# Defect Detection and Segmentation Framework for Remote Field Eddy Current Sensor Data

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Proposed Approach

#### 2.1. Signal Deconvolution

Algorithm 1: Signal deconvolution |

#### 2.2. Localization of Bell and Spigot Joints

#### 2.2.1. Feature Construction

#### 2.2.2. Classifiers Description

- Naive Bayes Classifiers require the features to be independent and identically distributed. First, a likelihood table is generated for any event by doing a frequency analysis on the training set. A probability of a class ${c}_{i}$ is then obtained by using the Bayes theorem as $p\left({c}_{i}\right|\mathit{f})={\textstyle \frac{p\left({c}_{i}\right)\prod p\left({f}_{j}\right|{c}_{i})}{p\left(\mathit{f}\right)}}$. The class with the maximum probability is then chosen. Naive Bayes classifiers are popular for text classification (e.g., spam filters) and have also been applied for medical diagnosis [15]. It is possible to train the classifier with a closed-form expression [16], which allows training with a linear computational complexity.
- Logistic Regression uses a logistic function—also known as a sigmoid function—defined as $p\left(\mathit{f}\right)={\textstyle \frac{1}{1+{e}^{{\mathit{w}}^{T}\mathit{f}}}}$ to generate a probability. A threshold on the probability is then used to yield a binary classification [17]. Logistic regression is used in many fields, such as medical [18,19] and social sciences [20].
- Random Forests are obtained by training a set of independent decision trees on a set of randomly sampled data. Once these decision trees are trained, a new sample is classified by considering the class which is most often obtained from all the independent decision trees [21]. The utilization of multiple classifiers is referred to as bagging and is used to avoid overfitting [22].
- Support Vector Machine finds the linear decision boundary which maximizes the distance between the closest points of each class—i.e., finds a fat margin—while minimizing the distance between the miss-classified samples and the decision boundary [23]. Additionally, to create a more flexible classification, a kernel trick [24] can be used to bring the features into a higher dimension (in our case the Support Vector Machine (SVM) is using a Radial Basis Functions (RBF) kernel).

#### 2.3. Defect Detection

#### 2.4. Defect Segmentation

#### 2.4.1. Region Growing

Algorithm 2: Region Growing |

#### 2.4.2. Active Contour Segmentation

**Remark (cylindrical space):**The active contour algorithm is designed for 2D matrices. As a result, the regularization term Equation (11) is integrated over the matrix edges. For the cylindrical RFEC data, this problem is overcome by rotating the matrix to be centered on the defect that has to be segmented and then applying the inverse transformation on the segmented data.

Algorithm 3: Active Contour Without Edges |

## 3. Results

#### 3.1. Artificial Dataset

#### 3.2. Real Dataset

#### 3.3. Classifiers Evaluation

#### 3.3.1. K-Fold Cross-Validation

#### 3.3.2. Confusion Matrix and Standard Metrics

#### 3.3.3. ROC Curves

#### 3.4. Signal Deconvolution

#### 3.5. Bell and Spigot Joint Detection

#### 3.6. Defect Detection

#### 3.7. Defect Segmentation

## 4. Discussion and Final Remarks

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Schematic of the RFEC tool considered in this article. The exciter coil generates an electromagnetic field which is expelled outwards from the pipe near the exciter coil—hence the direct field is quickly attenuated. At a remote distance along the axial direction, the remote field flows inwards to the pipe and is measured by an array of receivers.

**Figure 2.**Flowchart of the framework used for the signal segmentation. In (

**a**), the flowchart shows the processing done on the complete dataset; in (

**b**) the flowchart shows the per-pipe analysis performed for each independent pipe sections.

**Figure 3.**While unwrapping the data, the sensor measurements located at the boundary regarding theta are duplicated on the other extremity of the data, to consider the cylindrical properties of the sensor measurement.

**Figure 4.**3D visualization of a part of the artificial pipeline. The artificial pipe segments are linked to each other using the 3D model of a Bell and Spigot joint.

**Figure 5.**(

**a**) Commercial RFEC tool used for the field data collection in this work, courtesy of PICA Corporation, Edmonton, AB, Canada; (

**b**) Pictures of an excavated pipe section with the Bell and Spigot joint visible on the left; (

**c**) Digitalization of a 3D model of the pipe using a laser scanner. The 3D model is then transformed into a 2.5D thickness map.

**Figure 6.**ROC curves of the B&S classification. In (

**a**) the ROC curves show the performance of the classifiers for the artificial dataset and in (

**b**) the ROC curves show the performance of the classifiers on the real dataset. Overall, for both dataset, the SVM classifier outperforms the other classifiers. In (

**a**), the SVM and the random forest classifiers have the same performance.

**Figure 7.**Samples from the signal deconvolution applied to the artificial (left column) and real (right column) dataset. The pipe profile is shown in the first row, the associated RFEC signal is shown in the second row, and the applied signal deconvolution is shown in the last row. For both dataset, darker colors relate to lower thicknesses—the yellow stripes correspond to joints.

**Figure 8.**B&S classification. In (

**a**), the geometry of the artificial pipe is shown with the B&S classification; In (

**b**), the signal is shown with the B&S joint for this dataset.

**Figure 9.**ROC curves of defect classification in real dataset comparing the different classifiers. SVM with an RBF kernel outperforms the other classifiers.

**Figure 10.**Relation between segmentation and classification evaluation. For a label L and a segmentation S, the true positives are defined as the intersection of the label and segmentation or $tp=L\cap S$, the false positives consist of the segmentation absent in the label or $fp=S\backslash L$, the false negatives are the label absent in the segmentation or $fp=L\backslash S$ , and the true negatives are the pixels absent in both the segmentation and label or $tn=\omega -(fp+tp+fn)$.

**Figure 11.**Segmentation on artificial data. Results of the segmentation, with (

**a**–

**d**) the ground truth and the manual segmentation; (

**e**–

**h**) and (

**i**–

**l**) the processed sensor data with (

**e**–

**h**) the region growing segmentation and (

**i**–

**l**) the active contour segmentation—darker colors relate to lower thicknesses.

**Figure 12.**Segmentation on real data. Results of the segmentation, with (

**a**–

**d**) the ground truth and the manual segmentation; (

**e**–

**h**) and (

**i**–

**l**) the processed sensor data with (

**e**–

**h**) the region growing segmentation and (

**i**–

**l**) the active contour segmentation—darker colors relate to lower thicknesses.

Predicted Condition | |||
---|---|---|---|

true | false | ||

true | true | $tp$ | $fn$ |

condition | false | $fp$ | $tn$ |

coef | Precision | Recall | Accuracy | $\mathit{\kappa}$ |
---|---|---|---|---|

SVM | 1.00 | 1.00 | 1.00 | 1.00 |

Random Forest | 1.00 | 1.00 | 1.00 | 1.00 |

Naive Bayes | 0.69 | 0.78 | 0.96 | 0.71 |

Logistic Regression | 0.72 | 0.67 | 0.95 | 0.67 |

**Table 3.**Classifiers’ performances for the real dataset (ranked according to $\kappa $). The threshold for SVM has been chosen in order to have a precision equal to 1. Hence, the other metrics are slightly biased.

coef | Precision | Recall | Accuracy | $\mathit{\kappa}$ |
---|---|---|---|---|

SVM | 1.00 | 0.21 | 0.97 | 0.34 |

Random Forest | 0.70 | 0.42 | 0.97 | 0.51 |

Naive Bayes | 0.06 | 0.86 | 0.49 | 0.04 |

Logistic Regression | 0.21 | 0.01 | 0.93 | 0.01 |

**Table 4.**Classifiers’ performances for defect detection in real dataset (ranked according to $\kappa $).

coef | Precision | Recall | Accuracy | $\mathit{\kappa}$ |
---|---|---|---|---|

SVM | 0.96 | 0.83 | 0.90 | 0.84 |

Random Forest | 0.87 | 0.87 | 0.92 | 0.80 |

Logistic Regression | 0.84 | 0.89 | 0.90 | 0.79 |

Naive Bayes | 0.74 | 0.87 | 0.84 | 0.69 |

Predicted Condition | |||
---|---|---|---|

defects | outliers | ||

true | defects | 298 | 59 |

condition | outliers | 12 | 693 |

**Table 6.**Comparison of the segmentation performance on the artificial dataset (ranked according to $\mathit{F}$-score).

coef | Precision | Recall | Accuracy | F-Score |
---|---|---|---|---|

Region Growing | 0.60 | 0.27 | 0.88 | 0.19 |

Active Contour | 0.77 | 0.69 | 0.99 | 0.66 |

**Table 7.**Comparison of the segmentation performance on the real dataset (ranked according to $\mathit{F}$-score).

coef | Precision | Recall | Accuracy | F-Score |
---|---|---|---|---|

Region Growing | 0.63 | 0.14 | 0.92 | 0.22 |

Active Contour | 0.53 | 0.48 | 0.93 | 0.48 |

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## Share and Cite

**MDPI and ACS Style**

Falque, R.; Vidal-Calleja, T.; Miro, J.V.
Defect Detection and Segmentation Framework for Remote Field Eddy Current Sensor Data. *Sensors* **2017**, *17*, 2276.
https://doi.org/10.3390/s17102276

**AMA Style**

Falque R, Vidal-Calleja T, Miro JV.
Defect Detection and Segmentation Framework for Remote Field Eddy Current Sensor Data. *Sensors*. 2017; 17(10):2276.
https://doi.org/10.3390/s17102276

**Chicago/Turabian Style**

Falque, Raphael, Teresa Vidal-Calleja, and Jaime Valls Miro.
2017. "Defect Detection and Segmentation Framework for Remote Field Eddy Current Sensor Data" *Sensors* 17, no. 10: 2276.
https://doi.org/10.3390/s17102276