Identification and prediction of stochastic dynamical systems in a polynomial chaos basis Export

@article{citeulike:6060587, abstract = {Non-parametric system identification techniques have been proposed for constructing predictive models of dynamical systems without detailed knowledge of the mechanisms of energy transfer and dissipation. In a class of such models, multi-dimensional Chebychev polynomials in the state variables are fitted to the observed dynamical state of the system. Due to the approximative nature of this non-parametric model as well as to various other sources of uncertainty such as measurement errors and non-anticipative excitations, the parameters of the model exhibit a scatter that is treated here in a probabilistic context. The statistics of these coefficients are related to the physical properties of the model being analyzed, and are used to endow the model predictions with a probabilistic structure. They are also used to obtain a parsimonious characterization of the predictive model while maintaining a desirable level of accuracy. The proposed methodology is quite simple and robust.}, author = {Ghanem, R. and Masri, S. and Pellissetti, M. and Wolfe, R.}, citeulike-article-id = {6060587}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.cma.2004.05.031}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S0045782504004098}, day = {08}, doi = {10.1016/j.cma.2004.05.031}, issn = {00457825}, journal = {Computer Methods in Applied Mechanics and Engineering}, keywords = {detection, dynamics, nonlinear, nonparametric, prediction, reduced, stochastic}, month = {April}, number = {12-16}, pages = {1641--1654}, posted-at = {2009-11-03 15:59:13}, priority = {2}, title = {Identification and prediction of stochastic dynamical systems in a polynomial chaos basis}, url = {http://dx.doi.org/10.1016/j.cma.2004.05.031}, volume = {194}, year = {2005} }

TY - JOUR ID - citeulike:6060587 L3 - citeulike-article-id:6060587 N2 - Non-parametric system identification techniques have been proposed for constructing predictive models of dynamical systems without detailed knowledge of the mechanisms of energy transfer and dissipation. In a class of such models, multi-dimensional Chebychev polynomials in the state variables are fitted to the observed dynamical state of the system. Due to the approximative nature of this non-parametric model as well as to various other sources of uncertainty such as measurement errors and non-anticipative excitations, the parameters of the model exhibit a scatter that is treated here in a probabilistic context. The statistics of these coefficients are related to the physical properties of the model being analyzed, and are used to endow the model predictions with a probabilistic structure. They are also used to obtain a parsimonious characterization of the predictive model while maintaining a desirable level of accuracy. The proposed methodology is quite simple and robust. IS - 12-16 JF - Computer Methods in Applied Mechanics and Engineering SN - 00457825 EP - 1654 TI - Identification and prediction of stochastic dynamical systems in a polynomial chaos basis VL - 194 SP - 1641 KW - detection KW - dynamics KW - nonlinear KW - nonparametric KW - prediction KW - reduced KW - stochastic AU - Ghanem, R AU - Masri, S AU - Pellissetti, M AU - Wolfe, R PY - 2005/04/08/ UR - http://dx.doi.org/10.1016/j.cma.2004.05.031 ER -