Deep multimodal autoencoder for crack criticality assessment

Abstract

In continuum mechanics, the prediction of defect harmfulness requires to solve approximately partial differential equations with given boundary conditions. In this contribution boundary conditions are learnt for tight local volumes (TLV) surrounding cracks in three-dimensional volumes. A nonparametric data-driven approach is used to define the space of defects, by considering defects observed via X-Ray computed tomography. The dimension of the ambient space for the observed images of defects is huge. A nonlinear dimensionality reduction scheme is proposed in order to train a reduced latent space for both the morphology of defects and their local mechanical effects in the TLV. A multimodal autoencoder enables to mix morphological and mechanical data. It contains a single latent space, termed mechanical latent space. But this latent space is fed by two encoders. One is related to the images of defects and the other to mechanical fields in the TLV. The latent variables are input variables for a geometrical decoder and for a mechanical decoder. In this work, mechanical variables are displacement fields. The autoencoder on mechanical variables enables projection-based model order reduction as proposed in the study of Lee and Carlberg. The main novelty of this paper is a submodeling approach assisted by artificial intelligence. Here, for defect images in the test set, Dirichlet boundary conditions are applied to TLV. These boundary conditions are forecasted by the mechanical decoder with a latent vector predicted by the morphological encoder. For that purpose, a mapping is trained to convert morphological latent variables into mechanical latent variables, denoted "direct mapping." An "inverse mapping" is also trained for error estimation with respect to morphological predictions. Errors on mechanical predictions are close to 5% with simulation speed-up ranging for 3 to 120. We show that latent variables forecasted by the images of defects are prone to a better understanding of the predictions.

Multimodal data augmentation for digital twining assisted by artificial intelligence in mechanics of materials

“…The augmentation ratio is 100 for each DT, prior to fulfilling the constraints for the construction of D aug . Here, mechanical variables are structured data similar to digital images (Launay et al, 2021a). But not all data augmentation techniques proposed in the literature for digital images are relevant for reduced digital twinning.…”

“…Such synthetic data support decisions in engineering for maintenance, operating optimization, or decommission of RIMC. With the development of non-destructive testing (NDT) in the manufacturing industry, we can expect a growing activity on image-based DTs (Seon et al, 2020;Launay et al, 2021a) for accurate descriptions of as-manufactured geometries and microstructural properties of structural components. Such data are crucial for lifetime predictions (Aublet et al, 2022).…”

“…Another issue is the curse of dimensionality related to the dimension of the geometrical ambient space, so a dense sampling of this space is unaffordable. So, learning regression for lifetime prediction from observational data, as in cross-modal predictions (Launay et al, 2021a), may not be relevant for such image-based modeling. In this work, we augment multimodal data in order to train a ROM-net (Daniel et al, 2020).…”

Learning Projection-Based Reduced-Order Models

“…• Important limitations of projection-based model reduction methods includes situations where the geometry has to be handled in the exploitation phase of the reduced-order models, for instance when the problem features contact boundary conditions, crack propagation or when the geometry is a variability of the problem to learn. Geometrical variabilities are handled in the authors' works [ 1,2,22,60,61,92].…”