0
Research Papers

Radial Basis Functions Update of Digital Models on Actual Manufactured Shapes

[+] Author and Article Information
Marco Evangelos Biancolini

Associate Professor
Department of Enterprise
Engineering “Mario Lucertini,”
University of Rome Tor Vergata,
Via del Politecnico 1,
Rome 00133, Italy
e-mail: biancolini@ing.uniroma2.it

Ubaldo Cella

Research Fellow
Department of Enterprise
Engineering “Mario Lucertini,”
University of Rome Tor Vergata,
Via del Politecnico 1,
Rome 00133, Italy
e-mail: ubaldo.cella@uniroma2.it

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 7, 2018; final manuscript received September 28, 2018; published online January 7, 2019. Assoc. Editor: Radu Serban.

J. Comput. Nonlinear Dynam 14(2), 021013 (Jan 07, 2019) (9 pages) Paper No: CND-18-1299; doi: 10.1115/1.4041680 History: Received July 07, 2018; Revised September 28, 2018

In the mechanical engineering world, there is a growing interest in being able to create so-called “digital twins” to assess the impact to performance or response. Part of the challenge is to be able to include and assess manufactured geometries as opposed to nominal design intent, particularly for components that are sensitive to small shape variations. In this paper, we show how the update of digital models adopted in computer aided engineering (CAE) can be conducted according to a mesh morphing workflow based on radial basis functions (RBF). The CAE mesh of the nominal design is updated onto the actual one as acquired from surveying a manufactured individual. The concept is demonstrated on a practical application, the wing structure of the RIBES experiment, showing how the new proposed method compares with a traditional one based on the reconstruction of the geometrical model.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Mongeau, M. , and Bes, C. , 2005, “ Aircraft Maintenance Jacking Problem Via Optimization,” IEEE Trans. Aerosp. Electron. Syst., 41(1), pp. 99–109. [CrossRef]
Radvar-Esfahlan, H. , and Tahan, S.-A. , 2012, “ Nonrigid Geometric Metrology Using Generalized Numerical Inspection Fixtures,” Precis. Eng., 36(1), pp. 1–9. [CrossRef]
Abenhaim, G. N. , Desrochers, A. , Tahan, A. S. , and Bigeon, J. , 2015, “ A Virtual Fixture Using a FE-Based Transformation Model Embedded Into a Constrained Optimization for the Dimensional Inspection of Nonrigid Parts,” Comput.-Aided Des., 62, pp. 248–258. [CrossRef]
Biancolini, M. E. , 2017, “ Compensation of Metrological Data,” Fast Radial Basis Functions Engineering Applications, Springer, Cham, Switzerland, Chap. 12.6.
Kemmler, S. , Dazer, M. , Leopold, T. , and Bertsche, B. , 2014, “ Method for the Development of a Functional Adaptive Simulation Model for Designing Robust Products,” Weimar Optimization and Stochastic Days, Weimar, Germany, Nov. 6–7, pp. 1–21.
MacDonald, C. , Dion, B. , and Davoudabadi, M. , 2017, “ Creating a Digital Twin for a Pump,” ANSYS Adv., 1, pp. 8–10. https://www.ansys.com/-/media/ansys/corporate/resourcelibrary/article/creating-a-digital-twin-for-a-pump-aa-v11-i1.pdf
Jakobsson, S. , and Amoignon, O. , 2007, “ Mesh Deformation Using Radial Basis Functions for Gradient-Based Aerodynamic Shape Optimization,” Comput. Fluids, 36(6), pp. 1119–1136. [CrossRef]
Rendall, T. , and Allen, C. , 2009, “ Efficient Mesh Motion Using Radial Basis Functions With Data Reduction Algorithms,” J. Comput. Phys., 228(17), pp. 6231–6249. [CrossRef]
de Boer, A. , van der Schoot, M. , and Bijl, H. , 2007, “ Mesh Deformation Based on Radial Basis Functions Interpolation,” Comput. Struct., 85(11–14), pp. 784–795. [CrossRef]
Biancolini, M. E. , 2012, “ Mesh Morphing and Smoothing by Means of Radial Basis Functions (RBF): A Practical Example Using Fluent and RBF Morph,” Handbook of Research on Computational Science and Engineering: Theory and Practice, J. Leng and W. Sharrock , eds., Information Science Reference, Hershey, PA.
Cenni, R. , Bertuzzi, G. , and Cova, M. , 2016, “ A CAD-MESH Mixed Approach to Enhance Shape Optimization Capabilities,” International CAE Conference, Parma, Italy, Oct. 17–18.
Sieger, D. , Menzel, S. , and Botsch, M. , 2014, “ RBF Morphing Techniques for Simulation-Based Design Optimization,” Eng. Comput., 30(2), pp. 161–174. [CrossRef]
Cella, U. , and Biancolini, M. E. , 2012, “ Aeroelastic Analysis of Aircraft Wind-Tunnel Model Coupling Structural and Fluid Dynamic Codes,” AIAA J. Aircr., 49(2), pp. 407–414. [CrossRef]
Andrejašič, M. , Eržen, D. , Costa, E. , Porziani, S. , Biancolini, M. E. , and Groth, C. , 2016, “ A Mesh Morphing Based FSI Method Used in Aeronautical Optimization Applications,” ECCOMAS Congress, Crete Island, Greece, June 5–10, Paper No. 7206.
Botsch, M. , and Kobbelt, L. , 2005, “ Real-Time Shape Editing Using Radial Basis Functions,” Comput. Graph. Forum, 24(3), pp. 611–621. [CrossRef]
Valentini, P. P. , and Biancolini, M. E. , 2018, “ Interactive Sculpting Using Augmented-Reality, Mesh Morphing, and Force Feedback: Force-Feedback Capabilities in an Augmented Reality Environment,” IEEE Consumer Electron. Mag., 7(2), pp. 83–90. [CrossRef]
Hardy, R. , 1990, “ Theory and Applications of the Multiquadric-Biharmonic Method 20 Years of Discovery 1968–1988,” Comput. Math. Appl., 19(8–9), pp. 163–208. [CrossRef]
Carr, J. C. , Beatson, R. K. , McCallum, B. C. , Fright, W. R. , McLennan, T. J. , and Mitchell, T. J. , 2003, “ Smooth Surface Reconstruction From Noisy Range Data,” First International Conference on Computer Graphics and Interactive Techniques in Australasia and South East Asia, Melbourne, Australia, Feb. 11–14, pp. 119–297.
Boyd, J. P. , and Gildersleeve, K. W. , 2011, “ Numerical Experiments on the Condition Number of the Interpolation Matrices for Radial Basis Functions,” Appl. Numer. Math., 61(4), pp. 443–459. [CrossRef]
Beatson, R. K. , Powell, M. J. D. , and Tan, A. M. , 2007, “ Fast Evaluation of Polyharmonic Splines in Three Dimensions,” IMA J. Numer. Anal., 27(3), pp. 427–450. [CrossRef]
Wendland, H. , 1995, “ Piecewise Polynomial, Positive Definite and Compactly Supported Radial Functions of Minimal Degree,” Adv. Comput. Math., 4(1), pp. 389–396. [CrossRef]
Kansa, E. J., 1992, “ Biographical Sketch of Rolland L. Hardy,” Comput. Math Appl., 24(12), pp. ix–x. [CrossRef]
Ponzini, R. , Biancolini, M. , Rizzo, G. , and Morbiducci, U. , 2012, “ Radial Basis Functions for the Interpolation of Hemodynamics Flow Pattern: A Quantitative Analysis,” Computational Modelling of Objects Represented in Images III: Fundamentals, Methods and Applications, Taylor & Francis, London, pp. 341–344.
Biancolini, M. , Brutti, C. , Chiappa, A. , and Salvini, P. , 2015, “ Post-Processing Strutturale Mediante Uso di Radial Basis Functions,” AIAS 44th National Congress, Messina, Italy, Sept. 2–5, Paper No. 482. https://www.researchgate.net/publication/316663106_POST-PROCESSING_STRUTTURALE_MEDIANTE_USO_DI_RADIAL_BASIS_FUNCTIONS
Vennell, R. , and Beatson, R. , 2009, “ A Divergence-Free Spatial Interpolator for Large Sparse Velocity Data Sets,” J. Geophys. Res.: Oceans, 114(C10), p. 10. [CrossRef]
Carr, J. C. , Beatson, R. K. , Cherrie, J. B. , Mitchell, T. J. , Fright, W. R. , McCallum, B. C. , and Evans, T. R. , 2001, “ Reconstruction and Representation of 3D Objects With Radial Basis Functions,” 28th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH'01), Los Angeles, CA, Aug. 12–17, pp. 67–76.
Biancolini, M. E. , 2017, “ RBF Implicit Representation of Geometrical Entities,” Fast Radial Basis Functions for Engineering Applications, Springer, Cham, Switzerland, Chap. 5.
Biancolini, M. E. , and Valentini, P. P. , 2018, “ Virtual Human Bone Modelling by Interactive Sculpting, Mesh Morphing and Force-Feedback,” Int. J. Interact. Des. Manuf., 12(4), pp. 1223–1234.
Babuška, I. , and Melenk, J. M. , 1998, “ The Partition of Unity Method,” Int. J. Numer. Methods Eng., 40(4), pp. 727–758. [CrossRef]
Biancolini, M. E. , 2017, “ Iterative Solvers,” Fast Radial Basis Functions for Engineering Applications, Springer, Cham, Switzerland, Chap. 3.7.
Biancolini, M. , Chiappa, A. , Giorgetti, F. , Groth, C. , Cella, U. , and Salvini, P. , 2018, “ A Balanced Load Mapping Method Based on Radial Basis Functions and Fuzzy Sets,” Int. J. Numer. Methods Eng., 115(12), pp. 1411–1429. [CrossRef]
Cella, U. , 2017, “ Setup and Validation of High Fidelity Aeroelastic Analysis Methods Based on RBF Mesh Morphing,” Ph.D. thesis, University of Rome Tor Vergata, Rome, Italy.
Nelder, J. A. , and Mead, R. , 1965, “ A Simplex Method for Function Minimization,” Comput. J., 7(4), pp. 308–313. [CrossRef]
Biancolini, M. E. , Cella, U. , Groth, C. , Chiappa, A. , Giorgetti, F. , and Nicolosi, F. , 2019, “ Progresses in Fluid-Structure Interaction and Structural Optimization Numerical Tools Within the EU CS RIBES Project,” Evolutionary and Deterministic Methods for Design Optimization and Control With Applications to Industrial and Societal Problems, E. Andrés-Pérez , L. M. González , J. Periaux , N. Gauger , D. Quagliarella , and K. Giannakoglou , eds., Springer International Publishing, Cham, Switzerland, pp. 529–544.
Drela, M. , 1989, “ Xfoil: An Analysis and Design System for Low Reynolds Number Airfoils,” Low Reynolds Number Aerodynamics, T. J. Mueller , ed., Springer, Berlin, pp. 1–12.

Figures

Grahic Jump Location
Fig. 1

Radial basis functions interactions between source points

Grahic Jump Location
Fig. 2

Example of implicit surface

Grahic Jump Location
Fig. 3

Example of PoU sphere centers distribution for three values of spacing

Grahic Jump Location
Fig. 4

CAD model of the RIBES wing

Grahic Jump Location
Fig. 5

HEXAGON metrology electronic harm used to measure the RIBES wing

Grahic Jump Location
Fig. 6

Measured sections of the RIBES wing

Grahic Jump Location
Fig. 7

Comparison between measured and nominal section of the RIBES wing

Grahic Jump Location
Fig. 8

Detail of a NURBS curve approximating the measured points

Grahic Jump Location
Fig. 9

Updated CAE models (CFD and FEM)

Grahic Jump Location
Fig. 10

Target surfaces for the RBF morphing action

Grahic Jump Location
Fig. 11

Differences between surfaces generated by CAD and mesh morphing strategies

Grahic Jump Location
Fig. 12

Comparison of two-dimensional pressure at the sections at 36% of the span

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In