Generation of response spectrum compatible accelerograms using the maximum entropy principle

Abstract : The research addressed here concerns 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 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 paper, 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 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 It StochasticDifferential Equation in order to estimate the integrals in high dimension of the problem.