# Diversion Detection in Small-Diameter HDPE Pipes Using Guided Waves and Deep Learning

^{*}

## Abstract

**:**

## 1. Introduction

- To propose, design, and test piezoelectric transducer arrays, electronic circuits, signal designing and processing, and DNN models required to develop a DNN-based UGW detection scheme.
- To implement and evaluate a DNN-based UGW detection scheme, for detecting diversions in HDPE pipes.

## 2. System Specifications

## 3. Signal Design and Processing

#### 3.1. Transmitted Signal Design

#### 3.2. Received Signal Processing

## 4. Data Collection

## 5. DNN Architectures

#### 5.1. CNN Based Model

#### 5.2. LSTM Based Models

#### 5.3. CNN-LSTM Based Models

#### 5.4. Multilayer Perceptron

## 6. Experimental Protocol and Results Discussion

#### 6.1. Experimental Protocols

- Accuracy: The accuracy is the percentage of data points that are classified correctly by the algorithm over the total number of data points. Mathematically, the accuracy can be expressed as$$\begin{array}{c}\hfill \mathrm{Accuracy}=\frac{{T}_{P}+{T}_{N}}{{T}_{P}+{F}_{P}+{T}_{N}+{F}_{N}},\end{array}$$
- AUC: The area under the receiver operating characteristic (ROC) curve (AUC) is a metric that measures the ability of a classifier to distinguish between classes across all possible classification thresholds. Therefore, it measures the performance of a model irrespective of the classification threshold.
- Precision: If it is required to evaluate a model only on classifying the positive samples, precision is used. Precision is the ratio of positive samples classified correctly to total positive samples, which can be expressed as$$\begin{array}{c}\hfill \mathrm{Precision}=\frac{{T}_{P}}{{T}_{P}+{F}_{P}},\end{array}$$
- Recall: The recall describes the ratio of correctly classified positive samples over the total number of the positive samples, which is given by$$\begin{array}{c}\hfill \mathrm{Recall}=\frac{{T}_{P}}{{T}_{P}+{F}_{N}},\end{array}$$
- F1-score: F1-score is the harmonic mean of the precision and the recall values, which can be expressed as$$\begin{array}{c}\hfill \mathrm{F}1-\mathrm{score}=2\times \frac{\mathrm{Recall}\times \mathrm{Precision}}{\mathrm{Recall}+\mathrm{Precision}}\end{array}$$

#### 6.2. Discussion of the Results

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Pipe samples: the pipe on the right has a diversion (tee-fitting), whereas the one on the left does not (control pipe).

**Figure 2.**Clamp design: The clamp has a total of eight slots, six of which form a ring where transducers can be placed 60 degrees apart, and two additional slots which are 180 degrees apart for deploying additional transducers. This clamp was modified from the original design in [33].

**Figure 3.**Experimental setup: The designed signal is transmitted via ultrasonic transmitters with the aid of an AWG (arbitrary waveform generator), a DC power supply, and a driving circuit, and received using ultrasonic receivers with the aid of an oscilloscope. Signal processing takes place in a computer.

**Figure 5.**Received signal before and after processing. (

**a**) Raw received signal y[n]. (

**b**) Received signal before and after processing.

**Figure 6.**Correlation envelopes of diversion and control samples. Each sub-figure shows a plot of 40 samples selected randomly from the datasets, in addition to the mean of all samples in the datasets. (

**a**) Diversion samples. (

**b**) Control samples.

**Figure 10.**CNN-LSTM based models’ architectures. (

**a**) CNN-LSTM model. (

**b**) CNN-(2-LSTM) model. (

**c**) (2-CNN)-LSTM model.

**Figure 11.**Training and validation loss and accuracy for different trained models (using 1 Sensor reading. (

**a**) LSTM model. (

**b**) 2 Stacked-LSTM model. (

**c**) CNN model. (

**d**) 2 Stacked-CNN model. (

**e**) CNN-LSTM model. (

**f**) CNN-(2LSTM) model. (

**g**) (2CNN)-LSTM model.

**Figure 12.**Training and validation loss and accuracy for different trained models (Using 2 Sensors’ readings. (

**a**) LSTM model. (

**b**) 2 Stacked-LSTM model. (

**c**) CNN model. (

**d**) 2 Stacked-CNN model. (

**e**) CNN-LSTM model. (

**f**) CNN-(2-LSTM) model. (

**g**) (2-CNN)-LSTM model.

Dataset | Control | Diversion | Total |
---|---|---|---|

Training | 718 | 886 | 1604 |

Validation | 104 | 125 | 229 |

Testing | 184 | 275 | 459 |

Model | Performance Metrics | ||||
---|---|---|---|---|---|

Accuracy | Recall | Precision | F1-Score | AUC | |

LSTM | 0.655 (±0.021) | 0.845 (±0.036) | 0.708 (±0.017) | 0.767 (±0.004) | 0.637 (±0.001) |

2-LSTM | 0.638 (±0.0242) | 0.909 (±0.04) | 0.627 (±0.025) | 0.74 (±0.003) | 0.627 (±0.048) |

CNN | 0.821 (±0.04) | 0.921 (±0.04) | 0.79 (±0.064) | 0.85 (±0.026) | 0.915 (±0.02) |

2-CNN | 0.837 (±0.0167) | 0.89 (±0.036) | 0.83 (±0.038) | 0.85 (±0.01) | 0.92 (±0.009) |

CNN-LSTM | 0.801 (±0.03) | 0.822 (±0.13) | 0.82 (±0.061) | 0.81 (±0.05) | 0.890 (±0.01) |

CNN-(2-LSTM) | 0.822 (±0.04) | 0.77 (±0.12) | 0.91 (±0.05) | 0.82 (±0.06) | 0.920 (±0.006) |

(2-CNN)-LSTM | 0.903 (±0.02) | 0.9014 (±0.06) | 0.905 (±0.04) | 0.921 (±0.025) | 0.926 (±0.006) |

Model | Performance Metrics | ||||
---|---|---|---|---|---|

Accuracy | Recall | Precision | F1-Score | AUC | |

LSTM | 0.544 (±0.037) | 0.817 (±0.291) | 0.58 (±0.150) | 0.61 (±0.104) | 0.562 (±0.067) |

2-LSTM | 0.58 (±0.0182) | 0.891 (±0.197) | 0.64 (±0.121) | 0.71 (±0.064) | 0.6185 (±0.118) |

CNN | 0.991 (±0.007) | 0.9991 (±0.002) | 0.995 (±0.004) | 0.999 (±0.0002) | 0.995 (±0.004) |

2-CNN | 0.997 (±0.003) | 0.997 (±0.003) | 0.998 (±0.003) | 0.998 (±0.002) | 0.997 (±0.0094) |

CNN-LSTM | 0.996 (±0.00065) | 0.992 (±0.007) | 0.998 (±0.001) | 0.999 (±0.0004) | 0.998 (±0.0045) |

CNN-(2-LSTM) | 0.993 (±0.00130) | 0.994 (±0.008) | 0.993 (±0.002) | 0.992 (±0.00098) | 0.994 (±0.0031) |

(2-CNN)-LSTM | 0.996 (±0.001) | 0.998 (±0.006) | 0.998 (±0.0023) | 0.999 (±0.00003) | 0.999 (±0.0023) |

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**MDPI and ACS Style**

Zayat, A.; Obeed, M.; Chaaban, A.
Diversion Detection in Small-Diameter HDPE Pipes Using Guided Waves and Deep Learning. *Sensors* **2022**, *22*, 9586.
https://doi.org/10.3390/s22249586

**AMA Style**

Zayat A, Obeed M, Chaaban A.
Diversion Detection in Small-Diameter HDPE Pipes Using Guided Waves and Deep Learning. *Sensors*. 2022; 22(24):9586.
https://doi.org/10.3390/s22249586

**Chicago/Turabian Style**

Zayat, Abdullah, Mohanad Obeed, and Anas Chaaban.
2022. "Diversion Detection in Small-Diameter HDPE Pipes Using Guided Waves and Deep Learning" *Sensors* 22, no. 24: 9586.
https://doi.org/10.3390/s22249586