1.程序功能描述
基于Lipschitz李式指数的随机信号特征识别和故障检测.
2.测试软件版本以及运行结果展示
MATLAB2013B版本运行
3.核心程序
% --- Executes on button press in pushbutton2. function pushbutton2_Callback(hObject, eventdata, handles) % hObject handle to pushbutton2 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) global Signal global Lipschitz % ߶ С 任 Ss = 1; Ls = 32; wt = cwt(Signal,Ss:Ls,'gaus2'); %ģ Max_Pos = func_WMMT(wt,10); % С 仯 ÿһ Ķ Ӧ ֵ [Max_List,Ptr,Lengths] = func_find_Max_nlevel(Max_Pos,10); % Lipschitzָ Lipschitz = func_cal_Lipschitz(Ptr,Max_List,wt,Lengths); axes(handles.axes2); for k=1:length(Ptr) vec = Max_List(:,Ptr(k):Ptr(k) + Lengths(k)-1); plot(vec(2,:),log2(vec(1,:))); hold on; end title('ģ '); xlabel('u'); ylabel('log2'); hold off axes(handles.axes3); plot(Lipschitz,'r'); axis([0,length(Lipschitz),0,10]); title('Lipschitzָ '); hold off % --- Executes on button press in pushbutton3. function pushbutton3_Callback(hObject, eventdata, handles) % hObject handle to pushbutton3 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % ָ ļ Թ źż global Signal global Lipschitz cnt = 0; PP = []; for i = 1:length(Lipschitz) if abs(Lipschitz(i)) >= 4 cnt = cnt + 1; PP(cnt) = i; end end Len = length(Signal); axes(handles.axes4); if isempty(PP) == 0 START = min(PP); ENDS = max(PP); plot(Signal);title(' ϼ '); hold on plot(14*START,-4:0.01:4,'r'); hold on plot(Len,-4:0.01:4,'r'); else plot(Signal);title(' '); end hold off % --- Executes on button press in pushbutton4. function pushbutton4_Callback(hObject, eventdata, handles) % hObject handle to pushbutton4 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) clc; clear; close all; % --- Executes on button press in pushbutton6. function pushbutton6_Callback(hObject, eventdata, handles) % hObject handle to pushbutton6 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) global Signal global Lipschitz KHI = func_KHI(Lipschitz); axes(handles.axes1); plot(KHI,'b-o'); title('KHIָ '); FGP1 = func_FGP1(Lipschitz); axes(handles.axes3); plot(FGP1,'b-o'); title('FGP1ָ '); FGP2 = func_FGP2(Lipschitz); axes(handles.axes2); plot(FGP2,'b-o'); title('FGP2ָ '); FGP3 = func_FGP3(FGP2,0.5); axes(handles.axes4); plot(FGP3,'b-o'); title('FGP3ָ ');
4.本算法原理
Lipschitz李式指数(Lipschitz Exponent, LE)是一种刻画信号局部动态行为的非线性度量方法,在随机信号特征识别与故障检测领域具有重要应用价值。
4.1 Lipschitz李式指数定义与性质
则称该过程在T 上具有 全局Lipschitz指数 α。若上述不等式仅对某个小邻域内的时间点成立,则称X(t) 在该邻域内具有 局部Lipschitz指数 α。α 越小,表示过程变化越剧烈;α=0 表示过程可能具有瞬时突变,而 α=1 则对应线性过程。
4.2 Lipschitz李式指数的估计
对于实际观测到的随机信号,其Lipschitz指数往往未知,需要通过数据驱动的方法进行估计。常用的估计方法包括:
局部平均方法(Local Average Method, LAM):
分形维数方法(Fractal Dimension Method, FDM):
利用分形维数与Lipschitz指数之间的关系,可以通过计算信号的盒计数法(Box-counting Dimension, BCD)或关联积分法(Correlation Integral Method, CIM)等分形维数估计方法间接得到Lipschitz指数。例如,对于一维信号,BCD定义为:
其中,N(ϵ) 是覆盖信号所需的边长为ϵ 的区间数。当信号具有Hölder连续性时,其Lipschitz指数与BCD满足关系:
4.3 Lipschitz李式指数在信号特征识别与故障检测中的应用
特征识别:Lipschitz指数反映了信号在不同尺度上的自相似性和局部波动特性,可用于识别信号的内在结构和动态行为模式。例如,在机械振动分析中,正常运行和故障状态下的振动信号可能具有不同的Lipschitz指数,从而用于区分不同的工作状态。
故障检测:当系统发生故障时,其产生的信号往往呈现出更为剧烈的变化,表现为Lipschitz指数的显著降低。因此,监测信号的Lipschitz指数变化可以作为一种有效的故障预警指标。具体实现时,可设定一个阈值 αthreshold,当估计的α^ 低于该阈值时触发报警:
此外,Lipschitz指数还可结合其他信号处理技术,如小波分析、希尔伯特黄变换等,构建多模态特征向量,进一步提高故障检测的准确性和鲁棒性。
标签:plot,李式,title,see,handles,matlab,信号,Lipschitz From: https://www.cnblogs.com/softcodes/p/18542717