in phase shifts are calculated. The two above mentioned quantities: PS ratios and phase shift differences are the main
QOI for the computer code validation.
3.1
Resampling
We want to eliminate temporal correlations between representative subsamples and treat
individual oscillations as independent. Therefore detector responses to individual oscillations
are our representative sub-samples. Well defined oscillation boundaries have to be defined for
signal sectioning. In case of the TUD AKR-2 oscillators, a single pulse per cycle is given for the
variable strength absorber, while the position of the vibrating absorber is logged continuously.
For distinguishing between individual oscillations, local maxima are selected for the variable
strength absorber, while zero-crossings are selected for the vibrating/linear absorber (Figure
5). For the CROCUS reactor Colibri oscillator, zero-crossings were selected for distinguishing
between individual oscillations (Figure 6). Based on these reference points, the original signal
2
1.0
1
Osc. signal
Osc. signal
0.8
0.6
0.4
0.2
0
1
0.0
2
0.2
0
10
20
30
t [s]
40
50
2
4
6
8
10
12
t [s]
(a) Variable strength absorber signal and reference (b) Vibrating absorber signal and reference points
points at 0.2 Hz.
at 0.714 Hz.
Figure 5: Absorber signal, both at 0.2 Hz and the reference points for distinguishing between
individual oscillations.
was split by individual oscillations and resampled as shown in Figure 7.
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 7–10, 2020
212.6
1.0
Osc. signal
0.5
0.0
0.5
1.0
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
t [s]
Figure 6: CROCUS Colibri position signal at amplitude of 1.5 mm and oscillation frequency of
0.97 Hz.
Original data: 1742 total sections
8
0.04
13
5
4
Detector signal
0.02
1
7
10
9
19
16
14
12
11
18
15
17
6
2
3
0.00
0.02
0.04
0.0
2.5
5.0
7.5
10.0
time [s]
12.5
15.0
17.5
20.0
Resampled data: 1742 total sections
659
0.04
42
298
694
1065
1029
929
1117
751
1314
149
1376
1259
1720
786
1387
Detector signal
0.02
1472
1299
620
0.00
0.02
0.04
0.0
2.5
5.0
7.5
10.0
time [s]
12.5
15.0
17.5
20.0
Figure 7: An example of original and resampled detector signal.
4
RESULTS
The QOI are frequency dependent P SD and phase angle φ mean values and their uncertainties, displayed in Figure 8, with clearly distinguishable base and higher harmonic frequency
peaks. The PSD distributions of base and 1st harmonic frequency averaged data over 10 samples along with fitted Gaussian distributions for comparison purposes are displayed in Figure 9.
For validation purposes we use relative values of QOI with respect to a chose detector. The P S
and φ uncertainties can be easily calculated from obtained distributions. The ratios represent
the detected spectral power with respect to the reference combination. Because of the provided
uncertainties, weighted mean and weighted relative standard deviation can be calculated, as
displayed in Figure 10.
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 7–10, 2020
212.7
Mean
10
2
10
3
10
4
10
5
10
6
Mean
Std.
Std.
2
Rad
PSD [
Hz
1
]
1
0
1
2
0
2
4
6
8
10
0
2
4
Frequency [Hz]
6
8
10
Frequency [Hz]
(a) PSD mean and uncertainty.
(b) Phase angle mean and uncertainty.
Figure 8: Intermediate results of P SD and phase angle φ between detectors 3 and 5 in CROCUS
reactor at oscillator frequency of 0.97 Hz and amplitude of 1.6 mm.
PSD histogram plot at 9.707e-01 Hz
PSD histogram plot at 1.941e+00 Hz
1.0
original_data
Gaussian fit
0.8
0.8
0.6
0.6
Norm. PDF
Norm. PDF
1.0
0.4
0.2
original_data
Gaussian fit
0.4
0.2
0.0
0.0
2.0
1.5
1.0
0.5
0.0
Final
0.5
1.0
1.5
2.0
(a) Base PSD peak distribution.
2.0
1.5
1.0
0.5
0.0
Final
0.5
1.0
1.5
2.0
(b) 1st harmonic PSD distribution-
Figure 9: P SD distributions of base and 1st harmonic peaks between detectors 3 and 5 in
CROCUS reactor at oscillator frequency of 0.97 Hz and amplitude of 1.6 mm.
5
CONCLUSIONS AND OUTLOOKS
A spectral analysis has been performed, based on a non-standard derivation of power
spectral densities, phase angles and coherences using bootstrapping with replacement. This
aims to identify and eliminate biases, temporal correlations and windowing effects by treating
each oscillation individually. Checks have been implemented to confirm the validity of the
analysis approach by tallying the distributions of QOI. Spectral power ratios and phase angle
estimates with uncertainties are provided to the code developers for validation in the framework
of the H2020 CORTEX project.
A full core mapping of CROCUS reactor is planned for the near future where in excess of 150
detectors will be used and a similar kind of analysis will be performed.
ACKNOWLEDGMENT
The authors would like to acknowledge the member contributions and the financial support of the CORTEX project in the framework of the Horizon 2020 EU Framework Programme.
The research leading to these results has received funding from the Euratom research and trainProceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 7–10, 2020
212.8
ing programme 2014-2018 under grant agreement No 754316.
PSD area normalized to detector 5
det 10
1.290e+00
4.135e+00
8.162e-01
1.152e+00
1.000e+00
1.572e+00
1.201e+00
8.471e-01
1.648e+00
det 11
1.435e+00
4.622e+00
7.412e-01
1.064e+00
1.000e+00
1.516e+00
1.454e+00
8.646e-01
2.054e+00
det 3
1.249e+00
3.267e+00
8.300e-01
1.202e+00
1.000e+00
1.591e+00
1.255e+00
8.747e-01
1.708e+00
det 4
1.206e+00
3.210e+00
8.225e-01
1.207e+00
1.000e+00
1.586e+00
1.271e+00
8.434e-01
1.716e+00
det 5
1.257e+00
3.620e+00
8.213e-01
1.200e+00
1.000e+00
1.582e+00
1.242e+00
8.571e-01
1.732e+00
det 6
1.248e+00
3.469e+00
8.260e-01
1.203e+00
1.000e+00
1.596e+00
1.240e+00
8.425e-01
1.767e+00
det 7
1.216e+00
4.237e+00
8.299e-01
1.228e+00
1.000e+00
1.580e+00
1.375e+00
8.937e-01
1.780e+00
det 8
1.242e+00
3.652e+00
8.382e-01
1.181e+00
1.000e+00
1.555e+00
1.295e+00
1.121e+00
1.905e+00
det 9
1.196e+00
4.293e+00
8.103e-01
1.190e+00
1.000e+00
1.614e+00
1.277e+00
9.429e-01
1.899e+00
W. Mean
1.239e+00
3.619e+00
8.211e-01
1.193e+00
1.000e+00
1.586e+00
1.261e+00
8.718e-01
1.748e+00
W. rel. Std
1.340e-01
2.139e-01
1.173e-01
1.174e-01
1.199e-01
1.153e-01
1.450e-01
1.723e-01
1.368e-01
det 10
det 11
det 3
det 4
det 5
det 6
det 7
det 8
det 9
100
Figure 10: P S ratios to reference detector 5 at base frequency for the experiment No. 3 at
CROCUS reactor at 0.97 Hz and amplitude of ±1.6 .
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Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 7–10, 2020