# Damage Detection in Multiple RC Structures Based on Embedded Ultrasonic Sensors and Wavelet Transform

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Theoretical Background on Propagation of Ultrasonic Waves

#### 2.2. Non-Decimated Wavelet Transform

#### 2.3. Continuous Wavelet Transform

## 3. Experimental Objects

#### 3.1. Benchmark RC Structure

#### 3.2. Reference Real Structure

## 4. Experimental Programs and Results

#### 4.1. Benchmark RC Structure

#### 4.2. Reference Real Structure

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

RC | Reinforced concrete |

BAM | Bundesanstalt für Materialforschung und -prüfung |

NDT | Non-Destructive Testing |

CWI | Coda wave interferometry |

AR | Autoregressive model |

CC | correlation coefficient |

NDWT | Non-Decimated Wavelet Transform |

CWT | Continuous wavelet transform |

FFT | Fast Fourier transform |

STFT | Short-time Fourier transform |

UPV | Ultrasonic pulse velocity |

AE | Acoustic emission |

DIC | Digital image correlation and tracking |

LVDT | Linear variable differential transducer |

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**Figure 3.**Ultrasonic signal (recorded by sensors combination S01R04) after wavelet decomposition in time (A) and frequency (B) domain. (

**a**) Approximation coefficients after high wavelet scaling. (

**b**) Detail coefficients after low wavelet scaling.

**Figure 4.**Measuring stand and arrangement of all sensors. (

**a**) Real and simulated 3D view of the beam reinforcement with arrangement of all sensors in the reinforcement. (

**b**) Measuring stand and beam load position.

**Figure 5.**BLEIB structure and location of all ultrasonic sensors. (

**a**) BLEIB structure and location of the cracks. (

**b**) Arrangement of all ultrasonic sensors location and quasi-static load position in the BLEIB.

**Figure 10.**NDWT feature extracted from ultrasonic pair S01R04 time histories. (

**a**) Values of NDWT feature (low-frequency components) from ultrasonic pair S01R04 time histories. (

**b**) Values of NDWT feature (high-frequency components) from ultrasonic pair S01R04 time histories.

**Figure 11.**Values of continuous wavelet transform (CWT) feature from ultrasonic pair S01R04 time histories.

**Figure 12.**NDWT feature extracted from ultrasonic pair S02R03 time histories. (

**a**) Values of NDWT feature (low-frequency components) from ultrasonic pair S02R03. (

**b**) Values of NDWT feature (high-frequency components) from ultrasonic pair S02R03.

**Figure 15.**NDWT feature extracted from ultrasonic sensors pair time histories in the BLEIB structure. (

**a**) Values of NDWT feature extracted from ultrasonic pair S11R13 time histories in BLEIB structure. (

**b**) Values of NDWT feature extracted from ultrasonic pair S12R14 time histories in BLEIB structure.

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**MDPI and ACS Style**

Chakraborty, J.; Wang, X.; Stolinski, M.
Damage Detection in Multiple RC Structures Based on Embedded Ultrasonic Sensors and Wavelet Transform. *Buildings* **2021**, *11*, 56.
https://doi.org/10.3390/buildings11020056

**AMA Style**

Chakraborty J, Wang X, Stolinski M.
Damage Detection in Multiple RC Structures Based on Embedded Ultrasonic Sensors and Wavelet Transform. *Buildings*. 2021; 11(2):56.
https://doi.org/10.3390/buildings11020056

**Chicago/Turabian Style**

Chakraborty, Joyraj, Xin Wang, and Marek Stolinski.
2021. "Damage Detection in Multiple RC Structures Based on Embedded Ultrasonic Sensors and Wavelet Transform" *Buildings* 11, no. 2: 56.
https://doi.org/10.3390/buildings11020056