Because the design response spectrum compatible acceleration time history (DRSCATH) is strongly affected by the assigned Fourier phase spectrum we propose a method to extract the uncertainty of Fourier phase spectrum form an observed acceleration time history at the design site. The stochastic characteristic of the mean phase gradient is expressed by the Levy-flight probability density function. We introduce a new type of stochastic process being able to represent these stochastic characteristics of the mean phase gradient by the use of Lebesgue-Stieltjes type integral formula. In which the Kernel plays a role to realize the self-affine and auto correlation feature of phase difference and the integration function represents the main stochastic characteristics of earthquake motion phase. Using this stochastic process we simulate many sample Fourier phase spectra, which can be used to evaluate the uncertainty of Fourier phase spectrums on nonlinear structural response.
We also can see some minor effects of the initial Fourier amplitude spectrum on a simulated DRSCATH and therefore discussed We also can see some minor effects of the initial Fourier amplitude spectrum on a simulated DRSCATH and therefore discussed nonlinear response of a structural system. The structure considered is a designed one using the yield seismic coefficient demand spectrum, in which the response ductility is kept a constant. Our main concern is to evaluate the uncertainty of response ductility of the designed structure caused by the uncertainty of Fourier phase spectrum.