Inverse Interval Field Quantification via Digital Image Correlation

Abstract:

This paper presents the application of a new method for the identification and quantification of interval valued spatial uncertainty under scarce data.Specifically, full-field strain measurements, obtained via Digital Image Correlation, are applied in conjunction with a quasi-static finite element model.To apply these high-dimensional but scarce data, extensions to the novel method are introduced.A case study, investigating spatial uncertainty in Young's modulus of PA-12 parts, produced via Laser Sintering, shows that an accurate quantification of the constituting uncertainty is possible, albeit being somewhat conservative with respect to deterministic values reported in literature.

• Periodical: Applied Mechanics and Materials (Volume 885)
• Pages: 304-310
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.885.304
• Online since: November 2018
• Authors: Matthias Faes*, David Moens
• Keywords: Interval Field Analysis, Inverse Uncertainty Quantification, Multivariate Uncertainty

References

[1] G. Stefanou. The stochastic finite element method: Past, present and future. Computer Methods in Applied Mechanics and Engineering, 198(9-12) (2009), 1031-1051.

DOI: 10.1016/j.cma.2008.11.007

[2] D. Moens, & M. Hanss. Non-probabilistic finite element analysis for parametric uncertainty treatment in applied mechanics: Recent advances. Finite Elements in Analysis and Design, 47(1) (2011), 4-16.

DOI: 10.1016/j.finel.2010.07.010

[3] M. Beer, S. Ferson, & V. Kreinovich. Imprecise probabilities in engineering analyses. Mechanical Systems and Signal Processing, 37(1-2) (2013), 4-29.

DOI: 10.1016/j.ymssp.2013.01.024

[4] W. Betz, I. Papaioannou, & D. Straub. Numerical methods for the discretization of random fields by means of the Karhunen-Loève expansion. Computer Methods in Applied Mechanics and Engineering, 271 (2014), 109-129.

DOI: 10.1016/j.cma.2013.12.010

[5] W. Verhaeghe, W. Desmet, D. Vandepitte & D. Moens. Interval fields to represent uncertainty on the output side of a static FE analysis. Computer Methods in Applied Mechanics and Engineering, 260 (2013), 50-62.

DOI: 10.1016/j.cma.2013.03.021

[6] F. Fedele, R. L. Muhanna, N. Xiao, R. L. Mullen, Interval-Based Approach for Uncertainty Propagation in Inverse Problems, Journal of Engineering Mechanics 4 (1) (2014) 1-7.

DOI: 10.1061/(asce)em.1943-7889.0000815

[7] S.-E. Fang, Q.-H. Zhang, W.-X. Ren, An interval model updating strategy using interval response surface models, Mechanical Systems and Signal Processing 60-61 (2015) 909-927.

DOI: 10.1016/j.ymssp.2015.01.016

[8] H. H. Khodaparast, J. E. Mottershead, K. J. Badcock, Interval model updating with irreducible uncertainty using the Kriging predictor, Mechanical Systems and Signal Processing 25 (4) (2011) 1204-1206.

DOI: 10.1016/j.ymssp.2010.10.009

[9] M. Broggi, M. Faes, E. Patelli, Y. Govers, D. Moens, M. Beer. Comparison of Bayesian and Interval Uncertainty Quantification: Application to the AIRMOD Test Structure. 2017 SSCI Proceedings (2017), 1684-1691.

DOI: 10.1109/ssci.2017.8280882

[10] E. Patelli, Y. Govers, M. Broggi, H. M. Gomes, M. Link & J.E. Mottershead. Sensitivity or Bayesian model updating: a comparison of techniques using the DLR AIRMOD test data. Archive of Applied Mechanics, 87(5) (2017), 905-925.

DOI: 10.1007/s00419-017-1233-1

[11] M. Faes, J. Cerneels, D. Vandepitte & D. Moens. Identification of Interval fields for spatial uncertainty representation in Finite Element models. Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering: Vol. 7. European Congress on Computational Methods in Applied Sciences and Engineering. Crete Island, Greece, 5-10 June (2016).

DOI: 10.7712/100016.2243.4995

[12] M. Faes, J. Cerneels, D. Vandepitte & D. Moens. Identification and quantification of multivariate interval uncertainty in finite element models. Computer Methods in Applied Mechanics and Engineering , 315 (2017), 896 - 920.

DOI: 10.1016/j.cma.2016.11.023

[13] M. Faes & D. Moens. Identification and quantification of spatial interval uncertainty in numerical models. Computers and Structures, 192 (2017), 16-33.

DOI: 10.1016/j.compstruc.2017.07.006

[14] M. Hanss. The transformation method for the simulation and analysis of systems with uncertain parameters. Fuzzy Sets and Systems, 130(3) (2002), 277-289.

DOI: 10.1016/s0165-0114(02)00045-3

[15] A. Sofi & G. Muscolino. Static analysis of Euler-Bernoulli beams with interval Young's modulus. Computers and Structures, 156 (2015), 72-82.

DOI: 10.1016/j.compstruc.2015.04.002

[16] A. Sofi, G. Muscolino & M. Zingales. One-dimensional heterogeneous solids with uncertain elastic modulus in presence of long-range interactions: Interval versus stochastic analysis. Computers and Structures,122 (2013), 217-229.

DOI: 10.1016/j.compstruc.2013.03.005

[17] D. Wu, and W. Gao Uncertain static plane stress analysis with interval fields. International Journal for Numerical Methods in Engineering, 110(2017) 1272-1300.

DOI: 10.1002/nme.5457

[18] C. B. Barber, D. P. Dobkin & H. Huhdanpaa. The quickhull algorithm for convex hulls. ACM Transactions on Mathematical Software, 22(4) (1996), 469-483.

DOI: 10.1145/235815.235821

[19] M. Pavan, M. Faes, D. Strobbe, B. Van Hooreweder, T. Craeghs, D. Moens, & W. Dewulf. On the influence of inter-layer time and energy density on selected critical-to-quality properties of PA12 parts produced via laser sintering. Polymer Testing, 61 (2017).

DOI: 10.1016/j.polymertesting.2017.05.027