Big Data in Experimental Mechanics and Model Order Reduction: Today’s Challenges and Tomorrow’s Opportunities

Abstract

Since the turn of the century experimental solid mechanics has undergone major changes with the generalized use of images. The number of acquired data has literally exploded and one of today's challenges is related to the saturation of mining procedures through such big data sets. With respect to Digital Image/Volume Correlation one of tomorrow's pathways is to better control and master this data flow with procedures that are optimized for extracting the sought information with minimum uncertainties and maximum robustness. In this paper emphasis is put on various hierarchical identification procedures. Based on such structures a posteriori model/data reductions are performed in order to ease and make the exploitation of the experimental information far more efficient. Some possibilities related to other Model Order Reduction techniques like the Proper Generalized Decomposition are discussed and new opportunities are sketched.

Digital Volume Correlation: Review of Progress and Challenges

“…They provide quantitative estimates of the influence of noise on the kinematic analysis. This is important inasmuch as the obtained estimates of the full covariance matrix can be further used to evaluate the uncertainty of parameters identified with the measured displacement fields [165]. Moreover, the explicit expression of the covariance matrix on the measured degrees of freedom allows the "best" metric to be tailored in order to perform this identification step.…”

“…Time regularization will have some interest provided a sufficient number of scans is available in the analysis. It will also make the calculations even more involved and some of the above routes may turn out to be very useful (e.g., PGD [165]). It is believed that projectionbased approaches are more suitable since they precisely provide much more temporal information than using fully reconstructed volumes at different levels of load.…”

“…Further, their processing is also becoming tedious. Model/data reduction strategies are one possible route to follow in order to ease and make the exploitation of such experimental data far more efficient [165]. Similarly, much more developments should be performed regarding time and memory savings.…”

Classic and inverse compositional Gauss‐Newton in global DIC

“…This approximation is sometimes justified in the literature (including some papers published by the authors) by the fact that, by virtue of the gray-level conservation principle, these two quantities would be equal in the neighborhood of the solution. 18,[31][32][33][34][35][36][37][38][39] There is actually no reason why these quantities should be equal in general. The relationship between these two gradients can only be written at convergence.…”

“…The resolution of this nonlinear least squares problem with a standard Gauss-Newton leads exactly to the same linear system (33) as with the mod.-GN method of the standard FE-DIC problem. It thus has the double advantage of leading to a constant operator while remaining within the strict framework of a Gauss-Newton (condition (14) systematically true).…”