# Characterization of Relative Movements between Blocks Observed in a Concrete Dam and Definition of Thresholds for Novelty Identification Based on Machine Learning Models

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## Abstract

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## 1. Introduction

## 2. Methodology Proposed for the Characterization of Relative Movements between Blocks and for Threshold Definition for Novelty Identification

#### 2.1. Methodology

- The adoption of the HTT formulation for the development of the prediction model requires the selection of the main physical quantities to be used. The water height and the concrete dam body temperature variations are the selected main inputs in the proposed model.
- The separation of effects in the analysis of the relative movements between blocks may not be verified, so a model capable of mapping the interaction between the inputs is recommended. In this sense, an MLP-NN model was found to be suitable. Once the MLP-NN model is obtained, the influence of the main loads on the responses, as well as the analysis of the residuals, r, can be analysed.
- The definition of thresholds for novelty identification based on the residuals can be defined: (i) based on one record at a time, (ii) based on a time window of records, (iii) and based on the simultaneity of the responses measured, as shown below.
- A threshold definition based on one record at a time is the most used type of threshold in dam engineering and consists of the adoption of a multiplier n applied to the standard deviation of the residuals, $sd.r.$, as follows: $n\times sd.r.$ Values of n equal to 3 and 4 correspond to a confidence level of 99.73% and 99.99%, respectively, since residuals are assumed to follow a Gaussian distribution.
- A threshold definition based on a time window of records of one physical quantity is based on the moving average of the residuals, $m.a.r.$, and the moving standard deviation of the residuals, $m.sd.r.$, adopting a time window of records over time. The size of the time window may depend on the case under study.
- A threshold definition based on the simultaneity of the responses measured allows the identification of novelties related to a cluster of data (with m features) related to the m quantities considered in the analysis. $DBSCAN$ is a method suitable for this approach, in which it is necessary to adopt, as an initial step, suitable values for Epsilon distance, $\u03f5$ and MinPoints, $MinP$ (Section 2.4). Hence, the residuals related to several physical quantities $({r}^{1},\dots {r}^{m})$, with m being the number of features measured simultaneously, are assessed to define clusters of the ones that present a behaviour far from that of the remaining data.

#### 2.2. Multilayer Perceptron Neural Network Algorithm

#### 2.3. Time-Window Threshold Definition Based on the Moving Average and Moving Standard Deviation of the Residuals

#### 2.4. Multivariate Threshold Definition Based on DBSCAN Algorithm

## 3. Case Study

#### 3.1. The Feiticeiro Dam

- Horizontal movements based on the pendulum method through the use of optical telecoordinometers (4–20 mA signal);
- Vertical movements through rod strain meters with a position transducer of the vibrating wire type;
- Discharges through level gauges with ultrasonic sensors (4–20 mA signal);
- Pressures through piezometers with pressure transducers of the vibrating wire type;
- Relative movements between blocks through 3D jointmeters with a position transducer of the vibrating wire type, located in the inspection galleries;
- Relative movements between blocks through 1D jointmeters with a resistance transducer of the Carlson type, embedded in the concrete dam body;
- Concrete strain through strain meters with resistance strain meter transducers of the Carlson type, embedded in the concrete dam body;
- Concrete temperature through thermometers with resistance thermometer transducers of the Carlson type.

#### 3.2. The Analysed Data

## 4. Results and Discussion

#### 4.1. Model Formulation, Construction, and Performance

#### 4.2. Threshold Definition for a Singular Record

#### 4.3. Threshold Definition for Novelty Identification Based on a Time Period Evolution of the Residuals

#### 4.4. Threshold Definition for Novelty Identification Based on Multivariate Data

## 5. Conclusions and Final Remarks

- The definition of univariate thresholds based on the residuals, one for each quantity, is the first recommended step. This approach, through the use of multiplicative factors associated with the standard deviation of the residual, allows an easy novelty identification that, in some cases, could be related to measurement errors.
- The second type of threshold proposed in this study can be defined by the adoption of a moving window with the moving average and the standard deviation of the residuals. This kind of approach allows the specialist to have immediate information concerning the evolution over time.
- Finally, the third type of threshold proposed can be defined based on multiple factors related to the behaviour of the residuals for all the quantities considered in the model. For this approach, a strategy based on the DBSCAN algorithm, which proved to be suitable for multivariate analysis, was used.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**MLP architecture where x represents the input layer, l represents the hidden layer, L represents the output layer, b represents the bias and w represents the weights, adapted from [5].

**Figure 4.**DBSCAN illustration with MinPoints = 4 and epsilon distance represented by circles. Core points, such as A, are represented in red, B and C, in yellow, are border points, and N is a noise point, represented in blue. From [34].

**Figure 6.**Feiticeiro dam. Thermometers and 3D jointmeters included in the automated monitoring system. Legend: MWL—Maximum reservoir water level.

**Figure 7.**Time series of the relative movements between blocks measured between April 2017 and June 2022.

**Figure 8.**Time series of the relative movements between blocks measured between the 1st and the 8th of August 2018.

**Figure 11.**Opening-closing mov. measured in BT3 vs. temperature measured in T37 (

**left**). Opening-closing mov. measured in BT3 vs. water level for temperature measured in T37 equal to 10 °C (

**right**).

**Figure 12.**Time series of the fitted values and recorded values for the movements measured through 3D jointmeters.

**Figure 13.**Time series of the relative movements between block measurements and fitted values between the 1st and the 8th of August 2018.

**Figure 18.**Novelty identification based on a multivariate analysis based on the DBSCAN method (adopting Epsilon = 0.12 and MinPoints = 7).

Block | Level (m) | Position | Block | Level | Position | ||
---|---|---|---|---|---|---|---|

T10 | J7–J8 | 122.1 | u.f. | T11 | J7–J8 | 122.1 | 1 m u.f. |

T15 | J7–J8 | 122.1 | 1 m d.f. | T16 | J7–J8 | 122.1 | d.f. |

T31 | J11–J12 | 112.0 | u.f. | T32 | J11–J12 | 112.0 | 1 m u.f. |

T33 | J11–J12 | 112.0 | oth | T35 | J11–J12 | 112.0 | oth |

T62 | J15–J16 | 122.1 | u.f. | T64 | J15–J16 | 122.2 | oth |

T65 | J15–J16 | 122.1 | 1/2 th. | T66 | J15–J16 | 122.2 | oth |

Measurements | Model | |||||
---|---|---|---|---|---|---|

Min | Max | r_{Min} | r_{Max} | sd | ${\mathit{R}}^{2}$ | |

[mm] | [mm] | [mm] | [mm] | [mm] | % | |

BT3 O/C | 0.16 | 2.56 | −0.22 | 0.35 | 0.060 | 99.81 |

BT5 O/C | 0.29 | 2.85 | −0.32 | 0.39 | 0.072 | 99.79 |

BT7 O/C | 1.03 | 3.57 | −0.29 | 0.33 | 0.068 | 99.92 |

BT8 O/C | 0.70 | 2.61 | −0.21 | 0.34 | 0.063 | 99.86 |

BT10 O/C | 0.25 | 2.15 | −0.21 | 0.30 | 0.056 | 99.77 |

BT12 O/C | 0.81 | 2.72 | −0.24 | 0.37 | 0.067 | 99.85 |

BT13 O/C | 0.48 | 2.21 | −0.22 | 0.28 | 0.048 | 99.86 |

^{2}—coefficient of determination.

MinPoints | Epsilon | ||||
---|---|---|---|---|---|

0.08 | 0.10 | 0.12 | 0.14 | 0.16 | |

5 | 79 | 9 | 5 | 3 | 0 |

6 | 102 | 12 | 5 | 3 | 1 |

7 | 116 | 14 | 5 | 3 | 1 |

8 | 126 | 22 | 5 | 3 | 1 |

9 | 140 | 22 | 5 | 3 | 1 |

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**MDPI and ACS Style**

Mata, J.; Miranda, F.; Antunes, A.; Romão, X.; Pedro Santos, J. Characterization of Relative Movements between Blocks Observed in a Concrete Dam and Definition of Thresholds for Novelty Identification Based on Machine Learning Models. *Water* **2023**, *15*, 297.
https://doi.org/10.3390/w15020297

**AMA Style**

Mata J, Miranda F, Antunes A, Romão X, Pedro Santos J. Characterization of Relative Movements between Blocks Observed in a Concrete Dam and Definition of Thresholds for Novelty Identification Based on Machine Learning Models. *Water*. 2023; 15(2):297.
https://doi.org/10.3390/w15020297

**Chicago/Turabian Style**

Mata, Juan, Fabiana Miranda, António Antunes, Xavier Romão, and João Pedro Santos. 2023. "Characterization of Relative Movements between Blocks Observed in a Concrete Dam and Definition of Thresholds for Novelty Identification Based on Machine Learning Models" *Water* 15, no. 2: 297.
https://doi.org/10.3390/w15020297