🍩 Database of Original & Non-Theoretical Uses of Topology

(found 2 matches in 0.000932s)

  1. Lean Blowout Detection Using Topological Data Analysis (2024)

    Arijit Bhattacharya, Sabyasachi Mondal, Somnath De, Achintya Mukhopadhyay, Swarnendu Sen
    Abstract Modern lean premixed combustors are operated in ultra-lean mode to conform to strict emission norms. However, this causes the combustors to become prone to lean blowout (LBO). Online monitoring of combustion dynamics may help to avoid LBO and help the combustor run more safely and reliably. Previous studies have suggested various techniques to early predict LBO in single-burner combustors. In contrast, early detection of LBO in multi-burner combustors has been little explored to date. Recent studies have discovered significantly different combustion dynamics between multi-burner combustors and single-burner combustors. In the present paper, we show that some well-established early LBO detection techniques suitable for single-burner combustor are less effective in early detecting LBO in multi-burner combustors. To resolve this, we propose a novel tool, topological data analysis (TDA), for real-time LBO prediction in a wide range of combustor configurations. We find that the TDA metrics are computationally cheap and follow monotonic trends during the transition to LBO. This indicates that the TDA metrics can be used to fine-tune the LBO safety margin, which is a desirable feature from practical implementation point of view. Furthermore, we show that the sublevel set TDA metrics show approximately monotonic changes during the transition to LBO even with low sampling-rate signals. Sublevel set TDA is computationally inexpensive and does not require phase-space embedding. Therefore, TDA can potentially be used for real-time monitoring of combustor dynamics with simple, low-cost, and low sampling-rate sensors.

  2. Pattern Characterization Using Topological Data Analysis: Application to Piezo Vibration Striking Treatment (2023)

    Max M. Chumley, Melih C. Yesilli, Jisheng Chen, Firas A. Khasawneh, Yang Guo
    Abstract Quantifying patterns in visual or tactile textures provides important information about the process or phenomena that generated these patterns. In manufacturing, these patterns can be intentionally introduced as a design feature, or they can be a byproduct of a specific process. Since surface texture has significant impact on the mechanical properties and the longevity of the workpiece, it is important to develop tools for quantifying surface patterns and, when applicable, comparing them to their nominal counterparts. While existing tools may be able to indicate the existence of a pattern, they typically do not provide more information about the pattern structure, or how much it deviates from a nominal pattern. Further, prior works do not provide automatic or algorithmic approaches for quantifying other pattern characteristics such as depths’ consistency, and variations in the pattern motifs at different level sets. This paper leverages persistent homology from Topological Data Analysis (TDA) to derive noise-robust scores for quantifying motifs’ depth and roundness in a pattern. Specifically, sublevel persistence is used to derive scores that quantify the consistency of indentation depths at any level set in Piezo Vibration Striking Treatment (PVST) surfaces. Moreover, we combine sublevel persistence with the distance transform to quantify the consistency of the indentation radii, and to compare them with the nominal ones. Although the tool in our PVST experiments had a semi-spherical profile, we present a generalization of our approach to tools/motifs of arbitrary shapes thus making our method applicable to other pattern-generating manufacturing processes.