gp_cd.m

对所采集到的非线性信号进行数据预处理,消除趋势项,球得其关联维数

% GP算法求关联维
% the function is used to calculate correlation dimention with G-P algorithm
% data:the time series
% N: the length of the time series
% tau: the time delay
% m:the embedded dimention m
clc
clear
close all
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 调入试验数据
load f511x1_del_moving.txt;
x=f511x1_del_moving;              % 时间序列(列向量)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 调入试验数据
x = fun_normalize_1(x);           % 归一化
data=x';                          % 注意：此处应为一个行向量
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('======= GP算法求关联维 ========');
tau = 14;                         % 希腊字母 tau 代表时延
m = 6;                            % 嵌入维    

logdelt = 0.2;
ln_r = [-7:logdelt:0];
delt = exp(ln_r);
for k=1:length(ln_r)
   r=delt(k); 
   %C(k)=fun_correlation_integral_distance(m,data,r,tau);  %输出变量为关联积分,用计算空间距离的方法
   C(k)=fun_correlation_integral_max(m,data,r,tau);     %输出变量为关联积分，用每维最大值的方法
   k
    if (C(k)<0.0001)
        C(k)=0.0001;
    end
    ln_C(k)=log(C(k));            %lnC(r)
end
C
subplot(211)
plot(ln_r,ln_C,'*:');grid;
xlabel('ln r'); ylabel('ln C(r)');
hold on;

subplot(212)
Y = diff(ln_C)./logdelt;
plot(Y,'+:'); grid;
xlabel('n'); ylabel('slope'); 
hold on;

%------------------------------------------------------
% 拟合线性区域
ln_Cr=ln_C;
ln_r=ln_r;
LinearZone = [10:25];
F = polyfit(ln_r(LinearZone),ln_Cr(LinearZone),1);
CorrelationDimension = F(1)