6533b7d0fe1ef96bd125b844
RESEARCH PRODUCT
Laplace’s Method of Integration in the Path Integral Approach for the Probabilistic Response of Nonlinear Systems
Antonina PirrottaAlberto Di Matteosubject
Nonlinear systemPath Integral Laplace’s method Nonstationary response Probability density function.Laplace transformLaplace's methodPath integral formulationProbabilistic logicApplied mathematicsProbability density functionWhite noiseSettore ICAR/08 - Scienza Delle CostruzioniExcitationMathematicsdescription
In this paper the response of nonlinear systems under stationary Gaussian white noise excitation is studied. The Path Integral (PI) approach, generally employed for evaluating the response Probability Density Function (PDF) of systems in short time steps based on the Chapman-Kolmogorov equation, is here used in conjunction with the Laplace’s method of integration. This yields an approximate analytical solution of the integral involved in the Chapman-Kolmogorov equation. Further, in this manner the repetitive integrations, generally required in the conventional numerical implementation of the procedure, can be circumvented. Application to a nonlinear system is considered, and pertinent comparisons with stationary analytical solutions are presented, demonstrating the efficiency and accuracy of the proposed approach.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-01-01 |