Institutional Repository
Technical University of Crete
Technical University of Crete
EN
|
EL
| URI: | http://purl.tuc.gr/dl/dias/3DB169C2-06D5-403C-AC02-237E910991F9 | ||
| Year | 2016 | ||
| Type of Item | Peer-Reviewed Journal Publication | ||
| License |
|
||
| Bibliographic Citation | I.C. Tsantili and D.T. Hristopulos, "Karhunen-Loève expansion of Spartan spatial random fields," Probabilist Eng. Mech., vol. 43, pp. 132-147, Jan. 2016. doi: 10.1016/j.probengmech.2015.12.002 https://doi.org/10.1016/j.probengmech.2015.12.002 | ||
| Appears in Collections |
Random fields (RFs) are important tools for modeling space-time processes and data. The Karhunen-Loève (K-L) expansion provides optimal bases which reduce the dimensionality of random field representations. However, explicit expressions for K-L expansions only exist for a few, one-dimensional, two-parameter covariance functions. In this paper we derive the K-L expansion of the so-called Spartan spatial random fields (SSRFs). SSRF covariance functions involve three parameters including a rigidity coefficient η1, a scale coefficient, and a characteristic length. SSRF covariances include both monotonically decaying and damped oscillatory functions; the latter are obtained for negative values of η1. We obtain the eigenvalues and eigenfunctions of the SSRF K-L expansion by solving the associated homogeneous Fredholm equation of the second kind which leads to a fourth order linear ordinary differential equation. We investigate the properties of the solutions, we use the derived K-L base to simulate SSRF realizations, and we calculate approximation errors due to truncation of the K-L series.
Copyright © DIAS 2013
