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Iterative Classification of Graph-Set-Based Designs (IC-GSBD) for the Down-Selection of Aircraft Thermal Management Systems

Anthony Sirico, Daniel R Herber

TL;DR

This paper's findings demonstrate that incorporating additional graph-based features using principle component analysis (PCA) enhances GDL model performance, and achieving an accuracy of 98% for determining a graph's compilability and simulatability while using only 5% of the data for training.

Abstract

In this paper, we present Iterative Classification of Graph-Set-Based Design (IC-GSBD), a framework utilizing graph-based techniques with geometric deep learning (GDL) integrated within a set-based design (SBD) approach for the classification and down-selection complex engineering systems represented by graphs. We demonstrate this approach on aircraft thermal management systems (TMSs) utilizing previous datasets created using an enumeration or brute-force graph generation procedure to represent novel aircraft TMSs as graphs. However, as with many enumerative approaches, combinatorial explosion limits its efficacy in many real-world problems, particularly when simulations and optimization must be performed on the many (automatically-generated) physics models. Therefore, the approach uses the directed graphs representing aircraft TMSs and GDL to predict on a subset of the graph-based dataset through graph classification. This paper's findings demonstrate that incorporating additional graph-based features using principle component analysis (PCA) enhances GDL model performance, achieving an accuracy of 98% for determining a graph's compilability and simulatability while using only 5% of the data for training. By applying iterative classification methods, we also successfully segmented the total set of graphs into more specific groups with an average inclusion of 75.5 of the top 100 highest-performing graphs, achieved by training on 40% of the data.

Iterative Classification of Graph-Set-Based Designs (IC-GSBD) for the Down-Selection of Aircraft Thermal Management Systems

TL;DR

This paper's findings demonstrate that incorporating additional graph-based features using principle component analysis (PCA) enhances GDL model performance, and achieving an accuracy of 98% for determining a graph's compilability and simulatability while using only 5% of the data for training.

Abstract

In this paper, we present Iterative Classification of Graph-Set-Based Design (IC-GSBD), a framework utilizing graph-based techniques with geometric deep learning (GDL) integrated within a set-based design (SBD) approach for the classification and down-selection complex engineering systems represented by graphs. We demonstrate this approach on aircraft thermal management systems (TMSs) utilizing previous datasets created using an enumeration or brute-force graph generation procedure to represent novel aircraft TMSs as graphs. However, as with many enumerative approaches, combinatorial explosion limits its efficacy in many real-world problems, particularly when simulations and optimization must be performed on the many (automatically-generated) physics models. Therefore, the approach uses the directed graphs representing aircraft TMSs and GDL to predict on a subset of the graph-based dataset through graph classification. This paper's findings demonstrate that incorporating additional graph-based features using principle component analysis (PCA) enhances GDL model performance, achieving an accuracy of 98% for determining a graph's compilability and simulatability while using only 5% of the data for training. By applying iterative classification methods, we also successfully segmented the total set of graphs into more specific groups with an average inclusion of 75.5 of the top 100 highest-performing graphs, achieved by training on 40% of the data.
Paper Structure (33 sections, 10 equations, 12 figures, 5 tables, 1 algorithm)

This paper contains 33 sections, 10 equations, 12 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Set-Based Design (SBD)
  4. Graph Theory
  5. Representation, Enumeration, and Analysis of Thermal Management Systems as Graphs
  6. Enumerative Methods with Network Structure Constraints
  7. Analysis of Physics-Based Models
  8. Geometric Deep Learning
  9. Graph Neural Networks
  10. Methodology
  11. Graph Classification
  12. Multi-Label Classification for Model Compilation and Simulatability
  13. Binary Classification for Best Graph Performance
  14. Datasets
  15. Feature Engineering Through Principal Component Analysis
  16. ...and 18 more sections

Figures (12)

  • Figure 1: The workflow for Set-Based Design.
  • Figure 2: A common air cycle machine (ACM) architecture represented in two forms.
  • Figure 3: The Principle Component Analysis features displayed for both the simulate and compile classifications.
  • Figure 4: Computed node embeddings for the ACM graph in Fig. \ref{['acmgraph']}.
  • Figure 5: An example confusion matrix.
  • ...and 7 more figures