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Simple heuristic for data-driven computational elasticity with material data involving noise and outliers: a local robust regression approach

  • Yoshihiro Kanno
Original Paper Area 2
  • 39 Downloads

Abstract

Data-driven computing in applied mechanics utilizes the material data set directly, and hence is free from errors and uncertainties stemming from the conventional material modeling. For data-driven computing in elasticity, this paper presents a simple heuristic that is robust against noise and outliers in a data set. For each structural element, we extract the material property from some nearest data points. Using the nearest neighbors reduces the influence of noise, compared with the existing method that uses a single data point. Also, the robust regression is adopted to reduce the influence of outliers. Numerical experiments on the static equilibrium analysis of trusses are performed to illustrate that the proposed method is robust against the presence of noise and outliers.

Keywords

Data-driven computing Model-free computational mechanics Outlier Local regression Robust statistics 

Mathematics Subject Classification

62J05 80M50 90C20 

Notes

Acknowledgements

This work is partially supported by JSPS KAKENHI 17K06633 and 18K18898.

References

  1. 1.
    Altman, N.S.: An introduction to kernel and nearest-neighbor nonparametric regression. Am Stat 46, 175–185 (1992)MathSciNetGoogle Scholar
  2. 2.
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)CrossRefzbMATHGoogle Scholar
  3. 3.
    Bessa, M.A., Bostanabad, R., Liu, Z., Hu, A., Apley, D.W., Brinson, C., Chen, W., Liu, W.K.: A framework for data-driven analysis of materials under uncertainty: countering the curse of dimensionality. Comput. Methods Appl. Mech. Eng. 320, 633–667 (2017)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Chen, H., Chiang, R.H.L., Storey, V.C.: Business intelligence and analytics: from big data to big impact. MIS Q. Arch. 36, 1165–1188 (2012)Google Scholar
  5. 5.
    Clément, A., Soize, C., Yvonnet, J.: Computational nonlinear stochastic homogenization using a nonconcurrent multiscale approach for hyperelastic heterogeneous microstructures analysis. Int. J. Numer. Meth. Eng. 91, 799–824 (2012)CrossRefGoogle Scholar
  6. 6.
    Cleveland, W.S.: Robust locally weighted regression and smoothing scatterplots. J. Am. Stat. Assoc. 74, 829–836 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Cleveland, W.S., Devlin, S.J.: Locally weighted regression: an approach to regression analysis by local fitting. J. Am. Stat. Assoc. 83, 596–610 (1988)CrossRefzbMATHGoogle Scholar
  8. 8.
    Conti, S., Müller, S., Ortiz, M.: Data-driven problems in elasticity. Arch. Ration. Mech. Anal. 229, 79–123 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Fahad, A., Alshatri, N., Tari, Z., Alamri, A., Khalil, I., Zomaya, A.Y., Foufou, S., Bouras, A.: A survey of clustering algorithms for big data: taxonomy and empirical analysis. IEEE Trans. Emerg. Topics Comput. 2, 267–279 (2014)CrossRefGoogle Scholar
  10. 10.
    Fan, W., Hu, C.: Big graph analyses: from queries to dependencies and association rules. Data Sci. Eng. 2, 36–55 (2017)CrossRefGoogle Scholar
  11. 11.
    Flach, P.: Machine Learning: The Art and Science of Algorithms that Make Sense of Data. Cambridge University Press, Cambridge (2012)CrossRefzbMATHGoogle Scholar
  12. 12.
    Gupta, M.R., Garcia, E.K., Chin, E.: Adaptive local linear regression with application to printer color management. IEEE Trans. Image Process. 17, 936–945 (2008)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd edn. Springer, New York (2009)CrossRefzbMATHGoogle Scholar
  14. 14.
    Huber, P.J.: Robust estimation of a location parameter. Ann. Math. Stat. 35, 73–101 (1964)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Huber, P.J., Ronchetti, E.M.: Robust Statistics, 2nd edn. Wiley, Hoboken (2009)CrossRefzbMATHGoogle Scholar
  16. 16.
    Ibañez, R., Abisset-Chavanne, E., Aguado, J.V., Gonzalez, D., Cueto, E., Chinesta, F.: A manifold learning approach to data-driven computational elasticity and inelasticity. Arch. Comput. Methods Eng. 25, 47–57 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Ibañez, R., Borzacchiello, D., Aguado, J.V., Abisset-Chavanne, E., Cueto, E., Ladeveze, P., Chinesta, F.: Data-driven non-linear elasticity: constitutive manifold construction and problem discretization. Comput. Mech. 60, 813–826 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Kirchdoerfer, T., Ortiz, M.: Data-driven computational mechanics. Comput. Methods Appl. Mech. Eng. 304, 81–101 (2016)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Kirchdoerfer, T., Ortiz, M.: Data driven computing with noisy material data sets. Comput. Methods Appl. Mech. Eng. 326, 622–641 (2017)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Kirchdoerfer, T., Ortiz, M.: Data-driven computing in dynamics. Int. J. Numer. Meth. Eng. 113, 1697–1710 (2018)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Klusemann, B., Ortiz, M.: Acceleration of material-dominated calculations via phase-space simplicial subdivision and interpolation. Int. J. Numer. Meth. Eng. 103, 256–274 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Lee, T., Ouarda, T.B.M.J., Yoon, S.: KNN-based local linear regression for the analysis and simulation of low flow extremes under climatic influence. Clim. Dyn. 49, 3493–3511 (2017)CrossRefGoogle Scholar
  23. 23.
    Maronna, R., Martin, D., Yohai, V.: Robust Statistics: Theory and Methods. Wiley, Chichester (2006)CrossRefzbMATHGoogle Scholar
  24. 24.
    Mattmann, C.A.: Computing: a vision for data science. Nature 493, 473–475 (2013)CrossRefGoogle Scholar
  25. 25.
    Miguel, E., Bradley, D., Thomaszewski, B., Bickel, B., Matusik, W., Otaduy, M.A., Marschner, S.: Data-driven estimation of cloth simulation models. Comput. Graph. Forum 31, 519–528 (2012)CrossRefGoogle Scholar
  26. 26.
    Nguyen, L.T.K., Keip, M.-A.: A data-driven approach to nonlinear elasticity. Comput. Struct. 194, 97–115 (2018)CrossRefGoogle Scholar
  27. 27.
    Prairie, J.R., Rajagopalan, B., Fulp, T.J., Zagona, E.A.: Statistical nonparametric model for natural salt estimation. J. Environ. Eng. 131, 130–138 (2005)CrossRefGoogle Scholar
  28. 28.
    Ruiters, R., Schwartz, C., Klein, R.: Data driven surface reflectance from sparse and irregular samples. Comput. Graph. Forum 31, 315–324 (2012)CrossRefGoogle Scholar
  29. 29.
    Siuly, S., Zhang, Y.: Medical big data: neurological diseases diagnosis through medical data analysis. Data Sci. Eng. 1, 54–64 (2016)CrossRefGoogle Scholar
  30. 30.
    Temizer, İ., Wriggers, P.: An adaptive method for homogenization in orthotropic nonlinear elasticity. Comput. Methods Appl. Mech. Eng. 196, 3409–3423 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Temizer, İ., Zohdi, T.I.: A numerical method for homogenization in non-linear elasticity. Comput. Mech. 40, 281–298 (2007)CrossRefzbMATHGoogle Scholar
  32. 32.
    Terada, K., Kato, J., Hirayama, N., Inugai, T., Yamamoto, K.: A method of two-scale analysis with micro-macro decoupling scheme: application to hyperelastic composite materials. Comput. Mech. 52, 1199–1219 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Tsai, C.W., Lai, C.F., Chao, H.C., Vasilakos, A.V.: Big data analytics: a survey. J. Big Data 21, Article No. 21 (2015)CrossRefGoogle Scholar
  34. 34.
    Wang, H., O’Brien, J.F., Ramamoorthi, R.: Data-driven elastic models for cloth: modeling and measurement. ACM Trans. Graph. 30, Article No. 71 (2011)Google Scholar

Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics and Informatics CenterThe University of TokyoTokyoJapan

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