# GNSS-Based Dam Monitoring: The Application of a Statistical Approach for Time Series Analysis to a Case Study

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. GNSS Equipment, Installation and Raw Data Processing

#### 2.2. Displacement Time Series Analysis

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Map of the monitored points on the dam, showing the orientation of the axes of the local reference system.

**Figure 2.**Steel pillars supporting the antennas for points PT3 (

**left**) and PT4 (

**right**). The other points are materialized with the same kinds of structures.

**Figure 3.**Fourier analysis on the x, y, z components of the point PT1. Dashed blue line is the empirical ASD, red solid line is the model ASD computed by the median filter, and yellow and green stars are the identified periodical components in the low and high-frequency ranges, respectively.

**Figure 4.**Estimated displacements for all the points. Solid lines represent the estimated displacements, including both the deterministic and stochastic components, while black dots joined by dashed lines represent the GNSS observations. The colors refer to the analyzed coordinate.

**Figure 5.**Time series of the reservoir water level (on the

**left**) and time series of air and water temperatures (on the

**right**).

**Figure 6.**Time series of filtered GNSS displacement (solid line) versus the estimated autoregressive model (dashed lines) for each point and coordinate.

**Figure 7.**Sketch of the evolution in time of the relative alignment between the four monitored points in the XY plane. Dam orthophoto as background.

Coordinate | PT1 | PT2 | PT3 | PT4 |
---|---|---|---|---|

x | cubic | cubic | cubic | cubic |

y | cubic | cubic | cubic | quadratic |

z | cubic | cubic | cubic | cubic |

**Table 2.**Estimated covariance models for all the components at all the points. Red lines represent the estimated models, while blue dots the empirical covariance functions. Units are days for the $\tau $ axis (abscissa) and ${\mathrm{mm}}^{2}$ for the covariance axis (ordinate). The ${\sigma}_{\eta}^{2}$ is the difference between the red curve and the blue dot at the origin ($\tau =0$).

PT1 | PT2 | PT3 | PT4 | |
---|---|---|---|---|

x | ||||

y | ||||

z |

**Table 3.**RMS of the differences between the estimated displacements and corresponding raw GNSS observations. Units are mm.

Coordinate | PT1 | PT2 | PT3 | PT4 |
---|---|---|---|---|

x | 0.51 | 0.50 | 0.51 | 0.53 |

y | 0.34 | 0.32 | 0.34 | 0.36 |

z | 0.93 | 0.88 | 0.88 | 0.79 |

**Table 4.**Linear correlation index computed between the filtered GNSS displacement time series and the reservoir water level.

Coordinate | PT1 | PT2 | PT3 | PT4 |
---|---|---|---|---|

x | −0.13 | −0.21 | −0.49 | −0.16 |

y | 0.68 | 0.76 | 0.63 | 0.06 |

z | 0.04 | 0.05 | −0.07 | −0.46 |

**Table 5.**Linear correlation index computed between the filtered GNSS displacement time series and the air temperature.

Coordinate | PT1 | PT2 | PT3 | PT4 |
---|---|---|---|---|

x | 0.83 | 0.78 | 0.52 | 0.82 |

y | −0.16 | −0.22 | −0.04 | −0.48 |

z | −0.66 | −0.59 | −0.66 | −0.74 |

**Table 6.**Linear correlation index computed between the filtered GNSS displacement time series and the autoregressive model of the displacement based on air temperature and water level.

Coordinate | PT1 | PT2 | PT3 | PT4 |
---|---|---|---|---|

x | 0.95 | 0.93 | 0.88 | 0.95 |

y | 0.79 | 0.90 | 0.67 | 0.53 |

z | 0.71 | 0.64 | 0.68 | 0.79 |

**Table 7.**Correlation of the displacement along the crest direction (X-axis) of all the possible couples of points.

PT Station | 2 | 3 | 4 |
---|---|---|---|

1 | 0.99 | 0.87 | 0.97 |

2 | 0.92 | 0.96 | |

3 | 0.85 |

**Table 8.**Correlation of the displacement along the stream direction (Y-axis) of all the possible couples of points.

PT Station | 2 | 3 | 4 |
---|---|---|---|

1 | 0.92 | 0.75 | 0.49 |

2 | 0.86 | 0.58 | |

3 | 0.70 |

**Table 9.**Correlation of the displacement along the vertical direction (Z-axis) of all the possible couple of points.

PT Station | 2 | 3 | 4 |
---|---|---|---|

1 | 0.96 | 0.97 | 0.69 |

2 | 0.97 | 0.70 | |

3 | 0.75 |

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**MDPI and ACS Style**

Reguzzoni, M.; Rossi, L.; De Gaetani, C.I.; Caldera, S.; Barzaghi, R.
GNSS-Based Dam Monitoring: The Application of a Statistical Approach for Time Series Analysis to a Case Study. *Appl. Sci.* **2022**, *12*, 9981.
https://doi.org/10.3390/app12199981

**AMA Style**

Reguzzoni M, Rossi L, De Gaetani CI, Caldera S, Barzaghi R.
GNSS-Based Dam Monitoring: The Application of a Statistical Approach for Time Series Analysis to a Case Study. *Applied Sciences*. 2022; 12(19):9981.
https://doi.org/10.3390/app12199981

**Chicago/Turabian Style**

Reguzzoni, Mirko, Lorenzo Rossi, Carlo Iapige De Gaetani, Stefano Caldera, and Riccardo Barzaghi.
2022. "GNSS-Based Dam Monitoring: The Application of a Statistical Approach for Time Series Analysis to a Case Study" *Applied Sciences* 12, no. 19: 9981.
https://doi.org/10.3390/app12199981