Localization of robot for transformer internal inspection based on EMD-wavelet packet threshold denoising and MVDR beamforming algorithm improved with diagonal loading reduction

Large oil-immersed power transformers, characterized by their metal-enclosed shells, feature complex and tightly confined internal spaces. This poses significant challenges for the localization of robot used in transformer internal inspections. To this end, this paper proposes an ultrasonic localization method for robot based on an improved empirical mode decomposition (EMD) and a minimum variance distortionless response (MVDR) beamforming algorithm. To address strong on-site noise interference, the received localization signals are first processed with the EMD method to extract high-quality intrinsic mode function (IMF) components. Subsequently, a dynamic threshold function is applied to perform wavelet packet denoising on these selected IMF components. The denoised high-quality IMF components are then reconstructed to obtain a clean and accurate localization signal. Considering the computational complexity and limited resolution performance of existing beamforming algorithms, the proposed MVDR beamforming algorithm improves target signal identification by subtracting a diagonal matrix constructed from the minimum eigenvalue from the covariance matrix, normalizing the output power in all directions, and applying a higher-order power transformation. To validate the effectiveness of the proposed method, both simulation analysis and on-site experiments were conducted. The results demonstrate that the improved EMD-wavelet packet denoising method enhances the signal-to-noise ratio (SNR) of the positioning signal with minimal distortion. Furthermore, the improved MVDR beamforming algorithm enhances target signal discrimination and reduces the probability of misidentification. In a transformer test chamber measuring 1.2 m × 1.0 m × 1.0 m, the relative positioning error is 3.53 %, which meets the requirements of engineering applications.