- Research article
- Open Access

# Unsupervised learning approach to automation of hammering test using topological information

- Jun Younes Louhi Kasahara†
^{1}Email authorView ORCID ID profile, - Hiromitsu Fujii†
^{1}, - Atsushi Yamashita†
^{1}and - Hajime Asama†
^{1}

**Received:**8 October 2015**Accepted:**8 May 2017**Published:**18 May 2017

## Abstract

In this paper we present an online unsupervised method based on clustering to find defects in concrete structures using hammering. First, the initial dataset of sound samples is roughly clustered using the k-means algorithm with the k-means++ seeding procedure in order to find the cluster best representative of the structure. Then the regular model for the hammering sound, the centroid of this cluster, which is assumed to be the non-defective sound model, is established and finally used as a reference to conduct diagnosis on the whole dataset. During the model generation phase, topological information on the spatial distribution of samples is used to attribute varying importance to each sample and therefore take into account meticulous diagnosis of certain areas. The algorithm is fast and reliable enough to allow efficient diagnosis by running it each time a new sample is acquired. Tests on two commonly found types of defects, namely delamination and void type defects, were conducted on experimental test blocks and yielded satisfying results. This method also performed well in field environments.

## Keywords

- Clustering
- Hammering
- Concrete
- Online
- k-means

## Background

The designation concrete covers a large spectrum of composite materials composed of aggregates bonded by a fluid cement, hardened over time. This material is extremely common in modern societies, especially in social infrastructures such as tunnels. As any other material, concrete can be greatly affected by aging and environmental conditions. In some cases, these factors may lead concrete structures to structural failure [1–3]. In order to guarantee their safe use, careful maintenance is needed. Among all the operations taken to maintain these structures, the diagnosis for defects is critical since it is a decision-making step.

Various attempts to adapt the hammering test in an automatic form have been made in order to obtain a faster, more reliable and objective method to find defects in concrete structures. References [6, 7] were focused in finding sound features enabling differentiation between defective and non-defective spots as well as on the exploration of new methods to replace or aid the human operator holding the hammer in order to get more regular and reliable sound samples. References [8–11] were more focused on the data analysis part of the problem and used supervised learning to correctly distinguish sounds from non-defective areas and sounds from defective areas. These approaches have given promising results, however their main drawback is the necessity to train the algorithm first using a training set. Depending on various factors, especially during the hardening phase, concrete can greatly differ from one structure to another, even if they were made from the same batch, thus choosing the adequate training set can be difficult. Our proposed method takes a new approach to this task using unsupervised learning, based on clustering, and therefore bypasses the need of training sets.

In our previous method [12], the major cluster from which the centroid to be used as model was determined by finding the cluster with the biggest number of samples in it. This method was acceptable when diagnosis was conducted following a regular grid. However, in practice, defective areas of the structure are more carefully examined: this could result in having more defective samples in the dataset and non-defective ones and thus, the method wrongly choosing the wrong centroid as regular model. In this paper, we introduce a weight system to balance the respective influence of samples in accordance with their spatial distribution on the tested structure surface. This enables proper balancing of each sample’s relevance given their mutual spatial proximity.

Concrete structure inspection is generally divided into two stages [13]. The first one, called primary inspection, is a rough one, conducted on the whole structure. If any defect is found during this process, the secondary inspection is conducted only at these spots to accurately identify the defect. Given the nature of our proposed method, adaptable and based on statistical irregularity detection, it can be considered particularly suited for the primary inspection of concrete structures.

In this paper, we propose a method to allow training set-free, real-time, adaptive hammering testing of concrete structures. This allows hammering testing to be conducted on a unknown structure, obtaining a primary inspection diagnosis and narrowing down spots for secondary inspection.

## Methods

### Concept

The main assumption is that most of the tested structure is non-defective. That means that defects, such as cracks and voids, do not occupy the majority of the tested surface. This assumption is acceptable since concrete structures subject to severe deterioration are blatant and therefore do not require to be tested, a simple inspection by naked eye is enough. Considering this, it becomes possible to characterize the non-defective sound as the regular sound found on the tested surface.

This approach has been motivated by two main reasons. First, interview conducted with actual professionals in charge of conducting hammering tests revealed that they were, in fact, more focused in hitting multiple spots on the structure at high speed and looking for sounds that stands out rather than relying in past experiences and knowledge. In this aspect, our proposed method is closer to what human operators do. Secondly, as stated earlier, it has been observed that concrete is extremely sensible to physical conditions such as temperature, humidity, etc., that especially during the hardening phase of the fabrication process. The result is that even among concrete blocks that were made from the same source, non-defective spots do not return similar hammering sounds at all. This was observed at various occasion with concrete test blocks we used in our experiments: even tough they were made in a single batch, non-defective spots in two different blocks returned different sounds.

- 1.
Regroup hammering samples that are similar.

- 2.
Find the major group of the tested structure.

- 3.
Extract the centroid of this group and establish it as the regular, non-defective model.

- 4.
Use the generated regular model as a reference to conduct diagnosis on the samples.

### Regrouping hammering samples

#### Description of a hammering sample

- 1.
The recorded sound.

- 2.
The location where the sample was recorded.

Given a sound sample \(X_{i}\) defined by (\(x_{0},\ldots,x_{N-1}\)), *N* being the sampling rate multiplied by the recording duration, collected on a particular location \(\mathbf {L}_{i}\) on the structure, its Fourier spectrum (\(a_{0},\ldots,a_{N-1}\)) is obtained using Fast Fourier Transform (FFT).

#### Metric

In order to compare sounds, i.e to give a value of how much two hammering sounds are similar, a meaningful distance measure between sound samples in the Fourier spectrum space has to be defined.

*A*and

*B*, respectively defined by (\(a_{0},\ldots,a_{N-1}\)) and (\(b_{0},\ldots,b_{N-1}\)), the sample Pearson correlation coefficient is defined as in Eq. (1).

#### Rough clustering using k-means++

In our case, we do not need quality clusters since clustering is not our goal, i.e. clustering is not conducted as a step for further cluster analysis. The final aim is to obtain the regular model. Moreover, to work toward a system with the capability to conduct diagnosis in real-time, a fast algorithm would be useful. Considering the usual dataset of hammering samples, usually around a few hundred in our application, we found the k-means algorithm, usually used in data consolidation or pre-clustering, being adequate: it is simple and computationally fast enough.

Even if defective samples can be spread out in feature vector space (defects are unpredictable and can be of several variations in a single structure), more compactness can be expected for non-defective samples: k-means should not fail to put at least one centroid in the non-defective sample group.

### Finding the major cluster

In our approach to this task, the cluster best describing the tested structure has to be found.

Defining the regular model based on the number of sample contained in each cluster would be enough in the case of samples being collected following a grid: each sample would then have the same weight in the final comparison. However, when collecting samples freely on the structure, defective areas tend to be tested meticulously and therefore, the number of samples from defective spots tend to surpass the number of samples from non-defective spots. If this happens, such simple implementation would wrongly recognize the defective sound as being the regular sound and thus the non-defective sound model.

*D*among \(N_{sample}\) samples, with its location \(\mathbf {L}_{i}\), the radius of the sample’s area is defined as half of the Euclidian distance to its nearest neighbor:

### Generation of the regular model and diagnosis

*Th*, a boolean value

*defective*for a sample \(X_{i}\) could be defined as:

The pseudo-algoritm presented in Algorithm (1) briefly sums-up the mechanics of our proposed method. The clustering step being fast enough, online implementation was possible by simply running it each time a new sample is added to the dataset.

## Results and discussion

### Experiments using a traditional hammer

The used setup is illustrated in Fig. 5 and experiments were conducted on concrete test blocks containing various man-made defects to simulate natural ones. For each block, defective spots are marked in red on the corresponding schematic.

Test blocks were hit at 210 locations once following a 14 by 14 square grid that covers the whole block. The used hammer was a KTC UDHT-2 (head diameter 16 mm, length 380 mm, weight 160 g), commonly used in hammering test by professionals and sound was recorded at 44.1 kHz using a Behringer ECM8000 microphone coupled with a RolandUA-25EX sound board and a laptop for data analysis. Fourier spectrums were computed by FFT with a window of 1024, thus in vectors of length 512 due to symmetry.

A simple trigger was implemented to conduct clipping to get each hammering sound as a single sample and the hammer head was painted in red in order to be tracked so that the Cartesian coordinates of each sample could be collected.

#### Delamination-type defects

Delamination is a phenomenon mostly observed in reinforced concrete structures. These structures are often subject to reinforcement corrosion: the reinforcement metal is oxidized and its volume increases. This results in internal stresses in the concrete structure and the apparition of cracks diagonal to the surface of the structure.

Tests were conducted with \(500 \times 500 \times 150\) mm concrete blocks presenting cracks at an angle of respectively 15°, 30° and 45°. The schematics of these test blocks are presented in Fig. 6. Using these schematics as ground truth, receiver operating characteristic (ROC) curve was calculated for each of these blocks (Fig. 7) by varying the threshold value *Th* used in Eq. 9. It can be noticed that the area under the ROC curve decreases from 0.94 to 0.80 as the crack angle increases from 15° to 45°. This could be attributed to the defect depth: the bigger the crack angle, the deeper the crack runs in the concrete, resulting the sound to be more and more muffled as the crack angle increases, rendering analysis more difficult (Table 1).

In [15], Computer Vision is used to detect cracks on the surface of concrete. Depending on the used preprocessing techniques, the area under the curve varied from 0.87 to 0.99. Our proposed method could therefore be considered acceptable.

In Fig. 8 the correlation distances from the model for non-defective and defective hammering samples of the 15°. delamination test block is shown (in total 210 samples). Except a dozen defective samples that were incorrectly given small distance to the model, it can be observed that our proposed approach successfully separates the two types of samples.

Always for the 15° delamination defect test block, in Fig. 9 the Fourier spectrums of the computed model for non-defective sample, a non-defective sample and a defective sample are shown. It can be seen that the produced model is a Fourier spectrum that more closely resembles the Fourier spectrum of a non-defective sample than of a defective sample.

Area under the ROC curve for each delamination type blocks: the maximun value obtainable is 1 and closer to it the method scores, the better it is

Delamination angle (°) | Area under the ROC curve |
---|---|

15 | 0.94 |

30 | 0.90 |

45 | 0.81 |

#### Void-type defects

For various reasons such as a foreign body or the infiltration of water/air, defects we could call void-type can appear on concrete structures in the field. Basically, during the hardening phase, the concrete was not able to completely fill the required volume. This type of defects is considered extremely dangerous since for one part they tend to make large portions of concrete beneath them to be instable and fall off, and for the other part because unlike delaminations, they are usually not visible at the surface of the structure. The hammering test is in this case a trusted tool for inspection.

Area under the ROC curve for void type block

Void | Area under the ROC curve |
---|---|

30 mm depth | 0.94 |

50 mm depth | 0.81 |

75 mm depth | 0.71 |

### Experiments on the field

*Th*was manually adjusted in order to get the best discrimination of defective samples.

## Conclusions

Our proposed method was able to successfully identify both delamination and void type defects without the need of any training set, in a real-time fashion and by allowing adaptive hammering testing. The method was also able to show a similar performance on the field, on an unknown and untested structure, and to this regard, it could be judged adequate for the purpose of primary inspection, successfully narrowing down areas for secondary inspection. For future work, we would like to improve this method to ensure increased robustness, especially on the field where sources of noise such as wind are abundantly present. Another point worth further investigating would be on the hammering force; although its influence can to be considered to have been mitigated by normalizations in our devised metric, there is no guarantee that it does not influence the shape of hammering sound spectrums. Therefore, it would be interesting to either measure the hammering force and incorporate this aspect in the diagnosis. Also, with the recent development of automatic hammering modules, that would enable consistent hammering with the same force for the whole structure, the performance of this method in combination with these robots should also be investigated.

## Notes

## Declarations

### Authors' contributions

JYLK developed the method and drafted the manuscript. HF was involved in discussion of ideas and results and manuscript drafting. AY and HA supervised the project and provided guidance. All members are involved in checking and approval of the paper. All authors read and approved the final manuscript.

### Acknowledgements

This work was supported in part by the Cross-ministerial Strategic Innovation Promotion Program (SIP) of the New Energy and Industrial Technology Development Organization (NEDO), Grant-in-Aid for JSPS Fellows 269039, and Institute of Technology, Tokyu Construction Co., Ltd.

### Competing interests

The authors declare that they have no competing interests.

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## Authors’ Affiliations

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