Advertisement

Advanced Field Data Post-processing Using RBF Interpolation

  • Marco Evangelos BiancoliniEmail author
Chapter

Abstract

In this chapter a collection of application faced with an advanced post-processing method based on RBF fields is presented. The idea is that field information known at discrete points in a continuum domain (displacement field of an elastic body subjected to load and deformed, local speed and pressure in a fluid) can be interpolated so that scattered information becomes continuous and, in some cases, differentiable. Examples based on the theory of elasticity are firstly provided: the post-processing of a FEA solution available as a displacement field can be used to compute strains and stresses with the benefit to make them mesh independent (and so ready to be used for the generation of various plot) and better resolved in the space despite the coarseness of the field. Experimental data can be processed according to the same principle so that RBF become an useful tool for strain and stress evaluation by image processing. The chapter then addresses another useful application of RBF mapping suitable for the compensation of metrological data: a complex environment that loads the structure and can adversely affect the quality of the measurement can be subtracted by the inverse mapping of the displacement field achieved by FEA so that measured points can be corrected and positioned in their undeformed configuration for an effective comparison with reference CAD geometry. The chapter is concluded showing how RBF can be used for the interpolation of experimentally acquired flow information related to hemodynamics and showing the potential of an upscaling post processing toward the reduction of the resolution of in vivo acquired flow field (and so the exposition time of the patient).

References

  1. Amodio D, Broggiato GB, Salvini P (1995) Finite strain analysis by image processing: smoothing techniques. Strain 31(3):151–157CrossRefGoogle Scholar
  2. Arad N, Dyn N, Reisfeld D, Yeshurun Y (1994) Image warping by radial basis functions: application to facial expressions. CVGIP Graph Models Image Process 56:161–172CrossRefGoogle Scholar
  3. Besnard G, Hild F, Roux S (2006) Finite-element displacement fields analysis; from digital images: application to Portevin–Le Châtelier bands. Exp Mech 46:789–803CrossRefGoogle Scholar
  4. Biancolini M, Salvini P (2012) Radial basis functions for the image analysis of deformations. In: Computational modelling of objects represented in images: fundamentals, methods and applications III proceedings of the international symposium, Rome, pp 361–365. ISBN: 978-041562134-2Google Scholar
  5. Biancolini ME, Brutti C, Chiappa A, Salvini P (2015) Post-processing strutturale mediante uso di radial basis functions. Associazione Italiana per L’Analisi delle Sollecitazioni – AIAS, 44° Convegno Nazionale, 2–5 Settembre, Università di MessinaGoogle Scholar
  6. Editor (1992) Biographical sketch of Rolland L. Hardy. Comput Math Appl 24(12):ix–xGoogle Scholar
  7. Flusser J, Suk T, Zitová B (2009) Moments and moment invariants in pattern recognition. Wiley, USAGoogle Scholar
  8. Halpern AB, Billington DP, Adriaenssens S (2013) The ribbed floor slab systems of Pier Luigi Nervi. In: Obrębski JB, Tarczewski R (eds) Proceedings of the International Association for Shell and Spatial Structures (IASS) symposium 2013, “BEYOND THE LIMITS OF MAN” 23–27 Sept, Wroclaw University of Technology, PolandGoogle Scholar
  9. Hardy RL (1971) Multiquadric equations of topography and other irregular surfaces. J Geophys Res 76(8):1905–1915CrossRefGoogle Scholar
  10. Hardy RL (1990) Theory and applications of the multiquadric-biharmonic method, 20 years of discovery, 1968–1988. Comput Math Appl 19(8/9):163–208MathSciNetCrossRefzbMATHGoogle Scholar
  11. Howland RCJ (1930) On the stress in the neighborhood of a circular hole in a strip under tension. Philos Trans R Soc Lond 229:49–86Google Scholar
  12. Innovmetric (2017) Polyworks. https://www.innovmetric.com/
  13. Jessop HT, Snell C, Allison IM (1959) The stress concentration factors in cylindrical tubes with transverse cylindrical holes. Aeronaut Q 10(4):326–344Google Scholar
  14. Maggiolini E, Livieri P, Tovo R (2015) Implicit gradient and integral average effective stresses: relationships and numerical approximations. Fatigue Fract Eng Mater Struct 38:190–199CrossRefGoogle Scholar
  15. Morbiducci U, Ponzini R, Rizzo G, Iannaccone F, Gallo D, Redaelli A (2011) Synthetic dataset generation for the analysis and the evaluation of image-based hemodynamics of the human aorta. Med Biol Eng Comput 50(2):145–154Google Scholar
  16. New River Kinematics (2017) Spatial analyzer. http://www.kinematics.com/spatialanalyzer/
  17. Poncet L, Bellesia B, Oliva AB, Rebollo EB, Cornelis M, Medrano JC, Harrison R, Lo Bue A, Moreno A, Foussat A, Felipe A, Echeandia A, Barutti A, Caserza B, Barbero P, Stenca S, Da Re A, Ribeiro JS, Brocot C, Benaoun S (2015) EU ITER TF coil: dimensional metrology, a key player in the double pancake integration, fusion engineering and design, vol 98–99, pp 1135–1139. In: Proceedings of the 28th symposium on fusion technology (SOFT-28)Google Scholar
  18. Ponzini R, Biancolini ME, Rizzo G, Morbiducci U (2012). Radial basis functions for the interpolation of hemodynamics flow pattern: a quantitative analysis. In: Computational modelling of objects represented in images III: fundamentals, methods and applications. Rome, Italy, 09/05/2012–09/07/2012. ISBN: 9780415621342Google Scholar
  19. Schultz KJ (1941) On the state of stress in perforated plates. Ph.D., Technische Hochschule, DelftGoogle Scholar
  20. Semeraro L (2017) Alignment and metrology challenges at ITER. In: “3rd PACMAN workshop”, CERNGoogle Scholar
  21. Sutton MA, Turner JL, Chao YJ, Bruch A, Chae TL (1991) Full field representation of discretely sampled surfaces deformation for displacements and strain analysis. Exp Mech 31(2):168–177CrossRefGoogle Scholar
  22. Sutton MA, Orteu JJ, Shreier HW (2009) Image correlation for shape, motion and deformation measurements. Springer, Berlin. ISBN 0387787461Google Scholar
  23. Tarisciotti C, Biancolini ME (2013) Quando le eqauzioni dell’elsaticità progettano le strutture. Analisi e Calcolo. N 59Google Scholar
  24. Vennell R, Beatson R (2009) A divergence-free spatial interpolator for large sparse velocity data sets. J Geophys Res 114:C10024.  https://doi.org/10.1029/2008JC004973CrossRefGoogle Scholar
  25. Zienkiewicz OC, Taylor RL, Zhu JZ (2005) The finite element method: its basis and fundamentals, 6th edn. Butterworth-Heinemann, UKGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Enterprise Engineering “Mario Lucertini”University of Rome “Tor Vergata”RomeItaly

Personalised recommendations