---
_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. <i>Mechanical Systems and
    Signal Processing</i>. 2026;247:113904. doi:<a href="https://doi.org/10.1016/j.ymssp.2026.113904">https://doi.org/10.1016/j.ymssp.2026.113904</a>
  apa: Itner, D., Dreiling, D., Gravenkamp, H., Henning, B., &#38; Birk, C. (2026).
    A modified Levenberg–Marquardt method for estimating the elastic material parameters
    of polymer waveguides using residuals between autocorrelated frequency responses.
    <i>Mechanical Systems and Signal Processing</i>, <i>247</i>, 113904. <a href="https://doi.org/10.1016/j.ymssp.2026.113904">https://doi.org/10.1016/j.ymssp.2026.113904</a>
  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={<a href="https://doi.org/10.1016/j.ymssp.2026.113904">https://doi.org/10.1016/j.ymssp.2026.113904</a>},
    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.” <i>Mechanical Systems and Signal Processing</i> 247 (2026):
    113904. <a href="https://doi.org/10.1016/j.ymssp.2026.113904">https://doi.org/10.1016/j.ymssp.2026.113904</a>.'
  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,” <i>Mechanical
    Systems and Signal Processing</i>, vol. 247, p. 113904, 2026, doi: <a href="https://doi.org/10.1016/j.ymssp.2026.113904">https://doi.org/10.1016/j.ymssp.2026.113904</a>.'
  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.” <i>Mechanical Systems and Signal Processing</i>,
    vol. 247, 2026, p. 113904, doi:<a href="https://doi.org/10.1016/j.ymssp.2026.113904">https://doi.org/10.1016/j.ymssp.2026.113904</a>.
  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'
...