# Defect Identification of Concrete Piles Based on Numerical Simulation and Convolutional Neural Network

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## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Low-Strain Pile Integrity Test

#### 2.2. Wavelet Packet Decomposition

#### 2.3. Finite Element Analysis of Pile

#### 2.3.1. Basic Theory and Modeling Parameters

#### 2.3.2. Specific Modeling Method

#### 2.4. Experimental Validation

#### 2.5. Batch Modeling Using Python Scripts

^{®}function, which determines the location and range of cracks by script parameters [43]. In the main loop, each r corresponds to each a and generated 100 sets of parameters. In the second loop, 4 aa corresponds to each parameter generated in the main loop. A total of 10 × 10 × 4 = 400 data were generated. The modeling idea was shown in Figure 13.

#### 2.6. Convolution Neural Network

#### 2.7. Data Enhancement and WPT

## 3. Result

## 4. Conclusions

- (1)
- The application of LSPIT is affected by many complex situations, such as the influence of environmental noise on low-strain data and the influence of rebound waves superimposed on each other in concrete piles, but these influences will not destroy the information contained in low-strain data. Therefore, signal processing by computer technology can help to extract the characteristic indexes of the signal and eliminate the influence of complex conditions on the signal.
- (2)
- After feature extraction and signal structure reconstruction of the signal, a CNN can be used as an auxiliary tool for defect identification of concrete pile defects by the low-strain reflection wave method.
- (3)
- The complex noise in the original signal has a negative impact on the performance of the CNN classifier. The performance and robustness of the CNN classifier were increased by WPT and data enhancement. Using WPT and data enhancement can improve the accuracy of signal recognition compared with using only velocity signals as a defect index.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Tree structures of wavelet packet transform (A represents low frequency, D represents high frequency, and the number represents the number of layers of decomposition).

**Figure 3.**Types of simulated pile foundation ((

**a**) neck defect; (

**b**) bulge imperfection; (

**c**) weak concrete; (

**d**) crack; (

**e**) broken pile)).

**Figure 6.**Numerical simulation data. ((

**a**) neck defect; (

**b**) bulge imperfection; (

**c**) weak concrete; (

**d**) crack; (

**e**) broken pile).

**Figure 8.**(

**a**) Experimental piles (bulge imperfection; neck defect; crack; weak concrete; broken); (

**b**) Placement of experimental pile.

**Figure 10.**Experimental data ((

**a**) neck defect; (

**b**) bulge imperfection; (

**c**) weak concrete; (

**d**) crack; (

**e**) broken pile).

**Figure 12.**Principle of model generation.( X represents the radial direction of the pile, Y represents the longitudinal direction of the pile).

**Figure 13.**Parameters of five kinds of defects (pile (

**a**) and pile (

**b**) have three variables: defect location aa, defect length, and defect radius *. The variables of pile (

**c**) are defect location aa, defect length, and the material properties of the defective part. The variable of pile (

**e**) is the position of defect aa. The variables of pile (

**d**) are the positions of defect aa, the angle of the crack, and the radius of the crack).

**Figure 16.**The waveform of Db2 wavelet function. (

**a1**–

**a8**) represent Low Frequency Data of Wavelet Decomposition, (

**d1**–

**d8**) represent High Frequency Data of Wavelet Decomposition, (

**S**) represents the original data).

**Figure 17.**Data processing (Represents the data in the form of graphics because the feature of the data cannot be seen through the conventional time domain diagram after folding, and the depth of the color in the diagram represents the size of the value. S: original data, a4: the fourth layer data of wavelet decomposition.).

**Figure 18.**Confusion matrix; Overall training and validation accuracy of the classifier for 200 epochs.

Parts | Length (m) | Radius (m) | Material | Density (kg/m^{3}) | Elastic Modulus (Pa) | Poisson Ratio |
---|---|---|---|---|---|---|

Pile | 1 | 0.05 | C30 concrete | 2500 | 3.0 × 10^{10} | 0.18 |

Soil around pile | 1 | 0.5 | clay | 2100 | 5.0 × 10^{7} | 0.25 |

Bottom soil of the pile | 0.5 | 0.5 | clay | 2100 | 5.0 × 10^{7} | 0.25 |

**Table 2.**Basic parameters of the models. (The area of crack is 1/3 of the pile’s cross-sectional area, The elastic modulus of weak concrete is 1.5 × 10

^{10}pa).

Types | Length (m) | Radius (m) | Length of Defect (m) | Position of Defect (m) | Radius of Defect (m) |
---|---|---|---|---|---|

Neck defect | 1 | 0.05 | 0.08 | 0.5 | 0.03 |

Bulge imperfection | 1 | 0.05 | 0.08 | 0.5 | 0.08 |

Weak concrete | 1 | 0.05 | 0.08 | 0.5 | 0.05 |

Crack | 1 | 0.05 | 0 | 0.5 | 0.05 |

Broken | 1 | 0.05 | 0 | 0.5 | 0.05 |

Parts | ${\mathit{L}}_{\mathit{d}}\text{}\left(\mathbf{Length}\right)$ | * (Radius) | Aa (Position) | Material (Pa) | Angle (°) | Amount |
---|---|---|---|---|---|---|

Neck defect | 0.12 → 0.02 m | 0.05 → 0.1 m | 0.2–0.8 m | 3 × 10^{10} | None | 400 |

Bulge imperfection | 0.12 → 0.02 m | 0.02 → 0.05 m | 0.2–0.8 m | 3 × 10^{10} | None | 400 |

Weak concrete | 0.12 → 0.02 m | 0.05 m | 0.2–0.8 m | 3 × 10^{9} →3 × 10^{10} | None | 400 |

Crack | 0 | 0.01–0.045 m | 0.2–0.8 m | - | 10° → 270° | 400 |

Broken | 0 | 0.05 m | 0.2–0.8 m | - | None | 400 |

Stage | Layers | Stride | Output Shape |
---|---|---|---|

0 | Conv3 × 3 | 1 | 18 × 18 × 6 |

1 | Pooling | 1 | 9 × 9 × 6 |

2 | Conv2 × 2 | 1 | 7 × 7 × 16 |

3 | Pooling | 1 | 3 × 3 × 16 |

4 | Conv3 × 3 | 1 | 1 × 1 × 120 |

6 | Flatten | 1 | 120 |

7 | Dense | - | 84 |

8 | Dropout | - | - |

9 | Dense | - | 5 |

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**MDPI and ACS Style**

Wu, C.-S.; Zhang, J.-Q.; Qi, L.-L.; Zhuo, D.-B.
Defect Identification of Concrete Piles Based on Numerical Simulation and Convolutional Neural Network. *Buildings* **2022**, *12*, 664.
https://doi.org/10.3390/buildings12050664

**AMA Style**

Wu C-S, Zhang J-Q, Qi L-L, Zhuo D-B.
Defect Identification of Concrete Piles Based on Numerical Simulation and Convolutional Neural Network. *Buildings*. 2022; 12(5):664.
https://doi.org/10.3390/buildings12050664

**Chicago/Turabian Style**

Wu, Chuan-Sheng, Jian-Qiang Zhang, Ling-Ling Qi, and De-Bing Zhuo.
2022. "Defect Identification of Concrete Piles Based on Numerical Simulation and Convolutional Neural Network" *Buildings* 12, no. 5: 664.
https://doi.org/10.3390/buildings12050664