Simulation of parameterized random fields, Part I
Gaussian cases
Abstract
Parameterized random fields play an important role to simulate complex uncertain physical models. In this kind of random fields, statistical properties of the classical random fields, e.g. marginal distributions and covariance functions, may be also related to (random) parameters. In-depth analysis and efficient simulations of parameterized random fields still require further research. This paper presents efficient numerical simulations of parameterized Gaussian random fields (PGRFs). To this end, a stochastic Karhunen–Loève expansion (SKLE) is first proposed to approximate PGRFs and used to provide an explicit representation of PGRFs. The stochastic integral equation arising in SKLE is solved efficiently by a reduced-order method. In this method, stochastic eigenvectors are represented as stochastic linear combinations of deterministic vectors. The deterministic vectors are calculated efficiently using deterministic eigenequations. Corresponding random variable coefficients of deterministic vectors and stochastic eigenvalues are solved via a reduced-order stochastic eigenequation built by the deterministic vectors. With the obtained stochastic eigenvectors, the SKLE of PGRFs can be reformulated as classical Karhunen–Loève-like expansions and PGRFs are revisited from different parameterized perspectives. Three numerical examples demonstrate the effectiveness of the proposed method.
Details
- Organisation(s)
-
Institute of Mechanics and Computational Mechanics
Institute for Risk and Reliability
- External Organisation(s)
-
Harbin Institute of Technology
University of Liverpool
Tongji University
- Type
- Article
- Journal
- Mechanical Systems and Signal Processing
- Volume
- 238
- ISSN
- 0888-3270
- Publication date
- 01.09.2025
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Control and Systems Engineering, Signal Processing, Civil and Structural Engineering, Aerospace Engineering, Mechanical Engineering, Computer Science Applications
- Electronic version(s)
-
https://doi.org/10.1016/j.ymssp.2025.113215 (Access:
Open
)
