基于超完备字典的压缩感知电能质量数据重构

摘要

针对应用压缩感知原理进行电能质量数据重构时,采用普通函数形成的正交基进行稀疏表示不能自适应地获得最佳稀疏表示这一问题,首次将K-奇异值分解字典学习引用到电能质量数据重构中.首先,对电能质量信号进行一二维转换,利用K-奇异值分解字典学习算法,建立了适合电能质量数据的超完备字典;并选取高斯随机矩阵作为测量矩阵,对电能质量扰动信号进行压缩采样.同时,利用压缩感知匹配追踪算法进行信号二维重构,并将其转换成一维信号.最后,利用所提出的新算法对几类常见电能质量信号进行了仿真验证.结果表明:在压缩比为25%时,利用新算法能够完成重构信号,其信噪均大于44.2 dB,能够满足实际应用时的分析要求.%In terms of the power quality data reconstruction with the compressed sensing principle, the orthogonal basis generated by normal function cannot be used to obtain the best sparse representation. Therefore, the K-Singular Value Decomposition (K-SVD) dictionary is applied to the power quality data reconstruction for the first time. First of all, the power quality signals are converted from One-Dimensional (1D) to Two-Dimensional (2D) and then overcomplete dictionary adaptable for power quality signals is established, which is based on the K-SVD dictionary. Meanwhile compressed sampling is carried out for power quality disturbance signals by taking the Gauss random matrix as the measurement matrix. In addition, 2D reconstruction is conducted for the signals with the Compressed Sensing Matching Pursuit (CoSaMP) algorithm, and 2D signals are converted to 1D signals. Finally, simulation verification is implemented for several common power quality signals with new algorithm. Experiment result shows that at the compression ratio of 25%, the new algorithm can be used to complete the reconstruction of the signals with signal-to-noise ratios more than 44.2 dB, which meets the analysis requirements in practical application.