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Koopman-Based Methods for EV Climate Dynamics: Comparing eDMD Approaches

Luca Meda, Stephanie Stockar

TL;DR

This work tackles nonlinear HVAC and cabin dynamics in battery electric vehicles by casting them in a Koopman Operator framework to obtain a linear representation in a lifted space. It systematically compares three eDMD dictionary approaches—polynomial, radial basis function (RBF), and neural network dictionary learning (eDMD-DL)—and demonstrates that physics-based dictionaries (polynomial and RBF) outperform the neural approach for this application. By incorporating power as a measurable output, the approach achieves accurate prediction of state trajectories and energy consumption over driving cycles, validated against a high-fidelity nonlinear HVAC model with Route 15 and other cycles showing energy errors near $2\%$ for RBF. The results suggest a scalable, data-driven pathway for real-time climate-control prediction and controller design in BEVs, extendable to other complex nonlinear systems.

Abstract

In this paper, data-driven algorithms based on Koopman Operator Theory are applied to identify and predict the nonlinear dynamics of a vapor compression system and cabin temperature in a light-duty electric vehicle. By leveraging a high-fidelity nonlinear HVAC model, the system behavior is captured in a lifted higher-dimensional state space, enabling a linear representation. A comparative analysis of three Koopman-based system identification approaches (polynomial libraries, radial basis functions (RBF), and neural network-based dictionary learning) is conducted. Accurate prediction of power consumption over entire driving cycles is demonstrated by incorporating power as a measurable output within the Koopman framework. The performance of each method is rigorously evaluated through simulations under various driving cycles and ambient conditions, highlighting their potential for real-time prediction and control in energy-efficient vehicle climate management. This study offers a scalable, data-driven methodology that can be extended to other complex nonlinear systems.

Koopman-Based Methods for EV Climate Dynamics: Comparing eDMD Approaches

TL;DR

This work tackles nonlinear HVAC and cabin dynamics in battery electric vehicles by casting them in a Koopman Operator framework to obtain a linear representation in a lifted space. It systematically compares three eDMD dictionary approaches—polynomial, radial basis function (RBF), and neural network dictionary learning (eDMD-DL)—and demonstrates that physics-based dictionaries (polynomial and RBF) outperform the neural approach for this application. By incorporating power as a measurable output, the approach achieves accurate prediction of state trajectories and energy consumption over driving cycles, validated against a high-fidelity nonlinear HVAC model with Route 15 and other cycles showing energy errors near for RBF. The results suggest a scalable, data-driven pathway for real-time climate-control prediction and controller design in BEVs, extendable to other complex nonlinear systems.

Abstract

In this paper, data-driven algorithms based on Koopman Operator Theory are applied to identify and predict the nonlinear dynamics of a vapor compression system and cabin temperature in a light-duty electric vehicle. By leveraging a high-fidelity nonlinear HVAC model, the system behavior is captured in a lifted higher-dimensional state space, enabling a linear representation. A comparative analysis of three Koopman-based system identification approaches (polynomial libraries, radial basis functions (RBF), and neural network-based dictionary learning) is conducted. Accurate prediction of power consumption over entire driving cycles is demonstrated by incorporating power as a measurable output within the Koopman framework. The performance of each method is rigorously evaluated through simulations under various driving cycles and ambient conditions, highlighting their potential for real-time prediction and control in energy-efficient vehicle climate management. This study offers a scalable, data-driven methodology that can be extended to other complex nonlinear systems.

Paper Structure

This paper contains 12 sections, 13 equations, 5 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Methodology
  3. Vapor Compression System and Cabin Modeling
  4. Koopman Operator Theory
  5. Data-driven Koopman-based Modeling
  6. Selection of Dictionary of Basis Functions
  7. Case Study
  8. Problem Description
  9. Data Generation
  10. Comparison of Libraries on Simulation Data
  11. Driving scenarios results
  12. Conclusions

Figures (5)

  • Figure 1: Vehicle air conditioning and cabin model
  • Figure 2: $RMSE_{avg}$ for the three system states compared between different dictionary choices with varying N
  • Figure 3: States and power prediction for the Koopman methods tested (N=35) compared to a 1500s validation sequence
  • Figure 4: Route 15 velocity profile
  • Figure 5: States and power prediction for RBF Koopman method on the Route 15 driving cycle