A novel local stochastic linearization method via two extremum entropy principles

The classical Gaussian stochastic linearization method for non-linear random vibration problems is reinterpreted on the basis of the maximum entropy principle. Starting from this theoretical result, the maximum entropy principle allows to formulate a local stochastic linearization method, based on the substitution of the original non-linear system by an equivalent locally linear one. The expressions of the equivalent coefficients are derived. The equivalence of this method with a non-Gaussian closure based on the maximum entropy method for stochastic dynamics is evidenced. In addition, an alternative stochastic linearization method is proposed, based on the minimum cross-entropy principle. Numerical applications show the superiority of the two proposed local stochastic linearization methods over the Gaussian one.

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