# A Deep Learning Approach to Detect Failures in Bridges Based on the Coherence of Signals

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Set Up

- Hydrometer: measures the river level identifying possible flooding that can be dangerous for the bridge’s structure.
- Echo sounder: measures the level of the river bed and can provide information about possible movements of the piers within its proximity.
- Cameras: identify possible detritus stacks at the base of the piers by documenting and characterising the annual process of plant transportation.

#### Dataset Acquisition

## 3. Multi-Input Machine Learning Modelling

#### 3.1. Iterative Models

#### 3.2. Autoencoder Model

- Encoder function: it applies different transformations to the input data ($\mathit{X}$) by means of successive layers, which generates a compressed representation of the input ($\mathit{H}$) in a new feature space usually called latent space. The mathematical expression is: $\mathit{H}=f\left(\mathit{X}\right)$.
- Decoder function: starting from the latent space, it applies different transformations to determine a reconstruction ($\mathit{R}$) of the input. The mathematical expression is: $\mathit{R}=g\left(\mathit{H}\right)$.

## 4. Data Preprocessing and Models Architecture

## 5. Results

- 1.
- 2.
- For each sensor, a moving average and a moving standard deviation are applied with a one-week window to evaluate the distributions of residuals in time.
- 3.
- For each month, the mean absolute error (MAE) of the scaled residuals is computed; that is, Equations (3) and (5) are applied before the true values, and the estimations are scaled back to the original range. This allows the evaluation of how the sensors detect unusual behaviours on a comparable scale.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ANN | Artificial neural network |

CNN | Convolutional neural network |

AI | Artificial intelligence |

AU | Autoencoder |

SHM | Structural health monitoring |

ReLU | Rectified linear unit |

MAE | Mean absolute error |

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**Figure 3.**A model (such as a neural network) takes the temperature as the input and gives an estimation of the readings of other sensors.

**Figure 4.**A model estimates the values of one group of sensors by taking all of the other groups as the input.

**Table 1.**Channels, sensors and measurement units of the acquisition system mounted on Candia Bridge.

Channels | Sensors | Measurement Unit |
---|---|---|

1–15 | Tiltmeters | rad |

16 | Hydrometer | m |

23, 24 | Temperatures | °C |

25 | Atmospheric pressure | bar |

26, 27 | Temperatures | °C |

28, 29 | Humidity | % |

30 | Wind speed | Km/h |

31 | Wind direction | ° |

32 | Rain rate | mm/h |

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**MDPI and ACS Style**

Bono, F.M.; Radicioni, L.; Cinquemani, S.; Benedetti, L.; Cazzulani, G.; Somaschini, C.; Belloli, M.
A Deep Learning Approach to Detect Failures in Bridges Based on the Coherence of Signals. *Future Internet* **2023**, *15*, 119.
https://doi.org/10.3390/fi15040119

**AMA Style**

Bono FM, Radicioni L, Cinquemani S, Benedetti L, Cazzulani G, Somaschini C, Belloli M.
A Deep Learning Approach to Detect Failures in Bridges Based on the Coherence of Signals. *Future Internet*. 2023; 15(4):119.
https://doi.org/10.3390/fi15040119

**Chicago/Turabian Style**

Bono, Francesco Morgan, Luca Radicioni, Simone Cinquemani, Lorenzo Benedetti, Gabriele Cazzulani, Claudio Somaschini, and Marco Belloli.
2023. "A Deep Learning Approach to Detect Failures in Bridges Based on the Coherence of Signals" *Future Internet* 15, no. 4: 119.
https://doi.org/10.3390/fi15040119