Spacer rods maintain conductor spacing in power transmission networks. Tilt defects cause uneven load distribution and potential grid failures. Traditional manual inspections are inefficient and error-prone. We propose a LiDAR-based defect identification method using surveying drones to address multi-target interference from bird nests, vibration dampers, and conductor clamps.
Our methodology integrates LiDAR imaging correction, spatial attention modeling, and interference elimination. Surveying UAVs capture point cloud data through these stages:
1. LiDAR Imaging Correction
We model geometric distortion between image plane \(J(u,v)\) and calibration plane \(A(x,y)\):
$$ \begin{cases} x = D_x(u,v) \\ y = D_y(u,v) \end{cases} $$
Phase distributions for calibration planes \(B\) and \(C\) are calculated as:
$$ \begin{cases} \phi_{Bx}(x,y) = -\gamma_{Bx}(x,y) – \upsilon_{xb}x + \upsilon_{Ax}x \\ \phi_{By}(x,y) = -\gamma_{By}(x,y) – \upsilon_{yb}y + \upsilon_{Ay}y \\ \phi_{Cx}(x,y) = -\gamma_{Cx}(x,y) – \upsilon_{xc}x + \upsilon_{Ax}x \\ \phi_{Cy}(x,y) = -\gamma_{Cy}(x,y) – \upsilon_{yc}y + \upsilon_{Ay}y \end{cases} $$
Harmonic relationships determine spatial coordinates for defect localization:
$$ \begin{cases} \upsilon_{x_B}^0 X_1 = \upsilon_{x_B} u_1 + \gamma_{x_B}(u_1,v_1) \\ \upsilon_{y_B}^0 Y_1 = \upsilon_{y_B} u_1 + \gamma_{y_B}(u_1,v_1) \\ \upsilon_{x_C}^0 X_2 = \upsilon_{x_C} u_1 + \gamma_{x_C}(u_1,v_1) \\ \upsilon_{y_C}^0 Y_2 = \upsilon_{y_C} u_1 + \gamma_{y_C}(u_1,v_1) \end{cases} $$
2. Defect Enhancement and Classification
We apply top-hat transforms to distinguish defect regions:
$$ g_{Fn}(x,y) = \beta g(x,y) – \lambda Q(x,y) + \mu H(x,y) $$
where \(\beta \leq 1\), \(\mu \geq 1\), \(\lambda \geq 1\). Enhanced features input into our SVDD model:
$$ \text{GSV} = \min \left( r^2 + C\sum_{j=1}^M \varpi_j \right) $$
subject to:
$$ \begin{cases} r^2 + \varpi_j \geq \| \mathbf{x}_j – \mathbf{b} \|^2 \\ \varpi_j \geq 0 \end{cases} $$
Using Lagrange multipliers and Gaussian kernel \(L(\mathbf{x}_j,\mathbf{x}_i)\):
$$ r^2 = L(\mathbf{x}_s,\mathbf{x}_s) + \sum_{j=1}^m \sum_{i=1}^m \mu_i \mu_j L(\mathbf{x}_j,\mathbf{x}_i) – 2\sum_{j=1}^n \mu_j L(\mathbf{x}_j,\mathbf{x}_s) $$
State discrimination function:
$$ g(\mathbf{x}_t) = \max_n \left( \sum_{j=1}^{M_n} \sum_{i=1}^{M_n} \mu_{jn} \mu_{jn} L(\mathbf{x}_j,\mathbf{x}_i) + L(\mathbf{x}_t,\mathbf{x}_t) – 2\sum_{j=1}^{M_n} \mu_{jn} L(\mathbf{x}_j,\mathbf{x}_t) – r_n^2 \right) $$
3. Performance Validation
We tested our method on transmission line datasets captured by surveying drones:
| Method | 300s FPS | 400s FPS | 500s FPS | 600s FPS |
|---|---|---|---|---|
| Reference [3] | 23.5 | 24.8 | 27.9 | 30.5 |
| Reference [4] | 28.6 | 30.4 | 35.8 | 39.4 |
| Reference [5] | 27.3 | 28.6 | 32.7 | 34.5 |
| Our Method | 35.8 | 40.2 | 44.7 | 48.6 |
| Spacer State | Precision (%) | Recall (%) | F1 Score |
|---|---|---|---|
| Normal | 98.85 | 98.75 | 0.99 |
| Tilted | 95.18 | 86.37 | 0.90 |
Key results from surveying UAV implementation:
- mAP consistently >0.85 across 600s testing
- Zero false positives/negatives under multi-target interference
- 48.6 FPS processing rate at 600s duration
4. Conclusion
Our UAV LiDAR solution effectively identifies spacer tilt defects under complex field conditions. The framework combines:
- Distortion-corrected LiDAR imaging
- Top-hat enhanced feature extraction
- Hypersphere-based spatial classification
Experimental validation confirms superior accuracy (95.18% precision) and real-time performance (48.6 FPS) compared to existing methods. The system enables reliable autonomous inspection using surveying drones across diverse grid environments.