Relevant bibliographies by topics / Topological categories

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Topological categories'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 February 2022

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Journal articles on the topic "Topological categories"

1

Diers, Yves. "Topological geometrical categories." Journal of Pure and Applied Algebra 168, no. 2-3 (March 2002): 177–87. http://dx.doi.org/10.1016/s0022-4049(01)00095-0.

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Shenggang Li. "Weak topological categories." Fuzzy Sets and Systems 93, no. 3 (February 1998): 363–73. http://dx.doi.org/10.1016/s0165-0114(96)00202-3.

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Schwarz, Friedhelm. "HEREDITARY TOPOLOGICAL CATEGORIES AND TOPOLOGICAL UNIVERSES." Quaestiones Mathematicae 10, no. 2 (January 1986): 197–216. http://dx.doi.org/10.1080/16073606.1986.9631604.

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Tholen, Walter. "Met-Like Categories Amongst Concrete Topological Categories." Applied Categorical Structures 26, no. 5 (February 12, 2018): 1095–111. http://dx.doi.org/10.1007/s10485-018-9513-7.

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Ad�mek, J., and G. E. Strecker. "Injectivity of topological categories." Algebra Universalis 26, no. 3 (October 1989): 284–306. http://dx.doi.org/10.1007/bf01211836.

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Rice, Michael D. "Reflexive objects in topological categories." Mathematical Structures in Computer Science 6, no. 4 (August 1996): 375–86. http://dx.doi.org/10.1017/s0960129500001079.

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This paper presents several basic results about the non-existence of reflexive objects in cartesian closed topological categories of Hausdorff spaces. In particular, we prove that there are no non-trivial countably compact reflexive objects in the category of Hausdorff k-spaces and, more generally, that any non-trivial reflexive Tychonoff space in this category contains a closed discrete subspace corresponding to a numeral system in the sense of Wadsworth. In addition, we establish that a reflexive Tychonoff space in a cartesian-closed topological category cannot contain a non-trivial continuous image of the unit interval. Therefore, if there exists a non-trivial reflexive Tychonoff space, it does not have a nice geometric structure.
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Dikranjan, D., E. Giuli, and A. Tozzi. "TOPOLOGICAL CATEGORIES AND CLOSURE OPERATORS." Quaestiones Mathematicae 11, no. 3 (January 1988): 323–37. http://dx.doi.org/10.1080/16073606.1988.9632148.

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Barr, Michael. "Topological $\ast$-autonomous categories, revisited." Tbilisi Mathematical Journal 10, no. 3 (June 2017): 51–64. http://dx.doi.org/10.1515/tmj-2017-0102.

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Gurski, Nick, Niles Johnson, and Angelica M. Osorno. "Topological Invariants from Higher Categories." Notices of the American Mathematical Society 66, no. 08 (September 1, 2019): 1. http://dx.doi.org/10.1090/noti1934.

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Cagliari, F., and S. Mantovani. "Localizations in universal topological categories." Proceedings of the American Mathematical Society 103, no. 2 (February 1, 1988): 639. http://dx.doi.org/10.1090/s0002-9939-1988-0943097-7.

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Dissertations / Theses on the topic "Topological categories"

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O'Sullivan, David Robert. "Topological C*-categories." Thesis, University of Sheffield, 2017. http://etheses.whiterose.ac.uk/16775/.

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Tensor C*-categories are the result of work to recast the fundamental theory of operator algebras in the setting of category theory, in order to facilitate the study of higher-dimensional algebras that are expected to play an important role in a unified model of physics. Indeed, the application of category theory to mathematical physics is itself a highly active field of research. C*-categories are the analogue of C*-algebras in this context. They are defined as norm-closed self-adjoint subcategories of the category of Hilbert spaces and bounded linear operators between them. Much of the theory of C*-algebras and their invariants generalises to C*-categories. Often, when a C*-algebra is associated to a particular structure it is not completely natural because certain choices are involved in its definition. Using C*-categories instead can avoid such choices since the construction of the relevant C*-category amounts to choosing all suitable C*-algebras at once. In this thesis we introduce and study C*-categories for which the set of objects carries topological data, extending the present body of work, which exclusively considers C*-categories with discrete object sets. We provide a construction of K-theory for topological C*-categories, which will have applications in widening the scope of the Baum-Connes conjecture, in index theory, and in geometric quantisation. As examples of such applications, we construct the C*-categories of topological groupoids, extending the familiar constructions of Renault.
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Razafindrakoto, Ando Desire. "Neighbourhood operators on Categories." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/80169.

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Thesis (PhD)--Stellenbosch University, 2013.
ENGLISH ABSTRACT: While the notions of open and closed subsets in a topological space are dual to each other, they take on another meaning when points and complements are no longer available. Closure operators have been extensively used to study topological notions on categories. Though this has recovered a fair amount of topological results and has brought an economy of e ort and insight into Topology, it is thought that certain properties, such as convergence, are naturally associated with neighbourhoods. On the other hand, it is interesting enough to investigate certain notions, such as that of closed maps, which in turn are naturally associated with closure by means of neighbourhoods. We propose in this thesis a set of axioms for neighbourhoods and test them with the properties of connectedness and compactness.
AFRIKAANSE OPSOMMING: Al is die twee konsepte van oop en geslote subversamelings in 'n topologiese ruimte teenoorgesteldes van mekaar, verander hul betekenis wanneer punte en komplemente nie meer ter sprake is nie. Die gebruik van afsluitingsoperatore is alreeds omvattend in die studie van topologiese konsepte in kategorieë, toegepas. Alhoewel 'n redelike aantal topologiese resultate, groeiende belangstelling en groter insig tot Topologie die gevolg was, word daar geglo dat seker eienskappe, soos konvergensie, op 'n natuurlike wyse aan omgewings verwant is. Nietemin is dit van belang om sekere eienskappe, soos geslote afbeeldings, wat natuurlik verwant is aan afsluiting, te bestudeer. In hierdie proefskrif stel ons 'n aantal aksiomas oor omgewings voor en toets dit gevolglik met die eienskappe van samehangendheid en kompaktheid.
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Wüthrich, Samuel. "I-adic towers in algebraic and topological derived categories /." [S.l.] : [s.n.], 2004. http://www.zb.unibe.ch/download/eldiss/04wuethrich_s.pdf.

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De, Renzi Marco. "Construction of extended topological quantum field theories." Thesis, Sorbonne Paris Cité, 2017. http://www.theses.fr/2017USPCC114/document.

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La position centrale occupée par les Théories Quantiques des Champs Topologiques (TQFTs) dans l’étude de la topologie en basse dimension est due à leur structure extraordinairement riche, qui permet différentes interactions et applications à des questions de nature géométrique. Depuis leur première apparition, un grand effort a été mis dans l’extension des invariants quantiques de 3-variétés en TQFTs et en TQFT Étendues (ETQFTs). Cette thèse s’attaque à ce problème dans deux cadres généraux différents. Le premier est l’étude des invariants quantiques semi-simples de Witten, Reshetikhin et Turaev issus de catégories modulaires. Bien que les ETQFTs correspondantes étaient connues depuis un certain temps, une réalisation explicite basée sur la construction universelle de Blanchet, Habegger, Masbaum et Vogel apparaît ici pour la première fois. L’objectif est de tracer la route à suivre dans la deuxième partie de la thèse, où la même procédure est appliquée à une nouvelle famille d’invariants quantiques non semi-simples due à Costantino, Geer et Patureau. Ces invariants avaient déjà été étendus en TQFTs graduées par Blanchet, Costantino, Geer and Patureau, mais seulement pour une famille explicite d’exemples. Nous posons la première pierre en introduisant la définition de catégorie modulaire relative, un analogue non semi-simple aux catégories modulaires. Ensuite, nous affinons la construction universelle pour obtenir des ETQFTs graduées étendant à la fois les invariants quantiques de Costantino, Geer et Patureau et les TQFTs graduées de Blanchet, Costantino, Geer et Patureau dans ce cadre général
The central position held by Topological Quantum Field Theories (TQFTs) in the study of low dimensional topology is due to their extraordinarily rich structure, which allows for various interactions with and applications to questions of geometric nature. Ever since their first appearance, a great effort has been put into extending quantum invariants of 3-dimensional manifolds to TQFTs and Extended TQFTs (ETQFTs). This thesis tackles this problem in two different general frameworks. The first one is the study of the semisimple quantum invariants of Witten, Reshetikhin and Turaev issued from modular categories. Although the corresponding ETQFTs were known to exist for a while, an explicit realization based on the universal construction of Blanchet, Habegger, Masbaum and Vogel appears here for the first time. The aim is to set a golden standard for the second part of the thesis, where the same procedure is applied to a new family of non-semisimple quantum invariants due to Costantino, Geer and Patureau. These invariants had been previously extended to graded TQFTs by Blanchet, Costantino, Geer an Patureau, but only for an explicit family of examples. We lay the first stone by introducing the definition of relative modular category, a non-semisimple analogue to modular categories. Then, we refine the universal construction to obtain graded ETQFTs extending both the quantum invariants of Costantino, Geer and Patureau and the graded TQFTs of Blanchet, Costantino, Geer and Patureau in this general setting
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Juer, Rosalinda. "1 + 1 dimensional cobordism categories and invertible TQFT for Klein surfaces." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:b9a8fc3b-4abd-49a1-b47c-c33f919a95ef.

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We discuss a method of classifying 2-dimensional invertible topological quantum field theories (TQFTs) whose domain surface categories allow non-orientable cobordisms. These are known as Klein TQFTs. To this end we study the 1+1 dimensional open-closed unoriented cobordism category K, whose objects are compact 1-manifolds and whose morphisms are compact (not necessarily orientable) cobordisms up to homeomorphism. We are able to compute the fundamental group of its classifying space BK and, by way of this result, derive an infinite loop splitting of BK, a classification of functors K → Z, and a classification of 2-dimensional open-closed invertible Klein TQFTs. Analogous results are obtained for the two subcategories of K whose objects are closed or have boundary respectively, including classifications of both closed and open invertible Klein TQFTs. The results obtained throughout the paper are generalisations of previous results by Tillmann [Til96] and Douglas [Dou00] regarding the 1+1 dimensional closed and open-closed oriented cobordism categories. Finally we consider how our results should be interpreted in terms of the known classification of 2-dimensional TQFTs in terms of Frobenius algebras.
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Wasserman, Thomas A. "A reduced tensor product of braided fusion categories over a symmetric fusion category." Thesis, University of Oxford, 2017. http://ora.ox.ac.uk/objects/uuid:58c6aae3-cb0e-4381-821f-f7291ff95657.

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The main goal of this thesis is to construct a tensor product on the 2-category BFC-A of braided fusion categories containing a symmetric fusion category A. We achieve this by introducing the new notion of Z(A)-crossed braided categories. These are categories enriched over the Drinfeld centre Z(A) of the symmetric fusion category. We show that Z(A) admits an additional symmetric tensor structure, which makes it into a 2-fold monoidal category. ByTannaka duality, A= Rep(G) (or Rep(G; w)) for a finite group G (or finite super-group (G,w)). Under this identication Z(A) = VectG[G], the category of G-equivariant vector bundles over G, and we show that the symmetric tensor product corresponds to (a super version of) to the brewise tensor product. We use the additional symmetric tensor product on Z(A) to define the composition in Z(A)-crossed braided categories, whereas the usual tensor product is used for the monoidal structure. We further require this monoidal structure to be braided for the switch map that uses the braiding in Z(A). We show that the 2-category Z(A)-XBF is equivalent to both BFC=A and the 2-category of (super)-G-crossed braided categories. Using the former equivalence, the reduced tensor product on BFC-A is dened in terms of the enriched Cartesian product of Z(A)-enriched categories on Z(A)-XBF. The reduced tensor product obtained in this way has as unit Z(A). It induces a pairing between minimal modular extensions of categories having A as their Mueger centre.
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Maier, Jennifer [Verfasser], and Christoph [Akademischer Betreuer] Schweigert. "A Study of Equivariant Hopf Algebras and Tensor Categories through Topological Field Theories / Jennifer Maier. Betreuer: Christoph Schweigert." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2013. http://d-nb.info/1032313412/34.

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Maier, Jennifer Verfasser], and Christoph [Akademischer Betreuer] [Schweigert. "A Study of Equivariant Hopf Algebras and Tensor Categories through Topological Field Theories / Jennifer Maier. Betreuer: Christoph Schweigert." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2013. http://d-nb.info/1032313412/34.

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Araújo, Manuel. "Coherence for 3-dualizable objects." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:a4b8f8de-a8e3-48c3-a742-82316a7bd8eb.

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A fully extended framed topological field theory with target in a symmetric monoidal n-catgeory C is a symmetric monoidal functor Z from Bord(n) to C, where Bord(n) is the symmetric monoidal n-category of n-framed bordisms. The cobordism hypothesis says that such field theories are classified by fully dualizable objects in C. Given a fully dualizable object X in C, we are interested in computing the values of the corresponding field theory on specific framed bordisms. This leads to the question of finding a presentation for Bord(n). In view of the cobordism hypothesis, this can be rephrased in terms of finding coherence data for fully dualizable objects in a symmetric monoidal n-category. We prove a characterization of full dualizability of an object X in terms of existence of a dual of X and existence of adjoints for a finite number of higher morphisms. This reduces the problem of finding coherence data for fully dualizable objects to that of finding coherence data for duals and adjoints. For n=3, and in the setting of strict symmetric monoidal 3-categories, we find this coherence data, and we prove the corresponding coherence theorems. The proofs rely on extensive use of a graphical calculus for strict monoidal 3-categories.
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Moreira, Charles dos Anjos. "Linguagem de categorias e o Teorema de van Kampen /." Rio Claro, 2017. http://hdl.handle.net/11449/152195.

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Orientador: Elíris Cristina Rizziolli
Banca: Aldício José Miranda
Banca: João Peres Vieira
Resumo: Esse trabalho trata de elementos da Topologia Algébrica, a qual tem como fundamental aplicação abordar questões acerca de Espaços Topológicos sob o ponto de vista algébrico. Uma das questões é tentar responder se dois espaços topológicos X e Y são homeomorfos. Neste sentido, o grupo fundamental é uma ferramenta algébrica útil por se tratar de um invariante topológico. Além disso, apresentamos o Teorema de van Kampen do ponto de vista da Linguagem de Categorias e Funtores
Abstract: This work treats of elements of the Algebraic Topology, which has as fundamental application to approach subjects concerning Topological Spaces under the algebraic point of view. One of the subjects is to try to answer if two topological spaces X and Y are homeomorphics. In this sense, the fundamental group is an useful algebraic tool for treating of an topological invariant. In addition, we presented the van Kampen's Theorem of the point of view of the language of Categories and Functors
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Books on the topic "Topological categories"

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Turaev, Vladimir, and Alexis Virelizier. Monoidal Categories and Topological Field Theory. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49834-8.

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Lowen, R. Approach spaces: The missing link in the topology-uniformity-metric triad. Oxford: Clarendon Press, 1997.

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Tanaka, Hiro Lee. Lectures on Factorization Homology, ∞-Categories, and Topological Field Theories. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61163-7.

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Theory of topological structures: An approach to categorical topology. Dordrecht: D. Reidel Pub. Co., 1988.

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Functorial knot theory: Categories of tangles, coherence, categorical deformations, and topological invariants. Singapore: World Scientific, 2001.

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Werner, Gähler, Preuss Gerhard 1940-, and Herrlich Horst, eds. Categorical structures and their applications: Proceedings of the North-West European Category Seminar, Berlin, Germany, 28-29 March 2003. Singapore: World Scientific, 2004.

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A non-Hausdorff completion: The Abelian category of C-complete left modules over a topological ring. New Jersey: World Scientific, 2015.

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On the algebraic foundation of bounded cohomology. Providence, R.I: American Mathematical Society, 2011.

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Pantev, Tony. Stacks and catetories in geometry, topology, and algebra: CATS4 Conference Higher Categorical Structures and Their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, July 2-7, 2012, CIRM, Luminy, France. Providence, Rhode Island: American Mathematical Society, 2015.

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Tulane University. Dept. of Mathematics, ed. Mathematical foundations of information flow: Clifford lectures on information flow in physics, geometry and logic and computation, March 12-15, 2008, Tulane University, New Orleans, Louisiana. Providence, R.I: American Mathematical Society, 2012.

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Book chapters on the topic "Topological categories"

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Preuss, Gerhard. "Topological Categories." In Theory of Topological Structures, 16–46. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2859-6_3.

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Mazzola, Guerino, René Guitart, Jocelyn Ho, Alex Lubet, Maria Mannone, Matt Rahaim, and Florian Thalmann. "Categories of Gestures over Topological Categories." In The Topos of Music III: Gestures, 937–64. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-64481-3_7.

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Turaev, Vladimir, and Alexis Virelizier. "Braided categories." In Monoidal Categories and Topological Field Theory, 53–63. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49834-8_3.

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Turaev, Vladimir, and Alexis Virelizier. "Fusion categories." In Monoidal Categories and Topological Field Theory, 65–87. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49834-8_4.

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Preuss, Gerhard. "Cartesian Closed Topological Categories." In Theory of Topological Structures, 134–51. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2859-6_6.

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Preuss, Gerhard. "Relations Between Special Topological Categories." In Theory of Topological Structures, 90–133. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2859-6_5.

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May, J., and J. Sigurdsson. "Well-grounded topological model categories." In Parametrized Homotopy Theory, 77–96. Providence, Rhode Island: American Mathematical Society, 2006. http://dx.doi.org/10.1090/surv/132/05.

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Turaev, Vladimir, and Alexis Virelizier. "Topological Quantum Field Theory." In Monoidal Categories and Topological Field Theory, 229–35. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49834-8_10.

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Turaev, Vladimir, and Alexis Virelizier. "Monoidal categories and functors." In Monoidal Categories and Topological Field Theory, 3–30. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49834-8_1.

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Bertrand, Toën. "Lectures on DG-Categories." In Topics in Algebraic and Topological K-Theory, 243–302. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15708-0_5.

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Conference papers on the topic "Topological categories"

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ALB, ALINA. "SOME COREFLECTIVE CATEGORIES OF TOPOLOGICAL MODULES." In Proceedings of the International Conference on Algebras, Modules and Rings. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774552_0001.

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May, J. P. "The construction of E∞ring spaces from bipermutative categories." In New topological contexts for Galois theory and algebraic geometry. Mathematical Sciences Publishers, 2009. http://dx.doi.org/10.2140/gtm.2009.16.283.

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May, J. P. "The construction of E∞ring spaces from bipermutative categories." In New topological contexts for Galois theory and algebraic geometry. Mathematical Sciences Publishers, 2009. http://dx.doi.org/10.2140/gtm.2009.16.285.

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Kapustin, Anton. "Topological Field Theory, Higher Categories, and Their Applications." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0133.

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DIKRANJAN, DIKRAN, WALTER THOLEN, and STEPHEN WATSON. "CLASSIFICATION OF CLOSURE OPERATORS FOR CATEGORIES OF TOPOLOGICAL SPACES." In Proceedings of the North-West European Category Seminar. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702418_0007.

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Bytsenko, Andrey A. "Expository remarks on topological field theories, branes, complexes and categories." In Fifth International Conference on Mathematical Methods in Physics. Trieste, Italy: Sissa Medialab, 2007. http://dx.doi.org/10.22323/1.031.0054.

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BLANCHET, CHRISTIAN. "INTRODUCTION TO QUANTUM INVARIANTS OF 3-MANIFOLDS, TOPOLOGICAL QUANTUM FIELD THEORIES AND MODULAR CATEGORIES." In Proceedings of the Summer School. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812705068_0004.

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Seepersad, Carolyn Conner, Janet K. Allen, David L. McDowell, and Farrokh Mistree. "Robust Topological Design of Cellular Materials." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/dac-48772.

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A robust topology exploration method is under development in which robust design techniques are extended to the early stages of a design process when a product’s layout or topology is determined. The performance of many designs is strongly influenced by both topology, or the geometric arrangement and connectivity of a design, and potential variations in factors such as the operating environment, the manufacturing process, and specifications of the design itself. While topology design and robust design are active research areas, little attention has been devoted to integrating the two categories of design methods. In this paper, we move toward a comprehensive robust topology exploration method by coupling robust design methods, namely, design capability indices with topology design techniques. The resulting design method facilitates efficient, effective realization of robust designs with complex topologies. The method is employed to design extruded cellular materials with robust, desirable elastic properties. For this class of materials, 2D cellular topologies are customizable and largely govern multifunctional performance. By employing robust, topological design methods, we obtain cellular material designs that are characterized by ranged sets of design specifications with topologies that reliably meet a set of design requirements and are relatively simple and robust to anticipated variability.
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Le´on, Jean-Claude, Rosalinda Ferrandes, and Franca Giannini. "Shape Processing and Reasoning for Multiple Product Views: Key Issues and Contributions to a General Framework." In ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2008. http://dx.doi.org/10.1115/esda2008-59489.

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The concept of product view and the corresponding required models is a basic constituent of a product development process. Integration across product views is addressed through an analysis of the key characteristics of current geometric modellers. Here, topological and geometric issues are identified and major shape modelling principles are studied. As a result, the core concepts of a framework for product view integration are proposed and justified. The notions of mixed shape representation and layered topological representation are briefly outlined as part of the proposed framework. Categories of operators enabling the required shape transformations are also shortly introduced as element of the proposed framework.
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Meng, Xiangdun, Feng Gao, and Jialun Yang. "The GF Sets: A New Kind of Performance Criterion of Mechanisms." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70795.

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The fundamental work of type synthesis of robot mechanisms is to research and develop the performance criterion for evaluating the characteristics of robot end-effectors and consequently come up with the classification of mechanisms. The motion characteristics of end-effectors contain translation and rotation. Traditionally, mechanisms are classified only according to the existence and quantity of these two kinds of motion characteristics without considering the succession of motion, which has remarkable influence on the topological performance property of end-effectors. In this paper, we propose the conception of rotational completeness, which describes the rotational ability of end-effectors, based on the axis movement theorem. The GF Sets are classified into three categories according to the rotational completeness of end-effectors. We enumerated all three classes of GF sets and illustrated the effectiveness of GF sets in evaluating the characteristics of robot end-effectors.
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Reports on the topic "Topological categories"

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Yan, Yujie, and Jerome F. Hajjar. Automated Damage Assessment and Structural Modeling of Bridges with Visual Sensing Technology. Northeastern University, May 2021. http://dx.doi.org/10.17760/d20410114.

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Abstract:
Recent advances in visual sensing technology have gained much attention in the field of bridge inspection and management. Coupled with advanced robotic systems, state-of-the-art visual sensors can be used to obtain accurate documentation of bridges without the need for any special equipment or traffic closure. The captured visual sensor data can be post-processed to gather meaningful information for the bridge structures and hence to support bridge inspection and management. However, state-of-the-practice data postprocessing approaches require substantial manual operations, which can be time-consuming and expensive. The main objective of this study is to develop methods and algorithms to automate the post-processing of the visual sensor data towards the extraction of three main categories of information: 1) object information such as object identity, shapes, and spatial relationships - a novel heuristic-based method is proposed to automate the detection and recognition of main structural elements of steel girder bridges in both terrestrial and unmanned aerial vehicle (UAV)-based laser scanning data. Domain knowledge on the geometric and topological constraints of the structural elements is modeled and utilized as heuristics to guide the search as well as to reject erroneous detection results. 2) structural damage information, such as damage locations and quantities - to support the assessment of damage associated with small deformations, an advanced crack assessment method is proposed to enable automated detection and quantification of concrete cracks in critical structural elements based on UAV-based visual sensor data. In terms of damage associated with large deformations, based on the surface normal-based method proposed in Guldur et al. (2014), a new algorithm is developed to enhance the robustness of damage assessment for structural elements with curved surfaces. 3) three-dimensional volumetric models - the object information extracted from the laser scanning data is exploited to create a complete geometric representation for each structural element. In addition, mesh generation algorithms are developed to automatically convert the geometric representations into conformal all-hexahedron finite element meshes, which can be finally assembled to create a finite element model of the entire bridge. To validate the effectiveness of the developed methods and algorithms, several field data collections have been conducted to collect both the visual sensor data and the physical measurements from experimental specimens and in-service bridges. The data were collected using both terrestrial laser scanners combined with images, and laser scanners and cameras mounted to unmanned aerial vehicles.
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