Compressive Sensing Approach to Harmonics Detection in the Ship Electrical Network

Abstract

The contribution of this paper is to show the opportunities for using the compressive sensing (CS) technique for detecting harmonics in a frequency sparse signal. The signal in a ship’s electrical network, polluted by harmonic distortions, can be modeled as a superposition of a small number of sinusoids and the discrete Fourier transform (DFT) basis forms its sparse domain. According to the theory of CS, a signal may be reconstructed from under-sampled incoherent linear measurements. This paper highlights the use of the discrete Radon transform (DRT) techniques in the CS scheme. In the reconstruction algorithm section, a fast algorithm based on the inverse DRT is presented, in which a few randomly sampled projections of the input signal are used to correctly reconstruct the original signal. However, DRT requires a very large set of measurements that can defeat the purpose of compressive data acquisition. To acquire the wideband data below the Nyquist frequency, the K-rank-order filter is applied in the sparse transform domain to extract the most significant components and accelerate the convergence of the solution. While most CS research efforts focus on random Gaussian measurements, the Bernoulli matrix with different values of the probability of ones is applied in the presented algorithm. Preliminary results of numerical simulation confirm the effectiveness of the algorithm used, but also indicate its limitations. A significant advantage of the proposed approach is the speed of analysis, which uses fast Fourier transform (FFT) and inverse FFT (IFFT) algorithms widely available in programming environments. Moreover, the data processing algorithm is quite simple, and therefore memory usage and burden of the data processing load are relatively low.

Keywords

• harmonics
• compressive sensing
• signal reconstruction
• discrete Radon transform
• sparse signal domain