# Localizing Perturbations in Pressurized Water Reactors Using One-Dimensional Deep Convolutional Neural Networks

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## Abstract

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## 1. Introduction

## 2. Related Work

## 3. The VVER-1000 Nuclear Reactor at Temelín

#### 3.1. Reactor Description

#### 3.2. Measurement Methodology

#### 3.3. Detectors Used for Structural Health Monitoring

## 4. The Simulated Data

#### 4.1. The FEMFFUSION Diffusion Code

#### 4.2. Neutron Noise Diffusion Equation

- Fluctuations are assumed to be small.$$|\delta X(\overrightarrow{r},t)|\ll {X}_{0}\left(\overrightarrow{r}\right),\phantom{\rule{1.em}{0ex}}\forall (\overrightarrow{r},t).$$
- The transient is assumed to be stationary.$$\left(\right)open="\langle "\; close="\rangle ">\delta X(\overrightarrow{r},t)$$
- Second-order terms are neglected.$$\delta X(\overrightarrow{r},t)\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\delta Y(\overrightarrow{r},t)\approx 0.$$

#### 4.3. Generic Absorber of Variable Strength

## 5. The Machine Learning Model

#### 5.1. Model Architecture

## 6. Results and Discussion

#### 6.1. Results

#### 6.1.1. The Efficiency of the Trained Models

#### 6.1.2. Prediction on the Plant Measurements

#### 6.2. Discussion

#### 6.2.1. The Other Available Measurements in the Core

#### 6.2.2. Some Considerations on the Frequency Resolution

#### 6.2.3. Spectra Observation of the Other Available Measurements to Validate the Prediction

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ANN | Artificial Neural Network |

APSD | Auto-Power Spectral Density |

BOC | Beginning of Cycle |

CNN | Convolutional Neural Network |

CPSD | Cross-Power Spectral Density |

DC | Direct Current component |

DMTS | Distributed Measuring Test System |

FA | Fuel Assembly |

IAEA | International Atomic Energy Agency |

IRI | Incompatible Rod Insertion |

JTFS | Joint Time–Frequency Spectrogram |

LSTM | Long Short-Term Memory unit |

ML | Machine Learning |

NPP | Nuclear Power Plant |

PWR | Pressurized Water Reactor |

RNN | Recurrent Neural Network |

RVMS | Reactor Vibration Monitoring System |

SPND | Self Power Neutron Detector |

SÚJB | State Office for Nuclear Safety (Czech Republic) |

UJV | Nuclear power engineering in Czech Republic (ÚJV Řež) |

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**Figure 2.**SPND positions in the core of the VVER-1000/320 reactor with data from the U1C09 cycle. (

**a**) Radial detector positions with marked fa1, fa3, fa4 and fa6 sets. (

**b**) Vertical detector positions in the TVSA-T fuel assembly.

**Figure 3.**JTFS from the $N205$ SPND (selected from the fa1 configuration set) during the U1C09 cycle.

**Figure 7.**Prediction on plant measurements when no filter is applied (sampling rate 100 $\mathrm{Hz}$). (

**a**) fa1. (

**b**) fa3. (

**c**) fa4. (

**d**) fa6.

**Figure 8.**Prediction on plant measurements for filtered bandwidth $[0\phantom{\rule{0.166667em}{0ex}};1.1]\phantom{\rule{0.166667em}{0ex}}\mathrm{Hz}$ and sampling rate of 100 $\mathrm{Hz}$ (Section 6.2.2). (

**a**) fa1. (

**b**) fa3. (

**c**) fa4. (

**d**) fa6.

**Figure 9.**Prediction on plant measurements for filtered bandwidth $[0\phantom{\rule{0.166667em}{0ex}};2]\phantom{\rule{0.166667em}{0ex}}\mathrm{Hz}$ and sampling rate of 100 $\mathrm{Hz}$. (

**a**) fa1. (

**b**) fa3. (

**c**) fa4. (

**d**) fa6.

**Figure 10.**Prediction on plant measurements for filtered bandwidth $[9\phantom{\rule{0.166667em}{0ex}};11]\phantom{\rule{0.166667em}{0ex}}\mathrm{Hz}$ and sampling rate of 100 $\mathrm{Hz}$. (

**a**) fa1. (

**b**) fa3. (

**c**) fa4. (

**d**) fa6.

**Figure 11.**Available measurements for the U1C09 cycle, used to verify the machine learning performance.

**Table 1.**Detector signal groups (letter N designating internal detectors, the first two digits their radial position and the last digit the axial position).

Group Name | Detectors |
---|---|

fa1 | $N221$, $N223$, $N225$, $N227$, $N241$, $N243$, $N245$, $N247$, $N271$, $N273$, |

$N275$, $N277$, $N201$, $N203$, $N205$, $N207$ | |

fa3 | $N411$, $N413$, $N415$, $N417$, $N381$, $N383$, $N385$, $N387$, $N471$, $N473$, |

$N475$, $N477$, $N401$, $N403$, $N405$, $N407$ | |

fa4 | $N151$, $N153$, $N155$, $N157$, $N081$, $N083$, $N085$, $N087$, $N061$, $N063$, |

$N065$, $N067$, $N111$, $N113$, $N115$, $N117$ | |

fa6 | $N571$, $N573$, $N575$, $N577$, $N541$, $N543$, $N545$, $N547$, $N511$, $N513$, |

$N515$, $N517$, $N561$, $N563$, $N565$, $N567$ |

Group Name | fa1 | fa3 | fa4 | fa6 |
---|---|---|---|---|

Accuracy | $93.25\%$ | $93.95\%$ | $93.74\%$ | $93.26\%$ |

Model Characteristic | 0.1 Hz | 1 Hz | 10 Hz |
---|---|---|---|

Prediction accuracy of the radial location | low | medium | high |

Spectral resolution | not well described | partially described | well described |

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**MDPI and ACS Style**

Pantera, L.; Stulík, P.; Vidal-Ferràndiz, A.; Carreño, A.; Ginestar, D.; Ioannou, G.; Tasakos, T.; Alexandridis, G.; Stafylopatis, A.
Localizing Perturbations in Pressurized Water Reactors Using One-Dimensional Deep Convolutional Neural Networks. *Sensors* **2022**, *22*, 113.
https://doi.org/10.3390/s22010113

**AMA Style**

Pantera L, Stulík P, Vidal-Ferràndiz A, Carreño A, Ginestar D, Ioannou G, Tasakos T, Alexandridis G, Stafylopatis A.
Localizing Perturbations in Pressurized Water Reactors Using One-Dimensional Deep Convolutional Neural Networks. *Sensors*. 2022; 22(1):113.
https://doi.org/10.3390/s22010113

**Chicago/Turabian Style**

Pantera, Laurent, Petr Stulík, Antoni Vidal-Ferràndiz, Amanda Carreño, Damián Ginestar, George Ioannou, Thanos Tasakos, Georgios Alexandridis, and Andreas Stafylopatis.
2022. "Localizing Perturbations in Pressurized Water Reactors Using One-Dimensional Deep Convolutional Neural Networks" *Sensors* 22, no. 1: 113.
https://doi.org/10.3390/s22010113