Information Theory for Generation of Accelerograms Associated with Shock Response Spectra

Abstract

In structural dynamics, the specification of the transient loads applied to equipment (or to secondary subsystems) consists of a given shock response spectrum (SRS). The transient dynamical analysis of such equipment is performed using a computational nonlinear dynamical model. A generator of accelerograms satisfying the given SRS is then required. Information theory is used to solve this challenging inverse problem that has been looked at by others but not in the way presented. The maximum entropy principle is used to construct the probability distribution of the nonstationary stochastic process for which the available information is constituted of the mean SRS and additional information on the variance. A random generator of independent realizations of the nonstationary stochastic process is developed using a new algorithm based on the stochastic analysis. The method presented is validated with an example.

Generation of Response Spectrum Compatible Accelerograms Using the Maximum Entropy Principle

“…A generator of independent realizations for MaxEnt distributions has been proposed in [4,5] in the class of the MCMC algorithms. This methodology consists in constructing the pdf of random vector A λ as the density of the invariant measure p A λ (a)da, associated with the stationary solution of a second-order nonlinear Itô Stochastic differential equation (ISDE).…”

“…Below, we directly introduce the generator of independent realizations using a discretization of the ISDE. Details concerning the construction of this generator can be found in [4,5].…”

“…As proposed in [4,5], the ISDE is discretized using a semi-implicit integration scheme in order to avoid the resolution of an algebraic nonlinear equation at each step while allowing significantly increase of the time step compared to a purely explicit scheme.…”

“…The Maximum Entropy (MaxEnt) principle [3] is a powerful method which allows us to construct a probability distribution of a random vector under some constraints defined by the available information. This method has recently been applied in [5] for the generation of spectrum-compatible accelerograms as trajectories of a non-Gaussian nonstationary centered random process represented by a high-dimension random vector for which the probability density function (pdf) is constructed using the MaxEnt principle under constraints relative to (1) the mean value, (2) the variance of the components and (3) the mean value of the Velocity Response Spectrum (VRS). The objective of this paper is to take into account additional constraints which characterize the natural features of a seismic accelerogram.…”

“…The objective of this paper is to take into account additional constraints which characterize the natural features of a seismic accelerogram. To achieve this objective, the methodology proposed in [5] is extended to take into account constraints relative to statistics on (1) the end values for the velocity and the displacement, (2) the PGA, (3) the Peak Ground Velocity (PGV), (4) the envelop of the random VRS and (5) the Cumulative Absolute Velocity (CAV). The MaxEnt pdf is constructed and a generator of independent realizations adapted to the high-stochastic dimension of an accelerogram is proposed.…”