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๐๐๐ The content of this article is as follows: ๐๐๐
Directory
๐ฅ1 Overview
๐2 Results
2.1 Stationary Signal
2.2 Noisy Non-Stationary Signal
2.3 Signal with Closed Modes
๐3 References
๐4 Matlab Code Implementation
1 Overview
This article explains a data-driven time-varying AM-FM signal adaptive signal decomposition method, data-driven adaptive linear frequency modulation mode decomposition, and its application in non-stationary conditions for machine fault diagnosis, mechanical systems and signal processing, adaptive linear frequency modulation mode tracking: algorithms and applications, nonlinear linear frequency modulation mode decomposition: a variational method.
Reproducing some results from the paper: Hongbing Wang, Shiqian Chen, et al. Data-driven adaptive chirp mode decomposition with application to machine fault diagnosis under non-stationary conditions, Mechanical Systems and Signal Processing, 2022. The algorithm used in the paper is an improved version of that in the paper: Shiqian Chen, et al. Adaptive chirp mode pursuit: Algorithm and applications, Mechanical Systems and Signal Processing, 2018. Some of the scripts are adopted from the paper: Shiqian Chen, et al. Nonlinear Chirp Mode Decomposition: A Variational Method, IEEE Transactions on Signal Processing, 2017. and the paper: Shiqian Chen, et al. Detection of rub-impact fault for rotor-stator systems: A novel method based on adaptive chirp mode decomposition, Journal of Sound and Vibration, 2019.
2 Results
2.1 Stationary Signal
2.2 Noisy Non-Stationary Signal
2.3 Signal with Closed Modes
้จๅไปฃ็ ๏ผ%%%%%%%%% Signal withClose modes %%%%%%%%%clc;clear;closeall;SampFreq =800;t =0:1/SampFreq:2-1/SampFreq;a1 =exp(-0.1*t); % Instantaneous amplitude (IA) 1Sig1 = a1.*cos(2*pi*(-60*t.^3+180*t.^2+100*t)); % mode 1IF1 =-180*t.^2+360*t+100;% instantaneous frequency (IF) 1a2 =exp(-0.2*t);% IA 2Sig2 = a2.*cos(2*pi*(-60*t.^3+180*t.^2+90*t)); % mode 2IF2 =-180*t.^2+360*t+90;% IF2a3 =exp(-0.3*t);% IA 3Sig3 = a3.*cos(2*pi*(-60*t.^3+180*t.^2+80*t)); % mode 3IF3 =-180*t.^2+360*t+80;% IF3Sig = Sig1 + Sig2 + Sig3;noise = addnoise(length(Sig),0,0);Sign = Sig+noise; figureset(gcf,'Position',[20100640500]);plot(t,Sign,'b-','linewidth',1);axis([02-44]);set(gca,'xtick',[0:1:2]);set(gca,'ytick',[-4:2:4]);xlabel('Time (s)','FontSize',24);ylabel('Amplitude','FontSize',24);set(gca,'FontSize',24,'FontName','Times New Roman','linewidth',2);set(gca,'looseInset',[0.020.020.020.02])%%Time-frequency distribution (TFD) by STFTfigure[Spec,f] = STFT(Sign',SampFreq,512,218);imagesc(t,f,abs(Spec)); set(gcf,'Position',[20 100 640 500]); axis([0 2 0 400]);xlabel('Time (s)','FontSize',24);ylabel('Frequency (Hz)','FontSize',24);set(gca,'YDir','normal');set(gca,'looseInset',[0.02 0.02 0.02 0.02])set(gca,'FontSize',24,'FontName','Times New Roman','linewidth',2);colormap('jet')%% DDACMDtic[iniIF,eIF,eIA,IMF] = DDACMD(Sign,SampFreq);toc%% Estimated IFfigureset(gcf,'Position',[20 100 640 500]);plot(t,IF1,'b-',t,iniIF(1,:),'k-.',t,eIF(1,:),'r--','linewidth',2) holdonplot(t,IF2,'b-',t,iniIF(2,:),'k-.',t,eIF(2,:),'r--','linewidth',2)holdonplot(t,IF3,'b-',t,iniIF(3,:),'k-.',t,eIF(3,:),'r--','linewidth',2) xlabel('Time (s)','FontSize',24);ylabel('Frequency (Hz)','FontSize',24);set(gca,'FontSize',24,'FontName','Times New Roman','linewidth',2);axis([020400]);set(gca,'looseInset',[0.020.020.020.02])%% Reconstructed modesfigureset(gcf,'Position',[20100640500]);axes('position',[0.130.800.840.17]);plot(t,IMF(1,:),'b-','linewidth',1);holdonplot(t,Sig1-IMF(1,:),'k--','MarkerIndices',1:60:length(t),'linewidth',1);axis([02-1.51.5]);set(gca,'xtick',[0:0.5:2]);set(gca,'ytick',[-101]);ylabel('m1','FontSize',24);set(gca,'FontSize',24,'FontName','Times New Roman','linewidth',2);axes('position',[0.130.490.840.17]);plot(t,IMF(2,:),'b-','linewidth',1);holdonplot(t,Sig2-IMF(2,:),'k--','MarkerIndices',1:60:length(t),'linewidth',1);axis([02-1.51.5]);set(gca,'xtick',[0:0.5:2]);set(gca,'ytick',[-101]);ylabel('m2','FontSize',24);set(gca,'FontSize',24,'FontName','Times New Roman','linewidth',2);axes('position',[0.130.180.840.17]);plot(t,IMF(3,:),'b-','linewidth',1);holdonplot(t,Sig3-IMF(3,:),'k--','MarkerIndices',1:60:length(t),'linewidth',1);axis([02-1.51.5]);set(gca,'xtick',[0:0.5:2]);set(gca,'ytick',[-101]);ylabel('m3','FontSize',24);set(gca,'FontSize',24,'FontName','Times New Roman','linewidth',2);xlabel('Time (s)','FontSize',24);%% Adaptive time-frequency spectrumband = [0 SampFreq/2];[ASpec,fbin] = TFspec(eIF(1:3,:),eIA(1:3,:),band);figureimagesc(t,fbin,abs(ASpec)); set(gcf,'Position',[20100640500]); axis([020400]);xlabel('Time (s)','FontSize',24);ylabel('Frequency (Hz)','FontSize',24);set(gca,'YDir','normal');set(gca,'looseInset',[0.020.020.020.02])set(gca,'FontSize',24,'FontName','Times New Roman','linewidth',2);colormap('jet')
3References
Some theoretical sources are from the internet. If there is any infringement, please contact for removal.
[1] Shiqian Chen (2023). Data-driven adaptive linear frequency modulation mode decomposition.
4 Matlab Code Implementation
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