doi:10.1016/j.cma.2004.12.009 
Copyright © 2005 Elsevier B.V. All rights reserved.
An enhanced hybrid method for the simulation of highly skewed non-Gaussian stochastic fields
Institute of Structural Analysis & Seismic Research, National Technical University of Athens, 9, Iroon Polytechniou Str., Zografou Campus, GR-15780 Athens, Greece
Received 5 May 2004;
revised 18 October 2004;
accepted 20 December 2004.
Available online 28 January 2005.
References and further reading may be available for this article. To view references and further reading you must
purchase this article.
Abstract
In this paper, an enhanced hybrid method (EHM) is presented for the simulation of homogeneous non-Gaussian stochastic fields with prescribed target marginal distribution and spectral density function. The presented methodology constitutes an efficient blending of the Deodatis–Micaletti method with a neural network based function approximation. Precisely, the function fitting ability of neural networks based on the resilient back-propagation (Rprop) learning algorithm is employed to approximate the unknown underlying Gaussian spectrum. The resulting algorithm can be successfully applied for simulating narrow-banded fields with very large skewness at a fraction of the computing time required by the existing methods. Its computational efficiency is demonstrated in three numerical examples involving fields that follow the beta and lognormal distributions.
Keywords: Non-Gaussian field; Translation field; Soft computing
Fig. 1. A schematic representation of the proposed hybrid method.
Fig. 2. Flow chart of neural network based simulation of non-Gaussian stochastic fields.
Fig. 3. Target SDFs for stochastic field tests 1, 2 and 3.
Fig. 4. Sample function of test 1 generated using (a) Deodatis–Micaletti algorithm, (b) the EHM methodology (Rprop training).
Fig. 5. (a) Marginal PDF of sample function of test 1 shown in Fig. 4a versus target beta marginal PDF, (b) marginal PDF of sample function of test 1 shown in Fig. 4b versus target beta marginal PDF.
Fig. 6. Comparison of PDF of an underlying “Gaussian” sample function with the corresponding exact PDF at first iteration.
Fig. 7. Comparison of PDF of the final non-Gaussian sample function with the target beta PDF (translation field case).
Fig. 8. (a) SDF of sample function of test 1 shown in Fig. 4a versus target SDF, (b) SDF of sample function of test 1 shown in Fig. 4b versus target SDF.
Fig. 9. SDF of sample function of test 1 resulting from different training procedures.
Fig. 10. Sample function of test 2 generated using (a) Deodatis–Micaletti algorithm, (b) the EHM methodology (Rprop training).
Fig. 11. (a) Marginal PDF of sample function of test 2 shown in Fig. 10a versus target lognormal marginal PDF, (b) marginal PDF of sample function of test 2 shown in Fig. 10b versus target lognormal marginal PDF.
Fig. 12. (a) SDF of sample function of test 2 shown in Fig. 10a versus target SDF, (b) SDF of sample function of test 2 shown in Fig. 10b versus target SDF.
Fig. 13. Sample function of test 3 generated using (a) Deodatis–Micaletti algorithm, (b) the EHM methodology (Rprop training).
Fig. 14. (a) Marginal PDF of sample function of test 3 shown in Fig. 13a versus target lognormal marginal PDF, (b) marginal PDF of sample function of test 3 shown in Fig. 13b versus target lognormal marginal PDF.
Fig. 15. (a) SDF of sample function of test 3 shown in Fig. 13a versus target SDF, (b) SDF of sample function of test 3 shown in Fig. 13b versus target SDF.
Table 1.
Test 1—computational performance of D–M and EHM methodology
Table 2.
Test 2—computational performance of D–M and EHM methodology
Table 3.
Test 2—statistical comparison of D–M and EHM methodology
Table 4.
Test 3—computational performance of D–M and EHM methodology
Table 5.
Test 3—statistical comparison of D–M and EHM methodology
Abstract
Purchase PDF (336 K)
E-mail Article
Add to my Quick Links
Cited By in Scopus (4)
Purchase PDF (1820 K)
