# Frequency Optimization for Enhancement of Surface Defect Classification Using the Eddy Current Technique

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Kernel PCA

**x**

_{i}into a feature space

**F**using a nonlinear transformation $\mathsf{\varphi}(\mathit{x})$

**F**are centered, i.e., $\frac{1}{N}{\displaystyle \sum _{i=1}^{N}\mathsf{\varphi}({\mathit{x}}_{i})=0}$, to perform PCA, the covariance matrix

**C**in the space

**F**is calculated by

_{k}and

**v**

_{k}stand for non-zero eigenvalue and eigenvector of the covariance matrix

**C**, respectively.

**K**, respectively.

**K**is that we can cope with $\mathsf{\varphi}({\mathit{x}}_{i})$ of arbitrary dimensionality without having to compute $\mathsf{\varphi}({\mathit{x}}_{i})$ explicitly [36].

#### 2.2. Support Vector Machine

**S**correctly. However, only the optimal hyperplane in canonical form can maximize the margin between the two classes, which is formulated as

_{i}is obtained, the decision function used to classify sampled dataset from sensors is

## 3. Experimental Setup and Specimens

## 4. Results and Discussion

#### 4.1. Effect on Detection Sensitivity

#### 4.2. Effect on the Contrast of Defect Features

#### 4.3. Effect on Classification Accuracy

#### 4.4. Discussions and Limitation

- (1)
- Determine the range of the defects to be identified before inspections;
- (2)
- Manufacture a sample defect with a maximum depth and length;
- (3)
- Observe probe signals when excitation frequency is adjusted continuously until maximum signals are retrieved for the fabricated sample defect;
- (4)
- The optimal frequency should be equal to the frequency corresponding to the observed maximum probe signals.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Fabricated specimens. (

**a**) Sample 1: Defects with different lengths; (

**b**) Sample 2: Defects with different depths.

**Figure 3.**Probe signals due to the defects with different depths. (

**a**) Probe signals of the defect D1; (

**b**) probe signals of the defect D2; (

**c**) probe signals of the defect D3; (

**d**) probe signals of the defect D4; (

**e**) probe signals of the defect D5.

**Figure 4.**Probe signals due to the defects with different lengths: (

**a**) Probe signals due to the defect L1; (

**b**) probe signals due to the defect L2; (

**c**) Probe signals due to the defect L3; (

**d**) Probe signals due to the defect L4; (

**e**) Probe signals due to the defect L5.

**Figure 5.**Defect features under different frequencies. (

**a**) 50 kHz; (

**b**) 150 kHz; (

**c**) 250 kHz; (

**d**) 350 kHz; (

**e**) 450 kHz; (

**f**) 550 kHz; (

**g**) 650 kHz; (

**h**) 750 kHz; (

**i**) 850 kHz.

Defects | Length (mm) | Width (mm) | Depth (mm) | |
---|---|---|---|---|

different lengths (Sample 1) | L1 | 4 | 1 | 2.5 |

L2 | 6 | |||

L3 | 8 | |||

L4 | 10 | |||

L5 | 12 | |||

different depths (Sample 2) | D1 | 20 | 1 | 0.5 |

D2 | 1.0 | |||

D3 | 1.5 | |||

D4 | 2.0 | |||

D5 | 2.5 |

Defect | 50 kHz | 150 kHz | 250 kHz | 350 kHz | 450 kHz | 550 kHz | 650 kHz | 750 kHz | 850 kHz |
---|---|---|---|---|---|---|---|---|---|

D1 | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% |

D2 | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% |

D3 | 80% | 100% | 100% | 100% | 100% | 100% | 90% | 70% | 90% |

D4 | 60% | 70% | 100% | 90% | 100% | 100% | 100% | 80% | 60% |

D5 | 60% | 60% | 100% | 100% | 100% | 100% | 100% | 70% | 70% |

L1 | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% |

L2 | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% |

L3 | 90% | 100% | 100% | 90% | 100% | 100% | 100% | 90% | 80% |

L4 | 60% | 70% | 100% | 100% | 100% | 100% | 100% | 70% | 80% |

L5 | 60% | 60% | 90% | 100% | 100% | 100% | 100% | 60% | 60% |

Total | 88% | 92% | 96% | 100% | 100% | 100% | 96% | 92% | 92% |

Classifier | Accuracy | ||||||||
---|---|---|---|---|---|---|---|---|---|

50 kHz | 150 kHz | 250 kHz | 350 kHz | 450 kHz | 550 kHz | 650 kHz | 750 kHz | 850 kHz | |

PCA-ANN | 90% | 93% | 95% | 96% | 95% | 97% | 94% | 93% | 92% |

PCA-SVM | 88% | 88% | 92% | 96% | 100% | 100% | 96% | 92% | 88% |

KPCA-ANN | 93% | 95% | 97% | 98% | 98% | 98% | 98% | 96% | 95% |

KPCA-SVM | 88% | 92% | 96% | 100% | 100% | 100% | 96% | 92% | 92% |

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**MDPI and ACS Style**

Fan, M.; Wang, Q.; Cao, B.; Ye, B.; Sunny, A.I.; Tian, G.
Frequency Optimization for Enhancement of Surface Defect Classification Using the Eddy Current Technique. *Sensors* **2016**, *16*, 649.
https://doi.org/10.3390/s16050649

**AMA Style**

Fan M, Wang Q, Cao B, Ye B, Sunny AI, Tian G.
Frequency Optimization for Enhancement of Surface Defect Classification Using the Eddy Current Technique. *Sensors*. 2016; 16(5):649.
https://doi.org/10.3390/s16050649

**Chicago/Turabian Style**

Fan, Mengbao, Qi Wang, Binghua Cao, Bo Ye, Ali Imam Sunny, and Guiyun Tian.
2016. "Frequency Optimization for Enhancement of Surface Defect Classification Using the Eddy Current Technique" *Sensors* 16, no. 5: 649.
https://doi.org/10.3390/s16050649