# 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

- Rausche, F. Non-destructive evaluation of deep foundations. In Proceedings of the 5th International Conference on Case Histories in Geotechnical Engineering, New York, NY, USA, 13–17 April 2004; pp. 1–9. [Google Scholar]
- Chow, Y.K.; Phoon, K.K.; Chow, W.F. Low strain integrity testing of piles: Three-dimensional effects. J. Geotech. Geoenvironmental Eng.
**2003**, 129, 1057–1062. [Google Scholar] [CrossRef] - Luo, W.; Chen, F.; Hu, J. Improvement of Low Strain Pile Integrity Test. In Proceedings of the ASEE (American Society of Engineering Education) Conference, Boston, MA, USA, 7–8 May 2010; pp. 583–589. Available online: https://monolith.asee.org/documents/zones/zone1/2008/student/ASEE12008_0082_paper.pdf (accessed on 11 April 2022).
- Liu, W.; Tian, S. Classification of pile integrity based on convolutional neural network. J. Nanchang Univ. (Eng. Ed. )
**2021**, 43, 263–268. [Google Scholar] [CrossRef] - Bao, L.S.; Ye, X.F.; Li, Q.; Wang, H. Research on the application of neural network based on genetic algorithm in pile foundation detection. Highw. Transp. Technol. (Appl. Technol. Version)
**2017**, 13, 228–231. [Google Scholar] - Tam, C.M.; Tong, T.K.L.; Lau, T.C.T. Diagnosis of prestressed concrete pile defects using probabilistic neural networks. Eng. Struct.
**2004**, 26, 1155–1162. [Google Scholar] [CrossRef] - Cui, D.M.; Yan, W.; Wang, X.Q. Towards intelligent interpretation of low strain pile integrity testing results using machine learning techniques. Sensors
**2017**, 17, 2443. [Google Scholar] [CrossRef] [Green Version] - Yan, T.N.; Wang, S.; Li, S.J. The application of artificial neural network method in pile foundation detection. Geol. Sci. Technol. Inf.
**1999**, (Suppl. S1), 38–41. [Google Scholar] - Cai, Q.Y.; Lin, J.H. Diagnosis of pile defects based on wavelet analysis and neural network. Vib. Impact
**2002**, 3, 13–16. [Google Scholar] [CrossRef] - Cai, Q.Y. Diagnosis of Pile Defects Based on Wavelet Analysis and Neural Network. Master’s Thesis, Huaqiao University, Quanzhou, China, 2001. [Google Scholar]
- Wang, C.H.; Zhang, W. Neural network model for pile integrity identification based on reflection wave method. Geotech. Mech.
**2003**, 6, 952–956. [Google Scholar] [CrossRef] - Liu, M.G.; Yue, X.H.; Yang, Y.B.; Li, Q. Intelligent identification of pile defects based on Sym wavelet and BP neural network. J. Rock Mech. Eng.
**2007**, 192 (Suppl. S1), 3484–3488. [Google Scholar] - Zhang, G.; Jiang, X.L.; Liu, Z.J. Pile defect intelligent identification based on wavelet analysis and neural networks. In Applied Mechanics and Materials; Trans Tech Publications Ltd.: Frienbach, Switzerland, 2014; Volume 608–609, pp. 899–902. [Google Scholar] [CrossRef]
- Protopapadakis, E.; Schauer, M.; Pierri, E. A genetically optimized neural classifier applied to numerical pile integrity tests considering concrete piles. Comput. Struct.
**2016**, 162, 68–79. [Google Scholar] [CrossRef] - Kang, W.; Zhao, Y.; Liu, L. Pile defect identification based on multi-higher order moment feature. J. GeoEng.
**2018**, 13, 69–77. [Google Scholar] - Vu, G.; Timothy, J.J.; Singh, D.S. Numerical simulation-based damage identification in concrete. Modelling
**2021**, 2, 355–369. [Google Scholar] [CrossRef] - Xie, Y.; Xiao, Y.; Liu, X. Time-frequency distribution map-based convolutional neural network (CNN) model for underwater pipeline leakage detection using acoustic signals. Sensors
**2020**, 20, 5040. [Google Scholar] [CrossRef] - Zhuo, D.B.; Cao, H. Joint damage identification based on wavelet time-frequency diagram and lightweight convolutional neural network. Eng. Mech.
**2021**, 38, 228–238. [Google Scholar] - Ritto, T.G.; Rochinha, F.A. Digital twin, physics-based model, and machine learning applied to damage detection in structures. Mech. Syst. Signal Processing
**2021**, 155, 107614. [Google Scholar] [CrossRef] - Karvelis, P.; Georgoulas, G.; Kappatos, V. Deep machine learning for structural health monitoring on ship hulls using acoustic emission method. Ships Offshore Struct.
**2021**, 16, 440–448. [Google Scholar] [CrossRef] - Rautela, M.; Senthilnath, J.; Moll, J. Combined two-level damage identification strategy using ultrasonic guided waves and physical knowledge assisted machine learning. Ultrasonics
**2021**, 115, 106451. [Google Scholar] [CrossRef] - Perry, B.J.; Guo, Y. Atadero, R. Streamlined bridge inspection system utilizing unmanned aerial vehicles (UAVs) and machine learning. Measurement
**2020**, 164, 108048. [Google Scholar] [CrossRef] - Li, Z.; Li, D.; Chen, Y. Deep learning-based guided wave method for semi-grouting sleeve detection. J. Build. Eng.
**2022**, 46, 103739. [Google Scholar] [CrossRef] - Rausche, F.; Moses, F.; Goble, G.G. Soil resistance predictions from pile dynamics. J. Soil Mech. Found. Div.
**1972**, 98, 917–937. [Google Scholar] [CrossRef] - Kim, H.J.; Mission, J.L.; Dinoy, P.R. Guidelines for impact echo test signal interpretation based on wavelet packet transform for the detection of pile defects. Appl. Sci.
**2020**, 10, 2633. [Google Scholar] [CrossRef] [Green Version] - Smith, E.A.L. Pile-driving analysis by the wave equation. J. Soil Mech. Found. Div.
**1960**, 86, 35–61. [Google Scholar] [CrossRef] - ASTM D5882-07; Standard Test Method for Low Strain Impact Integrity Testing of Deep Foundations. ASTM International: West Conshohocken, PA, USA, 2007.
- Dai, Y.W. Reliability Method for Damage Identification of Solid Concrete Piles Based on Low Strain Reflection Wave Method. Ph.D. Thesis, South China University of Technology, Guangzhou, China, 2018. [Google Scholar]
- Yuan, Q.; Zhou, W.; Zhang, L. Epileptic seizure detection based on imbalanced classification and wavelet packet transform. Seizure
**2017**, 50, 99–108. [Google Scholar] [CrossRef] [PubMed] - Han, J.G.; Ren, W.X.; Sun, Z.S. Wavelet packet based damage identification of beam structures. Int. J. Solids Struct.
**2005**, 42, 6610–6627. [Google Scholar] [CrossRef] [Green Version] - Bettayeb, F.; Haciane, S.; Aoudia, S. Improving the time resolution and signal noise ratio of ultrasonic testing of welds by the wavelet packet. NDT E Int.
**2005**, 38, 478–484. [Google Scholar] [CrossRef] - Yen, G.G.; Lin, K.C. Wavelet packet feature extraction for vibration monitoring. IEEE Trans. Ind. Electron.
**2000**, 47, 650–667. [Google Scholar] [CrossRef] [Green Version] - Schauer, M.; Langer, S. Numerical simulations of pile integrity tests using a coupled FEM SBFEM approach. PAMM
**2012**, 12, 547–548. [Google Scholar] [CrossRef] - Huang, Y.H.; Ni, S.H.; Lo, K.F. Assessment of identifiable defect size in a drilled shaft using sonic echo method: Numerical simulation. Comput. Geotech.
**2010**, 37, 757–768. [Google Scholar] [CrossRef] - Doebling, S.W.; Farrar, C.R.; Prime, M.B. Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in Their Vibration Characteristics: A Literature Review. Available online: https://www.osti.gov/biblio/249299 (accessed on 11 April 2022).
- Liao, S. Nondestructive Testing of Piles. Ph.D. Thesis, The University of Texas at Austin, Austin, TX, USA, 1994. [Google Scholar]
- Kim, H.J.; Mission, J.L.C.; Park, I.S. Analysis of static axial load capacity of single piles and large diameter shafts using nonlinear load transfer curves. KSCE J. Civ. Eng.
**2007**, 11, 285–292. [Google Scholar] [CrossRef] - ABAQUS User’s Manual-Version 6.7; SIMULIA Dassault Systemes: Vélizy-Villacoublay, France, 2007.
- Li, J.B. Numerical Simulation and Application of Elastic Wave Method for Bridge Pile Detection in South Sichuan Intercity Railway. Master’s Thesis, Southwest Jiaotong University, Chengdu, China, 2020. [Google Scholar]
- Ni, S.H.; Lo, K.F.; Lehmann, L. Time–frequency analyses of pile-integrity testing using wavelet transform. Comput. Geotech.
**2008**, 35, 600–607. [Google Scholar] [CrossRef] - Lu, Z.T.; Wang, Z.L.; Liu, D.J. Study on low-strain integrity testing of pipe-pile using the elastodynamic finite integration technique. Int. J. Numer. Anal. Methods Geomech.
**2013**, 37, 536–550. [Google Scholar] [CrossRef] - Cooke, R.W.; Price, G.; Tarr, K. Jacked piles in London clay: Interaction and group behaviour under working conditions. Geotechnique
**1980**, 30, 97–136. [Google Scholar] [CrossRef] - Gschossmann, S.; Oberascher, T.; Schagerl, M. Quantification of subsurface cracks in a thin aluminium beam by the use of nonlinear guided wave theory–a numerical and model-based approach. In Proceedings of the 9th EWSHM, Manchester, UK, 10–13 July 2018; pp. 10–13. [Google Scholar]
- Sun, Y.; Ma, S.; Sun, S. Partial discharge pattern recognition of transformers based on mobilenets convolutional neural network. Appl. Sci.
**2021**, 11, 6984. [Google Scholar] [CrossRef] - Cao, K. Research on pile defects based on low strain reflection wave method. Master’s Thesis, Hebei University, Baoding, China, 2018. [Google Scholar]
- Dozat, T. Incorporating Nesterov Momentum into Adam. Available online: https://openreview.net/pdf?id=OM0jvwB8jIp57ZJjtNEZ (accessed on 11 April 2022).
- Nair, V.; Hinton, G.E. Rectified linear units improve restricted boltzmann machines. In Proceedings of the ICML, Haifa, Israel, 21–24 June 2010. [Google Scholar]
- Zhang, B.; Muradov, K.; Dada, A. Principal component analysis-assisted selection of optimal denoising method for oil well transient data. J. Pet. Explor. Prod.
**2021**, 11, 509–530. [Google Scholar] [CrossRef]

**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