Corresponding author: Ivan V. Maksimov (iv_maksimov@mail.ru)

Academic editor: Boris Balakin

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 (

One of the main condition monitoring systems of VVER reactor plants is the Loose Parts Monitoring System (

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:

U.S. Nuclear Regulatory Commission (NRC) Regulatory Guide 1.133 (1981) (Regulatory Guide 1.133 1981);

American Society of Mechanical Engineers (ASME) Standard OM-2017 (Operation and Maintenance 2015);

International Electrotechnical Commission (IEC) Standard IEC-609887 (IEC 60988 Nuclear power plants 2009).

Localizing the impact source is one of the most important functions of the

To date, a large number of studies on impact source localization methods have been performed (

One of the most well-known methods using

Another method (

The proposed algorithm automatically performs localization to a point on the surface of the

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 root-mean-square (RMS) value of the signal by means of a piecewise smooth function:

where _{n}_{S}_{TOA}_{max}), with _{n}_{TOA}_{S}_{TOA}_{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 (

To determine the TOA, the present work involves the method for detecting changes in the parameters of a random process. The original signal is pre-filtered (_{t}_{1}, ..., _{tN}_{TOA}_{TOA}

where _{ti}_{…}_{tj}_{i}_{…}_{j}

The function _{ti}_{…}_{tj}

where |_{i}_{…}_{j}^{2}_{i}_{…}_{j}

This method is illustrated in Fig.

Estimation of the time of arrival of the acoustic signal: a) with an acoustic effect; b) without an acoustic effect (1 – signal, 2 – objective function).

When loose parts collide with the surface of the

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 ∆_{1}_{i}_{1}_{i}

Graphic representation of the TDOA-based acoustic anomaly localization method: 1, 2, 3 are the sensor sensors numbered according to the time of arrival.

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

a geometric model of the RP surface; and

positions of the sensors on the RP equipment.

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. _{i}

Geometric model of the

2. Binding of sensor positions to the nearest control points. The coordinates of the sensors on the _{i}

3. Calculation of the shortest distances between the control points and sensors using Dijkstra’s algorithm (

As a result, we obtain the matrix

where _{i}_{j}_{i}_{j}

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 _{i}

where _{i}

the distance matrix D calculated by the formula (5);

the initial value of the acoustic wave velocity in the RP equipment material, which is assumed to be equal to 2500 m/s.

The values of the TDOA vector represent a vector, the size of which corresponds to the number of sensors

The algorithm for calculating the coordinate of the acoustic anomaly occurrence includes as follows:

1. For each control point _{i}_{i}

where

2. For each vector _{i}

_{i}_{i}

4. For the obtained control point _{i}_{j}_{j}

where _{ij}_{0} is the distance from _{i}_{j}_{0} that was the first to record the impact with respect to the time of arrival;

5. For the calculated velocities _{j}

6. The calculated average velocity ^{m}^{m}^{m}

As a result of the algorithm implementation, the coordinate of the acoustic anomaly source ^{m}

The geometric

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 | U-shaped bend | 29 | 624 | 2241 | 8803 |

2 | Pipeline cold patch | 38 | 708 | 2351 | 5998 |

3 | Pipeline hot patch | 38 | 473 | 2494 | 3769 |

4 | U-shaped 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

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.

* Russian text published: Izvestiya vuzov. Yadernaya Energetika (ISSN 0204-3327), 2019, n. 4, pp. 28–38.