Generation of spectrum - compatible accelerograms using information theory

The research addressed here is devoted to the generation of seismic accelerograms compatible with a given response spectrum and other associated properties. The time sampling of the stochastic accelerogram yields a time series represented by a random vector in high stochastic dimension. The probability density function (pdf) of this random vector is constructed using the Maximum Entropy (MaxEnt) principle under constraints defined by the available information. In this research, a new algorithm, adapted to the high stochastic dimension, is proposed to identify the Lagrange multipliers introduced in the MaxEnt principle to take into account the constraints. This novel algorithm is developed in the context of the methodology based on (1) the minimization of an appropriate convex functional and (2) the construction of the probability distribution defined as the invariant measure of an Itô Stochastic Differential Equation (belonging to the class of MCMC methods) in order to estimate the integrals in high dimension of the problem. The algorithm is validated through an application for which the available information is relative to the variance of each component of the random vector representing the accelerogram, statistics on the response spectrum such as the mean value and the envelopes, statistics on the Peak Ground Acceleration (PGA) and the velocity and displacement traces (behavior of the signals at the final time) .