TY - JOUR
T1 - Response and reliability analysis of nonlinear uncertain dynamical structures by the probability density evolution method
AU - Nielsen, Søren R. K.
AU - Peng, Yongbo
AU - Sichani, Mahdi Teimouri
PY - 2016
Y1 - 2016
N2 - The paper deals with the response and reliability analysis of hysteretic or geometric nonlinear uncertain dynamical systems of arbitrary dimensionality driven by stochastic processes. The approach is based on the probability density evolution method proposed by Li and Chen (Stochastic dynamics of structures, 1st edn. Wiley, London, 2009; Probab Eng Mech 20(1):33–44, 2005), which circumvents the dimensional curse of traditional methods for the determination of non-stationary probability densities based on Markov process assumptions and the numerical solution of the related Fokker–Planck and Kolmogorov–Feller equations. The main obstacle of the method is that a multi-dimensional convolution integral needs to be carried out over the sample space of a set of basic random variables, for which reason the number of these need to be relatively low. In order to handle this problem an approach is suggested, which reduces the number of basic random variables to merely a single one. Correspondingly, the response and reliability problems reduce to the solution of one-dimensional quadratures.
AB - The paper deals with the response and reliability analysis of hysteretic or geometric nonlinear uncertain dynamical systems of arbitrary dimensionality driven by stochastic processes. The approach is based on the probability density evolution method proposed by Li and Chen (Stochastic dynamics of structures, 1st edn. Wiley, London, 2009; Probab Eng Mech 20(1):33–44, 2005), which circumvents the dimensional curse of traditional methods for the determination of non-stationary probability densities based on Markov process assumptions and the numerical solution of the related Fokker–Planck and Kolmogorov–Feller equations. The main obstacle of the method is that a multi-dimensional convolution integral needs to be carried out over the sample space of a set of basic random variables, for which reason the number of these need to be relatively low. In order to handle this problem an approach is suggested, which reduces the number of basic random variables to merely a single one. Correspondingly, the response and reliability problems reduce to the solution of one-dimensional quadratures.
KW - Evolutionary phase model
KW - Nonlinear dynamical systems
KW - Probability density evolution method
KW - Reliability analysis
KW - Stochastic response
KW - Evolutionary phase model
KW - Nonlinear dynamical systems
KW - Probability density evolution method
KW - Reliability analysis
KW - Stochastic response
U2 - 10.1007/s40435-015-0155-4
DO - 10.1007/s40435-015-0155-4
M3 - Journal article
SN - 2195-268X
VL - 4
SP - 221
EP - 232
JO - International Journal of Dynamics and Control
JF - International Journal of Dynamics and Control
IS - 2
M1 - 12
ER -