=Paper=
{{Paper
|id=Vol-2744/paper11
|storemode=property
|title=Compression and Visualization of the Operational Parameters Archive
|pdfUrl=https://ceur-ws.org/Vol-2744/paper11.pdf
|volume=Vol-2744
|authors=Andrey Zagrebayev,Victor Pilyugin,Stanislav Ten
}}
==Compression and Visualization of the Operational Parameters Archive==
https://ceur-ws.org/Vol-2744/paper11.pdf
Compression and Visualization of the Operational
Parameters Archive1
Andrey Zagrebayev[0000-0003-0576-3587], Victor Pilyugin[0000-0001-8648-1690],
Stanislav Ten[0000-0001-9279-1732]
National Research Nuclear University MEPhI, Kashirskoe hwy 31, 115409, Moscow, Russia
{amzagrebayev, vvpilyugin}@mephi.ru
tenstanislav@email.com
Abstract. This article describes the mathematical apparatus for express analysis
of the archive of operational parameters. The developed algorithms based on the
methods of reducing the dimension of the space of variables and the “Chernoff
Faces” method allow visualizing the dynamics of changes in generalized limiting
parameters, as well as visually determining the approximation or intersection of
permitted values by parameters, which in turn can provide scientific and practical
use in improving quality of operational personnel work and analysis of situations
requiring additional attention and more detailed analysis.
Keywords: Operational Parameters Archive, Scientific Visualization, Data
Analysis.
1 Introduction
The safe operation of powerful nuclear power reactors is ensured by the availability of
information and computer systems that make it possible to measure, calculate and con-
trol the most important parameters of a nuclear power unit [1-4].
At power units with RBMK reactors such a system is called “SKALA”, which allows
controlling about 10,000 parameters in almost real time mode. This information is par-
tially visualized on a unit control board and enables operators to efficiently and safely
manage a nuclear power unit.
Moreover, in addition to the functions of directly providing information for the op-
erational management of the technological process, the information and computer com-
plex archives the current measured and calculated parameters. This enables a posteriori
analysis of the quality of process control in order to obtain new scientific and practical
results.
List as an example some of the tasks that require knowledge and analysis of the
history of the power unit's behavior:
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0).
2 A. Zagrebayev et al.
• Diagnosis of emergency situations at power unit, evaluation of operational staff
work quality;
• evaluation of efficiency of held events for algorithm and control systems improve-
ment;
• creation of real data information base for development of mathematical software of
a training apparatus;
• creation of adapting mathematical models of processes, ongoing in nuclear power
installation;
• creation of self-organizing programs of “operator advisor” type, using work experi-
ence of operational staff in regular and emergency situations (solving problems of
artificial intelligence);
• identification of reasons of separate items of reactor core and main technological
equipment break down (solving problems of predictive analytics).
2 Problem definition
Depending on the problem, requirements for pattern, type, amount of stored infor-
mation and also for the level of its specification may significantly differ. For example,
to solve the problem of assessing the quality of work of operational staff, it is necessary
to store information on the type and number of monitored parameters, the values of
which are beyond the limits established by the regulation, the number and type of op-
erator’s effects on the control object (movement of control and protection systems (for
CPS), coolant flow rate adjustment, etc.), the degree of spatial stability of the three-
dimensional energy release field, etc. While solving the problem of identification of
break down reasons, for example, of fuel elements and a channel, information for the
period from several days to several years may be needed. In this case a behavior back-
story of such parameters as each channel capacity, its power generation, coolant flow
rate through the channel, fuel elements’ burst can detection system data and integrity
control of technological channels [1], linear load on a fuel element, stock before the
heat transfer crisis, number of transpositions of fuel cartridges and etc. are of interest.
However, despite the fact that the above problems are actually of different types,
power unit operational parameters archive should enable each problem to be solved and
moreover, should be an information database for solving newly arising problems. At
the current level of development of computer systems at nuclear power plants, it is
possible to organize the storage of all experimental and calculated information with
high detail in time over a long period of operation, however, this raises problems with
express analysis of a large amount of data. The way out of this situation can be the use
of the method of scientific visualization, when the initial analyzed data is assigned to
one or another form of its graphic interpretation, which can subsequently be analyzed
visually, and the results of the analysis of this graphic interpretation are then interpreted
in relation to the original data.
A modern storage facility for parameters of a nuclear power unit with an RBMK
reactor and a special created module for visualizing archive data in a user-friendly form
Compression and Visualization of the Operational Parameters Archive… 3
for viewing the archive database from remote workstations are described in [5]. This
module also serves for easy export of data for subsequent analysis and calculations.
The module interface is presented in Fig. 1. In the main window of the program the
current state of the database is analyzed and a list of available "time slices" is generated.
The header of the main window displays information about the time of the last update
is presented. On the toolbar there is a button to update the list of available "time slices"
manually. In the center of the program window the cartogram of the parameter selected
from the list is displayed. Periodically (by default every 30 seconds) the program auto-
matically updates the list of available "time slices”.
Fig. 1. The window of the visualization module after selecting the required information
From the "SKALA-MICRO" system such parameters as core fueling, the coolant flow
rate in each channel, information about the position of control rods, the readings of the
neutron flux sensors and the estimated parameters reactor power, energy-producing of
fuel assembly and reactivity margin are extracted.
Despite the advantages of the visualization module above, that are the presentation
of information in the form of cartograms and graphs of detailed behavior of local pa-
rameters, there are some problems from the express analysis point of view of the pa-
rameters’ temporal behavior. It would be desirable to visualize the generalized param-
eters of a nuclear power unit containing the most important information about the tech-
nological process in the integral.
This opportunity is fundamentally possible, since there really are single objects, for
example, neutron fields, graphite masonry temperatures, etc., although they are meas-
ured by sensors discretely located in space. This is on the one hand. On the other hand,
the archive of operational parameters contains parameters correlated with each other,
since different control systems provide dissimilar information, but about the same ob-
ject.
4 A. Zagrebayev et al.
Thus, there is, firstly, a need to compress information and obtain a number of pa-
rameters, the physical meaning of which simplifies the visual analysis of the process
history, and secondly, the development (or application) of modern methods of visuali-
zation of multidimensional objects and processes.
This work illustrates the proposed approach with specific examples.
3 Visualization of multidimensional data
It is proposed to use the least squares method [6] and the method of selecting significant
ordinates [7] as the algorithms for compressing information on the neutron field. The
first one is used to compress intra-reactor information in space, and the second one is
to compress single and integral parameters in time.
Let us briefly consider the technique of compressing information in space. Suppose
that the field of some operational parameter of the reactor core is described by a spatio-
temporal function Ф(𝑟⃗, 𝑡). Approximate the readings of discretely located sensors
based on the least squares method.
Represent the function Ф(𝑟⃗, 𝑡) in the form (1), and seek a solution based on the min-
imum condition for functional (2).
Ф(𝑟⃗, 𝑡) = ∑𝑚
𝑖=1 𝐵𝑖 (𝑡 )𝜑𝑖 (𝑟
⃗) ; (1)
𝐹 = ∑𝑚 ⃗𝑖 , 𝑡) − 𝐶𝑖 )2 → 𝑚𝑖𝑛,
𝑖=1(Ф(𝑟 (2)
here 𝐶𝑖 is the value of the operational parameter at the points where the sensors are
installed; 𝑟⃗𝑖 - coordinates of the reactor core points where the sensors are installed;
𝜑𝑖 (𝑟⃗), 𝑖 = 1, . . . , 𝑚 - a number of linearly independent functions that are selected in
advance; 𝐵𝑖 (𝑡) - time coefficients to be found.
With this formulation of the problem, the solution is obtained in the form
⃗⃗ = (𝑆 𝑇 𝑆)−1 𝑆 𝑇 𝐶⃗, 𝐵
𝐵 ⃗⃗ = 𝑀𝐶⃗, 𝑀 = (𝑆 𝑇 𝑆)−1 𝑆 𝑇 , (3)
𝐶1
𝐶
where 𝐶⃗ = ( 2 ) is a parameter measurement vector;
…
𝐶𝑁
𝐵1
𝐵
⃗⃗ = ( 2 ) is a vector of unknown coefficients;
𝐵
…
𝐵𝑚
Compression and Visualization of the Operational Parameters Archive… 5
𝜑1 (𝑟⃗1 ) 𝜑2 (𝑟⃗1 ) . . . 𝜑𝑚 (𝑟⃗1 )
𝜑 (𝑟⃗ ) 𝜑2 (𝑟⃗2 ) . . . 𝜑𝑚 (𝑟⃗2 )
𝑆=( 1 2 ) is a matrix of values of decomposition func-
... ... ... ...
𝜑1 (𝑟⃗𝑁 ) 𝜑2 (𝑟⃗𝑁 ) . . . 𝜑𝑚 (𝑟⃗𝑁 )
tions at measurement points.
Thus, instead of the initial N values of the measurement vector 𝐶⃗, m values of the Bi
coefficients are obtained. The number of Bi coefficients is 1-2 orders of magnitude
smaller than the number N, and satisfactory accuracy is achieved.
The choice of decomposition functions during data compression by the least squares
method may be arbitrary in the general case, but in order to achieve maximum approx-
imation accuracy, it is desirable to choose them most closely describing the behavior
of the reactor parameters. On the one hand, it is known [1] that such functions are ei-
genfunctions for solving equations describing the dynamics of the parameters under
consideration. On the other hand, finding the exact solution that describes the behavior
of the parameters in the reactor is a difficult mathematical task, since a nuclear power
reactor is a complex object with distributed parameters.
In [8] there is the following method of experimental determination of the best set of
test functions, based on the transition from the initial expansion of the parameters in
some functions that approximately describe their behavior to the canonical expansion
obtained from the original.
It is necessary to find such decomposition functions {𝜑𝑖′ (𝑟⃗)} in order to present the
function Ф(𝑟⃗, 𝑡) in the form:
Ф(𝑟⃗, 𝑡) = ∑𝑀 ′ )
𝑖=1 𝑉𝑖 (𝑡 )𝜑𝑖 (𝑟
⃗ , (4)
in this case 𝑉𝑖 are not correlated with each other, in contrast to 𝐵𝑖 in formula (1).
𝑀[𝑉𝑖 𝑉𝑗 ] = 0 with 𝑖 ≠ 𝑗; 𝑀[𝑉𝑖 𝑉𝑗 ] = 𝐷[𝑉𝑗 ] = 𝐷𝑗 with 𝑖 = 𝑗, and also 𝑀[𝑉𝑖 ] = 0.
The new set of functions is calculated using the following formulas:
̃ 𝑖 (𝑟⃗) = 𝜑𝑖 (𝑟⃗) + ∑𝑁
Ф 𝑠=𝑖+1 𝑎𝑠𝑖 𝜑𝑠 (𝑟
⃗), 𝑖 = 1, . . . , 𝑁 − 1;
{ (5)
̃ 𝑁 (𝑟⃗) = 𝜑𝑁 (𝑟⃗)
Ф
𝐾
𝑎𝑖1 = 𝐾 𝑖1 ;
11
1 𝑝−1
𝑎𝑖𝑝 = 𝐷 [𝐾𝑖𝑝 − ∑𝜆=1 𝑎𝑖𝜆 𝑎𝑝𝜆 𝐷𝜆 ];
𝑝 (6)
𝑖 = 2, 𝑁;
{𝑝 = 2, 𝑖 − 1,
𝑝−1
where 𝐷𝑝 = 𝐾𝑝𝑝 − ∑𝜆=1 (𝑎𝑝𝜆 )2 𝐷𝜆 .
Kij values are correlation moments: 𝐾𝑖𝑗 = 𝑀[(𝐵𝑖 − 𝑚𝑖 )(𝐵𝑗 − 𝑚𝑗 )].
(𝑖)
∑𝑁
𝑖=1 𝐵𝑗
Here 𝑚𝑗 = 𝑁 , N is the sample size.
The desired function Ф(𝑟⃗, 𝑡) is expressed as following:
Ф(𝑟⃗, 𝑡) = ∑𝑀 ⃗) + ∑𝑀
𝑖=1 𝑚𝑖 𝜑𝑖 (𝑟
̃ ⃗).
𝑖=1 𝑉𝑖 Ф𝑖 (𝑟 (7)
6 A. Zagrebayev et al.
To find the coefficients, it is necessary to apply the least squares method described
above.
Due to the fact that the canonical decomposition obtained by the described method
allows the best description of the macro-field of reactor parameters, it is advisable to
recalculate the functions Ф(𝑟⃗, 𝑡) in relation to the dynamic archive in order to achieve
the most accurate decomposition, since in this case fewer decomposition functions will
be required to fulfil the conditions for the accuracy of decomposition.
This approach to visualizing the archive of operational parameters is illustrated by
the following examples.
3.1 Motion path in principal components
Compression of several correlated limiting parameters of the fuel channel by the
method of principal components and further dynamic visualization of the state in three-
dimensional space.
The limiting parameters that ensure the normal operation of the fuel assembly are:
• Power of the fuel assembly;
• coolant flow rate;
• power safety factor;
• safety factor for linear load;
• fuel temperature;
• temperature of the shell of fuel elements, etc.
Exceeding the settings of at least one of the parameters leads to an unplanned decrease
in emergency power. In this work, as a result of compression, three integral parameters
that characterize the state of the fuel assembly are left. This state in dynamics is dis-
played as the movement in time of a point in three-dimensional space limited by toler-
ances (see Fig. 2).
Compression and Visualization of the Operational Parameters Archive… 7
Fig. 2. Visualization of the motion path in the principal components (different angles)
3.2 Adaptation of the “Chernoff Faces” method to the archive
A convenient approach to visualizing the behavior of parameters is “Chernoff Faces”,
invented by Herman Chernoff in 1973, display multivariate data in the shape of a hu-
man face. The individual parts, such as eyes, ears, mouth and nose represent values of
the variables by their shape, size, placement and orientation [9]. The idea behind using
faces is that humans easily recognize faces and notice small changes without difficulty.
Typically, “Chernoff Faces” are used when it is necessary to group (cluster) objects
according to several criteria, or when it is necessary to analyze presumably complex
relationships between variables.
Applied to the express analysis of the operational parameters archive, the
Chernoff method significantly expands the range of visualized states of the reactor and
the power unit as a whole.
As an example, let’s use this approach to display power dynamics in local regions
of the core. Local regions in this case are understood as quadrants of the reactor core.
𝑡
Let 𝑊(𝑥,𝑦) be the power of the fuel assembly having coordinates on the core
scheme at time t (Fig. 3).
Further, the cartogram of the reactor is divided into 4 parts (quadrants), as shown
in Fig. 3. Each quadrant corresponds to a set of coordinates of the channels located in
this quadrant:
𝑄𝑖 = {(𝑥1 , 𝑦1 ), (𝑥1 , 𝑦2 ), … , (𝑥2 , 𝑦1 ), (𝑥2 , 𝑦2 ), … , (𝑥𝑝 , 𝑦𝑞 ), … },
𝑖 = 1, … , 4 – quadrant number
The average power value for each quadrant is taken for each time moment t.
𝑡
𝑊(𝑥 𝑝 ,𝑦𝑞)
̅𝑖𝑡 = ∑(𝑥 ,𝑦 )∈𝑄
𝑊 , (8)
𝑝 𝑞 𝑖 𝑛
n - number of channels in quadrant, 𝑖 = 1, … ,4 - number of quadrant.
As a result, for each moment of time, each quadrant corresponds to a parameter
which is the average value of power 𝑊 ̅𝑖𝑡 .
Then, the normalization procedure is applied for each quadrant according to the
formula for the entire time slice (given time slice):
𝑋−𝑋𝑚𝑖𝑛
𝑋𝑛𝑜𝑟𝑚 = , (9)
𝑋𝑚𝑎𝑥 −𝑋𝑚𝑖𝑛
𝑋 is the initial value is the value at the time t, 𝑋𝑚𝑖𝑛 is the minimum value for the entire
time slice, 𝑋𝑚𝑎𝑥 is the maximum value for the entire time slice.
The normalized value is denoted by 𝑊 ̂ 𝑡.
̅ 𝑖
At the mapping stage, 4 face characteristics were selected for visualization:
• 𝑃1 for the tilt of the eyebrows;
• 𝑃2 for the eye width;
8 A. Zagrebayev et al.
• 𝑃3 for the length of the nose;
𝑃4 for the bend of a smile.
Fig. 3. Scheme of reactor core divided into quadrants
Each of the characteristics 𝑃𝑖 lies in the range [0, 1]. The “average face” is displayed
separately, it has the average values of the parameters for the entire time slice (the
specified time slice) displayed. Fig. 4 shows an example of such a face which charac-
teristics of 0.5, i.e.
𝑃1 = 0.5, 𝑃2 = 0.5, 𝑃3 = 0.5, 𝑃4 = 0.5
Fig. 4. “Average face”
Compression and Visualization of the Operational Parameters Archive… 9
Further, each characteristic is associated with a normalized quadrant average power
value:
̂
̅𝑖𝑡
𝑃𝑖 = 𝑊
and for each point in time t, a corresponding face is displayed.
The final result of visualization for power using the “Chernoff Faces” method is
observed in Fig. 5. A similar procedure was carried out for the coolant flow rate (Fig.
6).
Fig. 5. Visualization results (Power).
Fig. 6. Visualization results (Flow rate).
10 A. Zagrebayev et al.
Analyzing the obtained results, it is possible to draw conclusions when some of the
parameters deviate strongly from their average values, when maximums or minimums
are reached, or implicit relationships between the parameters (when visualizing more
parameters) can be found. The result obtained at this stage is intermediate and is used
as a demonstration of possible options for visualizing the archive. Such an approach,
while using a larger number of parameters, would visually highlight clusters of similar
facial expressions or find hidden dependencies of the parameters among themselves.
3.3 Temporal Networks
Temporal Networks is another popular method for visualizing structured, dynamically
changing data over time.
A temporal network, also known as a time-varying network, is a network which links
are active only at certain points in time. Each link carries information on when it is
active, along with other possible characteristics such as weight. Time-varying networks
are of particular relevance to spreading processes, like the spread of information and
disease, since each link is a contact opportunity and the time ordering of contacts is
included [10].
At the moment, work is underway in the field of studying the visualization methods
acceptable for use with respect to the existing archive, including the Temporal Net-
works method that can be used to visualize the interaction of parameters in time and
can help understand, predict and optimize the behavior of system. Representation of
data in the form of graphs of vertices connected by edges could reveal new non-trivial
patterns of changes in parameters, possible correlations, and also could be used for
clustering. At the same time, it becomes possible to assess how local patterns interact
and produce global behavior, which is one of the main tasks of archive analysis.
Nowadays, Temporal Networks is actively used in the scientific community, while
there is already corresponding software for working with dynamically changing data,
as well as many articles on the application of this method to various data.
4 Conclusion
Currently, on the basis of the proposed methods, a computer software package that pro-
vides flexible customization of the desired visualization has been developed. The pro-
gram module includes components for export and data processing, two-dimensional
and three-dimensional visualization with the specified settings. The software is imple-
mented using modern effective data analysis tools and provides convenient user inter-
action functionality.
The proposed software can be used both by the operational staff of the NPP as an
auxiliary one in order to increase the efficiency of monitoring the operation of the
power unit, and also in order to analyze the existing archive database.
It is planned to continue work on improving the quality and stability of the developed
software package, as well as expanding the functionality and adding new features.
Compression and Visualization of the Operational Parameters Archive… 11
References
1. Dollezhal' N.A., Emel'yanov I.Ya. Kanal'nyi yadernyi ehnergeticheskii reaktor. [Channel
Nuclear Power Reactor] Atomizdat Publ., 1980.
2. M.A. Abramov, V.I. Avdeev, E.O. Adamov et al.Edited by Yu.M. Cherkashova. Kanal'nyi
yadernyi ehnergeticheskii reaktor RBMK.[Channel Nuclear Power Reactor RBMK] GUP
NIKIEhT Publ., 2006. 632 p.
3. Ovchinnikov F.Ya., Golubev L.I., Dobrynin V.D., Klochkov V.I., Semenov V.V., Tsybenko
V.M. Ehkspluatatsionnye rezhimy vodo-vodyanykh ehnergeticheskikh yadernykh
reaktorov. [Operational modes of water-cooled nuclear power reactors] Atomizdat Publ.,
1975.
4. Nuclear Power Engineering. Problems. Solution / Edited by M.N. Strikhanov. - Part 1. - M.:
Social Forecasts and Marketing Center, 2011. - 424 p.
5. A.M. Zagrebayev, R.N. Ramazanov, Nuclear Reactor RBMK Archive Data Visualization.
Scientific Visualization, 2015, Q.2, V.7, Num. 2, pp. 1-11
6. Yurova L.N., Naumov V.I., Savander V.I., Zagrebayev A.M. Kompaktnoe predstavlenie
vynutrireaktornoi informatsii o potoke neitronov / Fizika yadernykh reaktorov. [Compact
representation of in-reactor neutron flux information. / Physics of nuclear reactors.] Atom-
izdat Publ., 1975, n.4, pp.19-23
7. Alimov A.L., Shchadilov A.E. Optimal'noe adaptivnoe szhatie tsifrovykh soobshchenii po
algoritmu kusochno-lineinoi approksimatsii. [Optimal adaptive compression of digital mes-
sages using piecewise linear approximation algorithm] Avtometriya Publ., 1983, №3, pp.14-
18.
8. A.M. Zagrebayev, V.A. Nasonova, N.V. Ovsyannikova. Matematicheskoe modelirovanie
yadernogo reaktora pri sluchainykh vozmushcheniyakh tekhnologicheskikh parametrov.
[Mathematical modeling of a nuclear reactor with random perturbations of technological
parameters] NRNU MEPhI Publ., 2009. – 400 p.
9. Wikipedia contributors. Chernoff face. Wikipedia, The Free Encyclopedia. Retrieved May
5, 2020. Available at:
https://en.wikipedia.org/w/index.php?title=Chernoff_face&oldid=958878449
10. Wikipedia contributors. Temporal network. Wikipedia, The Free Encyclopedia. Retrieved
August 11, 2020. Available at:
https://en.wikipedia.org/w/index.php?title=Temporal_network&oldid=960041057