| Seismic signals are characterized by strong excitations, short durations, non-linearity and non-stationarity having both the amplitude and frequency content vary as a function of the recorded time. Various classical detection and estimation techniques, like the time-frequency representations and the Fourier-based techniques have been used to analyze such signals, but these techniques have variety of limitations and they fail to correctly estimate the concerned signals. The Damped-Amplitude and Polynomial-Frequency Model has been introduced to help in adapting to the seismic signals where the amplitude is damped. This model is based on approximating the frequency by low-order polynomials and the amplitude by damped exponentials. Its amplitude in turn is characterized by a damping coefficient; which was firstly assumed to be time-invariant. However the results of the studied signals showed rapid amplitude fluctuations and frequency content variations of each component that could be justified by the fact that the dynamic response of the structure is highly sensitive to the dynamic characteristics of the ground motion. Accordingly and to be more adapted with the physical model of the building motion that is characterized by damped exponential functions, the damping coefficient was then assumed to be time-variant leading to the foundation of a new model that keeps the same approximation for the frequency like the aforementioned model, and changes that of the amplitude by approximating its damping-coefficient by low-order polynomials. This model was then named Polynomial Damping Function Model. Results on different seismic signals show that the time-variant assumption is more efficient than the time-invariant one. |
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