# Experimental Validation of a High Precision GNSS System for Monitoring of Civil Infrastructures

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Benchmark Structure and Test Configuration

#### 2.2. Analysis of the GNSS Signal

_{0}, y

_{0}and z

_{0}are the coordinates of the origin of the ENU reference system expressed in the ECEF-r coordinate system.

#### 2.3. Validation

#### 2.3.1. Time Domain

#### 2.3.2. Frequency Domain

## 3. Results on a Real Bridge

#### 3.1. Benchmark Structure and Test Configuration

#### 3.2. Validation

## 4. Discussion

#### 4.1. Statistical Analysis of the Noise of the GNSS Signal

#### 4.1.1. Small Scale Benchmark Structure

#### 4.1.2. Road Bridge

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) GNSS-based monitoring system installed on the structure; (

**b**) Northwest view of the structure.

**Figure 2.**(

**a**) Schematic representation of the plan view of the benchmark structure, with the monitored points numbered from 1 to 5; (

**b**) Configuration of the GNSS-based monitoring system with the first three monitored points and the local Cartesian reference system highlighted.

**Figure 3.**(

**a**) Manual excitation applied close to the first monitored point (highlighted in the figure) and performed along the y-axis during tests number 2 and 4; (

**b**) manual excitation applied close to the fifth monitored point (highlighted in the figure) and performed along the x-axis during test number 3.

**Figure 4.**The meridian plane of the geodetic datum showing the semimajor and semiminor axes (a, b), the height (h), the latitude (ϕ) and the plumb line from the point of interest P to the z axis.

**Figure 5.**(

**a**) Ellipsoid showing ECEF-g and ECEF-r reference systems, the normal through point P and the geodetic longitude of P; (

**b**) Meridian plane containing point P, showing the normal through P, the geodetic latitude of P, the height of P and both the semiminor and semimajor axes of the ellipsoid, b and a, respectively.

**Figure 6.**Schematic representation of the ellipsoid showing the four coordinate systems involved in the transformation process: ECEF-g (in blue), ECEF-r (in red), ENU (in green) and local (in black).

**Figure 10.**Comparison of the displacements of monitored point 1 acquired by the GNSS (in blue) and the accelerometer (in red) during test 2.

**Figure 11.**Portions of signal that were considered to evaluate the natural frequency of the structure.

**Figure 12.**Graphical comparison of the PSDs evaluated from the GNSS and the accelerometric signals. The PSDs were obtained from the first set of free oscillations acquired during test 2.

**Figure 17.**First two bending mode shapes of a simply supported beam, with L being the length of the beam along the longitudinal direction indicated with x.

**Figure 19.**Schematic representation of the plan view of the second span of the road bridge, with the monitored points numbered from 1 to 3.

**Figure 23.**(

**a**) Displacements of GNSS1 along the x-axis; (

**b**) Displacements of GNSS1 along the y-axis; (

**c**) Displacements of GNSS1 along the z-axis.

**Figure 24.**(

**a**) Normal distribution of GNSS1 x signal; (

**b**) Normal distribution of GNSS1 y signal; (

**c**) Normal distribution of GNSS1 z signal.

**Figure 26.**(

**a**) Displacements of GNSS2 along the x-axis; (

**b**) Displacements of GNSS2 along the y-axis; (

**c**) Displacements of GNSS2 along the z-axis.

**Figure 27.**(

**a**) Normal distribution of GNSS2 x signal; (

**b**) Normal distribution of GNSS2 y signal; (

**c**) Normal distribution of GNSS2 z signal.

Test | Direction of Excitation | Point of Application ^{1} |
---|---|---|

1 | - | - |

2 | y | 1 |

3 | x | 5 |

4 | y | 1 |

^{1}Refer to the schematic representation in Figure 2a.

Name | Symbol | Value |
---|---|---|

Semimajor axis | a | 6,378,137 m |

Semiminor axis | b | 6,356,752.31424518 m |

Flatness | f | 3.3528107 × 10^{−3} |

Eccentricity | e | 81.8191908 × 10^{−3} |

**Table 3.**Comparison of the peak displacements acquired by the GNSS and the accelerometers. The peak displacements were caused by the first excitation during test 2.

Points | Peak Displacements [mm] | |||
---|---|---|---|---|

GNSS [mm] | Accelerometer [mm] | Difference [mm] | Percentage Difference [%] | |

1 | 25.4 | 18.7 | 6.7 | 26.4 |

2 | 13.2 | 8.9 | 4.3 | 32.6 |

3 | 5.8 | 3.4 | 2.4 | 41.4 |

4 | 12.8 | 9.1 | 3.7 | 28.9 |

5 | 14.6 | 9.9 | 4.7 | 32.2 |

Mean values | 4.4 | 32.3 | ||

Mean values without GNSS 3 | 4.9 | 30 |

**Table 4.**Comparison of the peak frequencies evaluated from the GNSS and the accelerometers. The peak frequencies were calculated by applying the PSD function to the first set of free oscillations acquired during test 2.

Points | Peak Frequencies | |||
---|---|---|---|---|

GNSS [Hz] | Accelerometer [Hz] | Difference [Hz] | Percentage Difference [%] | |

1 | 4.6 | 4.6 | 0.0 | 0.0 |

2 | 4.6 | 4.6 | 0.0 | 0.0 |

3 | 3.3 | 4.3 | 1.0 | 23.3 |

4 | 4.3 | 4.6 | 0.3 | 6.5 |

5 | 4.6 | 4.6 | 0.0 | 0.0 |

Mean values | 4.28 | 4.54 | 0.26 | 6.0 |

Mean values without GNSS 3 | 4.5 | 4.6 | 0.08 | 1.6 |

Max | Min | Mean | Variance | Standard Deviation | Percentile 99.95% | Percentile 0.05% | Threshold | |
---|---|---|---|---|---|---|---|---|

[mm] | [mm] | [mm] | [mm^{2}] | [mm] | [mm] | [mm] | [mm] | |

x | 4.41 | −7.20 | 0.00 | 0.30 | 0.55 | 2.11 | −2.11 | +/−2.11 |

y | 4.07 | −6.35 | 0.00 | 0.24 | 0.48 | 1.94 | −1.92 | +/−1.93 |

z | 7.30 | −12.45 | 0.00 | 1.35 | 1.16 | 4.28 | −4.40 | +/−4.34 |

Max | Min | Mean | Variance | Standard Deviation | Percentile 99.5% | Percentile 0.5% | Threshold | |
---|---|---|---|---|---|---|---|---|

[mm] | [mm] | [mm] | [mm^{2}] | [mm] | [mm] | [mm] | [mm] | |

x | 10.55 | −6.52 | 0.06 | 2.87 | 1.70 | 5.04 | −4.32 | +/− 4.68 |

y | 8.21 | −7.80 | −0.09 | 3.29 | 1.81 | 4.96 | −4.89 | +/− 4.93 |

z | 22.84 | −36.04 | −0.17 | 11.06 | 3.33 | 9.26 | −8.27 | +/− 8.77 |

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**MDPI and ACS Style**

Cinque, D.; Saccone, M.; Capua, R.; Spina, D.; Falcolini, C.; Gabriele, S.
Experimental Validation of a High Precision GNSS System for Monitoring of Civil Infrastructures. *Sustainability* **2022**, *14*, 10984.
https://doi.org/10.3390/su141710984

**AMA Style**

Cinque D, Saccone M, Capua R, Spina D, Falcolini C, Gabriele S.
Experimental Validation of a High Precision GNSS System for Monitoring of Civil Infrastructures. *Sustainability*. 2022; 14(17):10984.
https://doi.org/10.3390/su141710984

**Chicago/Turabian Style**

Cinque, Daniele, Mauro Saccone, Roberto Capua, Daniele Spina, Corrado Falcolini, and Stefano Gabriele.
2022. "Experimental Validation of a High Precision GNSS System for Monitoring of Civil Infrastructures" *Sustainability* 14, no. 17: 10984.
https://doi.org/10.3390/su141710984