Parametric Time-frequency Analysis (TFA)

Transcription

1 Parametric Time-frequency Analysis (TFA) Yang Yang Shanghai Jiao Tong University August, 2015

2 OUTLINE Background Theory and methods Applications

3 Non-stationary signals Vibration signals Radar signals Bioelectric signal Nonstationary signals Seismic data and guided waves Electronic signal and speech

4 Time domain Frequency domain Fourier transform-global transform Stationary signal Piece-wised stationary signal Non-stationary signal Amp 0 Amp 0 Amp Time/Sec Time/Sec Time/Sec Amp Amp Amp Freq / Hz Freq / Hz Freq / Hz

5 Non-stationary signal and time-frequency analysis Instantaneous frequency(if) 1937:Carson & Fry 1958:Ville Group delay(gd) IF t GD f t 1 d 2 dt 1 d f 2 df Controversy Uniqueness Shekel Prestley Huang Physical meaning Mandel Cohen Mono-component signal IF LGD Multi-component signal IF of cmp1 IF of cmp2

6 Time-frequency analysis(tfa) Background: TFA->TFR(time-frequency representation) & TFD(time-frequency distribution TFA Nonparametric TFA Semiparametric TFA Parametric TFA Post-processor Sparse decomposition Global TF transform Key issues of TFA: Concentration improvement and cross-term suppression

7 TFAs Short-time Fourier transform(stft) Wavelet transform Joseph Fourier ( ) Dennis Gabor ( ) Alfréd Haar ( ) Jean Morlet Ingrid Daubechies Widely used TFA Wigner-Ville distribution (WVD) Sparse decomposition Eugene p Wigner Stephane Mallat Yves Meyer

8 TFAs Problem: 1&2-Poor concentration, incorrect instantaneous amplitude (IA) 3-Interference of cross-term 4-Poor characterization of IF 1. STFT 2. Continues wavelet transform 40 Freq/Hz True IF Time / Sec 3.WVD 4.Sparse decomposition

9 Chirplet transform (CT) Signal model Effect of chirplet parameter on Gaussian window function Chirplet transform Mother chirplet 高斯窗 STFT Wavelet transform Chirplet transform 时移 TF resolution Frequency/Hz p1 p2 p3 Frequency/Hz p1 p2 p3 Frequency/Hz p1 p2 p3 频移 Time/Sec Time/Sec Time/Sec Section (t=120sec) Normalized envelope Normalized envelope Normalized envelope 线性调频 Frequency/Hz Frequency/Hz Frequency/Hz

10 CT and general parametric TFA 频率旋转算子 频率平移算子 Frequency c c IF(t) ct Frequency IF t; s IFs t P t 0 ω 0 θ ω 0 s IF P t Time t 0 Time

11 General parametric TFA Problem: Parametric TFAs lack of general theoretical framework to implement Contribution: General parametric TF transform and dual definition Theory and methods Parametric TFA Kernel construction and estimation Multi-component TFR fusion Signal decomposition Rotation operator Shift operator Applications Vibration analysis of rotatory machines with variable speed Dispersion analysis of guided waves Nonlinear system identification General parameterized time-frequency transform, IEEE Transactions on Signal Processing, 62(11), pp , 2014

12 Parametric TFA Problem: Traditional TFAs need to balance the tradeoffs between concentration and cross-term and between time and frequency resolution Contribution: New parametric TFAs are constructed using different kernels and corresponding kernel parameter estimators are developed TFR fusion Theory and methods Parametric TFA Kernel construction and estimation Multi-component Signal decomposition Applications Vibration analysis of rotatory machines with variable speed Polynomial chirplet transform (PCT) Spline chirplet transform (SCT) Generalized warblet transform (GWT) Dispersion analysis of guided waves Nonlinear system identification Spline-kernelled chirplet transform for the analysis of signals with time-varying frequency and its application, IEEE Transactions on Industrial Electronics, 59(3), pp , Characterize highly oscillating frequency modulation using generalized Warblet transform, Mechanical Systems and Signal Processing, 26, pp , 2012

13 Parameter estimation TFD dependent estimator (TF domain) Model-based estimator(parameter space) FCIP G s ; P 4 First PCT Second PCT Final PCT

14 Multi-component signal How to analyze multi-component signals? t IF 1 f IF 2

15 Parametric TFA Problem: Traditional TFA suffers from the poor concentration or interference of cross-term in the case of multi-component signals Contribution: TFR fusion and signal decomposition were developed for multi-component signals TFR fusion Theory and methods Parametric TFA Kernel construction and estimation Multi-component Signal decomposition TFR manipulation Applications Vibration analysis of rotatory machines with variable speed Signal decomposition Dispersion analysis of guided waves Nonlinear system identification Application of parameterized time-frequency analysis on multicomponent frequency modulated signals, IEEE Transactions on Instrumentation and Measurement, 63(12), pp , Multicomponent signal analysis based on polynomial chirplet transform, IEEE Transactions on Industrial Electronics, 60(9), pp , 2013

16 Multi-component signal Image processing High-pass 2D filter Connectivity labeling Rotate and filter Rotate Filter and recover

17 Application1-Hydraulic turbine Theory and methods Parametric TFA Kernel construction and estimation Hydraulic turbine TFR fusion Multi-component Signal decomposition Applications Vibration analysis of rotatory machines with variable speed Dispersion analysis of guided waves Shut-down stage Continuous and non-stationary process Rich information Multiple non-stationary components Nonlinear system identification

18 Application1-Hydraulic turbine Problem: Traditional TFA cannot characterize timefrequency pattern of multi-component nonstationary signal accurately Contribution: The proposed multi-component signal analysis method provides better solution of analyzing such signal in TF domain Components separation & parametric TFA 1X 2X STFT Wavelet transform 3X 4X WVD Sparse decomposition TFR combination Residual Vibration signal analysis using parameterized time-frequency method for feature extraction of varying-speed rotary machinery, Journal of Sound and Vibration,332(20), pp , 2015.

19 Application2-Lamb wave analysis Specimen Structure health detection GCC mirror GCL biconvex lens Theory and methods Parametric TFA Nd:Yad Pulse laser 532nm Kernel construction and estimation Trigger Frequency conversion unit Laser Doppler Velocimeter 0-2MHz TFR fusion Multi-component Signal decomposition Digital oscilloscope 2.5GS/s,100MHz Dispersion curves Gourp velocity/km/s A0 S0 A1 S1 A fd/mhz.mm S2 A3 S3 Applications Vibration analysis of rotatory machines with variable speed Dispersion analysis of guided waves Nonlinear system identification

20 Application2-Guided wave analysis TFR manipulation based on parametric TFA of frequency domain Simulated Lamb wave signal STFT Wavelet transform A 1 A 0 S 0 WVD D-STFT FPCT FGWT+TFR fusion Local Dispersion estimation of mode A0 Local Dispersion estimation of mode S0 Frequency-varying group delay estimation using frequency domain polynomial chirplet transform, Mechanical Systems and Signal Processing, 46(1), pp , 2014.

21 Application3-System identification System identification Theory and methods Parametric TFA Kernel construction and estimation Dynamic system modeling TFR fusion Multi-component Signal decomposition System control Applications Vibration analysis of rotatory machines with variable speed Nonlinear (time-varying) system 1. varying restoring forces 2. varying natural frequencies Dispersion analysis of guided waves Nonlinear system identification

22 Application3-System identification 1. Extract TF features using parametric TFA(IF &IA); 2. Estimate mode shape; 3. reconstruct backbone; 4. Estimate nonlinear stiffness and coupling coef STFT PCT Real value Backbone and coupling TFR of TFR of

23 Publications 1. Yang Y., Dong X.J., Peng Z.K., Zhang W. M., Meng G., Vibration signal analysis using parameterized time-frequency method for feature extraction of varying-speed rotary machinery, Journal of Sound and Vibration,332(20), pp , Yang Y., Dong X.J., Zhang W.M., Peng Z.K., Meng G., Component Extraction for Non-stationary Multi-component Signal Using Parameterized De-chirping and Band-pass Filter, IEEE Signal Processing Letters, Yang Y., Peng Z.K., Dong X.J., Zhang W.M., General parameterized time-frequency transform, IEEE Transactions on Signal Processing, 62(11), pp , Yang Y., Peng Z.K., Dong X.J., Zhang W.M., Application of parameterized time-frequency analysis on multicomponent frequency modulated signals, IEEE Transactions on Instrumentation and Measurement, 63(12), pp , Yang Y., Zhang W.M., Peng Z.K., Meng G., Multicomponent signal analysis based on polynomial chirplet transform, IEEE Transactions on Industrial Electronics,, 60(9), pp , Yang Y., Peng Z.K., Zhang W.M., Meng G., Spline-kernelled chirplet transform for the analysis of signals with timevarying frequency and its application, IEEE Transactions on Industrial Electronics, 59(3), pp , Yang Y., Peng Z.K., Zhang W.M., Meng G., Frequency-varying group delay estimation using frequency domain polynomial chirplet transform, Mechanical Systems and Signal Processing, 46(1), pp , Yang Y., Peng Z.K., Zhang W.M., Meng G., Characterize highly oscillating frequency modulation using generalized Warblet transform, Mechanical Systems and Signal Processing, 26, pp , Yang Y., Liao Y.X., Meng G., Zhang W.M., A hybrid feature selection scheme for unsupervised learning and its application in bearing fault diagnosis, Expert Systems with Applications, 38(9), pp , 2011.

24 Thanks!