1. Software version

MATLAB2013b

2. System Overview

        Lee index (Lipschitz exponent), German mathematicians Rudolf Lipschitz name , It is a smoothness index that describes better than the general continuous differentiability . Continuity with certain conditions is called Lee continuity . Lee index α It can be used to describe the singularity of signals . Generally speaking ,α The bigger it is , The smoother the signal is at this point ;α The smaller it is , Then the singularity of the signal at this point is greater . Li exponent is an exponent specially used to describe the smoothness of functions . A function is smooth or nonsingular if it is infinitely derivable , But if it has a discontinuity somewhere or a derivative of some order is discontinuous , It is usually called singularity of function , The singularity of the signal is usually Use Li index To portray . It is closely related to wavelet transform , The characteristics of signal singularity are described by wavelet transform , It's not hard for us to get out of , Li exponent also has the function of describing singular signals . The result of detecting the singularity of the signal by Li exponent is simple and clear , Convenient for observation , It has great practical significance .

3. part matlab Program

clc;
clear;
close all;
warning off;
addpath 'func\'

%%
% Parameter initialization 
Len         = 2048;% The length of the signal 
Noise_Power = 0.5; % The amount of interference generated in the test 
select      = 2;   % Select signal 

%%
% Generate analog fault signals 
[s_normal,s_error] = func_sig_gen(Len,Noise_Power);
figure;
subplot(211);plot(s_normal);title(' Normal signal ');
subplot(212);plot(s_error);title(' Fault signal ');
%%
% Calculate the Li index 
if select == 1
   signal = s_normal;
end
if select == 2
   signal = s_error;
end

% Multi scale wavelet transform 
Ss      = 1;   
Ls      = 32;
wt      = CWT(signal,Ss:Ls,'gaus2');

% Modular maxima 
Max_Pos = func_WMMT(wt,10);

% Connect the corresponding maximum value of each level after wavelet change 
[Max_List,Ptr,Lengths] = func_find_Max_nlevel(Max_Pos,10);
 
% Draw the modulus maximum curve 
figure;
for k=1:length(Ptr)
	vec = Max_List(:,Ptr(k):Ptr(k) + Lengths(k)-1);
    plot(vec(2,:),log2(vec(1,:)));
    hold on;
end
axis([0,Len,0,6]);
xlabel('u');
ylabel('log2');

% Calculation Lipschitz Index  
Lipschitz = func_cal_Lipschitz(Ptr,Max_List,wt,Lengths); 
figure;
plot(Lipschitz,'r');


%%
% Detect the fault signal according to the calculation result of Li index 
cnt = 0;
PP  = [];
for i = 1:length(Lipschitz)
    if abs(Lipschitz(i)) >= 4
       cnt = cnt + 1; 
       PP(cnt) = i;
    end
end

if isempty(PP) == 0
    START = min(PP);
    ENDS  = max(PP);
    figure;
    plot(signal);title(' Fault detection ');
    hold on
    plot(14*START,-10:0.1:10,'r');
    hold on
    plot(Len,-10:0.1:10,'r');
else
    figure;
    plot(signal);title(' No fault ');    
end

4. Some simulation conclusions

First load the data ：

Then calculate the Li index ：

Carry out fault detection and analysis according to Li index ：

A16-17