EMD(Empirical Mode Decomposition)经验模态分解
EMD(Empirical Mode Decomposition)经验模态分解软件:MATLAB
function imf = emd(x)
% Empiricial Mode Decomposition (Hilbert-Huang Transform)
% imf = emd(x)
% Func : findpeaks
x = transpose(x(:));% 转置
imf = [];
while ~ismonotonic(x) %当x不是单调函数,分解终止条件
x1 = x;
sd = Inf;%均值
%直到x1满足IMF条件,得c1
while (sd > 0.1) || ~isimf(x1) %当标准偏差系数sd大于0.1或x1不是固有模态函数时,分量终止条件
s1 = getspline(x1); % 上包络线
s2 = -getspline(-x1); % 下包络线
x2 = x1-(s1+s2)/2; % 此处的x2为文章中的h
sd = sum((x1-x2).^2)/sum(x1.^2);
x1 = x2;
end
imf= ;
x = x-x1;
end
单调性判断:
function u = ismonotonic(x)
%u=0表示x不是单调函数,u=1表示x为单调的
u1 = length(findpeaks(x))*length(findpeaks(-x));
if u1 > 0
u = 0;
else
u = 1;
end是否是本征模态函数IMF:
function u = isimf(x)
%u=0表示x不是固有模式函数,u=1表示x是固有模式函数
N= length(x);
u1 = sum(x(1:N-1).*x(2:N) < 0);
u2 = length(findpeaks(x))+length(findpeaks(-x));
if abs(u1-u2) > 1,
u = 0;
else
u = 1;
end三次样条插值:
function s = getspline(x)
%三次样条函数拟合成元数据包络线
N = length(x);
p = findpeaks(x);
s = spline(,,1:N);寻找极值点:
function n = findpeaks(x)
% Find peaks.找到极值
% n = findpeaks(x)
% 二阶导数<0表示曲线是凸弧,一阶导数的斜率在减小
% 二阶导数>0表示曲线是凹弧
n = find(diff(diff(x) > 0) < 0);
u = find(x(n+1) > x(n));
n(u) = n(u)+1;
请问哪一组数据是残差呢?
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