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Physics-based Approximation and Prediction of Speedlines in Compressor Performance Maps

Abdul-Malik Akiev, Danyal Ergür, Alexander Schirger, Matthias Müller, Alexander Hinterleitner, Thomas Bartz-Beielstein

Abstract

Speedlines in compressor performance maps (CPMs) are critical for understanding and predicting compressor behavior under various operating conditions. We investigate a physics-based method for reconstructing compressor performance maps from sparse measurements by fitting each speedline with a superellipse and encoding it as a compact, interpretable vector (surge, choke, curvature, and shape parameters). Building on the formulation of Llamas et al., we develop a robust two-stage fitting pipeline that couples global search with local refinement. The approach is validated on industrial data-sets for different turbocharger types. We discuss prediction quality for inter- and extrapolation, metric sensitivities and outline opportunities for physics-informed constraints, alternative function families, and hybrid physics-ML mappings to improve boundary behavior and, ultimately, enable full CPM reconstruction from limited data.

Physics-based Approximation and Prediction of Speedlines in Compressor Performance Maps

Abstract

Speedlines in compressor performance maps (CPMs) are critical for understanding and predicting compressor behavior under various operating conditions. We investigate a physics-based method for reconstructing compressor performance maps from sparse measurements by fitting each speedline with a superellipse and encoding it as a compact, interpretable vector (surge, choke, curvature, and shape parameters). Building on the formulation of Llamas et al., we develop a robust two-stage fitting pipeline that couples global search with local refinement. The approach is validated on industrial data-sets for different turbocharger types. We discuss prediction quality for inter- and extrapolation, metric sensitivities and outline opportunities for physics-informed constraints, alternative function families, and hybrid physics-ML mappings to improve boundary behavior and, ultimately, enable full CPM reconstruction from limited data.
Paper Structure (20 sections, 4 equations, 4 figures, 3 tables)

This paper contains 20 sections, 4 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background and Motivation
  3. Method
  4. Superellipse Model
  5. Prediction Using \\ beta Vectors
  6. Evaluation and Error Assessment
  7. Experiments
  8. Dataset and Preprocessing
  9. Fitting Optimization Study
  10. Prediction Method Validation
  11. Industrial Dataset Evaluation
  12. Results
  13. Fitting Optimization Study
  14. Interpolation Within CPMs
  15. Extrapolation beyond CPMs
  16. ...and 5 more sections

Figures (4)

  • Figure 1: Comparison of DirectEllipse and LlamasEllipse models using the best performing configuration on the tca88 dataset
  • Figure 2: Comparison of optimization strategies. The boxplots show the distribution of RMSE and maximum error across all speedlines in the tca88 dataset. Individual data points (red) show the actual error values for each speedline.
  • Figure 3: Interpolation results for tcaA88 compressor. Left: Visualization of predicted speedlines (dashed) compared to actual data (solid) for speeds within the training range. Right: Evolution of model coefficients ($\beta$ vectors) across different speeds, showing the polynomial interpolation used for prediction.
  • Figure 4: Extrapolation results for TCA88 compressor. Left: Visualization of predicted speedlines (dashed) compared to actual data (solid) for speeds outside the training range. Right: Evolution of model coefficients ($\beta$ vectors) across different speeds, showing the polynomial interpolation used for prediction.