Positive-instantaneous frequency representation for transient signals has always been a great concern due to its theoretical and practical importance,although the involved concept itself is paradoxical.The desire and ...Positive-instantaneous frequency representation for transient signals has always been a great concern due to its theoretical and practical importance,although the involved concept itself is paradoxical.The desire and practice of uniqueness of such frequency representation(decomposition)raise the related topics in approximation.During approximately the last two decades there has formulated a signal decomposition and reconstruction method rooted in harmonic and complex analysis giving rise to the desired signal representations.The method decomposes any signal into a few basic signals that possess positive instantaneous frequencies.The theory has profound relations to classical mathematics and can be generalized to signals defined in higher dimensional manifolds with vector and matrix values,and in particular,promotes kernel approximation for multi-variate functions.This article mainly serves as a survey.It also gives two important technical proofs of which one for a general convergence result(Theorem 3.4),and the other for necessity of multiple kernel(Lemma 3.7).Expositorily,for a given real-valued signal f one can associate it with a Hardy space function F whose real part coincides with f.Such function F has the form F=f+iHf,where H stands for the Hilbert transformation of the context.We develop fast converging expansions of F in orthogonal terms of the form F=∑k=1^(∞)c_(k)B_(k),where B_(k)'s are also Hardy space functions but with the additional properties B_(k)(t)=ρ_(k)(t)e^(iθ_(k)(t)),ρk≥0,θ′_(k)(t)≥0,a.e.The original real-valued function f is accordingly expanded f=∑k=1^(∞)ρ_(k)(t)cosθ_(k)(t)which,besides the properties ofρ_(k)andθ_(k)given above,also satisfies H(ρ_(k)cosθ_(k))(t)ρ_(k)(t)sinρ_(k)(t).Real-valued functions f(t)=ρ(t)cosθ(t)that satisfy the conditionρ≥0,θ′(t)≥0,H(ρcosθ)(t)=ρ(t)sinθ(t)are called mono-components.If f is a mono-component,then the phase derivativeθ′(t)is defined to be instantaneous frequency of f.The above described positive-instantaneous fre展开更多
光伏出力的随机波动性对电网稳定运行产生一定影响,针对这一问题,提出了基于自适应变分模态分解的混合储能系统(hybrid energy storage system,HESS)平滑光伏出力波动方法。首先,针对典型光伏出力场景,结合光伏功率波动标准及储能元件特...光伏出力的随机波动性对电网稳定运行产生一定影响,针对这一问题,提出了基于自适应变分模态分解的混合储能系统(hybrid energy storage system,HESS)平滑光伏出力波动方法。首先,针对典型光伏出力场景,结合光伏功率波动标准及储能元件特性,对光伏原始功率自适应的进行变分模态分解,从而实现功率初级分配;其次,在储能系统内部,监测超级电容荷电状态,通过模糊控制对储能元件初级功率进行二次修正。研究结果表明:所提控制策略能够自适应地实现光伏出力的最佳分解及合理分配,在有效减少光伏出力波动的同时避免了储能元件出现冗余容量;基于模糊控制的初级功率优化修正,使储能元件在荷电状态(state of charge,SOC)安全范围内工作,极大延长了储能元件的经济寿命。研究结果为变分模态分解算法的广泛应用提供了坚实基础,同时为实现大规模光伏电站的可靠并网及进一步开展光伏功率在线控制提供了一定的理论依据。展开更多
基金Macao University Multi-Year Research Grant(MYRG)MYRG2016-00053-FSTMacao Government Science and Technology Foundation FDCT 0123/2018/A3.
文摘Positive-instantaneous frequency representation for transient signals has always been a great concern due to its theoretical and practical importance,although the involved concept itself is paradoxical.The desire and practice of uniqueness of such frequency representation(decomposition)raise the related topics in approximation.During approximately the last two decades there has formulated a signal decomposition and reconstruction method rooted in harmonic and complex analysis giving rise to the desired signal representations.The method decomposes any signal into a few basic signals that possess positive instantaneous frequencies.The theory has profound relations to classical mathematics and can be generalized to signals defined in higher dimensional manifolds with vector and matrix values,and in particular,promotes kernel approximation for multi-variate functions.This article mainly serves as a survey.It also gives two important technical proofs of which one for a general convergence result(Theorem 3.4),and the other for necessity of multiple kernel(Lemma 3.7).Expositorily,for a given real-valued signal f one can associate it with a Hardy space function F whose real part coincides with f.Such function F has the form F=f+iHf,where H stands for the Hilbert transformation of the context.We develop fast converging expansions of F in orthogonal terms of the form F=∑k=1^(∞)c_(k)B_(k),where B_(k)'s are also Hardy space functions but with the additional properties B_(k)(t)=ρ_(k)(t)e^(iθ_(k)(t)),ρk≥0,θ′_(k)(t)≥0,a.e.The original real-valued function f is accordingly expanded f=∑k=1^(∞)ρ_(k)(t)cosθ_(k)(t)which,besides the properties ofρ_(k)andθ_(k)given above,also satisfies H(ρ_(k)cosθ_(k))(t)ρ_(k)(t)sinρ_(k)(t).Real-valued functions f(t)=ρ(t)cosθ(t)that satisfy the conditionρ≥0,θ′(t)≥0,H(ρcosθ)(t)=ρ(t)sinθ(t)are called mono-components.If f is a mono-component,then the phase derivativeθ′(t)is defined to be instantaneous frequency of f.The above described positive-instantaneous fre
文摘光伏出力的随机波动性对电网稳定运行产生一定影响,针对这一问题,提出了基于自适应变分模态分解的混合储能系统(hybrid energy storage system,HESS)平滑光伏出力波动方法。首先,针对典型光伏出力场景,结合光伏功率波动标准及储能元件特性,对光伏原始功率自适应的进行变分模态分解,从而实现功率初级分配;其次,在储能系统内部,监测超级电容荷电状态,通过模糊控制对储能元件初级功率进行二次修正。研究结果表明:所提控制策略能够自适应地实现光伏出力的最佳分解及合理分配,在有效减少光伏出力波动的同时避免了储能元件出现冗余容量;基于模糊控制的初级功率优化修正,使储能元件在荷电状态(state of charge,SOC)安全范围内工作,极大延长了储能元件的经济寿命。研究结果为变分模态分解算法的广泛应用提供了坚实基础,同时为实现大规模光伏电站的可靠并网及进一步开展光伏功率在线控制提供了一定的理论依据。
文摘为了改善传统姿态解算方法精度不高的问题,提出一种基于互补滤波和改进自适应卡尔曼的姿态解算融合算法。利用互补滤波将微电子机械系统(Micro-Electro-Mechanical System,MEMS)陀螺仪、加速度计和电子罗盘解算得到的姿态角进行融合,得到当前载体的状态方程和观测方程。采用上三角-对角(Upper Triangular and Diagonal,UD)分解改进自适应卡尔曼滤波算法,进行基于误差方差最小迭代估计的数据融合,对噪声进行过滤,同时抑制滤波发散,得到最优的估计姿态角。将高精度激光惯导系统作为参考,分析自适应卡尔曼滤波算法和基于互补滤波和改进自适应卡尔曼算法的解算效果。实验结果表明,该算法能够显著提高姿态角解算精度。
