# SARClust—A New Tool to Analyze InSAR Displacement Time Series for Structure Monitoring

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}. Furthermore, the SAR image archives currently available enable assessment to hundreds of displacement observation epochs for each point. The large volume of data achieved and the direction of the observed displacements (along the sensor line-of-sight—LOS), turns the interpretation of the displacement time series into a difficult task for InSAR non-experts, as is often the case for structure engineers. The retrieval of information from the displacement time series is particularly important when applied to structure monitoring. Structures react to loads they are subjected to and often present non-linear displacements due to variations of those loads (e.g., temperature). In cases where the structure is affected by some damage, its reaction will present a displacement anomaly. Therefore, displacement time series are important to assist structure experts in the identification of possible structural damages.

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data Sources

#### 2.3. Methods for Data Processing and Displacement Detection

#### 2.3.1. PSI Analysis

#### 2.3.2. Selection of PSs on Buildings

^{2}. Furthermore, the analysis was performed only for PSs located on buildings, in order to exclude points in objects such as lampposts, advertisement signs or other elements on the streets. The selection was performed based on an aerial orthophotograph with 0.50 m spatial resolution, subjected to an Object-Based Image Analysis (OBIA) at Orfeo software [35]. A supervised classification using the k-Nearest Neighbors algorithm with 32 neighbors was used to separate building from non-building objects with a global accuracy of 97% [36]. Only PSs located inside objects classified as buildings were considered for further analysis.

#### 2.3.3. SARClust Rationale

#### 2.3.4. Displacement Time Series Error Mitigation

#### 2.3.5. Merging of Ascending and Descending Data

_{V}, d

_{E}and d

_{N}are vertical, easting and northing displacements, respectively, ${\theta}^{ASC}$ and ${\theta}^{DESC}$ are the incidence angles for ascending and descending passes and ${\alpha}_{H}^{ASC}$ and ${\alpha}_{H}^{DESC}$ are the satellite headings also for ascending and descending passes. Let β be the angle between LOS projection on the horizontal plane and the east–west direction, given by Equation (3):

_{H}be the displacement along a direction of interest (DOI) on the horizontal plane and γ be the azimuth of the direction perpendicular to DOI. Easting and northing displacements are given by Equations (6) and (7):

_{V}and d

_{H}can be obtained through Equations (10) and (11):

#### 2.3.6. Dissimilarity Matrix

#### 2.3.7. Number of Clusters Selection

## 3. Results and Discussion

#### 3.1. Displacement Maps

#### 3.2. Cluster Analysis

#### 3.3. Visual Inspection

#### 3.4. Comparison to Other Radar Interpretation Tools

#### 3.5. Computational Performance

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Study area: (

**a**) location of Lisbon (black rectangle) in Portugal; (

**b**) digital elevation model at Lisbon region—the large rectangles are the areas for Persistent Scatterer Interferometry processing in ascending and descending passes, and the small rectangle is the downtown area; (

**c**) aerial orthophotograph of the downtown area provided by the Portuguese National System for Geographical Information.

**Figure 3.**Match of query and reference displacement time series in DTW, with a constraint window of two epochs.

**Figure 4.**Chart of relative linkage distance as a function of the number of clusters. Blue and green circles correspond to the automatic and manual solutions for the number of clusters to analyze, respectively.

**Figure 5.**Dendrogram showing the PS organization into clusters and the cutting of its branches corresponding to different solutions of number of clusters to analyze. The blue line corresponds to the automatic clustering solution and the green line represents the manual one.

**Figure 6.**Raster data for cluster centroids: (

**a**) slope, (

**b**) curvature, (

**c**) distance to faults, (

**d**) distance to the subway network and (

**e**) distance to the water line. The background image is an aerial orthophotograph of the downtown area provided by the Portuguese National System for Geographical Information.

**Figure 7.**(

**a**) Vertical and (

**b**) east–west cumulative displacement maps for the downtown area. The background image is an aerial orthophotograph of the downtown area provided by the Portuguese National System for Geographical Information.

**Figure 8.**Cluster spatial distribution for (

**a**) automatic and (

**b**) manual clustering solutions. The background image is an aerial orthophotograph of the downtown area provided by the Portuguese National System for Geographical Information.

**Figure 9.**Vertical and horizontal displacement time series for all PSs in each cluster (black lines), for the three-cluster solution. Green lines are the cluster-representative displacement time series.

**Figure 10.**Vertical displacement time series for all PSs in each cluster (black lines), for the ten-cluster solution. Green lines are the cluster-representative displacement time series.

**Figure 11.**Horizontal displacement time series for all PSs in each cluster (black lines), for the ten-cluster solution. Green lines are the cluster-representative displacement time series.

**Figure 12.**Comparison between vertical displacement time series representative of clusters 1 (green) and 3 (blue) and monthly temperature (red).

**Figure 13.**Spatial relationship between PSs from clusters 4, 5, 8 and 10, slope and inauguration dates of subway segments. The background image is an aerial orthophotograph of the downtown area provided by the Portuguese National System for Geographical Information.

**Figure 14.**Examples of cracks on buildings associated to centimeter-level displacement clusters, in August 2019. Pictures (

**a**,

**b**) correspond to PSs (

**a**,

**b**) in Figure 13, respectively.

Cluster | Percentage of PSs (%) | Altitude (m) | Vertical Displacement (mm) | Horizontal Displacement (mm) | Slope (°) | Curvature (m^{−1}) | Distance to | ||
---|---|---|---|---|---|---|---|---|---|

Faults (m) | Subway (m) | River (m) | |||||||

1 | 71.0 | 19 | 0.2 | −2.8 | 6 | −0.042 | 674 | 132 | 588 |

2 | 0.9 | 6 | 6.9 | −7.5 | 6 | −0.137 | 630 | 73 | 382 |

3 | 25.7 | 22 | 1.2 | 0.7 | 6 | −0.023 | 810 | 104 | 737 |

4 | 0.2 | 16 | −21.9 | 31.6 | 10 | 0.811 | 723 | 30 | 469 |

5 | 0.3 | 13 | 14.2 | −21.2 | 6 | 1.045 | 772 | 47 | 635 |

6 | 0.6 | 22 | −9.2 | 10.5 | 5 | −0.628 | 687 | 157 | 656 |

7 | 0.7 | 24 | −10.2 | −16.0 | 8 | 0.289 | 685 | 127 | 565 |

8 | 0.1 | 6 | −35.6 | 46.9 | 13 | 2.119 | 768 | 40 | 885 |

9 | 0.3 | 9 | 12.1 | 10.8 | 9 | 0.249 | 601 | 92 | 526 |

10 | 0.1 | 46 | 28.9 | 31.1 | 7 | 0.182 | 684 | 20 | 337 |

PS-Time Classes | SARClust Clusters | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |

0 | 447 | 1 | 141 | 0 | 0 | 2 | 1 | 0 | 0 | 0 |

1 | 159 | 1 | 57 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |

2 | 14 | 2 | 11 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |

3 | 70 | 4 | 38 | 2 | 2 | 2 | 1 | 0 | 3 | 0 |

4 | 0 | 1 | 1 | 0 | 0 | 1 | 3 | 0 | 0 | 0 |

5 | 2 | 0 | 2 | 0 | 1 | 1 | 0 | 1 | 0 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Roque, D.; Falcão, A.P.; Perissin, D.; Amado, C.; Lemos, J.V.; Fonseca, A.
SARClust—A New Tool to Analyze InSAR Displacement Time Series for Structure Monitoring. *Sustainability* **2023**, *15*, 3728.
https://doi.org/10.3390/su15043728

**AMA Style**

Roque D, Falcão AP, Perissin D, Amado C, Lemos JV, Fonseca A.
SARClust—A New Tool to Analyze InSAR Displacement Time Series for Structure Monitoring. *Sustainability*. 2023; 15(4):3728.
https://doi.org/10.3390/su15043728

**Chicago/Turabian Style**

Roque, Dora, Ana Paula Falcão, Daniele Perissin, Conceição Amado, José V. Lemos, and Ana Fonseca.
2023. "SARClust—A New Tool to Analyze InSAR Displacement Time Series for Structure Monitoring" *Sustainability* 15, no. 4: 3728.
https://doi.org/10.3390/su15043728