---
_id: '63800'
abstract:
- lang: eng
text: In this contribution, we address the estimation of the frequency-dependent
elastic parameters of polymers in the ultrasound range, which is formulated as
an inverse problem. This inverse problem is implemented as a nonlinear regression-type
optimization problem, in which the simulation signals are fitted to the measurement
signals. These signals consist of displacement responses in waveguides, focusing
on hollow cylindrical geometries to enhance the simulation efficiency. To accelerate
the optimization and reduce the number of model evaluations and wait times, we
propose two novel methods. First, we introduce an adaptation of the Levenberg–Marquardt
method derived from a geometrical interpretation of the least-squares optimization
problem. Second, we introduce an improved objective function based on the autocorrelated
envelopes of the measurement and simulation signals. Given that this study primarily
relies on simulation data to quantify optimization convergence, we aggregate the
expected ranges of realistic material parameters and derive their distributions
to ensure the reproducibility of optimizations with proper measurements. We demonstrate
the effectiveness of our objective function modification and step adaptation for
various materials with isotropic material symmetry by comparing them with the
Broyden–Fletcher–Goldfarb–Shanno method. In all cases, our method reduces the
total number of model evaluations, thereby shortening the time to identify the
material parameters.
author:
- first_name: Dominik
full_name: Itner, Dominik
last_name: Itner
- first_name: Dmitrij
full_name: Dreiling, Dmitrij
id: '32616'
last_name: Dreiling
- first_name: Hauke
full_name: Gravenkamp, Hauke
last_name: Gravenkamp
- first_name: Bernd
full_name: Henning, Bernd
id: '213'
last_name: Henning
- first_name: Carolin
full_name: Birk, Carolin
last_name: Birk
citation:
ama: Itner D, Dreiling D, Gravenkamp H, Henning B, Birk C. A modified Levenberg–Marquardt
method for estimating the elastic material parameters of polymer waveguides using
residuals between autocorrelated frequency responses. Mechanical Systems and
Signal Processing. 2026;247:113904. doi:https://doi.org/10.1016/j.ymssp.2026.113904
apa: Itner, D., Dreiling, D., Gravenkamp, H., Henning, B., & Birk, C. (2026).
A modified Levenberg–Marquardt method for estimating the elastic material parameters
of polymer waveguides using residuals between autocorrelated frequency responses.
Mechanical Systems and Signal Processing, 247, 113904. https://doi.org/10.1016/j.ymssp.2026.113904
bibtex: '@article{Itner_Dreiling_Gravenkamp_Henning_Birk_2026, title={A modified
Levenberg–Marquardt method for estimating the elastic material parameters of polymer
waveguides using residuals between autocorrelated frequency responses}, volume={247},
DOI={https://doi.org/10.1016/j.ymssp.2026.113904},
journal={Mechanical Systems and Signal Processing}, author={Itner, Dominik and
Dreiling, Dmitrij and Gravenkamp, Hauke and Henning, Bernd and Birk, Carolin},
year={2026}, pages={113904} }'
chicago: 'Itner, Dominik, Dmitrij Dreiling, Hauke Gravenkamp, Bernd Henning, and
Carolin Birk. “A Modified Levenberg–Marquardt Method for Estimating the Elastic
Material Parameters of Polymer Waveguides Using Residuals between Autocorrelated
Frequency Responses.” Mechanical Systems and Signal Processing 247 (2026):
113904. https://doi.org/10.1016/j.ymssp.2026.113904.'
ieee: 'D. Itner, D. Dreiling, H. Gravenkamp, B. Henning, and C. Birk, “A modified
Levenberg–Marquardt method for estimating the elastic material parameters of polymer
waveguides using residuals between autocorrelated frequency responses,” Mechanical
Systems and Signal Processing, vol. 247, p. 113904, 2026, doi: https://doi.org/10.1016/j.ymssp.2026.113904.'
mla: Itner, Dominik, et al. “A Modified Levenberg–Marquardt Method for Estimating
the Elastic Material Parameters of Polymer Waveguides Using Residuals between
Autocorrelated Frequency Responses.” Mechanical Systems and Signal Processing,
vol. 247, 2026, p. 113904, doi:https://doi.org/10.1016/j.ymssp.2026.113904.
short: D. Itner, D. Dreiling, H. Gravenkamp, B. Henning, C. Birk, Mechanical Systems
and Signal Processing 247 (2026) 113904.
date_created: 2026-01-29T08:53:42Z
date_updated: 2026-02-02T12:44:47Z
department:
- _id: '49'
doi: https://doi.org/10.1016/j.ymssp.2026.113904
intvolume: ' 247'
keyword:
- Material parameter estimation
- Waveguide
- Nonlinear optimization
- Inverse problem
- Least squares
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/S0888327026000610/pdfft?md5=16e8493b44527f4ab0a6d13f634a01c3&pid=1-s2.0-S0888327026000610-main.pdf
oa: '1'
page: '113904'
project:
- _id: '89'
name: Vollständige Bestimmung der akustischen Materialparameter von Polymeren
publication: Mechanical Systems and Signal Processing
publication_identifier:
issn:
- 0888-3270
publication_status: published
status: public
title: A modified Levenberg–Marquardt method for estimating the elastic material parameters
of polymer waveguides using residuals between autocorrelated frequency responses
type: journal_article
user_id: '32616'
volume: 247
year: '2026'
...
---
_id: '55159'
abstract:
- lang: eng
text: "We introduce a method based on Gaussian process regression to identify discrete
variational principles from observed solutions of a field theory. The method is
based on the data-based identification of a discrete Lagrangian density. It is
a geometric machine learning technique in the sense that the variational structure
of the true field theory is reflected in the data-driven model by design. We provide
a rigorous convergence statement of the method. The proof circumvents challenges
posed by the ambiguity of discrete Lagrangian densities in the inverse problem
of variational calculus.\r\nMoreover, our method can be used to quantify model
uncertainty in the equations of motions and any linear observable of the discrete
field theory. This is illustrated on the example of the discrete wave equation
and Schrödinger equation.\r\nThe article constitutes an extension of our previous
article arXiv:2404.19626 for the data-driven identification of (discrete) Lagrangians
for variational dynamics from an ode setting to the setting of discrete pdes."
author:
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
citation:
ama: Offen C. Machine learning of discrete field theories with guaranteed convergence
and uncertainty quantification.
apa: Offen, C. (n.d.). Machine learning of discrete field theories with guaranteed
convergence and uncertainty quantification.
bibtex: '@article{Offen, title={Machine learning of discrete field theories with
guaranteed convergence and uncertainty quantification}, author={Offen, Christian}
}'
chicago: Offen, Christian. “Machine Learning of Discrete Field Theories with Guaranteed
Convergence and Uncertainty Quantification,” n.d.
ieee: C. Offen, “Machine learning of discrete field theories with guaranteed convergence
and uncertainty quantification.” .
mla: Offen, Christian. Machine Learning of Discrete Field Theories with Guaranteed
Convergence and Uncertainty Quantification.
short: C. Offen, (n.d.).
date_created: 2024-07-10T13:43:50Z
date_updated: 2024-08-12T13:43:32Z
ddc:
- '510'
department:
- _id: '636'
external_id:
arxiv:
- '2407.07642'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2024-07-10T13:39:32Z
date_updated: 2024-07-10T13:39:32Z
description: |-
We introduce a method based on Gaussian process regression to identify discrete
variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a geometric machine learning technique in the sense that the variational structure of the true field theory is reflected in the data-driven model by design.
We provide a rigorous convergence statement of the method.
The proof circumvents challenges posed by the ambiguity of discrete Lagrangian densities in the inverse problem of variational calculus.
Moreover, our method can be used to quantify model uncertainty in the equations of motions and any linear observable of the discrete field theory.
This is illustrated on the example of the discrete wave equation and Schrödinger equation.
The article constitutes an extension of our previous article for the data-driven identification of (discrete) Lagrangians for variational dynamics from an ode setting to the setting of discrete pdes.
file_id: '55160'
file_name: L_Collocation.pdf
file_size: 4569314
relation: main_file
title: Machine learning of discrete field theories with guaranteed convergence and
uncertainty quantification
file_date_updated: 2024-07-10T13:39:32Z
has_accepted_license: '1'
keyword:
- System identification
- inverse problem of variational calculus
- Gaussian process
- Lagrangian learning
- physics informed machine learning
- geometry aware learning
language:
- iso: eng
oa: '1'
page: '28'
project:
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication_status: submitted
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Christian-Offen/Lagrangian_GP_PDE
status: public
title: Machine learning of discrete field theories with guaranteed convergence and
uncertainty quantification
type: preprint
user_id: '85279'
year: '2024'
...
---
_id: '13892'
abstract:
- lang: eng
text: Several ultrasonic approaches for material determination are formulated in
terms of an (nonlinear) inverse problem, e.g. immersion technique (Castaings et
al. (2000)) or plate-waveguide techniques (Marzani et al. (2012)). In this contribution
we focus on cylindrical waveguides for ultrasonic material determination and especially
on the sensitivity of recorded transmission signals to the material properties.
We utilize composite scaled sensitivities to determine the information content
that can be achieved by the setup to certain parameters and discuss the limitations
of the approach.
author:
- first_name: Fabian
full_name: Bause, Fabian
last_name: Bause
- first_name: Hauke
full_name: Gravenkamp, Hauke
last_name: Gravenkamp
- first_name: Jens
full_name: Rautenberg, Jens
last_name: Rautenberg
- first_name: Bernd
full_name: Henning, Bernd
id: '213'
last_name: Henning
citation:
ama: 'Bause F, Gravenkamp H, Rautenberg J, Henning B. Model based sensitivity analysis
in the determination of viscoelastic material properties using transmission measurements
through circular waveguides. In: ; 2015:204-207.'
apa: Bause, F., Gravenkamp, H., Rautenberg, J., & Henning, B. (2015). Model
based sensitivity analysis in the determination of viscoelastic material properties
using transmission measurements through circular waveguides (pp. 204–207).
bibtex: '@inproceedings{Bause_Gravenkamp_Rautenberg_Henning_2015, title={Model based
sensitivity analysis in the determination of viscoelastic material properties
using transmission measurements through circular waveguides}, author={Bause, Fabian
and Gravenkamp, Hauke and Rautenberg, Jens and Henning, Bernd}, year={2015}, pages={204–207}
}'
chicago: Bause, Fabian, Hauke Gravenkamp, Jens Rautenberg, and Bernd Henning. “Model
Based Sensitivity Analysis in the Determination of Viscoelastic Material Properties
Using Transmission Measurements through Circular Waveguides,” 204–7, 2015.
ieee: F. Bause, H. Gravenkamp, J. Rautenberg, and B. Henning, “Model based sensitivity
analysis in the determination of viscoelastic material properties using transmission
measurements through circular waveguides,” 2015, pp. 204–207.
mla: Bause, Fabian, et al. Model Based Sensitivity Analysis in the Determination
of Viscoelastic Material Properties Using Transmission Measurements through Circular
Waveguides. 2015, pp. 204–07.
short: 'F. Bause, H. Gravenkamp, J. Rautenberg, B. Henning, in: 2015, pp. 204–207.'
date_created: 2019-10-16T14:23:19Z
date_updated: 2022-01-06T06:51:46Z
department:
- _id: '49'
keyword:
- Sensitivity inverse problem ultrasonic material determination
language:
- iso: eng
page: 204-207
status: public
title: Model based sensitivity analysis in the determination of viscoelastic material
properties using transmission measurements through circular waveguides
type: conference
user_id: '15911'
year: '2015'
...
---
_id: '13893'
abstract:
- lang: eng
text: In this contribution, we present an efficient approach for the transient and
time-causal modeling of guided waves in viscoelastic cylindrical waveguides in
the context of ultrasonic material characterization. We use the scaled boundary
finite element method (SBFEM) for efficient computation of the phase velocity
dispersion. Regarding the viscoelastic behavior of the materials under consideration,
we propose a decomposition approach that considers the real-valued frequency dependence
of the (visco-)elastic moduli and, separately, of their attenuation. The modal
expansion approach is utilized to take the transmitting and receiving transducers
into account and to propagate the excited waveguide modes through a waveguide
of finite length. The effectiveness of the proposed simulation model is shown
by comparison with a standard transient FEM simulation as well as simulation results
based on the exact solution of the complex-valued viscoelastic guided wave problem.
Two material models are discussed, namely the fractional Zener model and the anti-Zener
model; we re-interpret the latter in terms of the Rayleigh damping model. Measurements
are taken on a polypropylene sample and the proposed transient simulation model
is used for inverse material characterization. The extracted material properties
may then be used in computer-aided design of ultrasonic systems.
author:
- first_name: Fabian
full_name: Bause, Fabian
last_name: Bause
- first_name: Hauke
full_name: Gravenkamp, Hauke
last_name: Gravenkamp
- first_name: Jens
full_name: Rautenberg, Jens
last_name: Rautenberg
- first_name: Bernd
full_name: Henning, Bernd
last_name: Henning
citation:
ama: Bause F, Gravenkamp H, Rautenberg J, Henning B. Transient modeling of ultrasonic
guided waves in circular viscoelastic waveguides for inverse material characterization.
Measurement Science and Technology. 2015;26(095602 (17pp)). doi:10.1088/0957-0233/26/9/095602
apa: Bause, F., Gravenkamp, H., Rautenberg, J., & Henning, B. (2015). Transient
modeling of ultrasonic guided waves in circular viscoelastic waveguides for inverse
material characterization. Measurement Science and Technology, 26(095602
(17pp)). https://doi.org/10.1088/0957-0233/26/9/095602
bibtex: '@article{Bause_Gravenkamp_Rautenberg_Henning_2015, title={Transient modeling
of ultrasonic guided waves in circular viscoelastic waveguides for inverse material
characterization}, volume={26}, DOI={10.1088/0957-0233/26/9/095602},
number={095602 (17pp)}, journal={Measurement Science and Technology}, author={Bause,
Fabian and Gravenkamp, Hauke and Rautenberg, Jens and Henning, Bernd}, year={2015}
}'
chicago: Bause, Fabian, Hauke Gravenkamp, Jens Rautenberg, and Bernd Henning. “Transient
Modeling of Ultrasonic Guided Waves in Circular Viscoelastic Waveguides for Inverse
Material Characterization.” Measurement Science and Technology 26, no.
095602 (17pp) (2015). https://doi.org/10.1088/0957-0233/26/9/095602.
ieee: F. Bause, H. Gravenkamp, J. Rautenberg, and B. Henning, “Transient modeling
of ultrasonic guided waves in circular viscoelastic waveguides for inverse material
characterization,” Measurement Science and Technology, vol. 26, no. 095602
(17pp), 2015.
mla: Bause, Fabian, et al. “Transient Modeling of Ultrasonic Guided Waves in Circular
Viscoelastic Waveguides for Inverse Material Characterization.” Measurement
Science and Technology, vol. 26, no. 095602 (17pp), 2015, doi:10.1088/0957-0233/26/9/095602.
short: F. Bause, H. Gravenkamp, J. Rautenberg, B. Henning, Measurement Science and
Technology 26 (2015).
date_created: 2019-10-16T14:24:43Z
date_updated: 2022-01-06T06:51:46Z
department:
- _id: '49'
doi: 10.1088/0957-0233/26/9/095602
intvolume: ' 26'
issue: 095602 (17pp)
keyword:
- viscoelasticity
- ultrasonics
- guided waves
- inverse problem
- scaled boundary finite element method
language:
- iso: eng
publication: Measurement Science and Technology
publication_identifier:
issn:
- 0957-0233
status: public
title: Transient modeling of ultrasonic guided waves in circular viscoelastic waveguides
for inverse material characterization
type: journal_article
user_id: '15911'
volume: 26
year: '2015'
...