Assessing observability of chaotic systems using Delay Differential Analysis

TL;DR

This paper introduces a numerical method using Delay Differential Analysis to assess the observability of chaotic systems from time series data, especially when the governing equations are unknown.

Contribution

It proposes a novel data-driven approach for evaluating observability through delay differential equations, validated against existing methods and tested for noise robustness.

Findings

DDA effectively ranks variables by observability using least squares error.

The approach correlates well with symbolic observability coefficients.

It demonstrates robustness against noise contamination.

Abstract

Observability can determine which recorded variables of a given system are optimal for discriminating its different states. Quantifying observability requires knowledge of the equations governing the dynamics. These equations are often unknown when experimental data are considered. Consequently, we propose an approach for numerically assessing observability using Delay Differential Analysis (DDA). Given a time series, DDA uses a delay differential equation for approximating the measured data. The lower the least squares error between the predicted and recorded data, the higher the observability. We thus rank the variables of several chaotic systems according to their corresponding least square error to assess observability. The performance of our approach is evaluated by comparison with the ranking provided by the symbolic observability coefficients as well as with two other data-based approaches using reservoir computing and singular value decomposition of the reconstructed space. We investigate the robustness of our approach against noise contamination.