Response Statistics of Nonlinear Dynamic Systems by Path Integration

The paper presents a method for calculating the response statistics of nonlinear dynamic systems excited by a white noise or filtered white noise process. The method, which is based on the path integral solution technique, is still under development, but experience so far indicates that it is singularly well suited for numerical calculation of the response statistics of nonlinear systems to which can be associated a Markov vector process whose probability density satisfies a Fokker-Planck-Kolmogorov (FPK) equation. The method is a viable alternative to the direct numerical solution of the FPK equation. A key feature of the method is the possibility of obtaining highly accurate solutions at very low probability levels. Also, there seems to be almost no limitation on the type of nonlinearity that can be accomodated. On the negative side there are clear limitations of the method concerning required computer resources.

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