KSVDSAMP自适应稀疏算法在电能质量信号重构中的应用
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摘要
针对现有固定正交稀疏基不足以灵活表示未知的电能质量信号特征,以及稀疏系数非自适应导致信号重构效果不佳、应用性不强的问题,提出一种基于字典学习的自适应压缩感知信号重构算法(KSVDSAMP),并将其应用于电能质量信号重构中。算法首先对大量电能质量信号的样本进行K均值分解得到信号特征,根据信号特征自适应的选取合适的稀疏函数表示未知信号,然后构建扰动信号的随机伯努利矩阵作为压缩感知框架下的测量矩阵,同时将回溯思想和逐步搜索原子字典更新相结合,通过设定固定的步长,在反复迭代的过程中,进行残差r的比较,最终重构出原始信号。实验结果表明,当信号压缩率在50%～90%时,提出的KSVDSAMP算法相较于现有的电能质量信号重构算法(FFTOMP、DCT),算法的重构信噪比均高出10～20 dB,验证了KSVDSAMP算法的有效性和优越性,为电能质量信号重构提供了一种新的方法。
Aiming at the existing problems that the existing fixed orthogonal sparsity basis are not sufficient to represent features of the unknown power quality signals and the sparse coefficient non-adaptive leads to the poor reconstructed effect of signals as well as weak applicability, a reconstructed algorithm of the adaptive compressed sensing signals based on dictionary learning(KSVDSAMP) is put forward and applied to the reconstruction of power quality signals. Three steps of the reconstructed algorithm are as follows: first of all, because signals features are non-adaptive to choose the appropriate sparse functions to show the unknown signals, this algorithm can realize the K-means value decomposition of lots of power quality signals to obtain signals features. Afterwards, the algorithm constructs the Random Bernoulli Matrices of disturbance signals as the measurement matrix under the frame of compressive sensing. Meanwhile, the algorithm combines the backtracking thought with searching atomic dictionary update step by step and compares the residuals in the process of repetitious iteration through setting the fixed step length. At last, the algorithm can reconstruct the original signals. The experimental results show that when the compression ratio of signals is 50%～90%, compared with the existing reconstructed algorithm of power quality signals(FFTOMP, DCT), the reconstructed signals-to-noise ratio of the mentioned algorithm(KSVDSAMP) is over 10～20 dB, which further proved the effectiveness and superiority of the mentioned algorithm(KSVDSAMP) and provided the reconstruction of power quality signals with a new method.
Aiming at the existing problems that the existing fixed orthogonal sparsity basis are not sufficient to represent features of the unknown power quality signals and the sparse coefficient non-adaptive leads to the poor reconstructed effect of signals as well as weak applicability, a reconstructed algorithm of the adaptive compressed sensing signals based on dictionary learning(KSVDSAMP) is put forward and applied to the reconstruction of power quality signals. Three steps of the reconstructed algorithm are as follows: first of all, because signals features are non-adaptive to choose the appropriate sparse functions to show the unknown signals, this algorithm can realize the K-means value decomposition of lots of power quality signals to obtain signals features. Afterwards, the algorithm constructs the Random Bernoulli Matrices of disturbance signals as the measurement matrix under the frame of compressive sensing. Meanwhile, the algorithm combines the backtracking thought with searching atomic dictionary update step by step and compares the residuals in the process of repetitious iteration through setting the fixed step length. At last, the algorithm can reconstruct the original signals. The experimental results show that when the compression ratio of signals is 50%～90%, compared with the existing reconstructed algorithm of power quality signals(FFTOMP, DCT), the reconstructed signals-to-noise ratio of the mentioned algorithm(KSVDSAMP) is over 10～20 dB, which further proved the effectiveness and superiority of the mentioned algorithm(KSVDSAMP) and provided the reconstruction of power quality signals with a new method.
引文
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[13] DONOHO D I. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.
[14] 朱云芳,戴朝华,陈维荣,等.压缩感知理论及其电能质量应用与展望[J].电力系统及其自动化学报,2015,27(1):80-85.
[15] CHAKRABORTY S, CHATTERJEE A, GOSWAMI S K. A sparse representation based approach for recognition of power system transients[J]. Engineering Applications of Artifical Intelligence, 2014, 30(3): 137-144.
[16] MANIKANDAN M S, SAMANTARAY S R, KAMWA I. Detection and classification of power quality disturbances using sparse signal decomposition on hybrid dictionaries[J]. IEEE Transactions on Instrumentation and Measurement, 2015, 64(1): 27-38.
[17] AHARON M, ELAD M, BRUCKSTDIN A M, et al. K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation[J]. IEEE Trans. on Signal Processing, 2006, 54(11): 4311-4322
[18] ELAD M, AHARON M. Image denoising via sparse and redundant representations over learned dictionaries[J]. IEEE Trans. On Image Process, 2006, (12): 3736-3745.
[19] 高放,孙长建,邵庆龙,等.基于K-均值聚类和传统递归最小二乘法的高光谱图像无损压缩[J].电子与信息学报,2016,38(11):2709-2714.
[2] 张达洄.电能质量在线监测系统在供配电网的应用[J].电气技术,2014(3):103-105.
[3] MAHELA O P, SHAIK A G, GUPTA. A critical review of detection and classification of power quality events[J]. Renewable and Sustainable Energy Reviews, 2015, 41: 495-505.
[4] HE S F, LI K C, ZHANG M. A new transient power quality disturbances detection using strong trace filter[J].IEEE Transactions on Instrumentation and Measurement, 2014, 63(2): 2863-2871.
[5] WEN H, GUO S, TENG Z. Frequency estimation of distorted and noisy signals in power systems by FFT-based approach[J]. IEEE Transactions on Power Systems, 2014, 29(2): 765-774.
[6] 冯浩,周雒维,刘毅. 基于复小波变换的暂态电能质量扰动检测与分类[J].电网技术,2010,34(3):91-95.
[7] 徐志超,杨玲君,李晓明.基于聚类改进S变换与直接支持向量机的电能质量扰动识别[J].电力自动化设备,2015,35(7):50-58,73.
[8] ZHAO F ZH, YANG R G. Power-quality disturbance recognition using S-transform[J]. IEEE Transactions on Power Delivery, 2007, 22(2): 944-950.
[9] 田振果,傅成华,吴浩,等.基于HHT的电能质量扰动定位与分类[J].电力系统保护与控制,2015,43(16):36-42.
[10] AFRONI M J, SUTANTO D, STIRLING D. Analysis of nonstationary power-quality waveforms using Iterative Hilbert Huang Transform and SAX algorithm[J]. IEEE Transactions on Power Delivery, 2013, 28(4): 2134-2144.
[11] SAQIB M A, SALEEM A Z. Power-quality issues and the need for reactive-power compensation in the grid integration of wind power[J]. Renewable and Sustainable Energy Reviews, 2015, 43(1): 51-64.
[12] 王学伟,王琳,苗桂君,等.暂态和短时电能质量扰动信号压缩采样与重构方法[J].电网技术,2012,36(3):191-196.
[13] DONOHO D I. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.
[14] 朱云芳,戴朝华,陈维荣,等.压缩感知理论及其电能质量应用与展望[J].电力系统及其自动化学报,2015,27(1):80-85.
[15] CHAKRABORTY S, CHATTERJEE A, GOSWAMI S K. A sparse representation based approach for recognition of power system transients[J]. Engineering Applications of Artifical Intelligence, 2014, 30(3): 137-144.
[16] MANIKANDAN M S, SAMANTARAY S R, KAMWA I. Detection and classification of power quality disturbances using sparse signal decomposition on hybrid dictionaries[J]. IEEE Transactions on Instrumentation and Measurement, 2015, 64(1): 27-38.
[17] AHARON M, ELAD M, BRUCKSTDIN A M, et al. K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation[J]. IEEE Trans. on Signal Processing, 2006, 54(11): 4311-4322
[18] ELAD M, AHARON M. Image denoising via sparse and redundant representations over learned dictionaries[J]. IEEE Trans. On Image Process, 2006, (12): 3736-3745.
[19] 高放,孙长建,邵庆龙,等.基于K-均值聚类和传统递归最小二乘法的高光谱图像无损压缩[J].电子与信息学报,2016,38(11):2709-2714.
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