# Detection of Building and Infrastructure Instabilities by Automatic Spatiotemporal Analysis of Satellite SAR Interferometry Measurements

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## Abstract

**:**

## 1. Introduction

^{2}over entire cities), all located in the three-dimensional (3D) space with metric precision. This is an important characteristic for building and infrastructure monitoring, because it makes it possible to associate the deformation measurement with the corresponding point over the structure.

## 2. PS Clustering and Detection of Spatially Anomalous Deformations

#### 2.1. PS Clustering

#### 2.2. Classification of Buildings and Detection of Spatially Anomalous Deformations

- Type 0 structures have no convergence points. Therefore, no stability analysis can be performed.
- Type I structures have just a single convergence point. Consequently, in such a case, the displacement value of the identified convergence point will be used to evaluate the structure settlement.
- Type II structures have at least two convergence points. For such a building, we can use two different criterions to identify potentially dangerous situations: the maximum measured settlement value and the maximum measured differential settlement value (see Figure 2 and the related explanation).
- Type III structures have at least a pair of convergence points with similar heights. In these cases, we can consider for the stability analysis also the value of angular distortion β (see Figure 2 and the related explanation). It is worth noting that the roof and the foundation can have different deformation trends even when no building tilting occurs. Therefore, the angular distortion can be calculated only by considering two points with similar heights.

_{A,LOS}and d

_{B,LOS}are the displacements measured on the convergence points A and B, respectively, along the satellite LOS (Line of Sight) direction during the monitoring period; Δ

_{LOS}is the absolute value of difference between these two measurements; and θ

_{inc}is the satellite incidence angle. It is worth highlighting that the Δ

_{LOS}value is divided by the cosine of the satellite incidence angle in order to obtain the vertical differential settlement ${\Delta}_{d}$.

#### 2.3. Detection of Spatially Anomalous Deformations: Real Data Analysis

_{max}, the maximum differential settlement ${\Delta}_{d,max}$, and the maximum angular distortion β

_{max}of the building. The two homogenous PS sets with the largest differential settlement were identified and marked by N (north) and S (south), respectively.

_{max}is 2.4‰ (which is a large value for general buildings). Even though the maximum measured settlement value was not very high, since both the maximum measured differential settlement and the maximum measured angular distortion were very large, the analyzed building was considered as potentially being in danger. This analysis was confirmed by a field survey, in which we obtained some photographic evidence (see Figure 7) showing cracks on the building.

## 3. Deformation Evolution Decomposition and Detection of Anomalous Temporal Trends

#### 3.1. Temporal Deformation Model

_{i}are the observed deformation values at the ith acquisition time t

_{i}. (i = N

_{0}, N

_{0}+ 1, N

_{0}+ 2…, N

_{m+1}); ν

_{j}and b

_{j}, (j = 1, 2, …, m + 1), which represent the velocity and constant deformation of the jth partition, respectively, are the coefficients of the piecewise linear deformation component; A and φ are the corresponding coefficients of the periodical deformation component, which are assumed to be the same during the whole monitoring period; ε

_{i}is the random noise at the ith acquisition time; and (N

_{1}, N

_{2}, …, N

_{m}) are the indices of m break points, which are explicitly treated as unknowns.

#### 3.2. Deformation Evolution Decomposition and Anomalous Trend Detection

_{j}, b

_{j}, A, and φ), together with the indices of break points (N

_{1}, N

_{2}, …, N

_{m}), when the deformation measurements d

_{i}at the ith acquisition times are available. The decomposition process is based on an iterative least-squares procedure. For each possible choice of partition (N

_{1}, N

_{2}, …, N

_{m}), the estimated parameters $\widehat{v}$

_{j}, $\widehat{b}$

_{j}, $\widehat{A}$, and $\widehat{\phi}$ can be obtained by minimizing the following objective function, i.e., the sum of squared residuals:

- (1)
- Set m = 0;
- (2)
- Estimate the multiple linear regression model:
- a)
- Set V = [v
_{1}, v_{2}, …, v_{m+1}] and B = [b_{1}, b_{2}, …, b_{m+1}] vectors to zero; - b)
- Compute the residual deformation after removing the piecewise linear model (based on the current m, V, and B values) from the original measured deformation;
- c)
- Estimate the periodic component coefficients A and φ on the obtained residual deformation component;
- d)
- Compute the residual deformation after removing the periodic deformation component (based on the current A and φ values) from the original measured deformation;
- e)
- Apply the dynamic programming method to the residual deformation without periodical component in order to estimate the vectors V, B, and N
_{break}= [N_{1}, N_{2}, …, N_{m}]; - f)
- Repeat steps (b–e) until N
_{break}= [N_{1}, N_{2}, …, N_{m}] does not change anymore;

- (3)
- Calculate the objective function value (see Equation 5), and if it is greater than a given threshold, add one to m and go back to Step (2).

#### 3.3. Anomalous Trend Detection: Real Data Analysis

## 4. Automatic Analysis of Large Areas for Building Stability Assessment

#### 4.1. Building Stability Assessment System

#### 4.2. Building Stability Assessment on Real Data in Large Areas

#### 4.2.1. Building 1

^{2}. Based on the InSAR results, the building was classified as a type III structure (see Table 1) and we were able to compute its maximum settlement, maximum differential settlement, and angular distortion factor. We computed a maximum mean annual velocity of about −11.9 mm/year in the monitoring period of June 2015–August 2018, which corresponds to a cumulative settlement d

_{max}of about −35.5 mm. The maximum measured differential settlement ${\Delta}_{d,max}$ was about −26.9 mm. The obtained maximum angular distortion β

_{max}was about 2.0‰ (quite close to the threshold that is normally used in China to consider a building as being affected by some instability issue). Moreover, by analyzing the settlement trend, it could be observed that the differential settlement value was gradually increasing in the temporal interval of our satellite measurements.

#### 4.2.2. Building 2

^{2}. Based on the InSAR results, the building was classified as a type III structure (see Table 1). We could compute a cumulative settlement d

_{max}of about −24.5 mm, a maximum measured differential settlement value ${\Delta}_{d,max}$ of −24.2 mm, and a maximum measured angular distortion value β

_{max}of about 0.7‰. Moreover, by the analysis of the deformation trend, it could be noted that the differential settlement was continuing to increase in the analyzed temporal interval.

#### 4.2.3. Building 3

^{2}. Based on the InSAR results, this building was classified as a type II structure (see Table 1). From the satellite measurements, we were able to estimate the maximum settlement and the maximum differential settlement (whereas the angular distortion factor could not be computed). We calculated a cumulative settlement d

_{max}of −25.7 mm and the maximum differential settlement ${\Delta}_{d,max}$ of about −32 mm. Moreover, by the analysis of the deformation trend, it could be noted that settlement rate persisted over the whole observation period.

#### 4.2.4. Building 4

^{2}. Based on the InSAR results, this building was classified as a type III structure (see Table 1). We calculated a cumulative settlement d

_{max}of about −14.4 mm and the maximum measured differential settlement ${\Delta}_{d,max}$ of about −14.5 mm. The maximum measured angular distortion was then computed to be 1.1‰. Although all the values of the three parameters were not so large, by the analysis of the deformation trend, the settlement rate reached −5 mm/month in the last 3 months of the analysis, showing an acceleration of the phenomenon.

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Schematic representation of differential settlement parameters used within the analysis. In the picture, d

_{A}and d

_{B}are the settlement of the two points (A and B) respectively.

**Figure 3.**COSMO-SkyMed persistent scatterer pair (PSP) InSAR measurements obtained in the considered area of Foshan, China.

**Figure 4.**PS points (small) and convergence points (big) in the target building. A homogenous PS set and its corresponding convergence point are represented with the same color. In the picture, X and Y indicate the local coordinates in the east–west and north–south directions, respectively.

**Figure 5.**Settlement evolutions of the PS and their convergence points in the (

**a**) north and (

**b**) south parts of the building, respectively.

**Figure 7.**Photos of the analyzed building. A large foundation ditch is present on the south of the building (

**a**). Cracks are visible on the building (

**b**), confirming our analysis from InSAR data.

**Figure 8.**Example of temporal analysis on simulated data: Original measured deformation (

**a**); retrieved periodic component (

**b**), piecewise linear component (

**c**), and random noise (

**d**).

**Figure 9.**COSMO-SkyMed PSP InSAR mean velocity measurements along a subway line in Shenzhen, China, corresponding to the period 14 September 2013–28 May 2017 (

**a**) and to the most recent temporal partition of the decomposition analysis (

**b**). A significant increase of velocity (especially in area A and B) is visible in the most recent observation period.

**Figure 10.**(

**a**) PS recent velocity measurements in area A of Figure 9b; (

**b**) measured deformation evolution of the PS circled in green in (

**a**); (

**c**) sum of periodic and piecewise linear components of the PS displacement; (

**d**) piecewise linear component of the PS displacement.

**Figure 11.**(

**a**) PS recent velocity measurements in area B of Figure 9b; (

**b**) measured deformation evolution of the PS circled in green in (

**a**); (

**c**) sum of periodic and piecewise linear components of the PS displacement; (

**d**) piecewise linear component of the PS displacement.

**Table 1.**Different building categories depending on the deformation information provided by satellite synthetic aperture radar interferometry (InSAR) measurements.

Building Type | Instruction | Maximum Measured Settlement (d _{max}) | Maximum Measured Differential Settlement (${\Delta}_{d,max}$) | Maximum Measured Angular Distortion (β _{max}) |
---|---|---|---|---|

0 | No convergence point | X | X | X |

I | Only one convergence point | ✓ | X | X |

II | At least two convergence points | ✓ | ✓ | X |

III | At least a pair of convergence points at similar heights | ✓ | ✓ | ✓ |

Building Type | Building Number | Percentage |
---|---|---|

Type 0 | 1192 | 9.7% |

Type I | 4771 | 38.9% |

Type II | 357 | 2.9% |

Type III | 5952 | 48.5% |

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## Share and Cite

**MDPI and ACS Style**

Zhu, M.; Wan, X.; Fei, B.; Qiao, Z.; Ge, C.; Minati, F.; Vecchioli, F.; Li, J.; Costantini, M.
Detection of Building and Infrastructure Instabilities by Automatic Spatiotemporal Analysis of Satellite SAR Interferometry Measurements. *Remote Sens.* **2018**, *10*, 1816.
https://doi.org/10.3390/rs10111816

**AMA Style**

Zhu M, Wan X, Fei B, Qiao Z, Ge C, Minati F, Vecchioli F, Li J, Costantini M.
Detection of Building and Infrastructure Instabilities by Automatic Spatiotemporal Analysis of Satellite SAR Interferometry Measurements. *Remote Sensing*. 2018; 10(11):1816.
https://doi.org/10.3390/rs10111816

**Chicago/Turabian Style**

Zhu, Mao, Xiaoli Wan, Bigang Fei, Zhuping Qiao, Chunqing Ge, Federico Minati, Francesco Vecchioli, Jiping Li, and Mario Costantini.
2018. "Detection of Building and Infrastructure Instabilities by Automatic Spatiotemporal Analysis of Satellite SAR Interferometry Measurements" *Remote Sensing* 10, no. 11: 1816.
https://doi.org/10.3390/rs10111816