A method for model identification and parameter estimation

Abstract

We propose and analyze a new method for the identification of a parameterdependent model that best describes a given system. This problem arises, for example, in the mathematical modeling of material behavior where several competing constitutive models are available to describe a given material, and one has to determine the best-suited constitutive model for a given material and application from experiments. We assume that the true model is one of N possible parameter-dependent models. To identify the correct model and the corresponding parameters we can perform experiments, where for each experiment we prescribe an input to the system and observe a part of the system state. Our approach consists of two stages. In the first stage, for each pair of models we determine the experiment, i.e., system input and observation, that best differentiates between the two models, and measure the distance between the two models. Then we conduct N(N − 1) or, depending on the approach taken, N(N − 1)/2 experiments and use the result of the experiments as well as the previously computed model distances to determine the true model. We provide sufficient conditions on the model distances and measurement errors which guarantee that our approach identifies the correct model. Given the model, we identify the corresponding model parameters in the second stage. The problem in the second stage is a standard parameter estimation problem and we use a method suitable for the given application.

Diffusion curves with diffusion coefficients

“…From it, we wish to calculate the diffusion coefficients, i.e., strength coefficients in the DCC model, for the medium. This is an inverse problem, called parameter identification [19]. In each of Figs.…”

Identification of optimal material models and parameters in finite strain plasticity

“…If one can choose between different material tests, then approaches from optimal experimental designs [1] can be used to select the best material test for parameter identification. Here, we propose a method which is an extension of [2] allowing for observation errors and errors in the loading. Another novelty of our approach is the use of automatic differentiation to compute the sensitivity with respect to deviations in the predefined conditions as well as the application to a set of finite strain plasticity models with isotropic/kinematic hardening.…”

A certified RB method for PDE-constrained parametric optimization problems

“…Several problems which can be cast in this framework have been already tackled with reduced order modeling techniques, such as optimal control [18,23], optimal design [24][25][26], parameter estimation [27], model identification [28], uncertainty quantification problems [29][30][31]. Often this has been done neither by relying on adjoint-based approaches, nor by developing a rigorous error analysis for the optimal solution.…”