🍩 Database of Original & Non-Theoretical Uses of Topology
(found 6 matches in 0.001267s)
Exploring Surface Texture Quantification in Piezo Vibration Striking Treatment (PVST) Using Topological Measures (2022)Melih C. Yesilli, Max M. Chumley, Jisheng Chen, Firas A. Khasawneh, Yang Guo
AbstractAbstract. Surface texture influences wear and tribological properties of manufactured parts, and it plays a critical role in end-user products. Therefore, quantifying the order or structure of a manufactured surface provides important information on the quality and life expectancy of the product. Although texture can be intentionally introduced to enhance aesthetics or to satisfy a design function, sometimes it is an inevitable byproduct of surface treatment processes such as Piezo Vibration Striking Treatment (PVST). Measures of order for surfaces have been characterized using statistical, spectral, and geometric approaches. For nearly hexagonal lattices, topological tools have also been used to measure the surface order. This paper explores utilizing tools from Topological Data Analysis for measuring surface texture. We compute measures of order based on optical digital microscope images of surfaces treated using PVST. These measures are applied to the grid obtained from estimating the centers of tool impacts, and they quantify the grid’s deviations from the nominal one. Our results show that TDA provides a convenient framework for characterization of pattern type that bypasses some limitations of existing tools such as difficult manual processing of the data and the need for an expert user to analyze and interpret the surface images.
A Classification of Topological Discrepancies in Additive Manufacturing (2019)Morad Behandish, Amir M. Mirzendehdel, Saigopal Nelaturi
AbstractAdditive manufacturing (AM) enables enormous freedom for design of complex structures. However, the process-dependent limitations that result in discrepancies between as-designed and as-manufactured shapes are not fully understood. The tradeoffs between infinitely many different ways to approximate a design by a manufacturable replica are even harder to characterize. To support design for AM (DfAM), one has to quantify local discrepancies introduced by AM processes, identify the detrimental deviations (if any) to the original design intent, and prescribe modifications to the design and/or process parameters to countervail their effects. Our focus in this work will be on topological analysis. There is ample evidence in many applications that preserving local topology (e.g., connectivity of beams in a lattice) is important even when slight geometric deviations can be tolerated. We first present a generic method to characterize local topological discrepancies due to material under-and over-deposition in AM, and show how it captures various types of defects in the as-manufactured structures. We use this information to systematically modify the as-manufactured outcomes within the limitations of available 3D printer resolution(s), which often comes at the expense of introducing more geometric deviations (e.g., thickening a beam to avoid disconnection). We validate the effectiveness of the method on 3D examples with nontrivial topologies such as lattice structures and foams.
Synthesis of Energy-Bounded Planar Caging Grasps Using Persistent Homology (2018)Jeffrey Mahler, Florian T. Pokorny, Sherdil Niyaz, Ken Goldberg
Raw Material Flow Optimization as a Capacitated Vehicle Routing Problem: A Visual Benchmarking Approach for Sustainable Manufacturing (2017)Michele Dassisti, Yasamin Eslami, Matin Mohaghegh
AbstractOptimisation problem concerning material flows, to increase the efficiency while reducing relative resource consumption is one of the most pressing problems today. The focus point of this study is to propose a new visual benchmarking approach to select the best material-flow path from the depot to the production lines, referring to the well-known Capacitated Vehicle Routing Problem (CVRP). An example industrial case study is considered to this aim. Two different solution techniques were adopted (namely Mixed Integer Linear Programming and the Ant Colony Optimization) in searching optimal solutions to the CVRP. The visual benchmarking proposed, based on the persistent homology approach, allowed to support the comparison of the optimal solutions based on the entropy of the output in different scenarios. Finally, based on the non-standard measurements of Crossing Length Percentage (CLP), the visual benchmarking procedure makes it possible to find the most practical and applicable solution to CVRP by considering the visual attractiveness and the quality of the routes.
Identification of Key Features Using Topological Data Analysis for Accurate Prediction of Manufacturing System Outputs (2017)Wei Guo, Ashis G. Banerjee
AbstractTopological data analysis (TDA) has emerged as one of the most promising approaches to extract insights from high-dimensional data of varying types such as images, point clouds, and meshes, in an unsupervised manner. To the best of our knowledge, here, we provide the first successful application of TDA in the manufacturing systems domain. We apply a widely used TDA method, known as the Mapper algorithm, on two benchmark data sets for chemical process yield prediction and semiconductor wafer fault detection, respectively. The algorithm yields topological networks that capture the intrinsic clusters and connections among the clusters present in the data sets, which are difficult to detect using traditional methods. We select key process variables or features that impact the system outcomes by analyzing the network shapes. We then use predictive models to evaluate the impact of the selected features. Results show that the models achieve at least the same level of high prediction accuracy as with all the process variables, thereby, providing a way to carry out process monitoring and control in a more cost-effective manner.