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To address the technical bottleneck of decoupling spatiotemporal feature, high hardware costs, and high computational complexity in ultrasonic detection of partial discharge (PD) in electrical equipment, this paper proposes a TDOA/DOA hybrid localization method based on kernel principal component analysis (KPCA) and modified noncircular FastICA (mnc-FastICA). By integrating spatiotemporal feature extraction with intelligent optimization mechanisms, this method achieves high-precision localization by using a small-scale sensor array. The key innovations are as follows. First, a KPCA-assisted pseudo-whitening preprocessing framework is constructed by using polynomial kernel mapping for nonlinear signal dimensionality reduction, which preserves the correlation between time delay (TDOA) and direction-of-arrival (DOA) features while suppressing environmental noise. Second, after the blind separation of ultrasonic signals via the mnc-FastICA algorithm, TDOA/DOA parameters are synchronously extracted through a combination of the generalized cross-correlation (GCC) method and array manifold analysis. Finally, a maximum likelihood estimation model integrating dual parameters is established, and the African vulture optimization algorithm (AVOA) is introduced to accelerate global optimal solution convergence. Experimental results demonstrate that with a compact hardware configuration of two orthogonal arrays (8 sensors in total), the proposed method achieves a TDOA estimation error of 2.34%, DOA estimation accuracy better than 2°, and localization errors as low as 1.54 cm. This approach effectively resolves the discrepancies among spatiotemporal feature coupling, hardware cost, and localization accuracy in PD detection, providing a novel solution for condition monitoring of electrical equipment.
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Keywords:
- hybrid TDOA/DOA /
- KPCA-mnc-FastICA /
- partial discharge /
- ultrasonic location
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图 1 信号混合与盲信号分离算法的过程
Figure 1. The process of signal mixed and blind signal separation.
图 2 PD信号源与阵列模型图
Figure 2. Model diagram of PD source and sensor arrays.
图 3 TDOA/DOA混合定位算法步骤
Figure 3. TDOA/DOA hybrid localization algorithm steps.
图 4 盲信号分离算法提取信号波形对比
Figure 4. Waveform extracted by KPCA-mnc-FastICA compared with original signal.
图 5 不同数量传感器阵元的DOA估计精度
Figure 5. DOA estimation accuracy versus number of sensor array.
图 6 NCC与分离信号SNR随输入SNR变化情况
Figure 6. Variation of NCC and SNR of separated signal with different input SNR.
图 7 不同SNR的TDOA提取方法性能对比
Figure 7. Performance of different TDOA estimation methods with different input SNR.
图 8 TDOA-chan定位结果
Figure 8. Positioning results of TDOA-chan.
图 9 不同信噪比的DOA估计精度 (a) 方位角; (b) 俯仰角
Figure 9. DOA estimation accuracy versus SNR: (a) Azimuth; (b) pitch.
图 10 不同信噪比下的各种方法定位估计精度
Figure 10. RMSE of positioning methods versus SNR.
图 11 不同阵元数目下的各种方法定位估计精度
Figure 11. RMSE of positioning methods versus number of sensor.
图 12 不同阵列数目下的各种方法定位估计精度
Figure 12. RMSE of positioning methods versus number of sensor array.
图 13 2个正交阵列的定位估计
Figure 13. Localization estimation of two orthogonal arrays.
图 14 试验平台 (a) 示意图; (b) 装置图
Figure 14. Schematic diagram of test platform: (a) Schematic diagram; (b) device diagram.
图 15 3个传感器阵列接收信号的盲信号分离信号 (a) 阵列1; (b) 阵列2; (c) 阵列3
Figure 15. The extracted signal obtained by blind signal separation of the received signal from the three sensor arrays: (a) Array 1; (b) array 2; (c) array 3.
表 1 PD源和3路传感器阵列坐标
Table 1. Coordinates of Needle-plate model and three sensor array.
设备类型 坐标/cm PD源 (20, 10, 10) 传感器阵列1 (0, 30, 15) 传感器阵列2 (40, 0, 5) 传感器阵列3 (60, 20, 20) 
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表 2 TDOA估计结果
Table 2. Results of TDOA estimation of the test.
时间差 理论时间差/ms 试验时间差/ms 误差/μs t21 0.1568 0.1530 –3.8 t31 0.2275 0.2221 –5.4
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表 3 DOA估计结果
Table 3. Results of DOA estimation of the test.
阵列 理论方位角/( º) 试验方位角/( º) 方位角误差/( º) 理论俯仰角/( º) 试验俯仰角/( º) 俯仰角误差/( º) 1 –45 –44 1 –10 –10 0 2 153 155 2 12 11 1 3 –165 –166 1 –13 –14 1
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表 4 局放定位结果
Table 4. Localization results of PD source.
阵列组合 阵列序号 估计坐标/cm 均方根误差/cm 1 1和2 (20.95, 11.21, 10.09) 1.54 2 1和3 (20.55, 11.79, 9.89) 1.88 3 2和3 (21.25, 12.11, 9.95) 2.45 4 1, 2和3 (21.13, 10.12, 10.14) 1.14
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