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Extraction of Process-Structure Evolution Linkages from X-ray Scattering Measurements Using Dimensionality Reduction and Time Series Analysis

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Abstract

The rapid development of robust, reliable, and reduced-order process-structure evolution linkages that take into account hierarchical structure are essential to expedite the development and manufacturing of new materials. Towards this end, this paper lays a theoretical framework that injects the established time series analysis into the recently developed materials knowledge systems (MKS) framework. This new framework is first presented and then demonstrated on an ensemble dataset obtained using small-angle X-ray scattering on semi-crystalline linear low density polyethylene films from a synchrotron X-ray scattering experiment.

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References

  1. National Science and Technology Council Executive Office of the President: Materials Genome Initiative for Global Competitiveness. http://www.whitehouse.gov/sites/default/files/microsites/ostp/materials_genome_initiative-final.pdf Accessed 2011-06-30

  2. Materials Genome Initiative National Science and Technology Council Committee on Technology Subcommittee on the Materials Genome Initiative: Materials Genome Initiative Strategic Plan. http://www.whitehouse.gov/sites/default/files/microsites/ostp/NSTC/mgi_strategic_plan_-_dec_2014.pdf Accessed 2014-12-30

  3. Allison J (2009) Integrated computational materials engineering (ICME): a transformational discipline for the global materials profession. Allied Publishers, New Delhi, p 223

    Google Scholar 

  4. Allison J (2011) Integrated computational materials engineering: a perspective on progress and future steps. JOM 63(4):15–18

    Article  Google Scholar 

  5. Olson GB (2000) Designing a new material world. Science 288(5468):993–998

    Article  Google Scholar 

  6. On Integrated Computational Materials Engineering, N.R.C.U.C. Integrated computational materials engineering: a transformational discipline for improved competitiveness and national security. National Academies Press, 2008

  7. Schmitz GJ, Prahl U (2012) Integrative computational materials engineering: concepts and applications of a modular simulation platform. John Wiley & Sons

  8. Robinson L (2013) TMS study charts a course to successful ICME implementation Springer

  9. Panchal JH, Kalidindi SR, McDowell DL (2013) Key computational modeling issues in integrated computational materials engineering. Comput Aided Des 45(1):4–25

    Article  Google Scholar 

  10. Kalidindi SR (2015) Data science and cyberinfrastructure: critical enablers for accelerated development of hierarchical materials. Int Mater Rev 60(3):150–168

    Article  Google Scholar 

  11. Kalidindi SR, Gomberg JA, Trautt ZT, Becker CA (2015) Application of data science tools to quantify and distinguish between structures and models in molecular dynamics datasets. Nanotechnology 26(34):344006

    Article  Google Scholar 

  12. Brough DB, Wheeler D, Warren JA, Kalidindi SR (2016) Microstructure-based knowledge systems for capturing process-structure evolution linkages. Curr Opinion Solid State Mater Sci, in press. doi:10.1016/j.cossms.2016.05.002

  13. Kalidindi SR, Niezgoda SR, Salem AA (2011) Microstructure informatics using higher-order statistics and efficient data-mining protocols. JOM 63(4):34–41

    Article  Google Scholar 

  14. Lajeunesse S (2004) Plastic bags. Chem Eng News 82(38): 51

    Article  Google Scholar 

  15. Faur-Csukat G (2006) A study on the ballistic performance of composites, vol 239. Wiley Online Library, pp 217–226

  16. Peacock A (2000) Handbook of polyethylene: structures: properties, and applications. CRC Press

  17. Kröner E (1986) Statistical modelling. Springer, pp 229– 291

  18. Kröner E (1977) Bounds for effective elastic moduli of disordered materials. J Mech Phys Solids 25(2):137–155

    Article  Google Scholar 

  19. Volterra V (2005) Theory of functionals and of integral and integro-differential equations. Courier Corporation

  20. Suits DB (1957) Use of dummy variables in regression equations. J Am Stat Assoc 52(280):548–551

    Article  Google Scholar 

  21. Galton F (1886) Regression towards mediocrity in hereditary stature. J Anthropol Inst G B Irel

  22. Cooley JW, Tukey JW (1965) An algorithm for the machine calculation of complex fourier series. Mathematics of computation 19(90):297–301

    Article  Google Scholar 

  23. Brough DB, Wheeler D, Kalidindi SR (2017) Materials knowledge systems in python—a data science framework for accelerated development of hierarchical materials. Integrating Materials and Manufacturing Innovation, in press

  24. Landi G, Niezgoda SR, Kalidindi SR (2010) Multi-scale modeling of elastic response of three-dimensional voxel-based microstructure datasets using novel DFT-based knowledge systems. Acta Mater 58(7):2716–2725

    Article  Google Scholar 

  25. Kalidindi SR, Niezgoda SR, Landi G, Vachhani S, Fast T (2010) A novel framework for building materials knowledge systems. Computers, Materials, & Continua 17(2):103–125

    Google Scholar 

  26. Yabansu YC, Patel DK, Kalidindi SR (2014) Calibrated localization relationships for elastic response of polycrystalline aggregates. Acta Mater 81:151–160

    Article  Google Scholar 

  27. Al-Harbi HF, Landi G, Kalidindi SR (2012) Multi-scale modeling of the elastic response of a structural component made from a composite material using the materials knowledge system. Model Simul Mater Sci Eng 20 (5):055001

    Article  Google Scholar 

  28. Gupta A, Cecen A, Goyal S, Singh AK, Kalidindi SR (2015) Structure–property linkages using a data science approach: application to a non-metallic inclusion/steel composite system. Acta Mater 91:239–254

    Article  Google Scholar 

  29. Cecen A, Fast T, Kalidindi SR (2016) Versatile algorithms for the computation of 2-point spatial correlations in quantifying material structure. Integrating Materials and Manufacturing Innovation 5(1):1–15

    Article  Google Scholar 

  30. Çeçen A, Fast T, Kumbur E, Kalidindi S (2014) A data-driven approach to establishing microstructure–property relationships in porous transport layers of polymer electrolyte fuel cells. J Power Sources 245:144–153

    Article  Google Scholar 

  31. Yabansu YC, Kalidindi SR (2015) Representation and calibration of elastic localization kernels for a broad class of cubic polycrystals. Acta Mater 94:26–35

    Article  Google Scholar 

  32. Fast T, Niezgoda SR, Kalidindi SR (2011) A new framework for computationally efficient structure–structure evolution linkages to facilitate high-fidelity scale bridging in multi-scale materials models. Acta Mater 59(2):699–707

    Article  Google Scholar 

  33. Niezgoda SR, Yabansu YC, Kalidindi SR (2011) Understanding and visualizing microstructure and microstructure variance as a stochastic process. Acta Mater 59(16):6387–6400

    Article  Google Scholar 

  34. Niezgoda SR, Kanjarla AK, Kalidindi SR (2013) Novel microstructure quantification framework for databasing, visualization, and analysis of microstructure data. Integrating Materials and Manufacturing Innovation 2(1):1–27

    Article  Google Scholar 

  35. Hotelling H (1933) Analysis of a complex of statistical variables into principal components. J Educ Psychol 24(6):417

    Article  Google Scholar 

  36. Mika S, Schölkopf B, Smola AJ, Müller K-R, Scholz M, Rätsch G (1998) Kernel PCA and de-noising in feature spaces, vol 4. Citeseer , p 7

  37. Kalidindi SR (2015) Hierarchical materials informatics: novel analytics for materials data. Elsevier

  38. Halko N, Martinsson P-G., Tropp JA (2011) Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions. SIAM Rev 53(2):217–288

    Article  Google Scholar 

  39. Niezgoda S, Fullwood D, Kalidindi S (2008) Delineation of the space of 2-point correlations in a composite material system. Acta Mater 56(18):5285–5292

    Article  Google Scholar 

  40. Scargle JD (1982) Studies in astronomical time series analysis. II-statistical aspects of spectral analysis of unevenly spaced data. Astrophys J 263:835–853

    Article  Google Scholar 

  41. Warner RM (1998) Spectral analysis of time-series data. Guilford Press

  42. Granger CWJ, Hatanaka M, et al. (1964) Spectral analysis of economic time series spectral analysis of economic time series

  43. Chan K-P, Fu AW-C (1999) Efficient time series matching by wavelets. IEEE, pp 126–133

  44. Grinsted A, Moore JC, Jevrejeva S (2004) Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Process Geophys 11(5/6):561–566

    Article  Google Scholar 

  45. Percival DB, Walden AT (2006) Wavelet methods for time series analysis vol. 4. Cambridge University Press

  46. Box GE, Jenkins GM, Reinsel GC, Ljung GM (2015) Time series analysis: forecasting and control. John Wiley & Sons

  47. Kalman RE (1960) A new approach to linear filtering and prediction problems. J Basic Eng 82(1):35–45

    Article  Google Scholar 

  48. Baum LE, Petrie T (1966) Statistical inference for probabilistic functions of finite state Markov chains. Ann Math Stat 37(6):1554–1563

    Article  Google Scholar 

  49. Rabiner LR (1989) A tutorial on hidden Markov models and selected applications in speech recognition. Proc IEEE 77(2):257–286

    Article  Google Scholar 

  50. Rabiner LR, Juang B-H (1986) An introduction to hidden Markov models. IEEE ASSP Mag 3(1):4–16

    Article  Google Scholar 

  51. Julier SJ, Uhlmann JK (1997) New extension of the Kalman filter to nonlinear systems. International Society for Optics and Photonics, pp 182–193

  52. Wan EA, Van Der Merwe R (2000) The unscented Kalman filter for nonlinear estimation. IEEE, pp 153–158

  53. Gustafsson F, Hendeby G (2012) Some relations between extended and unscented Kalman filters. IEEE Trans Signal Process 60(2):545–555

    Article  Google Scholar 

  54. Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735–1780

    Article  Google Scholar 

  55. Lipton ZC, Berkowitz J, Elkan C (2015) A critical review of recurrent neural networks for sequence learning. arXiv preprint arXiv:1506.00019

  56. Pankratz A (2009) Forecasting with univariate Box-Jenkins models: concepts and cases vol. 224. John Wiley & Sons

  57. Masreliez C, Martin R (1977) Robust Bayesian estimation for the linear model and robustifying the Kalman filter. IEEE Trans Autom Control 22(3):361–371

    Article  Google Scholar 

  58. Salti S, Di Stefano L (2013) On-line support vector regression of the transition model for the Kalman filter. Image Vis Comput 31(6):487–501

    Article  Google Scholar 

  59. Haaland B, Min W, Qian PZ, Amemiya Y (2010) A statistical approach to thermal management of data centers under steady state and system perturbations. J Am Stat Assoc 105(491):1030–1041

    Article  Google Scholar 

  60. Kalidindi SR, De Graef M (2015) Materials data science: current status and future outlook. Annu Rev MaterRes 45:171–193

    Article  Google Scholar 

  61. Friedman JH (1991) Multivariate adaptive regression splines. Ann Stat, 1–67

  62. Lewis PA, Stevens JG (1991) Nonlinear modeling of time series using multivariate adaptive regression splines (mars). J Am Stat Assoc 86(416):864–877

    Article  Google Scholar 

  63. De Gooijer JG, Ray BK, Kräger H (1998) Forecasting exchange rates using TSMARS. J Int Money Financ 17(3):513–534

    Article  Google Scholar 

  64. Narayanan T, Diat O, Bösecke P (2001) SAXS and USAXS on the high brilliance beamline at the ESRF. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers. Detectors and Associated Equipment 467:1005– 1009

    Article  Google Scholar 

  65. Cebe P, Hsiao BS, Lohse DJ (2000) Scattering from polymers: characterization by X-rays, neutrons, and light. ACS Publications

  66. Gurun B, Bucknall DG, Thio YS, Teoh CC, Harkin-Jones E (2011) Multiaxial deformation of polyethylene and polyethylene/clay nanocomposites: in situ synchrotron small angle and wide angle x-ray scattering study. J Polym Sci B Polym Phys 49(9):669– 677

    Article  Google Scholar 

  67. Gurun B, Thio Y, Bucknall D (2009) Combined multiaxial deformation of polymers with in situ small angle and wide angle x-ray scattering techniques. Rev Sci Instrum 80(12):123906

    Article  Google Scholar 

  68. Samon JM, Schultz JM, Hsiao BS, Seifert S, Stribeck N, Gurke I, Saw C (1999) Structure development during the melt spinning of polyethylene and poly (vinylidene fluoride) fibers by in situ synchrotron small-and wide-angle x-ray scattering techniques. Macromolecules 32(24):8121–8132

    Article  Google Scholar 

  69. Guáqueta C, Sanders LK, Wong GC, Luijten E (2006) The effect of salt on self-assembled actin-lysozyme complexes. Biophys J 90(12):4630–4638

    Article  Google Scholar 

  70. Chmelař J, Pokornỳ R, Schneider P, Smolnó K, Bělskỳ P, Kosek J (2015) Free and constrained amorphous phases in polyethylene: interpretation of 1 H NMR and SAXS data over a broad range of crystallinity. Polymer 58:189–198

    Article  Google Scholar 

  71. Noda I, Ozaki Y (2005) Two-dimensional correlation spectroscopy: applications in vibrational and optical spectroscopy. John Wiley & Sons

  72. Smirnova DS, Kornfield JA, Lohse DJ (2011) Morphology development in model polyethylene via two-dimensional correlation analysis. Macromolecules 44(17):6836–6848

    Article  Google Scholar 

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Acknowledgments

DBB and SRK acknowledge support from the NSF-IGERT Award 1258425 and NIST 70NANB14H191. AK and DGB acknowledge support from the ExxonMobil Chemical Company.

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Correspondence to Surya R. Kalidindi.

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Brough, D.B., Kannan, A., Haaland, B. et al. Extraction of Process-Structure Evolution Linkages from X-ray Scattering Measurements Using Dimensionality Reduction and Time Series Analysis. Integr Mater Manuf Innov 6, 147–159 (2017). https://doi.org/10.1007/s40192-017-0093-4

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