Assessing observability of chaotic systems using Delay Differential Analysis | JoVE Visualize

Area of Science:

Complex Systems Dynamics
Data-driven Modeling
Systems Engineering

Background:

Observability is crucial for understanding system states but often requires known system dynamics.
Experimental data frequently lacks explicit governing equations, hindering traditional observability quantification.
Developing data-driven methods for observability assessment is essential for analyzing real-world systems.

Purpose of the Study:

To propose and validate a novel numerical approach for assessing system observability using only time-series data.
To introduce Delay Differential Analysis (DDA) as a method for quantifying observability without prior knowledge of system dynamics.
To compare the performance of DDA against established observability assessment techniques.

Main Methods:

Employed Delay Differential Analysis (DDA) to approximate time-series data using delay differential equations.
Quantified observability by calculating the least squares error between DDA-approximated and recorded data.
Ranked system variables based on their least squares error to assess observability.
Validated the approach by comparing results with symbolic observability coefficients, reservoir computing, and singular value decomposition.
Investigated the robustness of the DDA method against noise contamination.

Main Results:

DDA successfully provided a numerical assessment of observability for chaotic systems using time-series data.
The least squares error in DDA accurately reflected the observability of system variables.
The proposed DDA approach demonstrated comparable or superior performance to existing data-based methods.
The method showed robustness in the presence of noise, indicating its practical applicability.

Conclusions:

Delay Differential Analysis (DDA) offers a viable and robust data-driven method for assessing system observability when system dynamics are unknown.
This approach enhances the ability to identify optimal discriminating variables from experimental data.
DDA provides a valuable tool for systems analysis in fields relying on experimental time-series measurements.