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.

Di Matteo, A., Pirrotta, A. (2020). Laplace’s Method of Integration in the Path Integral Approach for the Probabilistic Response of Nonlinear Systems. In Proceedings of XXIV AIMETA Conference 2019 (pp. 1687-1695). Springer International Publishing [https://doi.org/10.1007/978-3-030-41057-5_135].

Laplace’s Method of Integration in the Path Integral Approach for the Probabilistic Response of Nonlinear Systems

Di Matteo
;
Pirrotta
2020-01-01

Abstract

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.
Settore ICAR/08 - Scienza Delle Costruzioni
Di Matteo, A., Pirrotta, A. (2020). Laplace’s Method of Integration in the Path Integral Approach for the Probabilistic Response of Nonlinear Systems. In Proceedings of XXIV AIMETA Conference 2019 (pp. 1687-1695). Springer International Publishing [https://doi.org/10.1007/978-3-030-41057-5_135].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/407301
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