Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

From Features to States: Data-Driven Selection of Measured State Variables via RFE-DMDc

Haoyu Wang, Andrea Alfonsi, Roberto Ponciroli, Richard Vilim

TL;DR

This work tackles data-driven state-variable selection for dynamical systems by seeking a minimal, physically interpretable set of measured variables that can serve as the surrogate state for linear control-oriented models. It introduces RFE-DMDc, which combines Recursive Feature Elimination with Dynamic Mode Decomposition with Control and includes a cross-subsystem balancing step to prevent dominance by high-gain subsystems. Through a truth-known RLC benchmark and a large Integrated Energy System with thousands of candidate variables, RFE-DMDc identifies compact state sets (≈10 variables) achieving test accuracy comparable to a GA-based baseline (GA-DMDc) but with an order of magnitude lower computational cost, while preserving physical interpretability. The method enhances sensor planning and Digital Twin deployment by prioritizing measured variables that maximize dynamical predictability with minimal sensing overhead.

Abstract

The behavior of a dynamical system under a given set of inputs can be captured by tracking the response of an optimal subset of process variables (\textit{state variables}). For many engineering systems, however, first-principles, model-based identification is impractical, motivating data-driven approaches for Digital Twins used in control and diagnostics. In this paper, we present RFE-DMDc, a supervised, data-driven workflow that uses Recursive Feature Elimination (RFE) to select a minimal, physically meaningful set of variables to monitor and then derives a linear state-space model via Dynamic Mode Decomposition with Control (DMDc). The workflow includes a cross-subsystem selection step that mitigates feature \textit{overshadowing} in multi-component systems. To corroborate the results, we implement a GA-DMDc baseline that jointly optimizes the state set and model fit under a common accuracy cost on states and outputs. Across a truth-known RLC benchmark and a realistic Integrated Energy System (IES) with multiple thermally coupled components and thousands of candidate variables, RFE-DMDc consistently recovers compact state sets (\(\approx 10\) variables) that achieve test errors comparable to GA-DMDc while requiring an order of magnitude less computational time. The selected variables retain clear physical interpretation across subsystems, and the resulting models demonstrate competitive predictive accuracy, computational efficiency, and robustness to overfitting.

From Features to States: Data-Driven Selection of Measured State Variables via RFE-DMDc

TL;DR

This work tackles data-driven state-variable selection for dynamical systems by seeking a minimal, physically interpretable set of measured variables that can serve as the surrogate state for linear control-oriented models. It introduces RFE-DMDc, which combines Recursive Feature Elimination with Dynamic Mode Decomposition with Control and includes a cross-subsystem balancing step to prevent dominance by high-gain subsystems. Through a truth-known RLC benchmark and a large Integrated Energy System with thousands of candidate variables, RFE-DMDc identifies compact state sets (≈10 variables) achieving test accuracy comparable to a GA-based baseline (GA-DMDc) but with an order of magnitude lower computational cost, while preserving physical interpretability. The method enhances sensor planning and Digital Twin deployment by prioritizing measured variables that maximize dynamical predictability with minimal sensing overhead.

Abstract

The behavior of a dynamical system under a given set of inputs can be captured by tracking the response of an optimal subset of process variables (\textit{state variables}). For many engineering systems, however, first-principles, model-based identification is impractical, motivating data-driven approaches for Digital Twins used in control and diagnostics. In this paper, we present RFE-DMDc, a supervised, data-driven workflow that uses Recursive Feature Elimination (RFE) to select a minimal, physically meaningful set of variables to monitor and then derives a linear state-space model via Dynamic Mode Decomposition with Control (DMDc). The workflow includes a cross-subsystem selection step that mitigates feature \textit{overshadowing} in multi-component systems. To corroborate the results, we implement a GA-DMDc baseline that jointly optimizes the state set and model fit under a common accuracy cost on states and outputs. Across a truth-known RLC benchmark and a realistic Integrated Energy System (IES) with multiple thermally coupled components and thousands of candidate variables, RFE-DMDc consistently recovers compact state sets ( variables) that achieve test errors comparable to GA-DMDc while requiring an order of magnitude less computational time. The selected variables retain clear physical interpretation across subsystems, and the resulting models demonstrate competitive predictive accuracy, computational efficiency, and robustness to overfitting.

Paper Structure

This paper contains 14 sections, 30 equations, 15 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Brief Overview of the Dynamic Mode Decomposition with Control algorithm
  3. Cost-Function–Driven GA--DMDc for State Selection
  4. Recursive Feature Elimination based Algorithm for State Variable Selection
  5. Pre-filtering stage
  6. RFE with a DMDc-based importance score
  7. Assessment of the performance of the proposed algorithm
  8. Validation on a Simple RLC Benchmark
  9. Description of the Multi-component System
  10. Results
  11. GA--DMDc: population sweep and baseline
  12. RFE--DMDc vs. GA--DMDc: accuracy and selected size
  13. Computational efficiency of the developed algorithms
  14. Conclusion

Figures (15)

  • Figure 1: Flowchart of the GA--DMDc baseline used for comparison with RFE--DMDc.
  • Figure 2: Subsystems interacting on each other with corresponding sets of process variables.
  • Figure 3: Series RLC circuit used for validation (parameter values shown).
  • Figure 4: RLC benchmark: predicted state and output trajectories from the data-driven model versus the analytic solution.
  • Figure 5: Graphical representation of the IES modelFlaticon.
  • ...and 10 more figures