# A gradient-based optimization approach for the detection of partially connected surfaces using vibration tests

## Abstract

The integrity of engineering structures is often compromised by embedded surfaces that result from incomplete bonding during the manufacturing process, or initiation of damage from fatigue or impact processes. Examples include delaminations in composite materials, incomplete weld bonds when joining two components, and internal crack planes that may form when a structure is damaged. In many cases the areas of the structure in question may not be easily accessible, thus precluding the direct assessment of structural integrity. In this paper, we present a gradient-based, partial differential equation (PDE)-constrained optimization approach for solving the inverse problem of interface detection in the context of steady-state dynamics. An objective function is defined that represents the difference between the model predictions of structural response at a set of spatial locations, and the experimentally measured responses. One of the contributions of our work is a novel representation of the design variables using a density field that takes values in the range [0, 1] and raised to an integer exponent that promotes solutions to be near the extrema of the range. The density field is combined with the penalty method for enforcing a zero gap condition and realizing partially bonded surfaces. Furthermore the use of themore »

- Authors:

- Duke Univ., Durham, NC (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1499696

- Report Number(s):
- SAND-2018-1899J

Journal ID: ISSN 0045-7825; 660838

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Computer Methods in Applied Mechanics and Engineering

- Additional Journal Information:
- Journal Volume: 345; Journal Issue: C; Journal ID: ISSN 0045-7825

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; Interface detection; Inverse problems; Finite element; Constrained optimization; Penalty method; Structural dynamics

### Citation Formats

```
Aquino, Wilkins, Bunting, Gregory, Miller, Scott T., and Walsh, Timothy F. A gradient-based optimization approach for the detection of partially connected surfaces using vibration tests. United States: N. p., 2018.
Web. doi:10.1016/j.cma.2018.11.002.
```

```
Aquino, Wilkins, Bunting, Gregory, Miller, Scott T., & Walsh, Timothy F. A gradient-based optimization approach for the detection of partially connected surfaces using vibration tests. United States. doi:10.1016/j.cma.2018.11.002.
```

```
Aquino, Wilkins, Bunting, Gregory, Miller, Scott T., and Walsh, Timothy F. Wed .
"A gradient-based optimization approach for the detection of partially connected surfaces using vibration tests". United States. doi:10.1016/j.cma.2018.11.002. https://www.osti.gov/servlets/purl/1499696.
```

```
@article{osti_1499696,
```

title = {A gradient-based optimization approach for the detection of partially connected surfaces using vibration tests},

author = {Aquino, Wilkins and Bunting, Gregory and Miller, Scott T. and Walsh, Timothy F.},

abstractNote = {The integrity of engineering structures is often compromised by embedded surfaces that result from incomplete bonding during the manufacturing process, or initiation of damage from fatigue or impact processes. Examples include delaminations in composite materials, incomplete weld bonds when joining two components, and internal crack planes that may form when a structure is damaged. In many cases the areas of the structure in question may not be easily accessible, thus precluding the direct assessment of structural integrity. In this paper, we present a gradient-based, partial differential equation (PDE)-constrained optimization approach for solving the inverse problem of interface detection in the context of steady-state dynamics. An objective function is defined that represents the difference between the model predictions of structural response at a set of spatial locations, and the experimentally measured responses. One of the contributions of our work is a novel representation of the design variables using a density field that takes values in the range [0, 1] and raised to an integer exponent that promotes solutions to be near the extrema of the range. The density field is combined with the penalty method for enforcing a zero gap condition and realizing partially bonded surfaces. Furthermore the use of the penalty method with a density field representation leads to objective functions that are continuously differentiable with respect to the unknown parameters, enabling the use of efficient gradient-based optimization algorithms. Numerical examples of delaminated plates are presented to demonstrate the feasibility of the approach.},

doi = {10.1016/j.cma.2018.11.002},

journal = {Computer Methods in Applied Mechanics and Engineering},

number = C,

volume = 345,

place = {United States},

year = {2018},

month = {11}

}