A Space-Time PGD-DIC Algorithm:

Passieux, Jean‐Charles; Bouclier, Robin; Périé, Jean‐Noël

doi:10.1007/s11340-018-0387-2

Cited by 21 publications

(28 citation statements)

References 38 publications

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“…However, because all spatial dimensions are kept together without separation, the problem requires a different setting than that introduced in Refs. [39,40], and is closer to other spacetime frameworks [46,47,41].…”

Section: Introductionmentioning

confidence: 62%

“…Cubic splines provide a higher (i.e., C 2 ) regularity. Band limited Fourier modes are also a convenient way to tune smoothness at will [41]. Let us call ψ i (t), the i = 1, ..., M functions generating the space of admissible time variations.…”

Section: Regularizationmentioning

confidence: 99%

“…Few tens of Matlab code lines were needed to implement this variant. This non intrusiveness allows standard (stereo)DIC kernels to be used [47,41]. To remove PGD from the previous algorithm, it suffices to consider in the "for" loop (i.e., lines 14-21) a number of modes N m equal to the number of temporal basis functions, and in this case the singular value decomposition that would be used as a mere change of basis is no longer needed.…”

Section: Mechanical Regularizationmentioning

confidence: 99%

“…Although the spirit of the approach developed in Ref. [41] is close to the method proposed herein, some very general differences are worth being emphasized:…”

Section: Introductionmentioning

confidence: 99%

“…Although this pioneering work led to an elegant formulation and solutions of high quality, the efficiency of the code revealed somewhat disappointing as compared to the initial ambition. Very recently, PGD-stereoDIC was extended to space time analyses [41]. A very strong time regularization was chosen in the form of one vibrational mode.…”

Section: Introductionmentioning

confidence: 99%

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Mode-enhanced space-time DIC: applications to ultra-high-speed imaging

Berny

Jailin²,

Bouterf³

et al. 2018

Meas. Sci. Technol.

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Digital Image Correlation (DIC), which consists in registering image pairs to measure displacement fields, can be tailored to analyze image sequences from videos taking advantage of a common reference image. In the present study it is no longer the first image of the sequence but rather a computed image from the entire video. The sought kinematics, which is separated in space and time, offers the opportunity to extract "modes," each of which is a spatial displacement field multiplied by a scalar function of time only. These modes are not chosen a priori but rather computed from a specific formulation of DIC so that they capture the displacements at best. The exploited mathematical technique to achieve this modal representation is a form of Proper Generalized Decomposition (PGD) that makes use of the DIC variational formulation, where both spatial and temporal regularizations can be included. Two image videos acquired with an ultra-high speed camera at 5 and 10 million frames per second are analyzed to illustrate the proposed technique. Very large computation time gains are obtained with no noticeable differences in the kinematic measurements. Moreover, it is shown that motions have a lower complexity, i.e., require less modes, than the direct Proper Orthogonal Decomposition (or Principal Component Analysis) Mode-enhanced space-time DIC: Applications to ultra high-speed imaging 2 performed on the entire video.

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Section: Introductionmentioning

confidence: 62%

Section: Regularizationmentioning

confidence: 99%

Section: Mechanical Regularizationmentioning

confidence: 99%

“…Although the spirit of the approach developed in Ref. [41] is close to the method proposed herein, some very general differences are worth being emphasized:…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Mode-enhanced space-time DIC: applications to ultra-high-speed imaging

Berny

Jailin²,

Bouterf³

et al. 2018

Meas. Sci. Technol.

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Non‐invasive Spline‐based Regularization of FE Digital Image Correlation Problems

2023

Iga

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Classic and inverse compositional Gauss‐Newton in global DIC

Passieux

Bouclier

2019

Numerical Meth Engineering

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Summary Today, effective implementations of digital image correlation (DIC) are based on iterative algorithms with constant linear operators. A relevant idea of the classic finite element (or, more generally, global) DIC solver consists in replacing the gradient of the deformed state image with that of the reference image, so as to obtain a constant operator. Different arguments (small strains, small deformations, equality of the two gradients close to the solution, etc) have been given in the literature to justify this approximation, but none of them are fully accurate. Indeed, the convergence of the optimization algorithm has to be investigated from its ability to produce descent directions. Through such a study, this paper attempts to explain why this approximation works and what is its domain of validity. Then, an inverse compositional Gauss‐Newton implementation of finite element DIC is proposed as a cost‐effective and mathematically sound alternative to this approximation.

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A Space-Time PGD-DIC Algorithm:

Cited by 21 publications

References 38 publications

Mode-enhanced space-time DIC: applications to ultra-high-speed imaging

Mode-enhanced space-time DIC: applications to ultra-high-speed imaging

Non‐invasive Spline‐based Regularization of FE Digital Image Correlation Problems

Classic and inverse compositional Gauss‐Newton in global DIC

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