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Voronoi-Based Vacuum Leakage Detection in Composite Manufacturing

Christoph Brauer, Arne Hindersmann, Timo de Wolff

Abstract

In this article, we investigate vacuum leakage detection problems in composite manufacturing. Our approach uses Voronoi diagrams, a well-known structure in discrete geometry. The Voronoi diagram of the vacuum connection positions partitions the component surface. We use this partition to narrow down potential leak locations to a small area, making an efficient manual search feasible. To further reduce the search area, we propose refined Voronoi diagrams. We evaluate both variants using a novel dataset consisting of several hundred one- and two-leak positions along with their corresponding flow values. Our experimental results demonstrate that Voronoi-based predictive models are highly accurate and have the potential to resolve the leakage detection bottleneck in composite manufacturing.

Voronoi-Based Vacuum Leakage Detection in Composite Manufacturing

Abstract

In this article, we investigate vacuum leakage detection problems in composite manufacturing. Our approach uses Voronoi diagrams, a well-known structure in discrete geometry. The Voronoi diagram of the vacuum connection positions partitions the component surface. We use this partition to narrow down potential leak locations to a small area, making an efficient manual search feasible. To further reduce the search area, we propose refined Voronoi diagrams. We evaluate both variants using a novel dataset consisting of several hundred one- and two-leak positions along with their corresponding flow values. Our experimental results demonstrate that Voronoi-based predictive models are highly accurate and have the potential to resolve the leakage detection bottleneck in composite manufacturing.

Paper Structure

This paper contains 18 sections, 1 theorem, 31 equations, 17 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. Mathematical model of the vacuum setup
  4. Predictive models for leak localization
  5. Classic Voronoi diagrams
  6. Refined Voronoi diagrams
  7. Strategies for multi-leak localization
  8. Experiments
  9. Data acquisition
  10. Metrics
  11. Data cleaning
  12. Experimental results on single-leak data
  13. Experimental results on multi-leak data
  14. Discussion
  15. Conclusion
  16. ...and 3 more sections

Key Result

Proposition B.1

Voronoi diagrams are polyhedral complexes. Moreover, they can be computed effectively in runtime $k \log(k)$ for point sets of cardinality $k$.

Figures (17)

  • Figure 1: Classic Voronoi diagram of a random set of points
  • Figure 2: Order-two refined Voronoi diagram of a random set of points
  • Figure 3: Experimental setup
  • Figure 4: Leak introduction and measurements (FM = Flow Meter)
  • Figure 5: Experimental data
  • ...and 12 more figures

Theorems & Definitions (12)

  • Definition 2.1
  • Example 2.2
  • Definition 2.3
  • Definition 2.4
  • Example 2.5
  • Definition 2.6
  • Example A.1
  • Proposition B.1
  • Example B.2
  • Definition C.1
  • ...and 2 more