自适应最稀疏时频分析(adaptive and sparsest time-frequency analysis,ASTFA)方法将信号分解转化为最优化问题,在优化的过程中实现信号的自适应分解.为了研究ASTFA的分解能力,在定义分解能力评价指标(Evaluation Index of Decompositi...自适应最稀疏时频分析(adaptive and sparsest time-frequency analysis,ASTFA)方法将信号分解转化为最优化问题,在优化的过程中实现信号的自适应分解.为了研究ASTFA的分解能力,在定义分解能力评价指标(Evaluation Index of Decomposition Capacity,EIDC)的基础上,以双谐波分量合成信号模型来研究幅值比、频率比、初始相位差对ASTFA的影响.同时,将ASTFA方法与经验模态分解(Empirical Mode Decomposition,EMD)、局部特征尺度分解(Local Characteristic-scale Decomposition,LCD)进行对比分析.研究结果表明,ASTFA方法的分解能力基本不受幅值比的影响,可分解的极限频率比较大,不受初始相位差的影响,该方法的分解能力具有明显的优越性.展开更多
Adaptive data analysis provides an important tool in extracting hidden physical information from multiscale data that arise from various applications.In this paper,we review two data-driven time-frequency analysis met...Adaptive data analysis provides an important tool in extracting hidden physical information from multiscale data that arise from various applications.In this paper,we review two data-driven time-frequency analysis methods that we introduced recently to study trend and instantaneous frequency of nonlinear and nonstationary data.These methods are inspired by the empirical mode decomposition method(EMD)and the recently developed compressed(compressive)sensing theory.The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary consisting of intrinsic mode functions of the form{a(t)cos(θ(t))},wherea is assumed to be less oscillatory than cos(θ(t))andθ0.This problem can be formulated as a nonlinear l0optimization problem.We have proposed two methods to solve this nonlinear optimization problem.The frst one is based on nonlinear basis pursuit and the second one is based on nonlinear matching pursuit.Convergence analysis has been carried out for the nonlinear matching pursuit method.Some numerical experiments are given to demonstrate the efectiveness of the proposed methods.展开更多
文摘自适应最稀疏时频分析(adaptive and sparsest time-frequency analysis,ASTFA)方法将信号分解转化为最优化问题,在优化的过程中实现信号的自适应分解.为了研究ASTFA的分解能力,在定义分解能力评价指标(Evaluation Index of Decomposition Capacity,EIDC)的基础上,以双谐波分量合成信号模型来研究幅值比、频率比、初始相位差对ASTFA的影响.同时,将ASTFA方法与经验模态分解(Empirical Mode Decomposition,EMD)、局部特征尺度分解(Local Characteristic-scale Decomposition,LCD)进行对比分析.研究结果表明,ASTFA方法的分解能力基本不受幅值比的影响,可分解的极限频率比较大,不受初始相位差的影响,该方法的分解能力具有明显的优越性.
基金supported by Air Force Ofce of Scientifc ResearchMultidisciplinary University Research Initiative+3 种基金USA(Grant No.FA9550-09-1-0613)Department of Energy of USA(Grant No.DE-FG02-06ER25727)Natural Science Foundation of USA(Grant No.DMS-0908546)National Natural Science Foundation of China(Grant No.11201257)
文摘Adaptive data analysis provides an important tool in extracting hidden physical information from multiscale data that arise from various applications.In this paper,we review two data-driven time-frequency analysis methods that we introduced recently to study trend and instantaneous frequency of nonlinear and nonstationary data.These methods are inspired by the empirical mode decomposition method(EMD)and the recently developed compressed(compressive)sensing theory.The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary consisting of intrinsic mode functions of the form{a(t)cos(θ(t))},wherea is assumed to be less oscillatory than cos(θ(t))andθ0.This problem can be formulated as a nonlinear l0optimization problem.We have proposed two methods to solve this nonlinear optimization problem.The frst one is based on nonlinear basis pursuit and the second one is based on nonlinear matching pursuit.Convergence analysis has been carried out for the nonlinear matching pursuit method.Some numerical experiments are given to demonstrate the efectiveness of the proposed methods.
