局域均值分解(Local mean decomposition,LMD)的主要思想是把一个时间序列的信号,分解成不同尺度的包络信号和纯调频信号,然后获得信号的时频分布。LMD算法用极值点来定义局部均值函数和局域包络函数,然后用滑动平均来平滑均值和包络函...局域均值分解(Local mean decomposition,LMD)的主要思想是把一个时间序列的信号,分解成不同尺度的包络信号和纯调频信号,然后获得信号的时频分布。LMD算法用极值点来定义局部均值函数和局域包络函数,然后用滑动平均来平滑均值和包络函数,针对用滑动平均平滑均值和包络函数误差较大的缺点,提出了采用三次样条对上、下极值点分别插值求得上下包络线,然后由上下包络线的平均获得局部平均函数,由上下包络线相减的绝对值获得局部包络的方法。通过对非线性和实例振动信号的实验研究表明,基于样条的LMD方法的分析精度比LMD方法高。展开更多
A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined...A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined by the introduced base functions, include the B-spline curves and can approximate the B-spline curves from both sides. The curves can be adjusted easily by using the shape parameter a, where dpi（a,t） is linear with respect to da for the fixed t. With the shape parameter chosen properly, the defined curves can be used to precisely represent straight line segments, parabola segments, circular arcs and some transcendental curves, and the corresponding tensor product surfaces can also represent spherical surfaces, cylindrical surfaces and some transcendental surfaces exactly. By abandoning positive property, this paper proposes a new C^2 continuous blended interpolation spline based on piecewise trigonometric polynomials associated with a sequence of local parameters. Illustration showed that the curves and surfaces constructed by the blended spline can be adjusted easily and freely. The blended interpolation spline curves can be shape-preserving with proper local parameters since these local parameters can be considered to be the magnification ratio to the length of tangent vectors at the interpolating points. The idea is extended to produce blended spline surfaces.展开更多
文摘局域均值分解(Local mean decomposition,LMD)的主要思想是把一个时间序列的信号,分解成不同尺度的包络信号和纯调频信号,然后获得信号的时频分布。LMD算法用极值点来定义局部均值函数和局域包络函数,然后用滑动平均来平滑均值和包络函数,针对用滑动平均平滑均值和包络函数误差较大的缺点,提出了采用三次样条对上、下极值点分别插值求得上下包络线,然后由上下包络线的平均获得局部平均函数,由上下包络线相减的绝对值获得局部包络的方法。通过对非线性和实例振动信号的实验研究表明,基于样条的LMD方法的分析精度比LMD方法高。
基金Project supported by the National Natural Science Foundation of China (Nos. 10171026 and 60473114), the Research Funds forYoung Innovation Group, Education Department of Anhui Prov-ince (No. 2005TD03) and the Natural Science Foundation of An-hui Provincial Education Department (No. 2006KJ252B), China
文摘A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined by the introduced base functions, include the B-spline curves and can approximate the B-spline curves from both sides. The curves can be adjusted easily by using the shape parameter a, where dpi（a,t） is linear with respect to da for the fixed t. With the shape parameter chosen properly, the defined curves can be used to precisely represent straight line segments, parabola segments, circular arcs and some transcendental curves, and the corresponding tensor product surfaces can also represent spherical surfaces, cylindrical surfaces and some transcendental surfaces exactly. By abandoning positive property, this paper proposes a new C^2 continuous blended interpolation spline based on piecewise trigonometric polynomials associated with a sequence of local parameters. Illustration showed that the curves and surfaces constructed by the blended spline can be adjusted easily and freely. The blended interpolation spline curves can be shape-preserving with proper local parameters since these local parameters can be considered to be the magnification ratio to the length of tangent vectors at the interpolating points. The idea is extended to produce blended spline surfaces.
