Comptes Rendus
Modal decomposition from partial measurements
Comptes Rendus. Mécanique, Volume 347 (2019) no. 11, pp. 863-872.

A data set over space and time is assumed to have a low-rank representation in separated spatial and temporal modes. The problem of evaluating these modes from a temporal series of partial measurements is considered. Each elementary instantaneous measurement captures only a “window” (in space) of the observed data set, but the position of this window varies in time so as to cover the entire region of interest and would allow for a complete measurement would the scene be static. A novel procedure, alternative to the Gappy Proper Orthogonal Decomposition (GPOD) methodology, is introduced. It is a fixed-point iterative procedure where modes are evaluated sequentially. Tested upon very sparse acquisition (1% of measurements being available) and very noisy synthetic data sets (10% noise), the proposed algorithm is shown to outperform two variants of the GPOD algorithm, with much faster convergence, and better reconstruction of the entire data set.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2019.11.011
Keywords: Modal analysis, Proper generalized decomposition, Dynamic stereo-vision, Dynamic tomography, Field recovery, Gappy proper orthogonal decomposition

Clément Jailin 1, 2; Stéphane Roux 1

1 LMT (ENS Paris-Saclay/CNRS/Université Paris-Saclay), 61, avenue du Président-Wilson, 94235 Cachan, France
2 Safran Tech, rue des Jeunes-Bois, 78772 Magny-les-Hameaux, France
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Clément Jailin; Stéphane Roux. Modal decomposition from partial measurements. Comptes Rendus. Mécanique, Volume 347 (2019) no. 11, pp. 863-872. doi : 10.1016/j.crme.2019.11.011. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.11.011/

[1] M.A. Sutton; W.J. Wolters; W.H. Peters; W.F. Ranson; S.R. McNeill Determination of displacements using an improved digital correlation method, Image Vis. Comput., Volume 1 (1983) no. 3, pp. 133-139

[2] M.A. Sutton; J.J. Orteu; H. Schreier Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications, Springer Science & Business Media, 2009

[3] B.K. Bay; T.S. Smith; D.P. Fyhrie; M. Saad Digital volume correlation: three-dimensional strain mapping using x-ray tomography, Exp. Mech., Volume 39 (1999) no. 3, pp. 217-226

[4] G. Besnard; S. Guérard; S. Roux; F. Hild A space–time approach in digital image correlation: movie-dic, Opt. Lasers Eng., Volume 49 (2011) no. 1, pp. 71-81

[5] A. Buljac; C. Jailin; A. Mendoza; J. Neggers; T. Taillandier-Thomas; A. Bouterf; B. Smaniotto; F. Hild; S. Roux Digital volume correlation: review of progress and challenges, Exp. Mech., Volume 58 (2018) no. 5, pp. 661-708

[6] R.A. Newcombe; A.J. Davison Live dense reconstruction with a single moving camera, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE, 2010, pp. 1498-1505

[7] S.J. Rothberg; M.S. Allen; P. Castellini; D. Di Maio; J.J.J. Dirckx; D.J. Ewins; J. Ben Halkon; P. Muyshondt; N. Paone; T. Ryan et al. An international review of laser doppler vibrometry: making light work of vibration measurement, Opt. Lasers Eng., Volume 99 (2017), pp. 11-22

[8] J.E. Dufour; F. Hild; S. Roux Shape, displacement and mechanical properties from isogeometric multiview stereocorrelation, J. Strain Anal. Eng. Des., Volume 50 (2015) no. 7, pp. 470-487

[9] M. Berny; T. Archer; A. Mavel; P. Beauchêne; S. Roux; F. Hild On the analysis of heat haze effects with spacetime dic, Opt. Lasers Eng., Volume 111 (2018), pp. 135-153

[10] M.A. Iadicola (Advancement of Optical Methods in Experimental Mechanics), Volume vol. 3, Springer (2016), pp. 247-253

[11] H. Leclerc; S. Roux; F. Hild Projection savings in ct-based digital volume correlation, Exp. Mech., Volume 55 (2015) no. 1, pp. 275-287

[12] C. Jailin; A. Buljac; A. Bouterf; F. Hild; S. Roux Fast 4d tensile test monitored via X-CT: single projection based digital volume correlation dedicated to slender samples, J. Strain Anal. Eng. Des., Volume 53 (2018) no. 7, pp. 473-484

[13] J. Neggers; O. Allix; F. Hild; S. Roux Big data in experimental mechanics and model order reduction: today's challenges and tomorrow's opportunities, Arch. Comput. Methods Eng., Volume 25 (2018) no. 1, pp. 143-164

[14] P. Netrapalli; U.N. Niranjan; S. Sanghavi; A. Anandkumar; P. Jain Non-convex robust pca, Advances in Neural Information Processing Systems, 2014, pp. 1107-1115

[15] F. Wen; L. Chu; P. Liu; R.C. Qiu A survey on nonconvex regularization-based sparse and low-rank recovery in signal processing, statistics, and machine learning, IEEE Access, Volume 6 (2018), pp. 69883-69906

[16] F. Mathieu; H. Leclerc; F. Hild; S. Roux Estimation of elastoplastic parameters via weighted femu and integrated-dic, Exp. Mech., Volume 55 (2015) no. 1, pp. 105-119

[17] A. Buljac; M. Shakoor; J. Neggers; M. Bernacki P-O Bouchard; L. Helfen; T.F. Morgeneyer; F. Hild Experimental-numerical validation framework for micromechanical simulations, Multiscale Modeling of Heterogeneous Structures, Springer, 2018, pp. 147-161

[18] C. Jailin; A. Buljac; A. Bouterf; F. Hild; S. Roux Fast four-dimensional tensile test monitored via x-ray computed tomography: elastoplastic identification from radiographs, J. Strain Anal. Eng. Des., Volume 54 (2019) no. 1, pp. 44-53

[19] R.G. Baraniuk Compressive sensing, IEEE Signal Process. Mag., Volume 24 (2007) no. 4

[20] M.F. Duarte; M.A. Davenport; D. Takhar; J.N. Laska; T. Sun; K.F. Kelly; R.G. Baraniuk Single-pixel imaging via compressive sampling, IEEE Signal Process. Mag., Volume 25 (2008) no. 2, pp. 83-91

[21] R. Everson; L. Sirovich Karhunen–Loève procedure for gappy data, J. Opt. Soc. Amer. A, Volume 12 (1995) no. 8, pp. 1657-1664

[22] K. Willcox Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition, Comput. Fluids, Volume 35 (2006) no. 2, pp. 208-226

[23] N.E. Murray; L.S. Ukeiley An application of gappy pod, Exp. Fluids, Volume 42 (2007) no. 1, pp. 79-91

[24] J.-C. Passieux; J.-N. Périé High resolution digital image correlation using proper generalized decomposition: PGD-DIC, Int. J. Numer. Methods Eng., Volume 92 (2012) no. 6, pp. 531-550

[25] M. Berny; C. Jailin; A. Bouterf; F. Hild; S. Roux Mode-enhanced space-time dic: applications to ultra-high-speed imaging, Meas. Sci. Technol., Volume 29 (2018) no. 12

[26] P. Ladevèze Nonlinear Computational Structural Mechanics: New Approaches and Non-Incremental Methods of Calculation, Springer Science & Business Media, 2012

[27] L.G. Perini; J.C. Passieux; J.N. Périé A multigrid pgd-based algorithm for volumetric displacement fields measurements, Strain, Volume 50 (2014) no. 4, pp. 355-367

[28] A.B. Stanbridge; D.J. Ewins Modal testing using a scanning laser doppler vibrometer, Mech. Syst. Signal Process., Volume 13 (1999) no. 2, pp. 255-270

[29] C. Jailin, T. Jailin, S. Roux, Measurement of 1–10 Hz 3D vibration modes with a CT-scanner, preprint, 2019.

[30] J.M. Beckers; M. Rixen Eof calculations and data filling from incomplete oceanographic datasets, J. Atmos. Ocean. Technol., Volume 20 (2003) no. 12, pp. 1839-1856

[31] C. Jailin Full field modal measurement with a single standard camera, Opt. Lasers Eng., Volume 107 (2018), pp. 265-272

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