Discussion of Feng et al. (2014). Statistical reconstruction of two-phase random media Comput. Struct. 137 (2014) 78-92

Clarifies misrepresentations of existing iterative methods in Feng et al.Demonstrates the efficiency of the ITAM method for random media simulation.Addresses compatibility and generality of random media simulation methods. The recent work of Feng et al. (2014) presents a new approach for generation of 2-phase random media using a translation-based stochastic field. The method is useful, elegant, and efficient. The intention of this discussion is to clarify some misrepresentations of prior work as they are presented in terms of the efficiency of iterative methods and the Iterative Translation Approximation Method (ITAM) of Shields et al. (2011) specifically. The ITAM approach is far more efficient than presented and represents a negligibly small increase in expense over the proposed approach. Some issues pertaining to compatibility and generalization of translation fields are also discussed.

[1]  M. Grigoriu.  Applied Non-Gaussian Processes , 1995 .

[2]  Michael D. Shields,et al.  Modeling strongly non-Gaussian non-stationary stochastic processes using the Iterative Translation Approximation Method and Karhunen-Loève expansion , 2015 .

[3]  Paolo Bocchini,et al.  A simple and efficient methodology to approximate a general non-Gaussian stationary stochastic process by a translation process , 2011 .

[4]  George Deodatis,et al.  A simple and efficient methodology to approximate a general non-Gaussian stationary stochastic vector process by a translation process with applications in wind velocity simulation , 2013 .

[5]  S. Torquato,et al.  Reconstructing random media , 1998 .

[6]  N. Higham.  Computing the nearest correlation matrix—a problem from finance , 2002 .

[7]  Defeng Sun,et al.  A Quadratically Convergent Newton Method for Computing the Nearest Correlation Matrix , 2006, SIAM J. Matrix Anal. Appl..

[8]  D. Owen,et al.  Statistical reconstruction of two-phase random media , 2014 .

[9]  Paolo Bocchini,et al.  Critical review and latest developments of a class of simulation algorithms for strongly non-Gaussian random fields , 2008 .

[10]  Paolo Bocchini,et al.  An Efficient Methodology That Simulates a Multi-Dimensional Non-Gaussian Field to Evaluate the Effect of the Spatial Distribution of Corrosion in a Steel Beam , 2014 .

[11]  M. Shinozuka,et al.  Digital Generation of Non‐Gaussian Stochastic Fields , 1988 .

[12]  D. Owen,et al.  Statistical reconstruction and Karhunen–Loève expansion for multiphase random media , 2016 .

[13]  George Deodatis,et al.  Estimation of evolutionary spectra for simulation of non-stationary and non-Gaussian stochastic processes , 2013 .

[14]  Nicholas J. Higham,et al.  A Preconditioned Newton Algorithm for the Nearest Correlation Matrix , 2010 .

[15]  George Deodatis,et al.  Simulation of Highly Skewed Non-Gaussian Stochastic Processes , 2001 .