Time-frequency-domain modal identification of ambient vibration structures using Wavelet Transform Numerical example.

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Presentation transcript:

Time-frequency-domain modal identification of ambient vibration structures using Wavelet Transform Numerical example

Natural frequency & damping Frequency Time Cutting slide Frequency domain Time domain Damping Ratios Identification Natural Frequencies Identification

Wavelet transform  Continuous wavelet transform (CWT) is defined as convolution operator of signal X(t) and wavelet function : Wavelet function : Complex conjugate of wavelet function : Wavelet transform coefficient : Wavelet scale and translation parameters  Info of time and frequency can be obtained. Relation of wavelet scale and Fourier frequency can be estimated s : Wavelet scale; f F : Fourier frequency f s : Sampling frequency; f  : Central wavelet frequency

Wavelet function  The complex Morlet wavelet is commonly used in the CWT: : Fourier transform of complex Morlet wavelet : Fourier frequency and central wavelet frequency

Damping & mode shapes  Output displacements of the MDOF system can be decomposed in the structural normalized coordinates  Wavelet transform coefficient of output response:  Mode shape can be estimated via the wavelet coefficients of output displacements at point k and reference point:  Decay envelope and logarithmic decrement can be extracted from this decay envelope and in tern of modulus: and

Damped natural frequencies Wavelet transform (Floor1) Frequency domain Wavelet transform (Floor5)  =80s Frequency domain 5.91Hz 9.12Hz 14.02Hz Difficulties in identifying high-order low-dominant frequencnies Difficulties in identifying high-order low-dominant frequencnies due to inflexible resolutions & used smoothing due to inflexible resolutions & used smoothing

Refined by bandwidth filtering Filtered at frequency bandwidths Filtered at frequency bandwidths 1) Hz 1) Hz 2) Hz 2) Hz 3) Hz 3) Hz 4) Hz 4) Hz 5) 25-50Hz 5) 25-50Hz

Refined wavelet transform Bandwidth 0-20Hz [Bandwidth Hz] [Bandwidth Hz] [Bandwidth Hz] Only 1 st mode dominated f1=1.72Hz f2=5.37Hz f3=8.99Hz Refined and localized by Refined and localized by multiresolution analysis multiresolution analysis Filtered at frequency Filtered at frequency bandwidths bandwidths ( Hz; Hz ( Hz; Hz Hz; Hz; Hz; Hz; 25-50Hz) 25-50Hz) Dominant for mode 1 Dominant for mode 3 Dominant for mode 2

Refined wavelet transform [Bandwidth Hz] [Bandwidth Hz] [Bandwidth Hz] f1=1.72Hz f2=5.37Hz f3=8.99Hz Mode 1 Mode 2 Mode 3 [Slide 1] [Slide 2] [Slide 1] [Slide 2] [Slide 1] [Slide 2] 1.76Hz 5.49Hz 8.95Hz Amplitude envelope slop Damped Natural Frequencies (Hz) FEMFDDFDD-RDTWT mode mode mode mode mode