Details
Original language | English |
---|---|
Pages (from-to) | 42-53 |
Number of pages | 12 |
Journal | Probabilistic Engineering Mechanics |
Volume | 38 |
Early online date | 10 Sept 2014 |
Publication status | Published - Oct 2014 |
Externally published | Yes |
Abstract
Although a number of methods have been developed to generate random fields, it remains a challenge to efficiently generate a large, multi-dimensional, multi-variate property field. For such problems, the widely used spectral representation method tends to require relatively longer computing time. In this paper, a modified linear estimation method is proposed, which involves mapping the linearly estimated field through a series of randomized translations and rotations from one realization to the next. These randomized translations and rotations enable the simulated property field to be stationary. The autocorrelation function of the simulated fields can be approximately described by a squared exponential function. The algorithms of the proposed method in both the rectangular and cylindrical polar coordinate systems are demonstrated and the results validated by Monte-Carlo simulations. Comparisons between the proposed method and spectral representation method show that the results from both methods are in good agreement, as long as the cut-off wave numbers of the spectral representation method are sufficiently large. However, the proposed method requires much less computational time than the spectral representation method. This makes it potentially useful for generating large multi-dimensional fields in random finite element analysis. Applications of the proposed method are exemplified in both rectangular and cylindrical polar coordinate systems.
Keywords
- Autocorrelation function, Material property, Random field, Random finite element analysis
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Engineering(all)
- Civil and Structural Engineering
- Energy(all)
- Nuclear Energy and Engineering
- Physics and Astronomy(all)
- Condensed Matter Physics
- Engineering(all)
- Aerospace Engineering
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
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In: Probabilistic Engineering Mechanics, Vol. 38, 10.2014, p. 42-53.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Modified linear estimation method for generating multi-dimensional multi-variate Gaussian field in modelling material properties
AU - Liu, Yong
AU - Lee, Fook-Hou
AU - Quek, Ser-Tong
AU - Beer, Michael
N1 - Funding Information: This research is supported by the National Research Foundation Singapore under its Competitive Research Programme (CRP award no. NRF-CRP 6-2010-03 ) and the NUS Research Scholarship.
PY - 2014/10
Y1 - 2014/10
N2 - Although a number of methods have been developed to generate random fields, it remains a challenge to efficiently generate a large, multi-dimensional, multi-variate property field. For such problems, the widely used spectral representation method tends to require relatively longer computing time. In this paper, a modified linear estimation method is proposed, which involves mapping the linearly estimated field through a series of randomized translations and rotations from one realization to the next. These randomized translations and rotations enable the simulated property field to be stationary. The autocorrelation function of the simulated fields can be approximately described by a squared exponential function. The algorithms of the proposed method in both the rectangular and cylindrical polar coordinate systems are demonstrated and the results validated by Monte-Carlo simulations. Comparisons between the proposed method and spectral representation method show that the results from both methods are in good agreement, as long as the cut-off wave numbers of the spectral representation method are sufficiently large. However, the proposed method requires much less computational time than the spectral representation method. This makes it potentially useful for generating large multi-dimensional fields in random finite element analysis. Applications of the proposed method are exemplified in both rectangular and cylindrical polar coordinate systems.
AB - Although a number of methods have been developed to generate random fields, it remains a challenge to efficiently generate a large, multi-dimensional, multi-variate property field. For such problems, the widely used spectral representation method tends to require relatively longer computing time. In this paper, a modified linear estimation method is proposed, which involves mapping the linearly estimated field through a series of randomized translations and rotations from one realization to the next. These randomized translations and rotations enable the simulated property field to be stationary. The autocorrelation function of the simulated fields can be approximately described by a squared exponential function. The algorithms of the proposed method in both the rectangular and cylindrical polar coordinate systems are demonstrated and the results validated by Monte-Carlo simulations. Comparisons between the proposed method and spectral representation method show that the results from both methods are in good agreement, as long as the cut-off wave numbers of the spectral representation method are sufficiently large. However, the proposed method requires much less computational time than the spectral representation method. This makes it potentially useful for generating large multi-dimensional fields in random finite element analysis. Applications of the proposed method are exemplified in both rectangular and cylindrical polar coordinate systems.
KW - Autocorrelation function
KW - Material property
KW - Random field
KW - Random finite element analysis
UR - http://www.scopus.com/inward/record.url?scp=84907706527&partnerID=8YFLogxK
U2 - 10.1016/j.probengmech.2014.09.001
DO - 10.1016/j.probengmech.2014.09.001
M3 - Article
AN - SCOPUS:84907706527
VL - 38
SP - 42
EP - 53
JO - Probabilistic Engineering Mechanics
JF - Probabilistic Engineering Mechanics
SN - 0266-8920
ER -