Details
| Original language | English |
|---|---|
| Article number | 113386 |
| Journal | Mechanical Systems and Signal Processing |
| Volume | 240 |
| Early online date | 30 Sept 2025 |
| Publication status | Published - 1 Nov 2025 |
Abstract
This paper presents two numerical algorithms to simulate non-Gaussian random fields that are parameterized by random parameters. The simulation of such kind of random fields is very challenging due to their parameterized non-Gaussian properties. For each sample realization of the random parameters, the parameterized non-Gaussian random field degrades into a classical non-Gaussian random field. In the first algorithm, we present a sample-based iterative algorithm to simulate the obtained classical non-Gaussian random field. Initial random samples are first generated to meet the sampled marginal distribution, and an iterative procedure is adopted to change the ranking of the random samples to match the target sampled covariance function. However, this method is computationally expensive since we have to simulate a non-Gaussian random field for each sample realization of the random parameters. To avoid this issue, we develop a reformulation-based algorithm in the second method. Parameterized marginal distributions are reformulated as non-parameterized marginal distributions via a conditional probability integral, and parameterized covariance functions are reformulated as non-parameterized covariance functions via an expectation operation on random parameters. In this way, the original parameterized non-Gaussian random field is transformed into a classical non-Gaussian random field. The sample-based iterative algorithm is then used to simulate the obtained non-Gaussian random field. Moreover, a multi-fidelity approach is presented to further reduce the computational effort of the above iteration by taking advantage of the Karhunen-Loève expansion. Specifically, the expanded random variables in Karhunen-Loève expansion are calculated on a low-fidelity model and the deterministic functions in Karhunen-Loève expansion are calculated on a high-fidelity model. Thus, the method has low computational effort and high fidelity simultaneously. Two numerical examples, including one- and three-dimensional parameterized non-Gaussian random fields, are used to verify the effectiveness of the proposed methods.
Keywords
- Conditional probability integral, Karhunen–Loève expansion, Multi-fidelity iteration, Parameterized non-Gaussian random fields
ASJC Scopus subject areas
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- Signal Processing
- Engineering(all)
- Civil and Structural Engineering
- Engineering(all)
- Aerospace Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computer Science Applications
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In: Mechanical Systems and Signal Processing, Vol. 240, 113386, 01.11.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Simulation of parameterized random fields, Part II
T2 - Non-Gaussian cases
AU - Zheng, Zhibao
AU - Dai, Hongzhe
AU - Beer, Michael
AU - Nackenhorst, Udo
N1 - Publisher Copyright: © 2025 The Author(s)
PY - 2025/11/1
Y1 - 2025/11/1
N2 - This paper presents two numerical algorithms to simulate non-Gaussian random fields that are parameterized by random parameters. The simulation of such kind of random fields is very challenging due to their parameterized non-Gaussian properties. For each sample realization of the random parameters, the parameterized non-Gaussian random field degrades into a classical non-Gaussian random field. In the first algorithm, we present a sample-based iterative algorithm to simulate the obtained classical non-Gaussian random field. Initial random samples are first generated to meet the sampled marginal distribution, and an iterative procedure is adopted to change the ranking of the random samples to match the target sampled covariance function. However, this method is computationally expensive since we have to simulate a non-Gaussian random field for each sample realization of the random parameters. To avoid this issue, we develop a reformulation-based algorithm in the second method. Parameterized marginal distributions are reformulated as non-parameterized marginal distributions via a conditional probability integral, and parameterized covariance functions are reformulated as non-parameterized covariance functions via an expectation operation on random parameters. In this way, the original parameterized non-Gaussian random field is transformed into a classical non-Gaussian random field. The sample-based iterative algorithm is then used to simulate the obtained non-Gaussian random field. Moreover, a multi-fidelity approach is presented to further reduce the computational effort of the above iteration by taking advantage of the Karhunen-Loève expansion. Specifically, the expanded random variables in Karhunen-Loève expansion are calculated on a low-fidelity model and the deterministic functions in Karhunen-Loève expansion are calculated on a high-fidelity model. Thus, the method has low computational effort and high fidelity simultaneously. Two numerical examples, including one- and three-dimensional parameterized non-Gaussian random fields, are used to verify the effectiveness of the proposed methods.
AB - This paper presents two numerical algorithms to simulate non-Gaussian random fields that are parameterized by random parameters. The simulation of such kind of random fields is very challenging due to their parameterized non-Gaussian properties. For each sample realization of the random parameters, the parameterized non-Gaussian random field degrades into a classical non-Gaussian random field. In the first algorithm, we present a sample-based iterative algorithm to simulate the obtained classical non-Gaussian random field. Initial random samples are first generated to meet the sampled marginal distribution, and an iterative procedure is adopted to change the ranking of the random samples to match the target sampled covariance function. However, this method is computationally expensive since we have to simulate a non-Gaussian random field for each sample realization of the random parameters. To avoid this issue, we develop a reformulation-based algorithm in the second method. Parameterized marginal distributions are reformulated as non-parameterized marginal distributions via a conditional probability integral, and parameterized covariance functions are reformulated as non-parameterized covariance functions via an expectation operation on random parameters. In this way, the original parameterized non-Gaussian random field is transformed into a classical non-Gaussian random field. The sample-based iterative algorithm is then used to simulate the obtained non-Gaussian random field. Moreover, a multi-fidelity approach is presented to further reduce the computational effort of the above iteration by taking advantage of the Karhunen-Loève expansion. Specifically, the expanded random variables in Karhunen-Loève expansion are calculated on a low-fidelity model and the deterministic functions in Karhunen-Loève expansion are calculated on a high-fidelity model. Thus, the method has low computational effort and high fidelity simultaneously. Two numerical examples, including one- and three-dimensional parameterized non-Gaussian random fields, are used to verify the effectiveness of the proposed methods.
KW - Conditional probability integral
KW - Karhunen–Loève expansion
KW - Multi-fidelity iteration
KW - Parameterized non-Gaussian random fields
UR - http://www.scopus.com/inward/record.url?scp=105017241045&partnerID=8YFLogxK
U2 - 10.1016/j.ymssp.2025.113386
DO - 10.1016/j.ymssp.2025.113386
M3 - Article
AN - SCOPUS:105017241045
VL - 240
JO - Mechanical Systems and Signal Processing
JF - Mechanical Systems and Signal Processing
SN - 0888-3270
M1 - 113386
ER -