This paper focuses on the development of analytical methods for uncertainty quantification of the models obtained by the Eigensystem Realization Algorithm (ERA) owing to the presence of noise in the input-output experimental data. Starting from first principles, analytical expressions are presented for the distribution of eigenvalues of the Hankel matrix by application of standard results in random matrix theory. This result naturally leads to a probabilistic method for model order determination (reduction). By application of further results from the theory of random matrices, we develop analytical expressions for the joint density of eigenvalues. These expressions enable us to construct the probability density functions of the identified linear models as a function of the uncertainties in test data. Numerical examples illustrate the applications of ideas presented in the paper.
|Original language||English (US)|
|Number of pages||17|
|Journal||Advances in the Astronautical Sciences|
|State||Published - Jan 1 2013|
All Science Journal Classification (ASJC) codes
- Aerospace Engineering
- Space and Planetary Science