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Fig. 9. Measured hurricane data and CWT-scalogram. Fig. 10. Ground motion record and wavelet scalogram.

Figure 9 Measured hurricane data and CWT-scalogram. Fig. 10. Ground motion record and wavelet scalogram.

Related Figures (21)

Fig. 1. A structural response signal, a view of the wavelet decomposition basis functions (left column), and a view of the Fourier decomposition basis functions (right column). of a random signal using wavelet decomposition and Fourier decomposition. The top plot is the measured response of a structure to environmental loads. The right column shows several sine-wave basis functions of vari- ous frequencies used by Fourier analysis. Each wave is represented by a single complex coefficient describing amplitude and phase. The left column is a qualitative view of several wavelet-basis functions that might be used to decompose the structural response. Each of the three plots in the left column consist of multiple trans- ations of a single parent wavelet function, which in this case resembles a windowed sine wave. The first of the three left plots is built from nine parent wavelets, the middle left plot consists of five wavelets, encompassing ower frequency information. The bottom left plot is built from three parent wavelets dilated still larger, cap- turing even lower frequency behavior. The essential dif- Fig. 1 gives a qualitative outlay of the representation
Fig. 1. A structural response signal, a view of the wavelet decomposition basis functions (left column), and a view of the Fourier decomposition basis functions (right column). of a random signal using wavelet decomposition and Fourier decomposition. The top plot is the measured response of a structure to environmental loads. The right column shows several sine-wave basis functions of vari- ous frequencies used by Fourier analysis. Each wave is represented by a single complex coefficient describing amplitude and phase. The left column is a qualitative view of several wavelet-basis functions that might be used to decompose the structural response. Each of the three plots in the left column consist of multiple trans- ations of a single parent wavelet function, which in this case resembles a windowed sine wave. The first of the three left plots is built from nine parent wavelets, the middle left plot consists of five wavelets, encompassing ower frequency information. The bottom left plot is built from three parent wavelets dilated still larger, cap- turing even lower frequency behavior. The essential dif- Fig. 1 gives a qualitative outlay of the representation
Fig. 2. From top left column-wise downward: measured TLP sure response to wind and wave field and its time-scale decomposition using wavelet transforms.
Fig. 2. From top left column-wise downward: measured TLP sure response to wind and wave field and its time-scale decomposition using wavelet transforms.
Fig. 4. TLP pitch response, high frequency wavelet coefficient, and wave frequency wavelet coefficients.
Fig. 4. TLP pitch response, high frequency wavelet coefficient, and wave frequency wavelet coefficients.
Fig. 3. Power spectral density of measured TLP surge response seen in Fig. 2.
Fig. 3. Power spectral density of measured TLP surge response seen in Fig. 2.
Fig. 5. Summation of wavelet coefficients to estimate power spectrum.
Fig. 5. Summation of wavelet coefficients to estimate power spectrum.
Fig.6. Wavelet and FFT based spectral estimations of earthquake acceleration record.
Fig.6. Wavelet and FFT based spectral estimations of earthquake acceleration record.
Fig. 7. Cospectrum of wind input and TLP surge response using FFT and wavelet transform estimation.
Fig. 7. Cospectrum of wind input and TLP surge response using FFT and wavelet transform estimation.
Fig. 8. Frequency modulated sine wave, DWT-scalogram, CWT-scalogram, and CWT-scalogram with high frequency transient noise added to signal between 1000 and 1200.
Fig. 8. Frequency modulated sine wave, DWT-scalogram, CWT-scalogram, and CWT-scalogram with high frequency transient noise added to signal between 1000 and 1200.
Fig. 11. Top floor building response to hurricane wind (top), scalogram of top floor response to stationary wind (middle), and scalogram of top floor response to wind with transient high frequency fluctuations (bottom).
Fig. 11. Top floor building response to hurricane wind (top), scalogram of top floor response to stationary wind (middle), and scalogram of top floor response to wind with transient high frequency fluctuations (bottom).
ig. 12. Left: scalogram of upstream wind velocity and correlated rooftop pressure, and coscalogram of these two processes. Right: scalogram f uncorrelated wind velocity and pressure records, and the coscalogram of these two records.
ig. 12. Left: scalogram of upstream wind velocity and correlated rooftop pressure, and coscalogram of these two processes. Right: scalogram f uncorrelated wind velocity and pressure records, and the coscalogram of these two records.
Fig. 13. Mesured bridge acceleration under the effect of vortex shedding, scalogram of response on course scale grid, and scalogram of same record on fine scale grid.
Fig. 13. Mesured bridge acceleration under the effect of vortex shedding, scalogram of response on course scale grid, and scalogram of same record on fine scale grid.
Fig. 14. Octave band filtered ground motion signals and their identified envelopes using DWT.
Fig. 14. Octave band filtered ground motion signals and their identified envelopes using DWT.
Fig. 15. Measured and simulated non-stationary ground motion signal using DWT.
Fig. 15. Measured and simulated non-stationary ground motion signal using DWT.
Fig. 16. Power spectral density of measured earthquake ground motion and wavelet simulated signals.
Fig. 16. Power spectral density of measured earthquake ground motion and wavelet simulated signals.
Fig. 17. Measured wind velocity and a simulation using DWT.
Fig. 17. Measured wind velocity and a simulation using DWT.
Fig. 18. Denoising of two superimposed sine waves contaminated by white noise using DWT thresholding.
Fig. 18. Denoising of two superimposed sine waves contaminated by white noise using DWT thresholding.
Clean signal and signal denoised by soft thresholding
Clean signal and signal denoised by soft thresholding
Clean pressure signal and signal denoised by hard thresholding Fig. 19. Noise reduction of a pressure record contaminated by white noise using DWT thresholding.
Clean pressure signal and signal denoised by hard thresholding Fig. 19. Noise reduction of a pressure record contaminated by white noise using DWT thresholding.
Related topics:
Time-Frequency AnalysisWavelet AnalysisSpectral DecompositionSeismic Load
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