# A Novel Attention Temporal Convolutional Network for Transmission Line Fault Diagnosis via Comprehensive Feature Extraction

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## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

#### 2.1. The Short Circuit Faults of Transmission Line

#### 2.2. The Basic PCA Method

**X**is scaled according to the normal operation dataset, the covariance

**S**of the dataset

**X**is first computed.

**D**represents a diagonal matrix, whose diagonal contains the decreasing order eigenvalues ${\tilde{\lambda}}_{1}>{\tilde{\lambda}}_{2}>\dots >{\tilde{\lambda}}_{rank(X)}$ of the matrix

**S**. The l eigenvectors ${\tilde{p}}_{1},{\tilde{p}}_{2},\dots ,{\tilde{p}}_{l}$ related to the first l largest eigenvalues ${\tilde{\lambda}}_{1}>{\tilde{\lambda}}_{2}>\dots >{\tilde{\lambda}}_{l}$ are retained to construct the loading matrix $\tilde{P}=[{\tilde{p}}_{1},{\tilde{p}}_{2},\dots ,{\tilde{p}}_{l}]\in {R}^{m\times l}$.

**X**is mapped into the PC and residual spaces.

**T**indicates the score matrix $T=[{t}_{1},{t}_{2},\cdots ,{t}_{l}]$ and ${t}_{i}\in {R}^{n}$ is the i-th score vector. Note that the vector ${\tilde{p}}_{i}$ is also called the i-th loading vector and $l$ also represents the principal component (PC) number retained in the principal space.

**E**in residual space is computed as

#### 2.3. The Basic Temporal Convolutional Network

## 3. The Developed CFP-Based Feature Extraction Technique

**X**is first scaled by subtracting its mean and dividing its standard deviation. Based on the normalized matrix

**X**, the PCA model seeks a loading vector

**p,**which can guarantee that the distance among all the samples in the PC space is maximized.

**X**, the local structure-preserving framework is combined with the PCA model in our work.

**W**is determined as:

**W**can represent the local neighbor relations of the training matrix

**X**.

**p**to hold the local neighbor relations of the training matrix

**X**by minimizing the distances of neighbor samples in the PC space.

**D**is a diagonal matrix with the i-th element as ${D}_{ii}={\displaystyle \sum _{j=1}^{{n}_{s}}{W}_{ji}},i=1,2,\cdots ,{n}_{s}$.

**p**, which simultaneously maximizes the PCA’s objective function and minimizes the optimization of the local structure-preserving framework.

**P**of the CFP is built by retaining these d eigenvectors $P=[{p}_{1},{p}_{2},\cdots ,{p}_{d}]\in {R}^{n\times d}$. These loading vectors are mutually orthogonal, which can effectively improve the discriminative ability of the CFP-based dimension reduction method when extracting the global and local structure features of original data.

**P**, the training matrix

**X**is decomposed by the suggested CFP model.

**X**. Thereafter, the built CFP is applied to extract the global and local structure features of the snapshot dataset ${X}_{F}$ and the historical fault datasets. To gain improved fault diagnosis effectiveness, these exploited global and local structure features are regarded as the input of the subsequently developed recognition model.

## 4. The Enhanced Attention TCN-Based Fault Diagnosis Model

#### 4.1. The Established SCA Network

**value**,

**query**and

**key**are derived from the imported global and local structure features extracted by the CFP by means of the three respective input layers. As exhibited in Figure 2, the input layers contain two fully connected layers to exploit the important interrelations between the input features and the three intermediate vectors. In addition, the fully connected layers are able to ensure that the input and output have the same dimension. That is, the dimension of the input global and local structure features is equal to that of the three intermediate vectors. Specifically, based on the matrices

**V**,

**Q**and

**K**of the three intermediate vectors, the output of the constructed SCA network is formulated as

**F**

_{score}denotes the attention scores calculated by the softmax layer in the SCA network.

**query**’s element q

_{i}with the elements in the vector

**key**. In this way, the score matrix can be achieved by repeating the above multiplication operation. Then, the vector

**c**’s element ${o}_{i}$ is worked out by multiplying the vector

**score**with the vector

**value**. Note that the vector

**score**’s elements denote the attention paid to the homologous elements in the vector

**value**, and the summation of these elements is equal to one.

**output**, the residual output vector

**output**

_{res}is further derived by superposing the vector

**input**on the vector

**output**, i.e., $outpu{t}_{res}=input+output$. The added skip connection can ensure the vector’s

**input**and

**output**

_{res}have the same data dimension by means of indirectly merging the data in channels.

#### 4.2. The Developed EATCN Fault Diagnosis Model Based on the SCA Network

**x**with n elements, the dilated convolution operation is expressed as

## 5. The EATCN-Based Fault Diagnosis Scheme for the Transmission Line

**X**, the developed CFP model is first established by infusing the local structure-preserving in the PCA model, and then the built CFP model is employed to extract the global and local structure features of the C class historical fault datasets. The skip connection structure and two fully connected layers are subsequently merged into the existing attention mechanism to establish a new SCA network, and the EATCN-based diagnosis model is set up through incorporating the suggested SCA network with each residual block in the conventional TCN model. Finally, the mined historical global and local structure features are imported into the EATCN network to train the fault diagnosis model. In the fault diagnosis stage, the constructed CFP is first adopted to exploit the global and local structure features of the fault snapshot dataset ${X}_{F}$, and the trained EATCN is applied to classify the extracted global and local structure features to recognize the pattern of the snapshot dataset ${X}_{F}$. Due to EATCN’s virtue of paying more attention to the exploited structure features, which are difficult to classify, the pattern of the snapshot dataset can be effectively and accurately identified.

## 6. The Experiments and Comparisons

#### 6.1. Introduction of the Experimental Data

**V**

_{7}to

**V**

_{8}and the region from

**V**

_{8}to

**V**

_{9}.

#### 6.2. Compared Approaches and Effectiveness Evaluation Index

#### 6.3. Comparison of the Fault Diagnosis Results

- (1)
- Fault diagnosis results comparison for the pattern ABC

**S**

_{ABC}of the short circuit fault ABC is gathered, the index FDR’s values of SVM, DBN, LSTM and EATCN for the dataset

**S**

_{ACG}are computed as 64.25%, 71.75%, 79.00% and 93.50%. It is observed that the SVM displays the worst fault identification effect, while the DBN and LSTM have better index values for FDR, i.e., 71.75% and 79.00%, which still needs to be enhanced. Different from SVM, DBN and LSTM, EATCN gains the best recognition capability for the dataset

**S**

_{ABC}with the largest value of the index FDR, i.e., 93.50%. This is due to EATCN’s outstanding performance in exploiting and classifying the global and local structure features contained in the running data of the transmission line. Again, the histogram of the fault identification results for these four fault diagnosis models is illustrated in Figure 8, which clearly reveals that the diagnosis effectiveness of the discussed EATCN is much better than that of the SVM, DBN and LSTM for discerning the fault pattern ABC.

- (2)
- Fault diagnosis results comparison for the pattern BC

**S**

_{BC}. Compared with the LSTM and EATCN, the DBN and SVM exhibit a much more unsatisfied fault identification effect to diagnose the fault pattern BC. On the contrary, LSTM reveals the improved diagnosis effect because LSTM’s index FDR value is 81.75%. In the end, the EATCN reveals the best fault recognition effect as its FDR value is 92.50%. To make a more vivid comparison, the values of the index FDR for the SVM, DBN, LSTM and EATCN are plotted in the histogram in Figure 9. According to the above analysis, the advantage of the EATCN is fully certified over the LSTM, DBN and SVM when identifying the pattern BC.

- (3)
- Fault diagnosis results comparison for the pattern ABG

**S**

_{ABG}is constructed, the SVM-, DBN-, LSTM- and EATCN-based fault diagnosis models are employed to identify the pattern of short circuit fault ABG by computing the performance index FDR. To be specific, the values of the index FDR for the SVM, DBN, LSTM and EATCN are, respectively, 71.50%, 83.50%, 87.25% and 94.25%, which proves that the EATCN possesses the highest value of the index FDR among these four fault diagnosis models. To make a more visualized analysis, the four different FDR values are further represented by a bar chart in Figure 10. In this way, it can be concluded that the EATCN-based diagnosis model outperforms the LSTM, DBN and SVM in terms of recognizing the fault pattern ABG.

- (4)
- Fault diagnosis results comparison for the eleven patterns

_{average}for the four diagnosis models on the eleven fault patterns are also exhibited in Table 2. From Table 2, the values of the index FDR

_{average}for the SVM, DBN, LSTM and EATCN are, respectively, computed as 73.68%, 80.75%, 86.64% and 94.98%. Thus, the EATCN-based identification approach demonstrates the largest value of the index FDR

_{average}for all eleven fault patterns among the four approaches, which testifies to the superiority of the EATCN’s overall fault recognition effectiveness. Furthermore, in comparison with the SVM, DBN and LSTM, the suggested EATCN also exhibits more remarkable diagnosis performance to discern the particular fault of the eleven fault patterns. For example, the index FDR’s value of the fault pattern AB is 94.75% for the EATCN, in contrast to only 85.50% for the LSTM, 79.25% for the DBN and 70.50% for the SVM. Analogously, the value of the index FDR for the fault pattern ABCG is 97.25% for the EATCN, in comparison with only 89.25% for the LSTM, 84.25% for the DBN and even 80.00% for the SVM. It can be concluded that the presented EATCN approach is excellent at recognizing the short circuit fault patterns of the transmission line. This is because the global and local structure features extracted by the EATCN promote an improvement in the transmission line’s fault identification task. To facilitate further visualized analysis, the values of the index FDR for the four algorithms under the eleven fault patterns are plotted in a histogram in Figure 13, which also proves the outstanding recognition performance of the EATCN over the SVM, DBN and LSTM for discerning all eleven short circuit faults.

_{average}for the four diagnosis models are also exhibited in Table 3. From Table 3, the values of the index P

_{average}for the SVM, DBN, LSTM and EATCN are, respectively, computed as 73.71%, 80.77%, 86.68% and 95.01%. Thus, the EATCN-based identification approach demonstrates the largest value of the index P

_{average}for all eleven fault patterns, which testifies to the superiority of the EATCN’s overall fault recognition effectiveness. In comparison with the SVM, DBN and LSTM, the suggested EATCN displays a more remarkable diagnosis performance to discern the particular fault of the eleven fault patterns. For example, the index’s precision value of the fault pattern ACG is 94.27% for the EATCN, in contrast to only 89.95% for the DBN, 84.92% for the LSTM and 82.03% for the SVM. Analogously, the value of the index precision for the fault pattern AB is 93.81% for the EATCN, in comparison with only 85.71% for the LSTM, 81.28% for the DBN and 75.40% for the SVM. It can be concluded that the presented EATCN is excellent at recognizing the short circuit fault patterns of the transmission line.

#### 6.4. Fault Diagnosis Effects of the Proposed EATCN under Different Noise Environments

_{average}values, while Table 5 exhibits the EATCN’s indices P and P

_{average}values for the eleven fault patterns, with the noise variance varying from 0.1 to 0.0001. When the value of noise variance is 0.1, which is the largest in our experiment, the EATCN achieves the worst fault diagnosis performance as the values of the FDR

_{average}and P

_{average}are both the smallest, i.e., 92.23% and 92.61%, respectively. However, the EATCN’s values of FDR

_{average}and P

_{average}at the largest noise variance environment can be acceptable because they are both above 92.00%. With the decrement in the noise variance, the EATCN’s fault diagnosis effect becomes better and better. But, when the noise variance decreases from 0.001 to 0.0001, the diagnosis effectiveness of the EATCN improves slightly because the FDR

_{average}only varies from 96.55% to 97.20% and the P

_{average}only increases from 96.71% to 97.55%. Based on the above analysis, the developed EATCN shows outstanding accuracy and robustness under different noise environments.

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

PCA | principal component analysis |

LSP | local structure-preserving |

CFP | comprehensive feature preserving |

TCN | temporal convolutional network |

SCA | skip connection attention |

EATCN | enhanced feature extraction-based attention TCN |

CNN | convolutional neural network |

LSTM | long short-term memory |

VRF | variable refrigerant flow |

LG | line to ground |

LL | double lines (line-to-line) |

LLG | double lines to ground |

LLL | triple lines |

LLLG | triple lines to ground |

PC | principal component |

GRU | gate recurrent unit |

ReLU | rectified linear unit |

LSP | local structure-preserving |

ATCN | attention temporal convolutional network |

NF | no fault (normal operation) |

AG | short fault of line a to ground |

BG | short fault of line b to ground |

CG | short fault of line c to ground |

AB | short fault of line a to line b |

BC | short fault of line b to line c |

AC | short fault of line a to line c |

ABG | short fault of line a and line b to ground |

BCG | short fault of line b and line c to ground |

ACG | short fault of line a and line c to ground |

ABC | short fault of line a, line b and line c |

ABCG | short fault of line a, line b and line c to ground |

SVM | support vector machine |

DBN | deep belief network |

X | original high-dimensional dataset |

$x(i)$ | the i-th sample of the matrix X |

$\overline{x}$ | mean value of the samples |

$x(j)$ | nearest neighbors of the $x(i)$ |

${X}_{\mathrm{sub}}(i)$ | local neighborhood dataset subset of the $x(i)$ |

$n$ | the number of samples |

$m$ | the number of measured variables |

S | covariance of the datasets of the PCA |

D | diagonal matrix of the PCA |

$\tilde{P}$ | loading matrix of the PCA |

T | score matrix of the PCA |

${t}_{i}$ | the i-th score vector of the matrix T |

$l$ | the number of retained leading vectors of the PCA |

E | residual matrix in PCA’s the residual space |

F(n) | convolution computation of the input vector’s n-th element |

${x}_{t}$ | input vector of the TCN |

q | filter with the size of k |

d | dilation coefficient |

p | loading vector of the CFP |

W | similarity matrix of the LSP |

${W}_{ij}$ | element of the similarity matrix W |

$w\{x(i),x(j)\}$ | neighborhood relationship between the samples $x(i)$ and $x(j)$ |

$L$ | Laplacian matrix of the LSP |

$J{(p)}_{PCA}$ | objective function of the PCA |

$J{(p)}_{LSP}$ | objective function of the LSP |

$J{(p)}_{CFP}$ | objective function of the CFP |

$\eta $ | tradeoff parameter of the CFP |

${\lambda}_{1},{\lambda}_{2},\cdots ,{\lambda}_{d}$ | first d largest eigenvalues of the CFP |

${p}_{1},{p}_{2},\cdots ,{p}_{d}$ | eigenvectors of related to ${\lambda}_{1},{\lambda}_{2},\cdots ,{\lambda}_{d}$ in the CFP |

P | loading vector of the CFP |

$Y$ | score matrix of the CFP |

$\tilde{X}$ | residual matrix of the CFP |

${x}_{F}$ | fault sample |

${y}_{F}$ | latent significant features |

${X}_{F}$ | snapshot dataset |

V | value vector of the SCA |

K | key vector of the SCA |

Q | query vector of the SCA |

F_{score} | attention scores of the SCA |

$FDR(i)$ | fault diagnosis rate of the i-th fault pattern |

$FD{R}_{\mathrm{average}}$ | average fault diagnosis rate |

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**Figure 11.**The confusion matrices of the SVM, DBN, LSTM and EATCN. (

**a**) The confusion matrix of the SVM. (

**b**) The confusion matrix of the DBN. (

**c**) The confusion matrix of the LSTM. (

**d**) The confusion matrix of the EATCN. The orange block is darker, the percentages of fault samples is more.

**Figure 13.**The identification results of the SVM, DBN, LSTM and EATCN for the eleven fault patterns.

Number | Fault Pattern | Fault Description |
---|---|---|

0 | NF | No fault (normal operation) |

1 | AG | Short fault of line A to ground |

2 | BG | Short fault of line B to ground |

3 | CG | Short fault of line C to ground |

4 | AB | Short fault of line A to line B |

5 | BC | Short fault of line B to line C |

6 | AC | Short fault of line A to line C |

7 | ABG | Short fault of line A and line B to ground |

8 | BCG | Short fault of line B and line C to ground |

9 | ACG | Short fault of line A and line C to ground |

10 | ABC | Short fault of line A, line B and Line C |

11 | ABCG | Short fault of line A, line B and Line C to ground |

Fault Pattern | SVM | DBN | LSTM | EATCN |
---|---|---|---|---|

AG | 75.50% | 82.75% | 86.50% | 93.25% |

BG | 81.50% | 85.00% | 87.25% | 95.00% |

CG | 61.75% | 82.00% | 90.75% | 96.25% |

AB | 70.50% | 79.25% | 85.50% | 94.75% |

BC | 76.50% | 70.75% | 81.75% | 92.50% |

AC | 72.25% | 80.00% | 85.50% | 93.75% |

ABG | 71.50% | 83.50% | 87.25% | 94.25% |

BCG | 75.75% | 81.75% | 88.75% | 95.50% |

ACG | 81.00% | 87.25% | 91.50% | 98.75% |

ABC | 64.25% | 71.75% | 79.00% | 93.50% |

ABCG | 80.00% | 84.25% | 89.25% | 97.25% |

FDR_{average} | 73.68% | 80.75% | 86.64% | 94.98% |

Fault Pattern | SVM | DBN | LSTM | EATCN |
---|---|---|---|---|

AG | 66.96% | 82.34% | 86.50% | 92.33% |

BG | 74.94% | 79.63% | 89.26% | 96.69% |

CG | 68.04% | 78.28% | 87.47% | 95.06% |

AB | 75.40% | 81.28% | 85.71% | 93.81% |

BC | 72.51% | 77.53% | 86.97% | 99.20% |

AC | 76.46% | 79.21% | 88.60% | 95.18% |

ABG | 73.71% | 79.71% | 85.54% | 93.55% |

BCG | 74.45% | 82.78% | 84.12% | 95.98% |

ACG | 82.03% | 89.95% | 84.92% | 94.27% |

ABC | 71.39% | 79.06% | 87.78% | 93.97% |

ABCG | 74.94% | 78.74% | 86.65% | 95.11% |

P_{average} | 73.71% | 80.77% | 86.68% | 95.01% |

Fault Pattern | Variance (0.1) | Variance (0.01) | Variance (0.001) | Variance (0.0001) |
---|---|---|---|---|

AG | 90.50% | 93.25% | 94.50% | 95.25% |

BG | 91.25% | 95.00% | 97.25% | 98.00% |

CG | 92.75% | 96.25% | 98.25% | 98.75% |

AB | 90.75% | 94.75% | 96.00% | 96.75% |

BC | 91.00% | 92.50% | 93.75% | 94.50% |

AC | 90.25% | 93.75% | 95.50% | 96.25% |

ABG | 91.50% | 94.25% | 96.25% | 97.00% |

BCG | 93.50% | 95.50% | 97.50% | 98.25% |

ACG | 98.00% | 98.75% | 100.00% | 100.00% |

ABC | 89.50% | 93.50% | 95.00% | 96.00% |

ABCG | 95.50% | 97.25% | 98.00% | 98.50% |

FDR_{average} | 92.23% | 94.98% | 96.55% | 97.20% |

Fault Pattern | Variance (0.1) | Variance (0.01) | Variance (0.001) | Variance (0.0001) |
---|---|---|---|---|

AG | 89.80% | 92.33% | 93.32% | 94.52% |

BG | 93.29% | 96.69% | 97.58% | 98.36% |

CG | 90.97% | 95.06% | 96.79% | 97.53% |

AB | 92.51% | 93.81% | 95.56% | 96.27% |

BC | 96.23% | 99.20% | 99.50% | 100.00% |

AC | 93.07% | 95.18% | 96.74% | 97.68% |

ABG | 91.83% | 93.55% | 95.98% | 96.39% |

BCG | 94.42% | 95.98% | 97.70% | 98.48% |

ACG | 91.46% | 94.27% | 97.26% | 98.36% |

ABC | 92.08% | 93.97% | 96.53% | 97.38% |

ABCG | 93.00% | 95.11% | 96.85% | 98.13% |

P_{average} | 92.61% | 95.01% | 96.71% | 97.55% |

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## Share and Cite

**MDPI and ACS Style**

E, G.; Gao, H.; Lu, Y.; Zheng, X.; Ding, X.; Yang, Y.
A Novel Attention Temporal Convolutional Network for Transmission Line Fault Diagnosis via Comprehensive Feature Extraction. *Energies* **2023**, *16*, 7105.
https://doi.org/10.3390/en16207105

**AMA Style**

E G, Gao H, Lu Y, Zheng X, Ding X, Yang Y.
A Novel Attention Temporal Convolutional Network for Transmission Line Fault Diagnosis via Comprehensive Feature Extraction. *Energies*. 2023; 16(20):7105.
https://doi.org/10.3390/en16207105

**Chicago/Turabian Style**

E, Guangxun, He Gao, Youfu Lu, Xuehan Zheng, Xiaoying Ding, and Yuanhao Yang.
2023. "A Novel Attention Temporal Convolutional Network for Transmission Line Fault Diagnosis via Comprehensive Feature Extraction" *Energies* 16, no. 20: 7105.
https://doi.org/10.3390/en16207105