# Multi-Feature Extraction-Based Defect Recognition of Foundation Pile under Layered Soil Condition Using Convolutional Neural Network

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Theoretical Basis of Pile Detection by Low Strain Reflection Wave Method

_{2}/Z

_{1}, impedance Z = ρAC; ρ is the pile density; A represents the pile’s cross-sectional area; $\mathrm{C}=\sqrt{\mathrm{E}/\mathsf{\rho}}$ is the velocity of stress wave transmission in the pile body.

#### 2.2. Numerical Simulation of Dynamic Test of Foundation Pile in Layered Soil

#### 2.2.1. Basic Theory and Model Establishment

_{s}, and the contact between the pile bottom and the soil at the pile bottom is set as the binding constraint [29].

_{d}and I represent the exciting force’s pulse and sufficient time, correspondingly in the formula. Taking T

_{d}= 0.2 ms, t = 0.1 ms, p(t) = 1 N into the formula 3, I = 0.0001 N·s can be obtained. It is writable as p(t) = 0.5(1-cos10,000 πt), the 40 sections of the hammering times T

_{d}, and the curve of the time change of the unit hammering load is obtained as shown in Figure 2. Loading under the load module, inputting the unit force amplitude curve and magnitude input 2.0 × 10

^{7}can realize loading.

_{d}× C)/10 = 0.07 m [31]. The specific mesh size needs to be divided based on a trial calculation to guarantee the calculation’s precision. The basic principle is that the calculated velocity–time curve does not change significantly with the expansion of the boundary. After trial calculation, the mesh size of soil around the pile is divided into 0.07 m, and the pile’s mesh size is 0.02 m. The element type is the C3D8R (3D 8-node reduced integral element). This type of element is often used because it is easy to converge in finite element simulation [32]. Figure 3 depicts the results of the mesh model pile and soil division.

#### 2.2.2. Finite Element Model (FEM) of Pile

#### 2.3. Experimental Verification

#### 2.4. Multi-Feature Extraction of Pile Dynamic Signal

#### 2.4.1. Time Domain Feature Extraction

#### 2.4.2. Frequency Domain Feature Extraction

_{k}corresponds to the frequency value at which y = [y

_{1},y

_{2},y

_{3},…y

_{M}] reflects the absolute amount of frequency, and N denotes the duration of the signal. M = N/2 denotes the length of the spectra, and Table 7 displays the typical frequency domain feature characteristics.

#### 2.4.3. ICEEMDAN Decomposition Sample Entropy and Information Entropy Feature Extraction

^{(i)}is i construction signal; β

_{0}denotes the standard error of the noise at the first decomposition of the signal; w

^{(i}

^{)}is the ith added zero-mean unit-variance white noise; E

_{1}(·) is the first IMF operator to calculate the signal.

^{(i)}, the local mean is calculated and averaged to obtain the first residual component:

_{1}(·) is an average local function.

_{1}:

_{k-1}from the residual r

_{k}:

_{1},x

_{2},…,x

_{N}} see below for details:

^{m}(k) and X

^{m}(s) is defined as, i.e., the maximum absolute value of the two corresponding elements’ differences. The expression is:

^{(d}

^{<r)}, and C

^{m}(r) can be defined as:

^{m}(r), denoted as ${\overline{C}}^{m}(r)$;

_{1}, x

_{2},…, x

_{n}} the probabilities of X are denoted as p

_{i}= P(xi) ( i = 1,2,…, n ), while the likelihood distribution fulfills Equation (14), the function is described as in Equation (15).

#### 2.4.4. Feature Set Construction

#### 2.5. Pile Defect Recognition Based on Multi-Feature Extraction and CNN

#### 2.5.1. Convolutional Neural Network (CNN)

#### 2.5.2. Construction of Pile Foundation Defect Recognition Network Using Multi-Feature Extraction and Convolutional Neural Network (CNN)

## 3. Results and Discussion

#### 3.1. CNN Pile Defect Recognition

#### 3.2. CNN Recognition Results for Different Domain Features

#### 3.3. Probabilistic Neural Network (PNN) Pile defect Identification

_{ai}is the ith training vector of the defect pattern, m is the training sample quantity of the defective pattern, and the δ smoothing parameter.

## 4. Conclusions and Future Work

- (1)
- When the ICEEMDAN technique is utilized to decompose reflected wave signals from foundation piles under paved soil conditions, it lays the foundation for the accuracy of CNN identification. The correlation coefficient criterion filters the valuable components, removing the redundant components.
- (2)
- The convolutional neural network was used to classify and identify each group, and the feature sets extracted from the three dimensions were fed into the network with an accuracy of more than 90%, proving the excellent reliability of the CNN model for the detection of the foundation pile problem.
- (3)
- When single-domain features for foundation pile recognition were fed into the CNN model, the results were 88.89% for time domain features, 77.22% for frequency domain features, and 86.11% for time–frequency domain features. The accuracy of the multi-feature extraction method in conjunction with CNN is 97.8%. This method has high accuracy and effectively distinguishes the kind of foundation pile when the soil surrounding the pile is stratified, increasing the inspectors’ effectiveness.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**Model dynamic test results: (

**a**) 1# model pile; (

**b**) 2# model pile; (

**c**) 3# model pile; (

**d**) 4# model pile; (

**e**) 5# model pile.

**Figure 7.**Pile models: (

**a**) 1# complete pile, 2# diameter expanding pile, 3# diameter shrinkage pile, 4# segregation pile, and 5# broken pile; (

**b**) Placement of model pile.

**Figure 9.**Comparison of finite element simulation results and experimental results: (

**a**) 1# model pile; (

**b**) 2# model pile; (

**c**) 3# model pile; (

**d**) 4# model pile; (

**e**) 5# model pile.

**Figure 10.**ICEEMDAN decomposition of reflective wave signal of complete pile: (

**a**) Soil boundary position near pile tip; (

**b**) Soil boundary position near pile base.

**Figure 11.**Correlation analysis variation tendency: (

**a**) Complete pile dynamic signal ICEEMDAN decomposition; (

**b**) Diameter expanding piles dynamic signal ICEEMDAN decomposition; (

**c**) Diameter shrinkage piles dynamic signal ICEEMDAN decomposition; (

**d**) Segregation pile dynamic signal ICEEMDAN decomposition; (

**e**) Pile breaking dynamic signal ICEEMDAN decomposition.

Part | Elastic Modulus E(GPa) | Density ρ(kg/m^{3}) | Poisson Ratio ν | Friction Coefficient fs |
---|---|---|---|---|

pile | 30 | 2400 | 0.17 | - |

soil layer 1 | 0.015 | 1930 | 0.32 | 0.5 |

soil layer 2 | 10 | 2250 | 0.25 | 0.6 |

segregation part | 15 | 2000 | 0.23 | - |

breakdown part | 1.293 | 0 | 0 | - |

Pile Number | The Scenario of the Soil around Pile | |||
---|---|---|---|---|

Elastic Modulus E (Pa) | Density ρ (kg/m^{3}) | Poisson Ratio ν | Elastic Modulus E (Pa) | |

1# | 1 × 10^{10} | 2250 | 0.25 | 0–0.3 |

0.015 × 10^{9} | 1930 | 0.32 | 0.3–1.5 | |

2# | 1 × 10^{10} | 2250 | 0.25 | 0–0.3 |

0.015 × 10^{9} | 1930 | 0.32 | 0.3–1.5 | |

3# | 1 × 10^{10} | 2250 | 0.25 | 0–0.3 |

0.015 × 10^{9} | 1930 | 0.32 | 0.3–1.5 | |

4# | 0.015 × 10^{9} | 1930 | 0.32 | 0–0.7 |

1 × 10^{10} | 2250 | 0.25 | 0.7–1.5 | |

5# | 0.015 × 10^{9} | 1930 | 0.32 | 0–0.7 |

1 × 10^{10} | 2250 | 0.25 | 0.7–1.5 |

Pile Number | Length of the Piles (m) | Soil Boundary Position (m) | Defect Position (m) |
---|---|---|---|

1# | 1.06 | 0.33 | - |

2# | 1.05 | 0.30 | 0.45–0.57 |

3# | 1.07 | 0.33 | 0.46–0.58 |

4# | 1.02 | 0.74 | 0.47–0.58 |

5# | 0.99 | 0.70 | 0.48 |

Material | Elastic Modulus E (Pa) | Density ρ (kg/m^{3}) | Poisson Ratio ν |
---|---|---|---|

C30 concrete | 3.0 × 10^{10} | 2400 | 0.17 |

C15 concrete | 1.5 × 10^{6} | 2400 | 0.2 |

soil layer 1 | 1 × 10^{10} | 2250 | 0.25 |

soil layer 2 | 0.015 × 10^{9} | 1930 | 0.32 |

Pile Number | Length of the Piles (m) | Soil Boundary Position (m) | Defect Position (m) |
---|---|---|---|

1# | 0.95 | 0.32 | - |

2# | 0.97 | 0.26 | 0.44–0.54 |

3# | 0.97 | 0.28 | 0.44–0.55 |

4# | 0.97 | 0.73 | 0.42–0.53 |

5# | 0.97 | 0.77 | 0.47 |

Characteristic Index | Expression |
---|---|

average value | $\overline{x}=\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{x}_{i}}$ |

mean square value | $x=\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{x}_{i}^{2}}$ |

variance | ${x}_{{\sigma}^{2}}=\frac{1}{N}{\displaystyle \sum _{i=1}^{N}({x}_{i}-}\overline{x}{)}^{2}$ |

root mean square value | ${x}_{rms}=\sqrt{\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{x}_{i}^{2}}}$ |

skewness | $\alpha =\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{x}_{i}^{3}}$ |

skewness factor | ${x}_{\alpha}=\frac{\alpha}{{x}_{rms}^{3}}$ |

kurtosis | $k=\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{x}_{i}^{4}}$ |

kurtosis factor | ${x}_{k}=\frac{k}{{x}_{rms}^{4}}$ |

Characteristic Index | Expression |
---|---|

mean frequency | ${F}_{mean}={\displaystyle \sum _{K=1}^{M}\frac{{y}_{K}}{M}}$ |

frequency center | ${F}_{c}={\displaystyle \sum _{k=1}^{M}\frac{{y}_{k}{f}_{k}}{\sqrt{{y}_{k}}}}$ |

root mean square frequency | ${F}_{rms}=\sqrt{\frac{{\displaystyle \sum _{k=1}^{M}{y}_{k}^{2}}}{M}}$ |

standard deviation frequency | ${F}_{std}=\sqrt{\frac{{\displaystyle \sum _{k=1}^{M}{\left({y}_{k}-{F}_{\mathrm{mean}}\right)}^{2}}}{M}}$ |

Scenarios | Time Domain | Frequency Domain | Time and Frequency Domain- Sample Entropy | Time and Frequency Domain- Information Entropy | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

$\overline{\mathit{x}}$ | x | x_{σ2} | x_{α} | x_{k} | F_{mean} | F_{c} | F_{rms} | F_{std} | IMF3 | IMF4 | IMF5 | IMF6 | IMF3 | IMF4 | IMF5 | IMF6 | |

1—G | 1.82 × 10^{−5} | 5.39 × 10^{−6} | 3.81 × 10^{−6} | 6.12 × 10^{−2} | 1 | 0 | 3.16 × 10^{−3} | 3.96 × 10^{−3} | 2.39 × 10^{−3} | 7.18 × 10^{−8} | 2.57 × 10^{−6} | 1.19 × 10^{−6} | 2.51 × 10^{−6} | 6.96 × 10^{−5} | 6.95 × 10^{−5} | 6.95 × 10^{−5} | 6.94 × 10^{−5} |

H—2 | 1.11 × 10^{−5} | 2.80 × 10^{−6} | 1.95 × 10^{−6} | 5.44 × 10^{−2} | 1 | 0 | 2.08 × 10^{−3} | 2.64 × 10^{−3} | 1.61 × 10^{−3} | 4.87 × 10^{−8} | 8.06 × 10^{−7} | 4.28 × 10^{−7} | 1.49 × 10^{−6} | 4.84 × 10^{−5} | 4.84 × 10^{−5} | 4.84 × 10^{−5} | 4.84 × 10^{−5} |

2—I | 2.25 × 10^{−5} | 7.03 × 10^{−6} | 5.04 × 10^{−6} | 6.25 × 10^{−2} | 1 | 0 | 4.16 × 10^{−3} | 5.92 × 10^{−3} | 4.21 × 10^{−3} | 1.65 × 10^{−6} | 6.10 × 10^{−6} | 1.45 × 10^{−6} | 2.31 × 10^{−6} | 1.19 × 10^{−4} | 1.19 × 10^{−4} | 1.19 × 10^{−4} | 1.19 × 10^{−4} |

H—3 | 2.97 × 10^{−5} | 1.00 × 10^{−5} | 7.29 × 10^{−6} | 6.56 × 10^{−2} | 1 | 0 | 4.91 × 10^{−3} | 6.02 × 10^{−3} | 3.49 × 10^{−3} | 4.85 × 10^{−8} | 1.15 × 10^{−5} | 9.23 × 10^{−7} | 2.48 × 10^{−6} | 1.52 × 10^{−4} | 1.51 × 10^{−4} | 1.52 × 10^{−4} | 1.52 × 10^{−4} |

3—I | 2.35 × 10^{−5} | 7.52 × 10^{−6} | 5.50 × 10^{−6} | 6.23 × 10^{−2} | 1 | 0 | 4.29 × 10^{−3} | 5.60 × 10^{−3} | 3.60 × 10^{−3} | 1.27 × 10^{−7} | 5.11 × 10^{−6} | 1.67 × 10^{−6} | 3.30 × 10^{−6} | 9.82 × 10^{−5} | 9.80 × 10^{−5} | 9.77 × 10^{−5} | 9.74 × 10^{−5} |

H—4 | 3.81 × 10^{−5} | 1.25 × 10^{−5} | 8.55 × 10^{−6} | 6.77 × 10^{−2} | 1 | 0 | 5.43 × 10^{−3} | 6.83 × 10^{−3} | 4.15 × 10^{−3} | 1.30 × 10^{−7} | 8.43 × 10^{−6} | 6.10 × 10^{−6} | 3.76 × 10^{−6} | 1.77 × 10^{−4} | 1.76 × 10^{−4} | 1.77 × 10^{−4} | 1.77 × 10^{−4} |

4—I | 3.19 × 10^{−5} | 1.15 × 10^{−5} | 8.56 × 10^{−6} | 6.36 × 10^{−2} | 1 | 0 | 5.44 × 10^{−3} | 6.88 × 10^{−3} | 4.21 × 10^{−3} | 1.14 × 10^{−7} | 1.41 × 10^{−5} | 3.25 × 10^{−6} | 4.82 × 10^{−7} | 1.52 × 10^{−4} | 1.52 × 10^{−4} | 1.52 × 10^{−4} | 1.52 × 10^{−4} |

H—5 | 2.44 × 10^{−4} | 9.94 × 10^{−5} | 6.12 × 10^{−5} | 9.69 × 10^{−2} | 1 | 0 | 2.15 × 10^{−2} | 2.79 × 10^{−2} | 1.79 × 10^{−2} | 5.52 × 10^{−7} | 5.17 × 10^{−5} | 6.30 × 10^{−5} | 6.53 × 10^{−6} | 8.15 × 10^{−4} | 8.14 × 10^{−4} | 8.14 × 10^{−4} | 8.14 × 10^{−4} |

5—I | 5.56 × 10^{−4} | 2.27 × 10^{−4} | 1.20 × 10^{−4} | 9.43 × 10^{−2} | 1 | 4.42 × 10^{−7} | 3.85 × 10^{−2} | 5.13 × 10^{−2} | 3.38 × 10^{−2} | 0 | 1.24 × 10^{−4} | 1.51 × 10^{−4} | 1.29 × 10^{−5} | 8.07 × 10^{−4} | 8.28 × 10^{−4} | 8.49 × 10^{−4} | 8.71 × 10^{−4} |

Label | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

Scenarios | 1-G | H-2 | 2-I | H-3 | 3-I | H-4 | 4-I | H-5 | 5-I |

CNN | Accuracy (%) | |||
---|---|---|---|---|

Time Domain | Frequency Domain | Time–Frequency Domain | Multi-Domain | |

Train | 89.00 | 81.89 | 88.56 | 98.67 |

Validation | 87.50 | 80.28 | 86.67 | 98.33 |

Test | 88.89 | 77.22 | 86.11 | 97.80 |

Scenarios | Number of Test Samples | Correct Recognition Number | Accuracy |
---|---|---|---|

1-G | 40 | 60 | 45.5% |

H-2 | 40 | 1 | 2.5% |

2-I | 40 | 9 | 25.0% |

H-3 | 40 | 0 | 0 |

3-I | 40 | 0 | 0% |

H-4 | 40 | 0 | 0% |

4-I | 40 | 0 | 0% |

H-5 | 40 | 33 | 84.6% |

5-I | 40 | 0 | 0% |

Average accuracy 28.6% |

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## Share and Cite

**MDPI and ACS Style**

Wu, C.-S.; Hao, T.-Q.; Qi, L.-L.; Zhuo, D.-B.; Feng, Z.-Y.; Zhang, J.-Q.; Peng, Y.-X. Multi-Feature Extraction-Based Defect Recognition of Foundation Pile under Layered Soil Condition Using Convolutional Neural Network. *Appl. Sci.* **2022**, *12*, 9840.
https://doi.org/10.3390/app12199840

**AMA Style**

Wu C-S, Hao T-Q, Qi L-L, Zhuo D-B, Feng Z-Y, Zhang J-Q, Peng Y-X. Multi-Feature Extraction-Based Defect Recognition of Foundation Pile under Layered Soil Condition Using Convolutional Neural Network. *Applied Sciences*. 2022; 12(19):9840.
https://doi.org/10.3390/app12199840

**Chicago/Turabian Style**

Wu, Chuan-Sheng, Tian-Qi Hao, Ling-Ling Qi, De-Bing Zhuo, Zhen-Yang Feng, Jian-Qiang Zhang, and Yang-Xia Peng. 2022. "Multi-Feature Extraction-Based Defect Recognition of Foundation Pile under Layered Soil Condition Using Convolutional Neural Network" *Applied Sciences* 12, no. 19: 9840.
https://doi.org/10.3390/app12199840