Towards an improved Eigensystem Realization Algorithm for low-error guarantees

TL;DR

This paper introduces an improved Eigensystem Realization Algorithm (ERA) that enhances model accuracy by optimizing time resolution and frequency analysis, demonstrating superior performance on large-scale systems compared to traditional ERA.

Contribution

The paper proposes a modified ERA that optimally selects time resolution and incorporates frequency analysis, resulting in more accurate low-dimensional models for large-scale systems.

Findings

Modified ERA achieves higher accuracy than traditional ERA.

Optimized time resolution improves model quality.

Effective on large-scale systems with fewer states.

Abstract

Eigensystem Realization Algorithm (ERA) is a tool that can produce a reduced order model (ROM) from just input-output data of a given system. ERA creates the ROM while keeping the number of internal states to a minimum level. This was first implemented by Juang and Pappa (1984) to analyze the vibration of aerospace structures from impulse response. We reviewed ERA and tested it on single input single output (SISO) system as well as on multiple input single output (MISO) system. ERA prediction agreed with the actual data. Unlike other model reduction techniques (Balanced truncation, balanced proper orthogonal decomposition), ERA works just as fine without the need of the adjoint system, that makes ERA a promising, completely data-driven, thrifty model reduction method. In this work, we propose a modified Eigensystem Realization Algorithm that relies upon an optimally chosen time resolution for the output used and also checks for good performance through frequency analysis. Four examples are discussed: the first two confirm the model generating ability and the last two illustrate its capability to produce a low-dimensional model (for a large scale system) that is much more accurate than the one produced by the traditional ERA.