SACoSaMP在电能质量数据重构中的应用
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摘要
为了解决电能质量信号的稀疏度未知和重构性能差的问题,提出采用稀疏度自适应压缩采样匹配追踪(SACoSaMP)算法应用于电能质量数据重构。SACoSaMP算法结合压缩采样匹配追踪(CoSaMP)算法抗干扰能力强和稀疏度自适应匹配追踪(SAMP)算法稀疏度自适应的优点。首先对信号进行稀疏度初始估计,然后在CoSaMP算法框架下进行稀疏度逐步增大的递归运算,以残差值比较为终止条件实现稀疏度自适应。最后采用重构信噪比、均方差误差百分比和能量恢复系数作为评价参数,比较在稀疏基和观测矩阵相同的情况下OMP、CoSaMP、SAMP和SACoSaMP算法的重构效果,仿真实验表明,SACoSaMP算法能量恢复系数高,重构信噪比高,均方误差小,同时具备稀疏度自适应的优点,为电能质量扰动信号数据重构提供了一种新的方向。
In order to solve the question that the sparsity of the power quality signal is unknown and the reconstruction performance is poor,this paper proposes a reconstruction method that the sparsity adaptive compressive sampling matching pursuit algorithm(SACoSaMP) is applied for the power quality data reconstruction.SACoSaMP combines the advantages of stronger anti-interference ability of the compressive sampling matching pursuit algorithm and adaptive sparse degrees of the sparsity adaptive matching pursuit algorithm.First of all,the signal sparse degree is initially estimated,and then the sparse degree gradually increases under the CoSaMP algorithm framework of recursive computation,with the comparison of residual value for the termination condition to implement adaptive sparse degrees.Finally,the reconfiguration signal-to-noise ratio,the mean square error percentage and the energy recovery coefficient are used as evaluation parameters.Effects of reconstruction algorithms OMP,CoSaMP,SAMP and SACoSaMP are compared under the same condition of sparse matrix and observation.According to the simulation results,SACoSaMP algorithm not only has a higher energy recovery coefficient,but also has a better signal-to-noise ratio of reconfiguration,and a smaller mean square error,Meanwhile,it has an advantage of adaptive sparse degree,which provides a new direction for data reconfiguration of the power quality disturbance signal.
In order to solve the question that the sparsity of the power quality signal is unknown and the reconstruction performance is poor,this paper proposes a reconstruction method that the sparsity adaptive compressive sampling matching pursuit algorithm(SACoSaMP) is applied for the power quality data reconstruction.SACoSaMP combines the advantages of stronger anti-interference ability of the compressive sampling matching pursuit algorithm and adaptive sparse degrees of the sparsity adaptive matching pursuit algorithm.First of all,the signal sparse degree is initially estimated,and then the sparse degree gradually increases under the CoSaMP algorithm framework of recursive computation,with the comparison of residual value for the termination condition to implement adaptive sparse degrees.Finally,the reconfiguration signal-to-noise ratio,the mean square error percentage and the energy recovery coefficient are used as evaluation parameters.Effects of reconstruction algorithms OMP,CoSaMP,SAMP and SACoSaMP are compared under the same condition of sparse matrix and observation.According to the simulation results,SACoSaMP algorithm not only has a higher energy recovery coefficient,but also has a better signal-to-noise ratio of reconfiguration,and a smaller mean square error,Meanwhile,it has an advantage of adaptive sparse degree,which provides a new direction for data reconfiguration of the power quality disturbance signal.
引文
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[11]于代楠,张敬傑,代芳琳,等.压缩传感在电能质量扰动信号分析中的应用[J].吉林大学学报(信息科学版),2014,32(6):618-623.Yu D N,Zhang J J,Dai F L.Application of Power Quality Disturbance Signal Based on Compressed Sensing[J].Journal of Jilin University(Information Science Edition),2014,32(6):618-623.
[12]曾嘉俊.电能质量扰动信号压缩采样的重构算法[J].电网技术,2014,37(11):170-172.
[13]闫鹏,王阿川.基于压缩感知的Co Sa MP算法自适应性改进[J].计算机工程,2012,39(6):28-33.Yan P,Wang A C.Adaptivity Improvement 0f Co Sa MP Algorithm Based 0n Compressive Sensing[J].Computer Engineering,2012,39(6):28-33.
[14]Candes E,Romberg J.Tan Robust Uncertainty Principles:Exact Signal Reconstruction from Highly Incomplete Frequency Information[J].IEEE Transactions on Information Theory,2006,52(2):489-509.
[15]刘国海,吴拥轩,沈跃.正则化自适应匹配追踪电能质量数据重构方法[J].仪器仪表学报,2015,36(8):1838-1844.Liu G H,Wu H X,Shen Y.Novel Reconstruction Method of Power Quality Data based on Regularized Adaptive Matching Pursuit Algorithm[J].Chinese Journal of Scientific Instrumen,2015,36(8):1838-1844.
[16]Cheng Y,Wei F,Hui F,Tao Y,Bo H.A Sparsity Subspace Pursuit Algorithm for Compressive Sampling[J].Acta Electronica Sinica,2010,38(8):1914-1917.
[17]朱延万,赵拥军,孙兵.一种改进的稀疏度自适应匹配追踪算法[J].信号处理,2012,28(1):80-86.Zhu Y W,Zhao Y J,Sun B.A Modified Sparsity Adaptive Matching Pursuit Algorithm[J].Signal Processing,2012,28(1):80-86.
[2]Donoho D L.Compressed Sensing[J].IEEE Transactions on Information Theory.2006,52(4):1289-1306.
[3]Candes E J.Compressive Sampling[C].Proceedings of the International Congress of Mathematics.Madrid,Spain:European Mathematical Society Publishing House,2006,18(1):56-64.
[4]焦李成,杨淑媛,刘芳,等.压缩感知回顾与展望[J].电子学报,2011,39(7):1651-1662.Jiao L C,Yang S Y,Liu F,et a1.Development and Prospect of Compressive Sensing[J].Acta Electronica Sinica,2011,39(7):1651-1662.
[5]杨海蓉,张成,丁大为,等.传感理论与重构算法[J].电子学报,2011,39(1):142-148.Yang H R,Zhang C,Ding D W,et al.The Theory of Compressed Sensing and Reconstruction Algorithm[J].Acta Electronica Sinica,2011,39(1):142-148.
[6]Joel A Tropp,Anna C Gilbert.Signal Recovery from Random Measurements via Orthogonal Matching Pursuit[J].IEEETransactions on Information Theory,2007,22(2):573-584.
[7]Needell D,Tropp J A.Co Sa MP:Iterative Signal Recovery from Incomplete and Inaccurate Samples[J].Applied Computational Harmonic Analysis,2008,26(3):301-321.
[8]Do T T,Gan L,Nguyen N,Tran T D.Sparsity Adaptive Matching Pursuit Algorithm for Practical Compressed Sensing[J].System and Computers,2008,41(4):581-587.
[9]Xiang P L,Feng Y.A Sparsity Adaptive Compressive Sampling Matching Pursuit Algorithm[C].Proceedings of the 6th International Asia Conference on Industrial Engineering and Management Innovation,2016,22(2):178-187.
[10]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.Wang X W,Wang L,Miao G J,et al.An Approach for Compressive Sampling and Reconstruction of Transient and Short-Time Power Quality Disturbance Signals[J].Power System Technology,2012,36(3):191-196.
[11]于代楠,张敬傑,代芳琳,等.压缩传感在电能质量扰动信号分析中的应用[J].吉林大学学报(信息科学版),2014,32(6):618-623.Yu D N,Zhang J J,Dai F L.Application of Power Quality Disturbance Signal Based on Compressed Sensing[J].Journal of Jilin University(Information Science Edition),2014,32(6):618-623.
[12]曾嘉俊.电能质量扰动信号压缩采样的重构算法[J].电网技术,2014,37(11):170-172.
[13]闫鹏,王阿川.基于压缩感知的Co Sa MP算法自适应性改进[J].计算机工程,2012,39(6):28-33.Yan P,Wang A C.Adaptivity Improvement 0f Co Sa MP Algorithm Based 0n Compressive Sensing[J].Computer Engineering,2012,39(6):28-33.
[14]Candes E,Romberg J.Tan Robust Uncertainty Principles:Exact Signal Reconstruction from Highly Incomplete Frequency Information[J].IEEE Transactions on Information Theory,2006,52(2):489-509.
[15]刘国海,吴拥轩,沈跃.正则化自适应匹配追踪电能质量数据重构方法[J].仪器仪表学报,2015,36(8):1838-1844.Liu G H,Wu H X,Shen Y.Novel Reconstruction Method of Power Quality Data based on Regularized Adaptive Matching Pursuit Algorithm[J].Chinese Journal of Scientific Instrumen,2015,36(8):1838-1844.
[16]Cheng Y,Wei F,Hui F,Tao Y,Bo H.A Sparsity Subspace Pursuit Algorithm for Compressive Sampling[J].Acta Electronica Sinica,2010,38(8):1914-1917.
[17]朱延万,赵拥军,孙兵.一种改进的稀疏度自适应匹配追踪算法[J].信号处理,2012,28(1):80-86.Zhu Y W,Zhao Y J,Sun B.A Modified Sparsity Adaptive Matching Pursuit Algorithm[J].Signal Processing,2012,28(1):80-86.