Statistical Feature Extraction Combined with Generalized Discriminant Component Analysis Driven SVM for Fault Diagnosis of HVDC GIS
Abstract
:1. Introduction
2. Experimental Platform and Insulation Defects
2.1. Experimental Platform
2.2. Insulation Defects
3. Statistical Features Extraction from the Inherent Physical Quantities
- A.
- Hn(q)
- B.
- Hn(WP)
- C.
- Hn(Δq)
- D.
- Hn(ln(Δt))
- E.
- Hq(CP)
- F.
- Hqn(ln(Δtsuc))
- G.
- Hqmax(Δtsuc)
- H.
- Hqn(ln(Δtpre))
- I.
- Hqmax(ln(Δtpre))
- J.
- Hn(q, ln(Δt))
- K.
- Hn(Δq,ln(Δt))
- L.
- Hn(Δq, ln|Δ(Δt)|)
4. GDCA and Its Kernelization Forms
- (0)
- Prepare Essential Parameters
- (0.1)
- Choose the projected dimensionality m;
- (0.2)
- Choose regularization parameters δ and ρ, which must satisfy the condition that δ > ρ, δ → 0+ and ρ → 0 (for simplicity, let ρ = αδ, δ → 0+ and α < 1).
- (1)
- Calculate the between-class scatter matrix SB, within-class scatter matrix SW, and center-adjusted scatter matrix SC
- (1.1)
- Use data preprocessing methods, such as standard normal density (SND) or min-max normalization (MMN), to preprocess the original recognition vectors [41];
- (1.2)
- Denote recognition vectors after preprocessing as xi∈ℝM×1 (i = 1, 2, ⋯, N), then calculate SB, SW and SC.
- (2)
- Calculate the projection matrix WGDCA
- (2.1)
- If m is not more than rank(SB), WGDCA is consisted of the eigenvectors of (SW + δI)−1(SC + ρI) corresponding to the rank(SB) larger eigenvalues arranged in descending order.
- (2.2)
- If m is larger than rank(SB), the signal-subspace projection matrix WPS is consisted of the eigenvectors of (SW + δI)−1(SC + ρI) corresponding to the rank(SB) larger eigenvalues arranged in descending order while the noise-subspace projection matrix WPN is consisted of the eigenvectors of (SW + δI)−1(SC + ρI) corresponding to the m-rank(SB) smaller eigenvalues arranged in ascending order. Finally, WGDCA = [WPS, WPN].
- (3)
- Normalize projection vectors
- (4)
- Calculate the feature sample matrix after projection
- (5)
- Whether to change the values of δ and ρ ? Return to 0.2 if yes and go to next step if no.
- (6)
- Whether to change m? Return to 0.1 if yes and output WGDCA and YGDCA if no.
5. Results and Discussions
5.1. Test Strategy
5.2. Criterion for Selecting Optimal Parameters of GDCA and Its Kernelization Forms
5.3. Recognition Effects of GDCA and Its Kernelization Forms Driven SVM
5.3.1. Recognition Effect of GDCA Driven SVM
5.3.2. Recognition Effect of GDCA’s Kernelization Forms Driven SVM
- ●
- Comparisons between KGDCA-Intrinsic-Space/KGDCA-Empirical-Space driven SVM and original SVM
- ●
- Comparisons between KGDCA-Intrinsic-Space/KGDCA-Empirical-Space driven SVM and GDCA driven SVM
- ●
- Effect of α on KGDCA-Intrinsic-Space/KGDCA-Empirical-Space driven SVM
5.4. Comparisons with Other Dimensionality Reduction Algorithms
5.5. Comparisons with Other Classifiers
5.5.1. Comparisons with Ten Kinds of Neural Networks
5.5.2. Comparisons with CRS
5.5.3. Comparisons with the Remaining Classifiers
- ●
- Without attribute reduction of NRS
- ●
- with attribute reduction of NRS
6. Conclusions
- (1)
- All the problems of BDCA mentioned in Section 1 can be resolved by GDCA as well as its kernelization forms proposed in this paper. The range of δ, in which GDCA outperforms BDCA with regard to all the estimation indicators, generally expands as α expands. Especially, GDCA (0 < α < 1) is superior to BDCA in the majority span of δ. In the overwhelmingly major combinations of γ and δ under all the values of α, KGDCA-Intrinsic-Space/KGDCA-Empirical-Space outperformed GDCA.
- (2)
- By establishing an effective criterion to optimally select the parameters involved in GDCA and its kernelization forms in advance without using the evaluation indicators of classification results, the time of pattern recognition can be shortened considerably to ensure the optimal recognition effect simultaneously.
- (3)
- The newly proposed pattern recognition method greatly improved the recognition accuracy in comparison with 36 kinds of state-of-the-art dimensionality reduction algorithms and 44 kinds of state-of-the-art classifiers.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
- ■
- Proof of Proposition 1
- ■
- Proof of Proposition 2
- ■
- Proof of Proposition 3
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Solid Insulation Air Gap Defect | Post Insulator Defects | Surface Defect | Floating Defect | Point Defect | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
label | 1 | 2 | 3 | label | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 1 | 2 | 3 |
Diameter/mm | 2 | 1 | 0.5 | Diameter/mm | 1 | 0.5 | 0.5 | 0.5 | 0.6 | 2.5 | 0.6 | 0.6 | 2.5 | 0.6 |
Height/mm | 2 | 1 | 0.5 | Length/mm | 60 | 60 | 30 | 60 | 20 | 20 | 20 | 30 | 30 | 30 |
Distance to HV electrode/mm | 10 | 10 | 10 | 1 | 1 | 0 | 0 | |||||||
Distance to LV electrode/mm | 10 | 1 | 0 |
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Zhou, R.; Gao, W.; Liu, W.; Ding, D.; Zhang, B. Statistical Feature Extraction Combined with Generalized Discriminant Component Analysis Driven SVM for Fault Diagnosis of HVDC GIS. Energies 2021, 14, 7674. https://doi.org/10.3390/en14227674
Zhou R, Gao W, Liu W, Ding D, Zhang B. Statistical Feature Extraction Combined with Generalized Discriminant Component Analysis Driven SVM for Fault Diagnosis of HVDC GIS. Energies. 2021; 14(22):7674. https://doi.org/10.3390/en14227674
Chicago/Turabian StyleZhou, Ruixu, Wensheng Gao, Weidong Liu, Dengwei Ding, and Bowen Zhang. 2021. "Statistical Feature Extraction Combined with Generalized Discriminant Component Analysis Driven SVM for Fault Diagnosis of HVDC GIS" Energies 14, no. 22: 7674. https://doi.org/10.3390/en14227674