Time-Frequency Analysis of Systems with Changing Dynamic Properties

Time-frequency analysis methods transform a time series into a two-dimensional representation frequency content with respect to time. The Fourier Transform identifies frequency content of a signal (as a sum of weighted sinusoidal functions) but not give useful information regarding changes in the character of the signal, as all information is encoded in the phase of the transform. A time-frequency representation, expressing frequency content at different sections of a record, allows analysis of evolving signals. The time-frequency transformation most commonly in seismology and civil engineering is a windowed Fourier Transform, or; by comparing the frequency content of the first portion of a record with last portion of the record, it is straightforward to identify the changes between two segments. Extending this concept to a sliding window gives the spectrogram, the Fourier transforms of successive portions of the record are assembled into a-frequency representation of the signal. The spectrogram is subject to an inherent limitation, in accordance with the uncertainty principle, that precludes perfect representation of instantaneous frequency content. The wavelet transform introduced to overcome some of the shortcomings of Fourier analysis, though methods are themselves unsuitable for many commonly encountered signals. Wigner-Ville Distribution, and related refinements, represent a class of advanced-frequency analysis tools that are distinguished from Fourier and wavelet by an increase in resolution in the time-frequency plane. I introduce several-frequency representations and apply them to various synthetic signals as well as from instrumented buildings. systems of interest to engineers, investigating the changing properties of a is typically performed by analyzing vibration data from the system, rather direct inspection of each component. Nonlinear elastic behavior in the forcedisplacement can decrease the apparent natural frequencies of the system- these changes typically occur over fractions of a second in moderate to strong excitation the system gradually recovers to pre-event levels. Structures can also suffer damage (e.g., plastic deformation or fracture), permanently decreasing the natural frequencies as the system loses stiffness. Advanced time-frequency provide a set of exploratory tools for analyzing changing frequency in a signal, which can then be correlated with damage patterns in a structure. building instrumentation allows for an unprecedented investigation into changing dynamic properties of structures: a framework for using time-frequency methods for instantaneous system identification is discussed.