A modified Levenberg-Marquardt method for estimating the elastic material parameters of polymer waveguides using residuals between autocorrelated frequency responses

TL;DR

This paper introduces a modified Levenberg-Marquardt method with an autocorrelation-based objective function to efficiently estimate elastic parameters of polymer waveguides from simulation and measurement data, reducing computation time.

Contribution

It presents a novel adaptation of the Levenberg-Marquardt algorithm and an improved objective function for faster, more reliable parameter estimation in polymer waveguide analysis.

Findings

The method reduces the number of model evaluations needed.

It shortens the time to identify material parameters.

The approach is effective across various isotropic materials.

Abstract

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 a state-of-the-art optimization method. In all cases, our method reduces the total number of model evaluations, thereby shortening the time to identify the material parameters.