一种基于人工蜂群算法的混沌信号盲分离方法

混沌信号所固有的非周期、宽带频谱和对初值极度敏感等特性使得对这类信号进行盲分离极为困难. 针对这一问题, 提出一种新的盲分离方法, 该方法通过相空间重构来构造代价函数, 将混沌信号的盲分离转化为一个无约束优化问题, 并利用人工蜂群算法进行求解. 不同于现有的独立成分分析方法仅使用混合信号的统计特性来解决分离问题, 该方法能充分利用混合信号内在的动态特性, 因而在处理混沌信号这种确定性信号时能获得更好的分离效果. 此外, 正交矩阵的参数化表示有效地降低了盲分离问题的复杂性, 使优化过程能快速收敛. 实验结果表明, 该方法具有较快的收敛速度和较高的数值精度, 在分离混沌信号时其整体性能优于现有的几种盲分离方法. 同时, 在分离混沌-高斯混合信号的实验中该方法也展现出优异良好的性能, 这表明该文的方法有应用潜力.

A blind source separation method for chaotic signals based on artificial bee colony algorithm

The inherent features, such as non-periodic, wide band spectrum, and extreflely sensitive to initial values etc. make it quite a challenge to blindly separate the mixed chaotic signals. A new blind source separation method based on the artificial bee colony algorithm is proposed in this paper. This method can recover chaotic sources from noisy observations on their linear mixtures without any prior information about the source equations. The proposed method is structured in the phase space of the demixed signals, which is reconstructed from the observations by using delay-embedding method. An objective function in the reconstructed phase space is designed so that the blind source separation problem is transformed into an optimization problem. The optimal demixing matrix is obtained by maximize the objective function with an artificial bee colony optimizer and the chaotic sources are then recovered by multiplying the observed mixtures and the optimal demixing matrix. Before the optimization procedure is made, a pre-whitening should be employed. Additionally, the parameterized repreflentation of orthogonal matrices through principal rotation is adopted to reduce the dimension of the optimization procedure so that the proposed blind source separation algorithm can converge quickly. Different from the traditional independent component analysis approaches which concern mainly the statistical features, the proposed blind source separation method utilizes the dynamics in the observed mixtures by means of phase space reconstruction. Therefore, better performance can be achieved when it is used to deal with chaotic signals.In computer simulation, two cases are taken into consideration: namely, the mixture is noiseless or not contaminated by noise. The correlation coefficient criterion and the performance index criterion are adopted to evaluate the separation performances. Simulation result shows that in most cases the proposed approach converges within a few tens of iterations and the chaotic sources can be accurately recovered. The impact of noise level and signal length on the separation performance is investigated in detail. The overall performance of the proposed approach is much better than the traditional independent component analysis approaches. Moreover, the capability of separating the mixed chaotic and Gaussian signals reflealed in the simulation indicates that the proposed approach has the potential to be applied in a wider range of applications.