2010
DOI: 10.1115/1.4002481
|View full text |Cite
|
Sign up to set email alerts
|

A Polynomial Chaos-Based Kalman Filter Approach for Parameter Estimation of Mechanical Systems

Abstract: In this study, a new computational approach for parameter identification is proposed based on the application of the polynomial chaos theory. The polynomial chaos method has been shown to be considerably more efficient than Monte Carlo in the simulation of systems with a small number of uncertain parameters. In the new approach presented in this paper, the maximum likelihood estimates are obtained by minimizing a cost function derived from the Bayesian theorem. Direct stochastic collocation is used as a less c… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

0
42
0

Year Published

2011
2011
2017
2017

Publication Types

Select...
4
3
1

Relationship

2
6

Authors

Journals

citations
Cited by 74 publications
(42 citation statements)
references
References 54 publications
0
42
0
Order By: Relevance
“…Table 1 shows the variation in the parameters for each simulation, and figures (3)(4)(5) show the parameter estimations for each simulation.…”
Section: Extended Kalman Filter Resultsmentioning
confidence: 99%
See 2 more Smart Citations
“…Table 1 shows the variation in the parameters for each simulation, and figures (3)(4)(5) show the parameter estimations for each simulation.…”
Section: Extended Kalman Filter Resultsmentioning
confidence: 99%
“…More explicit derivation of this equation can be found in reference [3]. The indexes are defined as: The subscript k indexes time.…”
Section: The Generalized Polynomial Chaos -Extended Kalman Filtermentioning
confidence: 99%
See 1 more Smart Citation
“…Sandu and coworkers introduced its application to multibody dynamical systems in [27,28,[36][37][38][39][40]. Significant work has been done applying it as a foundational element in parameter [23][24][25][26][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59] and state estimation [60,61], as well as system identification [62]. Relatively recent work has applied gPC to both classical and optimal control system design [41,63,64].…”
Section: 25mentioning
confidence: 99%
“…The required size of the sample significantly increases with the complexity of the physics (multi-parameter estimation) and the model nonlinearities (complex physics), thus emphasizing the need for a reducedcost EnKF. Efforts have therefore been devoted to designing more efficient EnKF schemes by reducing sampling errors (Szunyogh et al, 2008;Saad, 2007;Xiu, 2008, 2009;Blanchard et al, 2010;Xiu, 2010;Rosić et al, 2013). For this purpose, and following work from Li and Xiu (2009), an EnKF strategy based on a PC approximation (PC-EnKF) is proposed in this paper; the polynomial surrogate model being used during the EnKF prediction step to generate a large number of model simulation trajectories at almost no cost and without loss of accuracy (Birolleau et al, 2014).…”
Section: Introductionmentioning
confidence: 99%