The Euclidean direction search (EDS) algorithm provides an efficient iterative approach for adaptation without computationally expensive matrix inversion. However, existing EDS-based algorithms are unsuitable for the non-circular complex signals. To address this problem, this paper integrates the widely linear model with the EDS algorithm, proposing the widely linear complex-valued EDS (WL-CEDS) algorithm, which extends the conventional EDS algorithm to the augmented complex statistics domain. Moreover, to confirm the convergence, the Lyapunov stability theory (LST) is used, with the theoretical steady-state complementary behavior analyzed. Simulations validate the correctness of the analysis, and confirm that WL-CEDS achieves significant performance improvement for non-circular signals compared to the conventional widely linear-based algorithms.

The presence of impulsive noise can significantly compromise the localization accuracy of partial discharge (PD). To address this problem, the direct data-reusing time-delay estimation (TDE) algorithm with the generalized Cauchy loss (GCL) function (DDR-TDE-GCL) is proposed. Leveraging the robustness of the GCL function, the proposed algorithm demonstrates a superior capability to combat impulsive interference. In addition, the direct TDE method is integrated into the data-reusing strategy. The integration enables the DDR-TDE-GCL algorithm to achieve high localization accuracy in cable systems while remaining noniterative. Moreover, the convergence behavior of the DDR-TDE-GCL algorithm is analyzed, proving that the estimation for the attenuation factor is unbiased and consistent. Simulations and experiments demonstrate that the DDR-TDE-GCL algorithm has an improved localization accuracy compared to existing algorithms for PD signals, achieving an average localization accuracy of 99.59%.

The iterative Wiener filter (IWF) algorithm can achieve a fast convergence rate. However, its performance may degrade when it encounters noisy input scenarios. To tackle this problem, a novel IWF algorithm incorporating bias-compensation (BC-IWF) is proposed, which can enhance the performance of the algorithm by estimating the input noise variance. The BC-IWF algorithm optimizes the step size for each iteration and updates along the direction of the gradient. To further reduce the steady-state error, a normalized IWF by making use of the bias-compensation scheme (BC-NIWF) algorithm is proposed. Moreover, the steady-state performance of the BC-NIWF algorithm is analyzed. Simulation results demonstrate the validity of the theoretical analysis and the BC-NIWF algorithm achieves improved misadjustment compared with the state-of-the-art algorithms.

Based on the total least-squares (TLS) model, the gradient-descent TLS Euclidean direction search (GD-TLS-EDS) algorithm is proposed when both input and output signals are corrupted by noises. Taking advantage of the effectiveness of the EDS algorithm, the GD-TLS-EDS algorithm has improved performance and comparable computational complexity. Moreover, based on the time difference of arrival technique, the traditional location methods may suffer from performance degradation in the location problem with noisy inputs, the GD-TLS-EDS algorithm is exploited to mitigate the noise from the original and reflected partial discharge signals and achieve the one-step location result by estimating the time difference in cable systems. Simulation and experimental studies demonstrate the GD-TLS-EDS algorithm has improved location accuracy as compared with the existing algorithms.

The Euclidean direction search (EDS) algorithm can reduce the complexity by avoiding the matrix inversion operation. However, it may fail to work in impulsive environments. To address this problem, a novel EDS based upon the maximum correntropy criterion (EDS-MCC) algorithm is proposed, which provides computational savings and robustness for combating impulsive noise. Additionally, the EDS-MCC algorithm is analyzed to obtain the theoretical performance by utilizing the energy conservation argument (ECA) and the Taylor expansion method. Simulations are exhibited to show the robustness of the EDS-MCC algorithm and verify the accuracy of the theoretical analysis.

Partial discharge (PD) location techniques are a useful tool for condition monitoring of electrical apparatus in power systems. However, the noisy PD measurements may significantly degrade the performance of location algorithms. This article deals with the PD location problem by using adaptive filtering techniques. Heretofore, scarce literature focuses on addressing the PD location based on such method. A novel adaptive algorithm, termed as total least-squares (TLS)-Matérn kernel (TLS-MK), is proposed. Benefiting from the merits of the Matérn kernel, the TLS model can effectively suppress the noise from the direct and reflected waves of the PD source. Meanwhile, the TLS-MK algorithm is used to estimate the time difference, which is used in the PD location. Moreover, the convergence behavior of the TLS-MK algorithm is analyzed. Simulations and experiments show that the proposed algorithm can enhance the location accuracy as compared to state-of-the-art methods for various PD signals.

The partial discharge (PD) classification for electric power equipment based on machine learning algorithms often leads to insufficient generalization ability and low recognition accuracy. To solve the problem, this article develops an improved Wasserstein generative adversarial network with gradient penalty (WGAN-GP) based data augmentation model. The improved WGAN-GP model can generate data samples to supplement the low-data input set in PD source classification. First, an improved WGAN-GP model with conditional generation is trained and various new data samples are generated. Then, the new data samples are utilized to expand the raw dataset. Finally, the expanded dataset is trained to get a new PD classifier. Experimental results demonstrate that the proposed model can generate new high-quality data samples more stably. Moreover, the proposed method can suppress the overfitting risk caused by low data or imbalanced data distributions and the classification accuracy is effectively improved.

Multi-frequency analysis is an effective tool for seismic data interpretation, such as fluvial channel characterization and sand bodies interpretation. Due to the broadband and non-stationary properties of seismic data, time-frequency transform is widely used for extracting multi-frequency components, e.g., S-transform and wavelet transform. However, how to fuse these extracted band-limited multi-frequency components for complex reservoir characterization is still a hot topic in exploration geophysics. In this study, we propose a multi-frequency analysis workflow for complex reservoir delineation based on the local tangent space alignment (LTSA). First, we utilize the generalized S-transform (GST) for extracting multi-frequency components, which is easy to implement and also a valid time-frequency analysis tool. Afterward, we adopt LTSA for blending the decomposed multi-frequency components. Finally, we apply the proposed workflow on a 3D post-stack field data for delineating complex carbonate reservoir. The results prove that the proposed workflow can effectively delineate carbonate reservoir, which is superior to the individual seismic attribute analysis and the contrastive blending method.