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Partial discharge (PD) is a primary factor leading to the deterioration of insulation in electrical equipment. However, it is hard for traditional methods to precisely extract PD signals in increasingly complex engineering environments. This paper proposes a new PD signal denoising method combining Aquila Optimizer–Variational Mode Decomposition (AO-VMD) and K-Singular Value Decomposition (K-SVD) algorithms. Firstly, the AO algorithm optimizes critical parameters of the VMD algorithm. For the PD signal overwhelmed by noise, the AO-VMD algorithm can decompose it and reconstruct it by using kurtosis. In this process, the majority of the noise is removed, and the characteristics of the original signal are shown. Subsequently, the K-SVD algorithm performs sparse decomposition on the signal after OA-VMD, constructs a learned dictionary, and captures the characteristics of the signal for continuous learning and updating. After the dictionary learning is completed, the best matching atoms from the dictionary are selected to precisely reconstruct the original noiseless signal. Finally, the proposed method is compared with three traditional algorithms, Adaptive Ensemble Empirical Mode Decomposition (AEEMD), SVD-VMD, and the Adaptive Wavelet Multilevel Soft Threshold algorithm, on the simulated signal and the actual engineering signal. The results both demonstrate that the algorithm proposed by this paper has superior noise reduction and signal extraction performance. [ABSTRACT FROM AUTHOR]

Direction‐of‐arrival (DOA) estimation methods for wideband linear frequency modulated (LFM) signals based on fractional Fourier transform (FRFT) typically use the single snapshot vector in the fractional Fourier (FRF) domain. However, the low‐rank problem of the second‐order statistics in the single snapshot vector can decrease the DOA estimation resolution and cause issues in DOA estimation for coherent sources. In order to address these problems, a weighted l1‐norm method based on FRFT is proposed. The proposed method utilises the energy aggregation property of FRFT for LFM signals. This allows for obtaining a single snapshot vector in the FRF domain. Subsequently, a sparse representation DOA estimation model is established by taking advantage of the sparsity of the target distribution in the spatial domain. The DOA estimation is then obtained by minimising the l1‐norm. To further enhance the DOA estimation performance, we construct a matrix by rearranging the elements of the eigenvectors corresponding to the nonzero eigenvalue of the covariance matrix in the FRF domain. The rank of this matrix is equal to the number of sources, ensuring the orthogonality of the subspace obtained by the reconstructed matrix. Finally, a weighted matrix is constructed by exploiting the subspace orthogonality principle to adjust the sparsity penalty of the l1 constraint model. Simulation results demonstrate that our method is capable of achieving high angular resolution and accuracy even at low SNR and can process coherent signals directly. [ABSTRACT FROM AUTHOR]

Traditional direction of arrival (DOA) estimation methods of wideband linear frequency modulated (LFM) signal based on the fractional Fourier transform (FRFT) highly depend on the peak value of LFM signal in the FRFT domain. However, the peak value can be affected by various factors, such as a low signal‐to‐noise ratio (SNR), a small number of snapshots, or the large incident angle of signals, which can lead to a decrease in DOA estimation accuracy. To tackle this problem, based on the energy‐concentrated property of LFM signal in the FRFT domain, the DOA estimation is accomplished by adopting the approach of slope fitting for the wideband array signal in the FRFT domain in this study. The method uses the correspondence between the peak position in the FRFT domain and the delay of the received signal on different uniform linear array elements. The least square method based on threshold outlier detection is used for slope fitting. Compared to conventional methods, the method of this study has high accuracy and relatively low complexity in the case of low SNR or large incident angle of the signal without relying on the peak value. The effectiveness of this method is verified by theoretical analysis and Monte‐Carlo simulations. The proposed method provides a new path for DOA estimation of LFM signal. [ABSTRACT FROM AUTHOR]