Infinite-dimensional integrated digital image correlation (IDIC)

Background

Digital image correlation (DIC) methods are common in laboratory experi­ments. Often termed two-dimensional digital image correlation (2D-DIC), the method uses a camera to acquire images of a planar object that is deforming nominally within the specimen surface plane that is being imaged. DIC algorithms typically perform the image registration by measuring changes in the two images using cross-correlation.

Since the 1980s, this technology has been extensively used in laboratory setting to learn about heterogeneous displacement fields. More recently, the displacement solution from DIC has been extended to determine material properties that are consistent with the displacement data (i.e. solving the inverse problem). The inverse problem is solved as a mathematical optimiza­tion problem, where one determines material properties that minimize the error between the corresponding displacement prediction of the physical model and the observed displacement data via DIC.

In Integrated DIC (IDIC), the image registration and subsequent inverse problem are unified into one simultaneous optimization problem whereby the displacements are not computed with statistical (e.g. cross-correlation) algorithms but are themselves constrained to obey the same physics as the corresponding inverse problem.  IDIC has not been applied to complex high-dimensional heterogeneous material properties and instead has been limited in its deployment to low-dimensional problems such as learning in a lab setting and not used in complex, large-scale material defect detection problems.

Technical description

Researchers at The University of Texas at Austin have invented a speedy, physics-driven DIC algorithm built to learning constitutive models and their respective parameters with robust error handling. In their approach, the inventors pose the IDIC problem for high-dimensional material property estimation problems that allow them to infer spatial variations in material properties at small scales, enhancing the ability to detect inclusions and other material defects (i.e., any heterogeneity).

The material defect detection problem in its high-dimensional representation is solved via the use of adjoint methods to efficiently compute gradients and Hessian actions associated with the joint optimization IDIC problem, leading to a state-of-the-art inverse problem solution via Newton systems. This is referred to as an Infinite-Dimensional IDIC formulationm as the convergence properties of these methods are known to be independent of the discretization dimension of the finite element (FE) method used to simulate the physics.

Computational costs of the dimension-independent IDIC and its respective Bayesian formulation may be intractable due to the computational costs of the PDE simulations via the FE method. Use of machine learning surrogates that learn the relationship between the material properties and the resulting displace­ment fields can be executed many orders of magnitude faster than the corresponding FE-based PDE simulation.

Features

• Captures heterogenous behavior by solving the IDIC problem in infinite dimensions
• Poses IDIC within the Bayesian inference setting to account for uncertainty
  • The inputs to IDIC are inherently noisy and the uncertainty in the displacement and parameter should be captured.
• Uses a dictionary of constitutive laws to mathematically learn which one best describes the system
  • A prior knowledge of the correct constitutive models is not always available, or
  • The prior knowledge directs researchers away from the best model.
• Uses modern computational techniques to handle the inverse problem in a fashion that both:
  • Scales independently of dimensions, and
  • Is accelerated by machine learning to be computationally efficient.

Benefits

• Higher quality IDIC predictions due to handling the problem in the infinite dimension while maintaining near real-time performance via acceleration with machine learning
• May lead to better damage identification or facilitate scientific advance­ment in selection of constitutive models
• Non-destructive evaluation of structures is an optimistic application for DIC such that real-time predictions are desirable.