Experimental Implementation of Energy Closure Analysis for Reduced Order Modeling

Reduced order models (ROMs) provide an efficient, kinematically condensed representation of computationally expensive high dimensional dynamical systems; however, their accuracy depends crucially on the accurate estimation of their dimension. We here demonstrate how the energy closure criterion, developed in our prior work, can be experimentally implemented to accurately estimate the dimension of ROMs obtained using the proper orthogonal decomposition (POD). We examine the effect of using discrete data with and without measurement noise, as will typically be gathered in an experiment or numerical simulation, on estimating the degree of energy closure on a candidate reduced subspace. To this end, we used a periodically kicked Euler-Bernoulli beam with Rayleigh damping as the model system, and studied ROMs obtained by applying POD to discrete displacement field data obtained from simulated numerical experiments. An improved method for quantifying the degree of energy closure is presented: the convergence of energy input to or dissipated from the system is obtained as a function of the subspace dimension, and the dimension capturing a predefined percentage of either energy is selected as the ROM-dimension. This method was found to be more robust to data discretization error and measurement noise. The data processing necessary for the experimental application of energy closure analysis is discussed in detail. We show ROMs formulated from the simulated data using our approach accurately capture the dynamics of the beam for different sets of parameter values.

Files

Metadata

Work Title Experimental Implementation of Energy Closure Analysis for Reduced Order Modeling
Access
Open Access
Creators
  1. Suparno Bhattacharyya
  2. Joseph Cusumano
Keyword
  1. Physics-informed model reduction, proper orthogonal decomposition (POD), reduced order model (ROM), dynamical systems, energy balance, energy closure analysis, solid mechanics, structural vibrations
License CC BY-NC 4.0 (Attribution-NonCommercial)
Work Type Article
Publication Date 2021
Subject
  1. Dynamical systems
  2. Structural vibration
Language
  1. English
Deposited July 04, 2021

Versions

Analytics

Collections

This resource is currently not in any collection.

Work History

Version 1
published

  • Created
  • Added Creator Suparno Bhattacharyya
  • Added Creator Joseph Cusumano
  • Added Bhattacharyya_Cusumano_Experimental Implementation of Energy closure analysis.pdf
  • Updated License Show Changes
    License
    • https://creativecommons.org/licenses/by-nc/4.0/
  • Published
  • Updated Work Title Show Changes
    Work Title
    • [Preprint] Experimental Implementation of Energy Closure Analysis for Reduced Order Modeling
    • Experimental Implementation of Energy Closure Analysis for Reduced Order Modeling
  • Updated