Corresponding author: Ivan V. Maksimov ( iv_maksimov@mail.ru ) Academic editor: Boris Balakin
© 2020 Ivan V. Maksimov, Vladimir V. Perevezentsev.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Maksimov IV, Perevezentsev VV (2020) A localization method for loose parts monitoring system of VVER reactor plants. Nuclear Energy and Technology 6(1): 2935. https://doi.org/10.3897/nucet.6.51252

As operational experience shows, it can hardly be excluded that some detached or loosened parts and even foreign objects (hereinafter referred to as the ‘loose parts’) may appear in the main circulation loop of VVER reactor plants. Naturally, the sooner such incidents are detected and evaluated, the more time will be available to eliminate or at least minimize damage to the reactor plant main equipment. The paper describes a method for localizing the impact of loose parts located in the coolant circulation circuit of a VVER reactor plant. To diagnose malfunctions of the reactor plant main equipment, it is necessary to accurately determine the place where the acoustic anomaly occurred. Therefore, if some loose parts make themselves felt, it is important to track the path of their movement along the main circulation circuit as well as their location using physical barriers.
The method is based on the representation of the surface, along which an acoustic wave travels, as a 3D model of the reactor plant (RP) main circulation circuit. The model has the form of a graph in which the vertices characterize the control points on the RP surface and the edges are the distances between them. The method uses information about the acoustic wave velocity and the time difference of arrivals (TDOAs) of the signal received by various sensors. It is shown that, when the effect is received by more than three sensors, along with an estimate of the impact coordinate, it becomes possible to estimate the average acoustic wave velocity. To determine time of arrival, the signal dispersion change point detection method is used. Provided that the average size between the control points on the RP surface was 300 mm, the average localization error was about 600 mm. The developed algorithm can be easily adapted to any VVER reactor plant. The obtained deviation values are acceptable for practical use.
Loose Parts Monitoring System (LPMS), diagnostics of NPPs, impact localization, acoustic wave, main circulation circuit, VVER reactor plant
One of the main condition monitoring systems of VVER reactor plants is the Loose Parts Monitoring System (LPMS), which function is detecting and evaluating the parameters of loose parts in the coolant circulation circuit. Loose parts can move with the coolant flow in the circulation circuit and cause damage to the RP primary circuit equipment. They can to some extent block the coolant flow, resulting in deteriorated heat transfer, possible overheating of the fuel element claddings, changes in the fuel temperature, and increased fuel swelling rate. Another negative consequence may be the risk of these parts falling into the movable mechanisms of the control and protection system working bodies. In case of their untimely detection in the coolant circulation circuit, the costs of measures taken to eliminate the damage caused by them increase significantly.
Currently, most NPPs with pressurized water reactors (PWR, VVER) are equipped with LPMSs. There are several international standards defining the requirements that LPMSs must meet:
Localizing the impact source is one of the most important functions of the LPMS when diagnosing the RP equipment (
To date, a large number of studies on impact source localization methods have been performed (
One of the most wellknown methods using TDOAs is the method of intersecting hyperbolas (
Another method (
The proposed algorithm automatically performs localization to a point on the surface of the RP primary circuit. It is based on calculating the shortest path along a 3D model of the surface of the RP primary circuit. The algorithm is flexible and easily adaptable to any pressurized water reactor plant.
One of the key factors in localizing the source of the acoustic anomaly is determining the time of arrival (TOA) of the impact wave for each sensor that recorded the effect. There are several approaches to the TOA determination. One method is to approximate the rootmeansquare (RMS) value of the signal by means of a piecewise smooth function:
$F\left(t\right)=\left\{\begin{array}{ll}{F}_{n}\left(t\right)=a,& t<{t}_{TOA}\\ {F}_{S}\left(t\right)=kt+b,& {t}_{TOA}<t<{t}_{\mathrm{max}}\end{array}\right.$, (1)
where F_{n} (t) is the constant value approximating the background noise; F_{S} (t) is the linear function approximating the leading edge in the interval from the TOA (t_{TOA}) to the RMS maximum time (t_{max}), with F_{n} (t_{TOA}) = F_{S} (t_{TOA}) = F (t_{TOA}).
Another widespread approach is based on statistical sequential analysis methods that are used to detect the acoustic effect. These include the Wald sequential probability ratio test (WSPRT) and the CUSUM test (
To determine the TOA, the present work involves the method for detecting changes in the parameters of a random process. The original signal is prefiltered (
$F\left({t}_{TOA}\right)=c\left({y}_{{t}_{1}\dots {t}_{TOA}}\right)+c\left({y}_{{t}_{TOA}\dots {t}_{N}}\right)$, (2)
where c (y_{ti}_{…}_{tj}) is the function that measures the uniformity (stability of parameters) of the signal part y_{i}_{…}_{j}.
The function c (y_{ti}_{…}_{tj}) for the signal dispersion change problem can be defined as
$c{\sigma}^{2}\left({y}_{i...j}\right)=\left{y}_{i...j}\right\times \mathrm{log}{\sigma}_{i\dots j}^{2}$, (3)
where y_{i}_{…}_{j} is the length of the signal part; σ^{2}_{i}_{…}_{j} is the signal part dispersion. The values of the objective function are expected to be low for uniform parts of the signals and large with significant dispersion changes. Therefore, the TOA of the impact wave is defined as follows:
${t}_{TOA}=\mathrm{arg}\mathrm{min}F\left({t}_{TOA}\right)$, (4)
This method is illustrated in Fig.
When loose parts collide with the surface of the RP equipment, an acoustic impact wave is generated. It is assumed that it spreads in the RP equipment material every which way at an equal velocity, which does not depend on the location of the source and direction. As a result, the wave travel time between two points on the surface is uniquely determined by the length of the shortest path along the surface between these points. Therefore, the time between the impact moment and its detection by the sensor depends on the distance and wave velocity.
To localize the anomaly in a linear section, it is enough to have signals from two sensors that recorded the burst. For a plane or surface, which can be represented as a plane, the TDOA pairs of sensors determine the geometric location of the points of the source possible position. To accurately determine the impact site, a signal of the third sensor is required. Then the location of the impact wave source is defined as the center of the circle passing through the coordinate of the sensor installation, corresponding to the sensor that was the first to record the impact wave, and tangent to the other two, with the radius ∆t_{1}_{i}×V, where ∆t_{1}_{i} is the TDOA of the acoustic wave between the sensor that was the first to record the impact and ith sensor with respect to the time of arrival; V is the velocity of sound in the medium (Fig.
The average wave velocity, considered in the target frequency range, is of the order of 2500 m/s (
To obtain the coordinate of the acoustic anomaly source localization in real time, it is necessary to prepare data for the calculation. The main data is taken from the RP and LPMS design documentation:
The geometric model is the shape of the boundaries of the pipelines and the main equipment of the MCC, i.e., the surface along which an acoustic wave travels. The positions of the sensors are the fixed sites in which the sensors are installed. They are described by coordinates on the geometric model.
The data preparation stage includes as follows:
1. Selection of control points on the geometric surface (Fig.
2. Binding of sensor positions to the nearest control points. The coordinates of the sensors on the RP equipment are compared with the control points. Triangulation of the surface should be carried out in such a way that the control points of the grid correspond to the coordinates of the sensors. As a result, we obtain the positions of the sensors S_{i}, i = 1, ..., N, where N is the number of the sensors.
3. Calculation of the shortest distances between the control points and sensors using Dijkstra’s algorithm (
As a result, we obtain the matrix D dimensioned [M × N] with elements
${D}_{ij}=dist\left({C}_{i},{S}_{j}\right)$, (5)
where C_{i} is the ith control point; S_{j} is the jth sensor; dist(C_{i}, S_{j}) is the the function of calculating the shortest distance over the geometric model surface.
The localization algorithm is performed every time an event associated with an unknown acoustic anomaly and (potentially) the presence of loose parts in the primary circuit is recorded. The input to the algorithm includes:
the vector of the TDOAs of the acoustic wave ∆t to each sensor S_{i}
$\Delta {t}_{i}=TO{A}_{i}\mathrm{min}\left(TOA\right)$, (6)
where TOA_{i} is the time of arrival of the acoustic wave;
The values of the TDOA vector represent a vector, the size of which corresponds to the number of sensors N. In cases when the time of arrival was not determined on the sensor, the TDOA value remains undetermined. The numbers of the sensors, in which the TDOA value was determined, form the set K.
The algorithm for calculating the coordinate of the acoustic anomaly occurrence includes as follows:
1. For each control point C_{i}, i = 1, ..., M the vector r_{i}is calculated:
${r}_{ij}={D}_{ij}\Delta {t}_{j}\times V$, (7)
where V is the initial approximation of the acoustic wave velocity; j ∈ K are the sensor numbers where the TDOA is determined.
2. For each vector r_{i}, i = 1, ..., M the functional value is calculated with the exception of empty values:
${\sigma}_{i}=\frac{1}{\leftK\right}\sum _{j\in K}{\left({r}_{ij}{r}_{i}^{m}\right)}^{2}$, (8)
3. The control point C_{i} is found at which the value of σ_{i} is minimal:
$i=\mathrm{arg}\mathrm{min}\left(\sigma \right)$, (9)
4. For the obtained control point C_{i}, the acoustic wave velocity V_{j} to the sensor S_{j} is recalculated:
${V}_{j}=\left({D}_{ij}{D}_{ij0}\right)/\Delta {t}_{j}$, (10)
where D_{ij}_{0} is the distance from C_{i} to the sensor S_{j}_{0} that was the first to record the impact with respect to the time of arrival; j ∈ K are the sensor numbers where the TDOA is determined.
5. For the calculated velocities V_{j}, the average wave velocity is calculated
${V}^{m}=\frac{1}{\leftK\right}\sum _{j\in K}{V}_{j}$, (11)
6. The calculated average velocity V ^{m} is compared with the initialized velocity V. If the velocity values coincide, then the algorithm is completed. If the values differ, the velocity V is taken equal to V ^{m}, and the algorithm is repeated until the velocities V and V ^{m} coincide.
As a result of the algorithm implementation, the coordinate of the acoustic anomaly source С and the average acoustic wave velocity V ^{m} are determined. To estimate the accuracy of determining the source localization, impacts of impact hammers (IH) located on the RP pipelines were considered (the arrangement of sensors and IHs is shown in Fig.
The geometric RP model in the form of a grid contained 30004 vertices (control points). The average distance between two control points was 30 cm.
In total, 143 IM impacts were made on different loops. The impacts were made under different operating modes of the power unit, and, accordingly, background acoustic noise was different, which affected the accuracy of determining the time of arrival. The experimental results are given in Table
Experimental results.
Loop No.  Location of IHs  Number of impacts  Average localization error, mm  Average acoustic wave velocity, m/s  Distance to the nearest sensor, mm 

1  Ushaped bend  29  624  2241  8803 
2  Pipeline cold patch  38  708  2351  5998 
3  Pipeline hot patch  38  473  2494  3769 
4  Ushaped bend  38  768  2161  8654 
Provided that the average cell size was 300 mm, the average localization error was 600 mm. As the distance from the impact site to the nearest sensor becomes longer, the error increases. The main error is associated with determining the time differences of arrival of the impact wave. The grid edge size introduces a constant error proportional to its length. Nevertheless, the deviation values are completely acceptable for practical use, and the developed algorithm can be used to estimate the acoustic anomaly source localization.
The authors propose an algorithm for localizing the acoustic anomaly source on the surface of the RP equipment along the triangulated surface of a 3D model of the coolant circulation circuit.
The algorithm consists of two parts. Data preparation is performed once for each power unit. Then, when an event is recorded in real time, the second part is executed, where the impact site and the average acoustic wave velocity are determined.
The analysis of the experimental data showed that the average error in the impact source localization is ~ 600 mm, which makes possible the practical application of the developed method.