Chatter detection in turning using persistent homology

Khasawneh, Firas A.; Munch, Elizabeth

doi:10.1016/j.ymssp.2015.09.046

Cited by 114 publications

(63 citation statements)

References 75 publications

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“…While this is obviously a very lossy point summary for a persistence diagram, it is quite useful in that, particularly for applications where the existence of a large circle is of interest, it often does what we need. See, e.g., [45,86].…”

Section: Point Summaries Of Persistence Diagramsmentioning

confidence: 99%

“…One particularly useful tool for this analysis is 1-dimensional persistent homology [32,33], which encodes how circular structures persist over the course of a filtration in a topological signature called a persistence diagram. This and its variants have been quite successful in applications, particularly for the analysis of periodicity [34][35][36][37][38][39][40][41], including for parameter selection [42,43], data clustering [44], machining dynamics [45][46][47][48][49], gene regulatory systems [50,51], financial data [52][53][54], wheeze detection [55], sonar classification [56], video analysis [57][58][59], and annotation of song structure [60,61].…”

Section: Introductionmentioning

confidence: 99%

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Persistent homology of complex networks for dynamic state detection

2019

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In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a compressed, multi-scale representation of the graph that can distinguish between dynamic states such as periodic and chaotic behavior. We show the approach for two graph constructions obtained from the time series. In the first approach the time series is embedded into a point cloud which is then used to construct an undirected k-nearest neighbor graph. The second construct relies on the recently developed ordinal partition framework. In either case, a pairwise distance matrix is then calculated using the shortest path between the graph's nodes, and this matrix is utilized to define a filtration of a simplicial complex that enables tracking the changes in homology classes over the course of the filtration. These changes are summarized in a persistence diagram-a two-dimensional summary of changes in the topological features. We then extract existing as well as new geometric and entropy point summaries from the persistence diagram and compare to other commonly used network characteristics. Our results show that persistence-based point summaries yield a clearer distinction of the dynamic behavior and are more robust to noise than existing graph-based scores, especially when combined with ordinal graphs.

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Section: Point Summaries Of Persistence Diagramsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Persistent homology of complex networks for dynamic state detection

2019

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“…It can also describe more complicated structure such as loops and voids that are not visible with other methods. Persistent homology has found success in the investigation of data from many different domains; these include image processing (Carlsson, Ishkhanov, de Silva, & Zomorodian, 2008;Perea & Carlsson, 2014;Adcock, Carlsson, & Carlsson, 2016), time series analysis (Perea, Deckard, Haase, & Harer, 2015;Khasawneh & Munch, 2016;Emrani, Gentimis, & Krim, 2014), phylogenetics (Chan, Carlsson, & Rabadan, 2013), neuroscience (Giusti, Pastalkova, Curto, & Itskov, 2015;Dabaghian, Mémoli, Frank, & Carlsson, 2012), and sensor networks (de Silva & Ghrist, 2007;Adams & Carlsson, 2015;Munch, Shapiro, & Harer, 2012). …”

Section: Persistent Homologymentioning

confidence: 99%

A User’s Guide to Topological Data Analysis

Munch

2017

Learning Analytics

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ABSTRACT. Topological data analysis (TDA) is a collection of powerful tools that can quantify shape and structure in data in order to answer questions from the data's domain. This is done by representing some aspect of the structure of the data in a simplified topological signature. In this article, we introduce two of the most commonly used topological signatures. First, the persistence diagram represents loops and holes in the space by considering connectivity of the data points for a continuum of values rather than a single fixed value. The second topological signature, the mapper graph, returns a 1-dimensional structure representing the shape of the data, and is particularly good for exploration and visualization of the data. While these techniques are based on very sophisticated mathematics, the current ubiquity of available software means that these tools are more accessible than ever to be applied to data by researchers in education and learning, as well as all domain scientists.

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“…If the expected value is taken of both sides of the equation (4), an x t perturbation process can be introduced around the E (y st ) = κ equilibrium point of the equation, where E (x t ) = 0, as shown in (8).…”

Section: The Stochastic Dimensionless Equation For Turningmentioning

confidence: 99%

“…The commonly used models involve deterministic delay differential equations, in which the parameters are usually considered to be constant [3][4][5][6][7][8]. During the measurements of these parameters, the average is considered and the variance is attributed to the quality of the measurement.…”

Section: Introductionmentioning

confidence: 99%

A Theoretical Investigation of the Effect of the Stochasticity in the Material Properties on the Chatter Detection During Turning

Sykora

Bachrathy

Stépàn

2017

Volume 8: 29th Conference on Mechanical Vibration and Noise

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In this work the effect of the inhomogeneous material properties are investigated in regenerative turning processes by introducing white noise in the cutting coefficient. The model is a one degree of freedom linear delayed oscillator with stochastic parameters. A full discretization method is used to calculate the time evolution of the second moment to determine the moment stability of the turning process. The resultant stability chart is compared with the deterministic turning model. NOMENCLATURE

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Chatter detection in turning using persistent homology

Cited by 114 publications

References 75 publications

Persistent homology of complex networks for dynamic state detection

Persistent homology of complex networks for dynamic state detection

A User’s Guide to Topological Data Analysis

A Theoretical Investigation of the Effect of the Stochasticity in the Material Properties on the Chatter Detection During Turning

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