# Structural Health Monitoring Impact Classification Method Based on Bayesian Neural Network

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Machine Learning Methodologies

## 3. Fundamental of Bayesian Neural Network

#### 3.1. Bayesian Neural Network

#### 3.1.1. Probabilistic Model

#### 3.1.2. Variational Inference

#### 3.1.3. Training and Prediction

#### 3.2. Multi-Artificial Neural Network

## 4. Data Acquisition and Pre-Processing

#### 4.1. Experimental Setup

_{2s}made of M21 T800s carbon fiber prepregs, as shown as Figure 3a [41]. The flat plate was placed on a silicone heating mat with a temperature control unit to adjust the temperature for different experiments (25 °C as a baseline). Eight vibration motors were placed along the four edges of the plate to simulate background noise/vibration and eight PZT sensors (PIC 255) were bonded to the periphery of the panel. The rectangular area bounded by the sensors was split into a 7 × 5 grid which represents 35 different impact locations, shown in Figure 3b. An 8-channel oscilloscope (NI PXI-5105) was connected to the sensors to record signals with a sampling rate of 2 MHz via 10× attenuation oscilloscope probes. In total, 100,000 samples were obtained from the experimental test campaign.

#### 4.2. Data Pre-Processing

#### 4.2.1. Noise Reduction

#### 4.2.2. Feature Extraction

## 5. Results and Discussion

#### 5.1. Perpendicular Impacts

#### 5.1.1. Single ANN

#### 5.1.2. Bayesian Neural Network

- $0.9<P\le 1$
**Reliable** - $0.1<P\le 0.9$
**Unreliable** - $0<P\le 0.1$
**False**

#### 5.1.3. Multi-ANN

#### 5.2. Angled Impacts

#### 5.2.1. Single Feature

#### 5.2.2. Multiple Features

## 6. Conclusions

- Both the BNN and single ANN can classify energy levels of perpendicular impacts with high accuracy using the feature of transferred energy, although the accuracy of the single ANN is higher than that of the BNN.
- Both the BNN and multi-ANN can quantify the uncertainty in the mode and calculate the confidence of predicted outcomes. For perpendicular impacts, the confidence of predicted outcomes in the multi-ANN is higher than that in the BNN, while the time and computational resource cost of the multi-ANN are significantly larger than those of the BNN.
- The time and computational resource cost of the multi-ANN increase linearly as the number of ANN used increases, while the cost of the BNN remains stable as the number of Monte Carlo sampling increases. For 100 ANN and 100 times Monte Carlo sampling, the cost of the multi-ANN is significantly larger than that of the BNN.
- For angled impacts, both the BNN and multi-ANN can only reach the accuracy of nearly 50% with the feature of transferred energy, while the multi-ANN tends to make more “False” predictions.
- The dynamics response that the perpendicular and inclined impacts generate in the plate are very different, even if they are of the same mass and height; therefore, if a metamodel is developed for perfect impact scenarios in the laboratory condition (i.e., perpendicular impacts), it cannot predict inclined impacts with high accuracy. It is observed that including other features that can directly relate to the characteristic response that each impact scenario generates in the structure, can improve the results, but this needs to be further investigated, including more variability in the impact scenarios. This conclusion also follows the findings in [22] where two step classification is proposed. Therefore, future work will investigate the variability not only of impact angle but also impactor material, mass and size to represent a more realistic variability.
- The mixed features of transferred energy and frequency at maximum amplitude cannot be used to predict energy levels of angled impacts as the results are totally random. The mixed features of transferred energy and time interval of the largest peak show a potential to help to identify both the angled and perpendicular impacts as the number of “False” predictions for angled impacts and “Unreliable” predictions for perpendicular impacts decreases meanwhile.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) ANN where each weight ${w}_{i,j}$ has a fixed value, (

**b**) BNN where each weight is assigned a distribution.

**Figure 3.**Experimental setup and configuration. (

**a**) Impact set up; (

**b**) Experimental configuration of the 8 PZT sensors and 35 impact locations.

**Figure 12.**The distribution of classified results with BNN. (

**a**) Single test sample. (

**b**) Three single testing samples.

**Figure 14.**The probabilistic results from 100 ANN. (

**a**) Probability of correct predictions. (

**b**) Their distribution. (

**c**) Results from three test samples.

**Figure 17.**The results of the BNN based on mixed data with transferred energy. (

**a**) Probability of correct predictions. (

**b**) Their distribution.

**Figure 18.**The results of multi-ANN based on mixed data with transferred energy. (

**a**) Probability of correct predictions. (

**b**) Their distribution.

**Figure 19.**The results of BNN with transferred energy and frequency. (

**a**) Probability of correct predictions. (

**b**) Their distribution.

**Figure 20.**The results of BNN with transferred energy and time interval. (

**a**) Probability of correct predictions. (

**b**) Their distribution.

Case | Material | Height/mm | Mass/g | Angle/° | Temperature/°C | Energy/mJ |
---|---|---|---|---|---|---|

A1 | Steel | 50 | 100 | 90 | 25 | 49 |

A2 | Steel | 50 | 200 | 90 | 25 | 98 |

A3 | Steel | 100 | 100 | 90 | 25 | 98 |

A4 | Steel | 100 | 200 | 90 | 25 | 196 |

B1 | Steel | 50 | 100 | 45 | 25 | 49 |

B2 | Steel | 100 | 100 | 45 | 25 | 98 |

Label | Energy/J(S1) … | Energy/J(S8) | Frequency/Hz(S1) … | Frequency/Hz(S8) | Time int/s(S1) … | Time int/s(S8) |
---|---|---|---|---|---|---|

0 | 0.04968 | 0.04552 | 20 | 58 | 0.01287 | 0.00788 |

0 | 0.04943 | 0.04592 | 20 | 58 | 0.01293 | 0.00806 |

0 | 0.04958 | 0.04609 | 20 | 58 | 0.01302 | 0.00791 |

0 | 0.04911 | 0.04601 | 20 | 58 | 0.01298 | 0.00794 |

0 | 0.04062 | 0.04641 | 20 | 20 | 0.03223 | 0.01758 |

… | … | … | … | … | … | … |

1 | 0.07705 | 0.03190 | 21 | 21 | 0.02126 | 0.01660 |

… | … | … | … | … | … | … |

2 | 0.10343 | 0.05218 | 21 | 20 | 0.02105 | 0.01538 |

Meta Model | Input Feature * | Training Set | Testing Set | Reliable Classification | Unreliable Classification | False Classification |
---|---|---|---|---|---|---|

BNN | 1 | A | A | 94% | 6% | 0% |

BNN | 1 | A | A+B | 70% (only 55% for B) | 8% | 22% |

BNN | 1+2 | A | A+B | 70% | 8% | 22% |

BNN | 1+3 | A | A+B | 54% | 39% | 7% |

Multi-ANN | 1 | A | A | 98% | 0% | 2% |

Multi-ANN | 1 | A | A+B | 70% (only 44% for B) | 2% | 28% |

Multi-ANN | 1+2 | A | A+B | 70% | 3% | 27% |

Multi-ANN | 1+3 | A | A+B | 70% | 18% | 12% |

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**MDPI and ACS Style**

Yu, H.; Seno, A.H.; Sharif Khodaei, Z.; Aliabadi, M.H.F.
Structural Health Monitoring Impact Classification Method Based on Bayesian Neural Network. *Polymers* **2022**, *14*, 3947.
https://doi.org/10.3390/polym14193947

**AMA Style**

Yu H, Seno AH, Sharif Khodaei Z, Aliabadi MHF.
Structural Health Monitoring Impact Classification Method Based on Bayesian Neural Network. *Polymers*. 2022; 14(19):3947.
https://doi.org/10.3390/polym14193947

**Chicago/Turabian Style**

Yu, Haofan, Aldyandra Hami Seno, Zahra Sharif Khodaei, and M. H. Ferri Aliabadi.
2022. "Structural Health Monitoring Impact Classification Method Based on Bayesian Neural Network" *Polymers* 14, no. 19: 3947.
https://doi.org/10.3390/polym14193947