# 3D Point Cloud Analysis for Damage Detection on Hyperboloid Cooling Tower Shells

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Problem Statement

#### 1.2. Related Work

- (1)
- reference planes;
- (2)
- point cloud processing, common in deformation monitoring applications;
- (3)
- local geometric features of surfaces of interest.

#### 1.2.1. Reference Plane

#### 1.2.2. Processed Point Clouds as in Deformation Monitoring Applications

#### 1.2.3. Local Surface Geometric Properties

## 2. Materials

#### 2.1. Test Cooling Tower

^{th}century and features typical flaws of the period together with age defects caused by the years-long operation. This type of cooling tower is the most popular in Poland. The reinforced concrete shell of the structure is a hyperboloid of revolution with variable thickness (0.4 m–0.12 m). The height of the structure from the ground is 65 m. Its diameter at the ring beam is 43 m and reaches 27 m at the crest. The shell is supported by 3 m high V-shaped inclined columns.

#### 2.2. Experimental Data

- black and white Z+F Professional 6˝ targets centred and levelled over the monitoring network points (Figure 3b);
- 150 mm steel reference spheres with adapters for fixed, stable mounting, precision levelled (Figure 3c).

## 3. Methods

#### 3.1. Overview of Research Methodology

#### 3.2. Data Pre-Processing

#### 3.3. Curvature Estimation

_{th}) empirically. If the boundary value was exceeded (because of excessive differentiation of value $\sqrt{N}$), it was indicative of inconsistency of (damage to) parts of the structure and identified areas in need of further analyses.

#### 3.4. Segmentation

_{th}). The extent of the healthy surface was identified using the region growing algorithm. It was originally designed for image analysis [76]. Now, it is a popular automatic point cloud segmentation tool [77,78,79,80]. The principle of the algorithm was to verify the conformity of values of consecutive points in a scalar field with values of the uniform surface. The algorithm threshold value c

_{th}was determined empirically with curvature value histograms estimated from principal component analysis after square root transformation. The parameter estimation employed the Weibull distribution, which offers sufficient flexibility to model diverse datasets and takes the form of the normal distribution, log-normal distribution, or exponential distribution depending on its parameters [81]. Local extrema of distribution plots for the damaged (series I) and healthy (series II and III) parts of the cooling tower shell (Figure 7) helped define the right inclusion criterion to specify the slight variability of the curvature of the uniform surface.

_{cth}) adapted to data quality, which represents the healthy shell of the cooling tower. The pseudocode for this method is given in Algorithm 1.

Algorithm 1: Point cloud segmentation based on curvature |

Input: Point cloud P = p_{1},p_{2}…, p_{n}; Point curvatures C; Curvature threshold c_{th}; Neighbour finding function F(∙) |

Process:1: Region list {R} ← ∅ 2: Available points list {L} ← {l..|P|}3: While {L} is not empty do4: Current region {R_{c}} ← ∅5: Current seeds {S_{c}} ← ∅6: Point with minimum curvature in {L} = P_{min}7: {S_{c}} ← {S_{c}} ∪ P_{min}8: {R_{c}} ← {R_{c}} ∪ P_{min} 9: {L} ← {L} \ P_{min}10: For i = 0 to size ({S_{c}}) do 11: Find nearest neighbors of current seed point{B _{c}} ← F(S_{c}{i})12: For j = 0 to size ({B_{c}}) do13: Current neighbor point P_{j} ← B_{c}{j}14: If P_{j}$\u03f5$L andc{P _{j}} < c_{th} then 15: {S_{c}} ← {S_{c}} ∪ P_{j} 16: {R_{c}} ← {R_{c}} ∪ P_{j}17: {L} ← {L} \ P_{j}18: End if19: End for20: End for21: Global segment list {R} ← {R} ∪ {R_{c}}22: End while23: Return the global segment list {R} |

Outputs: a set of homogeneous regions R = {R_{i}} |

_{min}) of the identified healthy surface (R

_{c}). Consecutive points of the cloud are added to it as the region grows (P

_{j}). Individual neighbour points of the seed are grouped into a region, a set of seeds (S

_{c}) if their curvature is sufficiently similar. This similarity is expressed by the predicate (c{P

_{j}} < c

_{th}), referred to as the uniformity criterion. If the uniformity criterion is satisfied for a cloud point (the point curvature is lesser than the curvature threshold), it becomes part of the identified surface. The growth continues until all cloud points are tackled. The result of Algorithm 1 is a region uniform in terms of curvature representing a healthy surface.

#### 3.5. Labelling

#### 3.6. Defect Vectorisation

## 4. Results and Discussion

#### 4.1. Experimental Results

_{min}) resulting from data resolution (r

_{min}→ k

_{min}= 6). Another key factor affecting the performance of the method was the transformation of the local curvature value with the square root function that guaranteed clear representation of the shape of defects (clear enough to facilitate quantitative analyses) and verification of the effective surface repairs aimed at restoring the protective properties of the concrete surround. The proposed original transform of the curvature value increased the range of the investigated local geometric feature of the surface, thus improving the operational applicability of the approach to damage detection (due to a significant increase of rooted curvature on edges of defects). Contrary to the currently applied solutions based on untransformed curvature (Figure 8) [28,54], the proposed solution faithfully represented the shape of damage (Figure 9). The implemented square root transformation of a local curvature estimated from principal component analysis facilitated further algorithm steps to develop a cartometric documentation of defects in the reinforced concrete shell of the cooling tower. Empirical analyses of the research material demonstrated an average five-fold increase in the standard deviation of values $\sqrt{N}$ of damaged areas of the reinforced concrete shell compared to the uniform (continuous) surface, while arithmetic means remained virtually the same. This relationship between basic statistical parameters facilitated the implementation of the coefficient of variation as the initial criterion for damage detection (CV

_{th}≤ 30%). Because of the extent of the analysed material, promising results of the experiment are presented for a selected sample of three test fields (with dimensions of 5 by 5 m). They are representative areas of the shell situated along a vertical line of the structure at 50, 30, and 10 m above ground (Figure 8 and Figure 9, Table 2).

_{th}= 0.02), which specifies the trivial variability of value $\sqrt{N}$ of the uniform surface helped specify the shell degradation degree (series I) and verify its continuity (smoothness) at repair sites (series II and III). Coherent components extracted with the CCL algorithm point cloud segmentation that represent individual defects of the reinforced concrete shell facilitated reliable determination of the extent of damage to specify the scope of necessary repairs (such as cavities, scaling, and blisters in the concrete surround). The convex hull with a parameter that restricted its maximum edge length (L = 0.01 m) provided cartometric vectorisation of defects by determining their extent in line with the course of defect edge using detailed TIN models. Figure 10 shows vectorised defects in three test fields in series I against reference TIN models.

#### 4.2. Evaluation Using Traditional Methods

^{2}accuracy, the extent of defects extracted from TLS data was determined from the width and length derived from contours.

^{2}, mean—0.003 m

^{2}, standard deviation—0.027 m

^{2}), which initially indicated satisfactory, regarding the industry, consistency of the defect surfaces estimated from point clouds and measured directly. The consistency of distributions of the determined surfaces of the reinforced concrete shell damage was confirmed with the Wilcoxon signed-rank test for two paired populations of equal sizes [88]. A test statistic for a small sub-sample (16 pairs) was calculated from the sum of ranks with the same signs. The surface distribution consistency hypothesis was verified at a five per cent significance level (q = 0.05). The test statistic determined for pairs of observations based on a sum of negative ranks was 57 (sum of positive ranks was 79). The test probability (p = 0.60), higher than the significance level, did not reject the zero hypothesis concerning the consistency of distribution in both datasets, thus indicating lack of statistically significant differences between extents of defects identified from point clouds and by direct measurement. The graphical analysis also confirmed that the zero hypothesis should not be rejected. The differences (within their possible limits of variability) were illustrated on a Bland-Altman plot made using PQStat (Figure 11) [89]. Fifteen out of the 16 differences (94%) were included in the 95% limits of agreement (0.1045 m

^{2}), and none of the differences exceeded the confidence interval for the specified limits (set for the representative sample based on its size).

#### 4.3. Future Work

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**The test object and repairs: (

**a**) the cooling tower before repairs; (

**b**) shell repair; (

**c**) the cooling tower after repairs.

**Figure 2.**Test object measurement series: (

**a**) Series I—before repairs; (

**b**) Series II—after repairs; (

**c**) Series III—after a winter.

**Figure 3.**Laser scanning of the test object: (

**a**) Cooling tower measurement with Z+F Imager 5010; (

**b**) Targets Z+F Professional; (

**c**) Steel reference spheres with adapters (protected by registered utility model No. W.126075, creator: Maria Makuch).

**Figure 4.**Terrestrial laser scanning (TLS) data excerpt with Triangulated Irregular Network (TIN): (

**a**) Series I—damaged shell; (

**b**) Series II—healthy shell; (

**c**) Series III—healthy shell.

**Figure 5.**Step-by-step research methodology: (

**a**) Step 1: Data pre-processing; (

**b**) Step 2: Curvature estimation; (

**c**) Step 3: Segmentation; (

**d**) Step 4: Labelling; (

**e**) Step 5: Defect vectorisation.

**Figure 6.**Example data with results of local curvature estimation ($\sqrt{N}$): (

**a**) Series I—damaged shell (CV = 67.16%); (

**b**) Series II—healthy shell (CV = 25.11%); (

**c**) Series III—healthy shell (CV = 23.61%).

**Figure 7.**Value $\sqrt{N}$ distribution charts with Weibull distribution density curves for sample data: (

**a**) Series I—damaged shell; (

**b**) Series II—healthy shell; (

**c**) Series III—healthy shell.

**Figure 8.**Example data with results of local curvature estimation, not transformed (N)—Series I: (

**a**) Test field 1; (

**b**) Test field 2; (

**c**) Test field 3.

**Figure 9.**Results of local curvature analysis with the square root function ($\sqrt{N}$); Test field 1: (

**a**) Series I; (

**b**) Series II; (

**c**) Series III; Test field 2: (

**d**) Series I; (

**e**) Series II; (

**f**) Series III; Test field 3: (

**g**) Series I; (

**h**) Series II; (

**i**) Series III.

**Figure 10.**Data sample (series I) demonstrating the conformity of extracted damage contours with reference TIN models: (

**a**) Test field 1; (

**b**) Test field 2; (

**c**) Test field 3.

Step | Algorithm/Function | Parameters |
---|---|---|

1: Data pre-processing | statistical outlier removal | k=20, 2σ |

2: Curvature estimation | principal component analysis, square root function | r=2r_{min} |

3: Segmentation | coefficient of variation, region growing | CV_{th} = 30%, c_{th} =0.02 |

4: Labelling | connected component labelling | o = 8, p = 10 |

5: Defect vectorization | convex hull | L = 0.01 m |

Test Field | SERIES I | SERIES II | SERIES III | ||||||
---|---|---|---|---|---|---|---|---|---|

$\overline{\mathit{x}}$ | σ | CV | $\overline{\mathit{x}}$ | σ | CV | $\overline{\mathit{x}}$ | σ | CV | |

1: 50 m above ground | 0.029 | 0.024 | 83% | 0.021 | 0.005 | 24% | 0.022 | 0.006 | 27% |

2: 30 m above ground | 0.049 | 0.034 | 71% | 0.017 | 0.004 | 22% | 0.018 | 0.004 | 22% |

3: 10 m above ground | 0.031 | 0.021 | 68% | 0.018 | 0.004 | 22% | 0.020 | 0.005 | 25% |

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## Share and Cite

**MDPI and ACS Style**

Makuch, M.; Gawronek, P. 3D Point Cloud Analysis for Damage Detection on Hyperboloid Cooling Tower Shells. *Remote Sens.* **2020**, *12*, 1542.
https://doi.org/10.3390/rs12101542

**AMA Style**

Makuch M, Gawronek P. 3D Point Cloud Analysis for Damage Detection on Hyperboloid Cooling Tower Shells. *Remote Sensing*. 2020; 12(10):1542.
https://doi.org/10.3390/rs12101542

**Chicago/Turabian Style**

Makuch, Maria, and Pelagia Gawronek. 2020. "3D Point Cloud Analysis for Damage Detection on Hyperboloid Cooling Tower Shells" *Remote Sensing* 12, no. 10: 1542.
https://doi.org/10.3390/rs12101542