Library Subscription: Guest
International Journal for Multiscale Computational Engineering

Published 6 issues per year

ISSN Print: 1543-1649

ISSN Online: 1940-4352

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.4 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.3 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 2.2 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.00034 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.46 SJR: 0.333 SNIP: 0.606 CiteScore™:: 3.1 H-Index: 31

Indexed in

Gain Access(open in a new tab)
More
Purchase $35.00(open in a new tab) Check subscription Download MARC record(open in a new tab) Get Permissions(open in a new tab)

STOCHASTIC DESIGN AND CONTROL IN RANDOM HETEROGENEOUS MATERIALS

Volume 9, Issue 4, 2011, pp. 425-443
DOI: 10.1615/IntJMultCompEng.v9.i4.60
Get accessGet access
Raphael Sternfels
School of Civil and Environmental Engineering, 372 Hollister Hall, Cornell University, Ithaca, New York 14853, USA
Phaedon-Stelios Koutsourelakis
Continuum Mechanics Group, Technical University of Munich, Boltzmannstrasse 15, 85748 Garching, Germany

ABSTRACT

This paper discusses a sampling framework that enables optimization of complex systems characterized by high-dimensional uncertainties and design variables. We are especially concerned with problems relating to random heterogeneous materials where uncertainties arise from the stochastic variability of their properties. In particular, we reformulate topology optimization problems to account for the design of truly random composites. In addition, we address the optimal prescription of input loads/excitations in order to achieve a target response by the random material system. The methodological advances proposed in this paper consist of an adaptive sequential Monte Carlo scheme that economizes the number of runs of the forward solver and allows the analyst to identify several local maxima that provide important information with regard to the robustness of the design. We further propose a principled manner of introducing information from approximate models that can ultimately lead to further reductions in computational cost.

KEY WORDS: uncertainty quantification, sequential Monte Carlo, random heterogenous materials, topology optimization
REFERENCES

  1. Amzal, B. A., Bois, F., Parent, E., and Robert, C. P., Bayesian-optimal design via interacting particle systems. DOI: 10.1198/016214505000001159

  2. Bendsoe, M. P. and Sigmund, O., Material interpolation schemes in topology optimization. DOI: 10.1007/s004190050248

  3. Berk, N. F., Scattering properties of leveled-wave model for random morphologies. DOI: 10.1103/PhysRevA.44.5069

  4. Besag, J., Markov Chain Monte Carlo for Statistical Inference.

  5. Burkardt, J., Du, Q., and Gunzburger, M., Reduced Order Modeling of Complex Systems.

  6. Charmpis, D. C., Schueller, G. I., and Pellissetti, M. F., The need for linking micromechanics of materials with stochastic finite elements: A challenge for materials science. DOI: 10.1016/j.commatsci.2007.02.014

  7. Chopin, N., Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference. DOI: 10.1214/009053604000000698

  8. Del Moral, P., Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications.

  9. Del Moral, P., Doucet, A., and Jasra, A., Sequential Monte Carlo for Bayesian Computation (with discussion).

  10. Del Moral, P., Doucet, A., and Jasra, A., Sequential Monte Carlo samplers. DOI: 10.1111/j.1467-9868.2006.00553.x

  11. Doucet, A., de Freitas, J. F. G., and Gordon, N. J.,, Sequential Monte Carlo Methods in Practice.

  12. Gersborg-Hansen, A., Bendsoe, M. P., and Sigmund, O., Topology optimization of heat conduction problems using the finite volume method. DOI: 10.1007/s00158-005-0584-3

  13. Ghanem, R. and Spanos, P., Stochastic Finite Elements: A Spectral Approach.

  14. Gibiansky, L. V. and Sigmund, O., Multiphase composites with extremal bulk modulus. DOI: 10.1016/S0022-5096(99)00043-5

  15. Guest, J. K. and Igusa, T., Structural optimization under uncertain loads and nodal locations. DOI: 10.1016/j.cma.2008.04.009

  16. Johansen, M. A., Doucet, A., and Davy, M., Particle methods for maximum likelihood parameter estimation in latent variable models. DOI: 10.1007/s11222-007-9037-8

  17. Kennedy, M. C. and O’Hagan, A., Predicting the output from a complex computer code when fast approximations are available. DOI: 10.1093/biomet/87.1.1

  18. Koutsourelakis, P. S., Probabilistic characterization and simulation of multi-phase random media. DOI: 10.1016/j.probengmech.2005.11.004

  19. Koutsourelakis, P. S., Accurate uncertainty quantification using inaccurate models. DOI: 10.1137/080733565

  20. Koutsourelakis, P. S. and Deodatis, G., Simulation of binary random processes with applications to two-phase random media. DOI: 10.1061/(ASCE)0733-9399(2005)131:4(397)

  21. Kück, H., de Freitas, N., and Doucet, A., SMC samplers for Bayesian pptimal nonlinear design.

  22. Liu, J. S., Monte Carlo strategies in scientific computing.

  23. MacEachern, S. N., Clyde, M., and Liu, J. S., Sequential importance sampling for nonparametric bayes models: The next generation.

  24. Müller, P., Simulation Based Optimal Design.

  25. Robert, C. P. and Casella, G., Monte Carlo Statistical Methods.

  26. Roberts, A. P. and Teubner, M., Transport properties of heterogeneous materials derived from gaussian random fields: Bounds and simulation. DOI: 10.1103/PhysRevE.51.4141

  27. Roberts, G. O. and Rosenthal, J. S., Optimal scaling for various metropolis hastings algorithms. DOI: 10.1214/ss/1015346320

  28. Romkes, A., Oden, J. T., and Vemaganti, K., Multi-scale goal-oriented adaptive modeling of random heterogeneous materials. DOI: 10.1016/j.mechmat.2005.06.028

  29. Schueller, G. I. and Jensen, H. A., Computational methods in optimization considering uncertainties–An overview. DOI: 10.1016/j.cma.2008.05.004

  30. Shinozuka, M. and Deodatis, G., Simulation of multi-dimensional stochastic processes by spectral representation.

  31. Sigmund, O., Materials with prescribed constitutive parameters–An inverse homogenization problem. DOI: 10.1016/0020-7683(94)90154-6

  32. Sigmund, O., Tailoring materials for specific needs. DOI: 10.1177/1045389X9400500602

  33. Sigmund, O., Tailoring materials with prescribed elastic properties. DOI: 10.1016/0167-6636(94)00069-7

  34. Sigmund, O., On the design of compliant mechanisms using topology optimization.

  35. Sigmund, O., A new class of extremal composites. DOI: 10.1016/S0022-5096(99)00034-4

  36. Sigmund, O., Topology optimization: A tool for the tailoring of structures and materials. DOI: 10.1098/rsta.2000.0528

  37. Sigmund, O., Manufacturing tolerant topology optimization. DOI: 10.1007/s10409-009-0240-z

  38. Sigmund, O. and Torquato, S., Composites with extremal thermal expansion coefficients. DOI: 10.1063/1.117961

  39. Sigmund, O. and Torquato, S., Design of materials with extreme thermal expansion using a three-phase topology optimization method. DOI: 10.1016/S0022-5096(96)00114-7

  40. Sigmund, O. and Torquato, S., Design of smart composite materials using topology optimization. DOI: 10.1088/0964-1726/8/3/308

  41. Stefanou, G. and Papadrakakis, M., Stochastic finite element analysis of shells with combined random material and geometric properties. DOI: 10.1016/j.cma.2003.10.001

  42. Sundararaghavan, V. and Zabaras, N., A multi-length scale sensitivity analysis for the control of texture-dependent properties in deformation processing. DOI: 10.1016/j.ijplas.2007.12.005

  43. Torquato, S., Random Heterogeneous Materials.

  44. Vel, S. S. and Goupee, A. J., Multiscale thermoelastic analysis of random heterogeneous materials, Part I: Microstructure characterization and homogenization of material properties. DOI: 10.1016/j.commatsci.2009.11.015

  45. Wadbro, E. and Berggren, M., Megapixel topology optimization on a graphics processing unit. DOI: 10.1137/070699822

  46. Xu, X. F., Chen, X., and Shen, L. H., A green-function-based multiscale method for uncertainty quantification of finite body random heterogeneous materials. DOI: 10.1016/j.compstruc.2009.05.009

  47. Yeong, C. L. Y. and Torquato, S., Reconstructing random media I and II.

  48. Zabaras, N. and Ganapathysubramanian, B., A scalable framework for the solution of stochastic inverse problems using a sparse grid collocation approach. DOI: 10.1016/j.jcp.2008.01.019

CITED BY

  1. Ng Leo Wai-Tsun, Huynh Dinh Bao Phuong, Willcox Karen, Multifidelity Uncertainty Propagation for Optimization Under Uncertainty, 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2012. Crossref

  2. Sternfels Raphael, Earls Christopher J, Reduced-order model tracking and interpolation to solve PDE-based Bayesian inverse problems, Inverse Problems, 29, 7, 2013. Crossref

  3. Olariu C. S., Lasquellec S., Brosseau C., Randomized scalable checkerboard geometries: The electrostatic problem, Journal of Applied Physics, 114, 7, 2013. Crossref

  4. Koutsourelakis P.S., Variational Bayesian strategies for high-dimensional, stochastic design problems, Journal of Computational Physics, 308, 2016. Crossref

  5. Rixner Maximilian, Koutsourelakis Phaedon-Stelios, Self-supervised optimization of random material microstructures in the small-data regime, npj Computational Materials, 8, 1, 2022. Crossref

  6. Willmann Harald, Nitzler Jonas, Brandstäter Sebastian, Wall Wolfgang A., Bayesian calibration of coupled computational mechanics models under uncertainty based on interface deformation, Advanced Modeling and Simulation in Engineering Sciences, 9, 1, 2022. Crossref

942 Article views 37 Article downloads Metrics
942 VIEWS 37 DOWNLOADS 6 Crossref CITATIONS Google
Scholar CITATIONS

Articles with similar content:

BAYESIAN INFERENCE OF STOCHASTIC REACTION NETWORKS USING MULTIFIDELITY SEQUENTIAL TEMPERED MARKOV CHAIN MONTE CARLO International Journal for Uncertainty Quantification, Vol.10, 2020, issue 6
Huy D. Vo, Thomas A. Catanach, Brian Munsky
MULTILEVEL MONTE CARLO ON A HIGH-DIMENSIONAL PARAMETER SPACE FOR TRANSMISSION PROBLEMS WITH GEOMETRIC UNCERTAINTIES International Journal for Uncertainty Quantification, Vol.9, 2019, issue 6
Laura Scarabosio
DIMENSIONALITY REDUCTION FOR COMPLEX MODELS VIA BAYESIAN COMPRESSIVE SENSING International Journal for Uncertainty Quantification, Vol.4, 2014, issue 1
Bert J. Debusschere, Habib N. Najm, Peter Thornton, Cosmin Safta, Khachik Sargsyan, Daniel Ricciuto
GOAL-ORIENTED MODEL ADAPTIVITY IN STOCHASTIC ELASTODYNAMICS: SIMULTANEOUS CONTROL OF DISCRETIZATION, SURROGATE MODEL AND SAMPLING ERRORS International Journal for Uncertainty Quantification, Vol.10, 2020, issue 3
Pedro Bonilla-Villalba, A. Kundu, S. Claus, Pierre Kerfriden
A STOCHASTIC DOMAIN DECOMPOSITION AND POST-PROCESSING ALGORITHM FOR EPISTEMIC UNCERTAINTY QUANTIFICATION International Journal for Uncertainty Quantification, Vol.13, 2023, issue 5
Mahadevan Ganesh, Alexandre M. Tartakovsky, Ramakrishna Tipireddy, S. C. Hawkins

Latest Issue

EFFECTIVE BIOMEDICAL SYSTEM FOR DETECTING, TRACKING, AND PREVENTING ASYMPTOMATIC COVID-19 PATIENTS NON-INVASIVELY USING IoT AND MIXED REALITY R. Prasanna , T. Ragupathi, N. Ganesh Kumar, Banu Priya Prathaban, S. Aswath, R. Rajesh Kanna

Forthcoming Articles

Multiscale 3D TransUNet-aided Tumor Segmentation and Multi-Cascaded Model for Lung Cancer Diagnosis System from 3D CT Images with Fused Feature Pool Formation GILBERT langat, Beiji Zou, Xiaoyan Kui, Kevin Njagi Fine-tuning MobileNetV3 with different weight optimization algorithms for classification of denoised blood cell images using convolutional neural network M. Mohana Dhas, N. Suresh Singh A Comparative Biomechanical Analysis of Posterior Lumbar Interbody Fusion Constructs with Four Established Scenarios Nitesh Kumar Singh, Nishant Singh Thermodynamics analysis of Casson hybrid nanofluid flow over a porous Riga plate with slip effect Himanshu Upreti, Satyaranjan R. Mishra, Alok Kumar Pandey, Pradyumna K. Pattnaik Diagnosis of kidney cyst, tumor and stone from CT scan images using feature fusion hypergraph convolutional neural network (F2HCN2) N. Sasikaladevi, S. Pradeepa, A. Revathi, S. Vimal, Ruben Gonzalez Crespo
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections Prices and Subscription Policies Begell House Contact Us Language English 中文 Русский Português German French Spain