# Parameter identification in elasto-plasticity: distance between parameters and impact of measurement errors

## TL;DR

This paper investigates how measurement errors affect parameter identification in finite-strain elasto-plasticity, introducing a mechanics-based distance to assess sensitivity and robustness, with an analytical approach to improve Monte Carlo simulations.

## Contribution

It introduces a mechanics-based distance for sensitivity analysis and a fast analytical method to evaluate robustness of parameter identification under measurement errors.

## Key findings

- Correlated measurement errors lead to more stable identification results.
- Trade-off observed between stability and accuracy in parameter estimation.
- The proposed approach efficiently estimates robustness of identification procedures.

## Abstract

A special aspect of parameter identification in finite-strain elasto-plasticity is considered. Namely, we analyze the impact of the measurement errors on the resulting set of material parameters. In order to define the sensitivity of parameters with respect to the measurement errors, a mechanics-based distance between two sets of parameters is introduced. Using this distance function, we assess the reliability of certain parameter identification procedures. The assessment involves introduction of artificial noise to the experimental data; the noise can be both correlated and uncorrelated. An analytical procedure to speed up Monte Carlo simulations is presented. As a result, a simple tool for estimating the robustness of parameter identification is obtained. The efficiency of the approach is illustrated using a model of finite-strain elasto-plasticity, which accounts for combined isotropic and kinematic hardening. It is shown that dealing with correlated measurement errors, most stable identification results are obtained for non-diagonal weighting matrix. At the same time, there is a conflict between the stability and accuracy.