Wavelets based time-frequency analysis techniques in structural engineering
Politis, Nikolaos P.
Spanos, Pol D.
Doctor of Philosophy thesis
Future design procedures for civil structures, especially those to be protected from extreme loads, will need to account for temporal evolution of their frequency content. Separate time analysis and frequency analysis by themselves do not fully describe the nature of these nonstationary dynamic loads. In the past few years, significant effort has been devoted to wavelets and time-frequency analysis. The appropriateness of emerging joint-time frequency analysis techniques for structural engineering problems is evaluated. Emphasis is focused on adaptive methods and the wavelet transform is also considered for validation purposes. In particular, the adaptive chirplet decomposition method and the empirical mode decomposition method are investigated. The required level of sophistication of the adaptive analysis is assessed. Mathematical expressions pertaining to time-frequency estimators are derived. Specifically, a transition from individual spectrograms to evolutionary power spectrum is attempted and function-specific decompositions are used for the estimation of the mean instantaneous frequency. Further, the Bootstrap method is employed for the assessment of the accuracy of the statistical estimators for the cases where limited data is available. An alternative approach utilizing function-specific decompositions for the derivation of well defined Hilbert spectra is suggested. Data pertaining to simulated and recorded earthquake signals, nonlinear structural responses due to earthquake excitations, and sea level recordings during the 2004 tsunami in Indian Ocean are used. The significance of the present study, over studies available in the literature for wavelets based structural analysis, hinges upon the consideration of adaptive and nonadaptive methods, the computational efficiency and effectiveness assessment of the suggested time-frequency estimators. It is expected that this study will enhance the interest in using advanced signal processing methods in structural systems analysis and design.
Civil engineering; Electronics; Electrical engineering