Ιδρυματικό Αποθετήριο
Πολυτεχνείο Κρήτης
Πολυτεχνείο Κρήτης
EN
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| URI: | http://purl.tuc.gr/dl/dias/3DB169C2-06D5-403C-AC02-237E910991F9 | ||
| Έτος | 2016 | ||
| Τύπος | Δημοσίευση σε Περιοδικό με Κριτές | ||
| Άδεια Χρήσης |
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| Βιβλιογραφική Αναφορά | 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 | ||
| Εμφανίζεται στις Συλλογές |
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.
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