Stochastic
seismic response of single-degree-of-freedom systems through wavelets
Biswajit Basua
and Vinay K. Guptab
a Department of Civil Engineering, Jadavpur University,
Calcutta-700032, India
b Department of Civil Engineering, Indian Institute of Technology,
Kanpur-208016, India
This paper proposes a wavelet-based approach for estimation of the
stochastic response of a single-degree-of-freedom (SDOF) system which is
subjected to an earthquake ground motion process modelled by its wavelet
coefficients. Expressions have been derived for (i) the representation of the
excitation process through wavelets, (ii) relationship between the wavelet
coefficients of the excitation and response processes, and (iii) instantaneous
mean-square value and power spectral density function (PSDF) of the response
process. The proposed formulation considers both amplitude and frequency
non-stationarities in the ground motion process, and is thus more generalized
than the earlier methods based on the use of frequency-independent modulating
functions. Compared with an alternative wavelet-based formulation (Basu B,
Gupta VK. Seismic response of SDOF systems by wavelet modelling of
non-stationary processes. J Eng Mech (ASCE) 1998;124(10):1142–50), this
formulation does not require the wavelet bases to be mutually orthogonal and
energy bands corresponding to different scales to be non-overlapping, for
computing the instantaneous mean-square value of the response process. This is
also applicable for very short excitations where the sudden application of
excitation may be of crucial importance. The proposed formulation has been
validated through statistical simulation in the case of an example ground
motion process and oscillators of different periods.
Author Keywords: Linear SDOF system; Stochastic seismic response; Wavelet coefficients; Littlewood–Paley basis; Frequency nonstationarity; Short excitations