基于量子进化的信号稀疏分解方法
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摘要
稀疏分解将信号表达为冗余字典中少量原子的线性组合,其分解的精度对其广泛应用具有重要影响。提出了基于量子进化算法的稀疏分解方法,利用增强型量子比特概率幅对Gabor原子进行染色体编码,采用简化形式的梯度进化操作和逐代缩减的变异操作进行种群个体的更新,以稀疏分解的残余信号与Gabor原子的内积作为适应度函数,筛选出每次稀疏分解的最佳原子。通过两个仿真信号的稀疏分解实验和轴承振动信号的故障特征提取实验,验证了所提方法较其他方法具有更高的分解精度。
Sparse decomposition expresses a signal as a linear combination of a small number of atoms in a redundant dictionary.The accuracy of the decomposition has an important influence on its wide application.A sparse decomposition method based on quantum evolution algorithm is proposed.The Gabor atoms are encoded by the enhanced qubit probability amplitude.Simplified gradient evolution operation and generation-by-generation reduction mutation operation are used to update the individual population.And the inner products of the residual signal of sparse decomposition and Gabor atoms are used as the fitness to filter out the best atoms for each sparse decomposition.Two experiments on sparse decomposition of simulation signals and the fault feature extraction experiments of the bearing vibration signals are carried out.It's proved that the proposed method has a higher decomposition accuracy than the other methods.
Sparse decomposition expresses a signal as a linear combination of a small number of atoms in a redundant dictionary.The accuracy of the decomposition has an important influence on its wide application.A sparse decomposition method based on quantum evolution algorithm is proposed.The Gabor atoms are encoded by the enhanced qubit probability amplitude.Simplified gradient evolution operation and generation-by-generation reduction mutation operation are used to update the individual population.And the inner products of the residual signal of sparse decomposition and Gabor atoms are used as the fitness to filter out the best atoms for each sparse decomposition.Two experiments on sparse decomposition of simulation signals and the fault feature extraction experiments of the bearing vibration signals are carried out.It's proved that the proposed method has a higher decomposition accuracy than the other methods.
引文
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[2]Narayanan S,Sahoo S K,Makur A.Greedy pursuits assisted basis pursuit for reconstruction of joint-sparse signals[J].Signal Processing,2018,148(3):485-491.
[3]Gerist S,Maheri M R.Multi-stage approach for structural damage detection problem using basis pursuit and particle swarm optimization[J].Journal of Sound and Vibration,2016,384(1):210-226.
[4]Qin Y,Mao Y F,Tang B P.Vibration signal component separation by iteratively using basis pursuit and its application in mechanical fault detection[J].Journal of Sound and Vibration,2013,332(20):5217-5235.
[5]Qin Q,Jiang Z N,Feng K,et al.A novel scheme for fault detection of reciprocating compressor valves based on basis pursuit,wave matching and support vector machine[J].Measurement,2012,45(5):897-908.
[6]Xu S P,Yang X H,Jiang S L.A fast nonlocally centralized sparse representation algorithm for image denoising[J].Signal Processing,2017,131(1):99-112.
[7]Ventura R F I,Vandergheynst P.Matching pursuit through genetic algorithms[R].Signal Processing Laboratories:Lausanne, Switzerland,2001.
[8]Li C,Su Y,Zhang Y,et al.Root imaging from ground penetrating radar data by CPSO-OMP compressed sensing[J].Journal of Forestry Research,2017,28(1):155-162.
[9]Yang M,Liu N B,Liu W.Image 1D OMP sparse decomposition with modified fruit-fly optimization algorithm[J].Cluster Computing,2017,20(4):3015-3022.
[10]Han K H,Kim J H.Quantum-inspired evolutionary algorithm for a class of combinatorial optimization[J].IEEE Transactions on Evolutionary Computation,2002,6(6):580-593.
[11]Li P C,Li S Y.Quantum-inspired evolutionary algorithm for continuous spaces optimization[J].Chinese Journal of Electronics,2008,17(1):80-84.
[12]Li P C,Li S Y.Quantum-inspired evolutionary algorithm for continuous spaces optimization based on Bloch coordinates of qubits[J].Neurocomputing,2008,72(3):581-591.
[13]Lv F M,Yang G W,Wang S B,et al. The research on controlling the iteration of quantum-inspired evolutionary algorithms for artificial neural networks[C].Algorithmic Aspects in Information and Management,2014:253-262.
[14]Meng Y Y,Liu X Y.Quantum inspired evolutionary algorithm for community detection in complex networks[J].Physics Letters A,2018,382(34):2305-2312.
[15]Li S,Zhang P L,Li B,et al. Quantum GA-PLS for feature selection method and its application[J].Chinese Journal of Quantum Electronics(量子电子学报)2014,31(2):194-201(in Chinese).
[16]Guo Q,Ruan G Q,Wan J.A sparse signal reconstruction method based on improved double chains quantum genetic algorithm[J].Symmetry,2017,9(9):178-195.
[17]Wu J L,Li F,Zheng B Y.Quantum bacterial foraging algorithm with adaptive phase rotation[J].Journal of Signal Processing(信号处理),2015,31(8):901-911(in Chinese).
[18]Li P C,Song K P,Shang F H.Double chains quantum genetic algorithm with application to neuro-fuzzy controller design[J].Advances in Engineering Software,2011,42(10):875-886.
[19]Zhang Y X,Qian X Y,Peng H D,et al.Real-coded quantum evolutionary algorithm based on allele[J].Chinese Journal of Scientific Instrument(仪器仪表学报)2015,36(9):2129-2137(in Chinese).