195
Views
2
CrossRef citations to date
0
Altmetric
Articles

Polynomial metamodeling with dimensional analysis and the effect heredity principle

Pages 195-213 | Accepted 22 Jun 2016, Published online: 19 Jul 2016

References

  • Albrecht, M. C., Nachtsheim, C. J., Albrecht, T. A., & Cook, R. D. (2013). Experimental design for engineering dimensional analysis. Technometrics, 55, 257–270.10.1080/00401706.2012.746207
  • Barenblatt, G. I. (1996). Scaling, self-similarity, and intermediate asymptotics. New York, NY: Cambridge University Press.10.1017/CBO9781107050242
  • Blatman, G., & Sudret, B. (2010). Efficient computation of global sensitivity indices using sparse polynomial chaos expansions. Reliability Engineering and System Safety, 95, 1216–1229.10.1016/j.ress.2010.06.015
  • Box, G. E. P., & Draper, N. R. (2007). Response surfaces, mixtures, and ridge analyses (2nd ed.). New Jersey, NJ: Wiley.10.1002/0470072768
  • Box, G. E. P., & Meyer, R. D. (1993). Finding the active factors in fractionated screening experiments. Journal of Quality Technology, 25, 94–105.
  • Bridgman, P. W. (1931). Dimensional analysis (2nd ed.). New Haven, CT: Yale University Press.
  • Cengel, Y. A. (2002). Heat transfer: A practical approach. New York, NY: McGraw-Hill.
  • Chen, V. C., Tsui, K. L., Barton, R. R., & Meckesheimer, M. (2006). A review on design, modeling and applications of computer experiments. IIE Transactions, 38, 273–291.10.1080/07408170500232495
  • Chen, W., Jin, R., & Sudjianto, A. (2006). Analytical global sensitivity analysis and uncertainty propagation for robust design. Journal of Quality Technology, 38, 333–348.
  • Chipman, H. (1996). Bayesian variable selection with related predictors. The Canadian Journal of Statistics, 24, 17–36.10.2307/3315687
  • Chipman, H., Hamada, M., & Wu, C. F. J. (1997). A Bayesian variable-selection approach for analyzing designed experiments with complex aliasing. Technometrics, 39, 372–381.10.1080/00401706.1997.10485156
  • Crestaux, T., Maître, O. L., & Martinez, J. M. (2009). Polynomial chaos expansion for sensitivity analysis. Reliability Engineering and System Safety, 94, 1161–1172.10.1016/j.ress.2008.10.008
  • Fang, K. T., & Lin, D. K. (2003). Uniform experimental designs and their applications in industry. In R. Khattree & C. R. Rao (Eds.), Statistics in industry (handbook of statistics) (Vol. 22, pp. 131–170). Amsterdam: North-Holland.10.1016/S0169-7161(03)22006-X
  • Gautschi, W. (2004). Orthogonal polynomials: Computation and approximation. New York, NY: Oxford University Press.
  • George, E. I., & McCulloch, R. E. (1993). Variable selection via Gibbs sampling. Journal of the American Statistical Association, 88, 881–889.10.1080/01621459.1993.10476353
  • George, E. I., & McCulloch, R. E. (1997). Approaches for Bayesian variable selection. Statistica Sinica, 7, 339–373.
  • Ghanem, R., & Spanos, P. D. (1991). Stochastic finite elements: A spectral approach. New York, NY: Springer-Verlag.10.1007/978-1-4612-3094-6
  • Gramacy, R. B., & Lee, H. K. H. (2012). Cases for the nugget in modeling computer experiments. Statistical Computing, 22, 713–722.10.1007/s11222-010-9224-x
  • Hamada, M., & Wu, C. F. J. (1992). Analysis of designed experiments with complex aliasing. Journal of Quality Technology, 24, 130–137.
  • Joseph, V. R. (2006). A Bayesian approach to the design and analysis of fractionated experiments. Technometrics, 48, 219–229.10.1198/004017005000000652
  • Li, R., & Lin, D. K. (2009). Variable selection for screening experiments. Quality Technology & Quantitative Management, 6, 271–280.
  • Le Maître, O. P., & Knio, O. M. (2010). Spectral methods for uncertainty quantification: With applications to computational fluid dynamics. New York, NY: Springer-Verlag.10.1007/978-90-481-3520-2
  • Lemieux, C. (2009). Monte Carlo and quasi-Monte-Carlo sampling. New York, NY: Springer-Verlag.
  • Matousek, J. (1998). On the L2-discrepancy for anchored boxes. Journal of Complexity, 14, 527–556.10.1006/jcom.1998.0489
  • Misic, T., Najdanovic-Lukic, M., & Nesic, L. (2010). Dimensional analysis in physics and the Buckingham theorem. European Journal of Physics, 31, 893–906.10.1088/0143-0807/31/4/019
  • Nguyen, N. K., & Piepel, G. F. (2005). Computer-generated experimental designs for irregular-shaped regions. Quality Technology & Quantitative Management, 2, 147–160.
  • Oakley, J. E., & O’Hagan, A. (2004). Probabilistic sensitivity analysis of complex models: A Bayesian approach. Journal of the Royal Statistical Society (Series B), 66, 751–769.10.1111/rssb.2004.66.issue-3
  • Peixoto, J. L. (1987). Hierarchical variable selection in polynomial regression models. The American Statistician, 41, 311–313.
  • Peixoto, J. L. (1990). A property of well-formulated polynomial regression models. The American Statistician, 44, 26–30.
  • Sacks, J., Welch, W. J., Mitchell, T. J., & Wynn, H. P. (1989). Design and analysis of computer experiments. Statistical Science, 4, 409–423.10.1214/ss/1177012413
  • Saltelli, A., Chan, K., & Scott, M. (Eds.). (2000). Sensitivity analysis. New York, NY: Wiley.
  • Santner, T. J., Williams, B. J., & Notz, W. I. (2003). The design and analysis of computer experiments. New York, NY: Springer-Verlag.10.1007/978-1-4757-3799-8
  • Shen, W., Davis, T., Lin, D. K., & Nachtsheim, C. J. (2014). Dimensional analysis and its application in statistics. Journal of Quality Technology, 46, 185–198.
  • Simpson, T. W., Mauery, T. M., Korte, J. J., & Mistree, F. (1998). Comparison of response surface and Kriging models for multidisciplinary design optimization. AIAA Paper, 98, 1–11.
  • Sonin, A. A. (2004). A generalization of the Π-theorem and dimensional analysis. PNAS, 101, 8525–8526.10.1073/pnas.0402931101
  • Steinberg, D. M., & Bursztyn, D. (2004). Data analytic tools for understanding random field regression models. Technometrics, 46, 411–420.10.1198/004017004000000419
  • Sudret, B. (2008). Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering and System Safety, 93, 964–979.10.1016/j.ress.2007.04.002
  • Tan, M. H. Y., & Wu, C. F. J. (2013). A Bayesian approach for model selection in fractionated split plot experiments with applications in robust parameter design. Technometrics, 55, 359–372.10.1080/00401706.2013.778790
  • Tan, M. H. Y. (2014). Bounded loss functions and the characteristic function inversion method for computing expected loss. Quality Technology & Quantitative Management, 11, 401–421.
  • Vignaux, G. A., & Scott, J. L. (1999). Simplifying regression models using dimensional analysis. Australia and New Zealand Journal of Statistics, 41, 31–34.10.1111/anzs.1999.41.issue-1
  • Wang, G. G., & Shan, S. (2007). Review of metamodeling techniques in support of engineering design optimization. Journal of Mechanical Design, 129, 370–380.10.1115/1.2429697
  • Welch, W., Yu, T., Kang, S. M., & Sacks, J. (1990). Computer experiments for quality control by parameter design. Journal of Quality Technology, 22, 15–22.
  • Xiu, D., & Karniadakis, G. E. (2002). The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM Journal of Scientific Computing, 24, 619–644.10.1137/S1064827501387826
  • Yuan, M., Joseph, V. R., & Lin, Y. (2007). An efficient variable selection approach for analyzing designed experiments. Technometrics, 49, 430–439.10.1198/004017007000000173

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.