<p>  </p> <p>For decades, agencies have collected infrastructure condition assessment data using dedicated equipment that require substantial capital investments and staff time to operate/drive. However, these techniques are challenging to scale network wide. The United States has over 8 million lane miles of roadways which generate almost 3 trillion vehicle miles annually.  Connected vehicles can now provide real-time data on a wide range of parameters such as vehicle speed, location, lane markings, and 3 axis acceleration. This dissertation develops techniques to validate, utilize and leverage connected vehicle data for infrastructure assessment and monitoring.  </p> <p><br></p> <p>Opportunities to employ connected vehicle data were examined in the following areas: quality of lane marking edge lines, width of lanes (particularly temporary lanes in construction zones), and pavement roughness. Quality of lane markings was evaluated using embedded lane keep assist data and equipment. In 2020 and 2021 over 5000 miles of pavement markings were evaluated on Indiana interstates. Comparisons between 2020 and 2021 data showed detection increase from 80.2% to 92.3%.  Although there are no industry standards for lane keep assist data, this study demonstrated both the importance and utility of partnering with the automotive industry to develop shared vision on acceptable lane quality. </p> <p><br></p> <p>A follow-up quantitative study was performed using a LiDAR vehicle to compare LiDAR values with those that are obtained from traditional retroreflectivity measurements used for contract acceptance and maintenance decisions. A comparison of LiDAR intensity to retroreflectivity (the industry standard) on 70 miles of US-52 and US-41 in Indiana was assessed and a linear regression found that the intensity values are comparable to retroreflectivity readings with an R2 of 0.87 and 0.63 for right edge and center skip lines respectively. These results suggest that LiDAR is a viable tool for monitoring of retroreflectivity of pavement markings that are strongly correlated with existing standards, but scale much better than traditional retroreflectivity measurement techniques.</p> <p><br></p> <p>The LiDAR data also provided the opportunity to evaluate how well modern vehicles measure lane width. This dissertation reports on over 200 miles of roadway and when compared to LiDAR and field measurements had a root mean square error of 0.24 feet. This data is valuable for agencies to quickly identify system wide where lane widths fall below acceptable design standards, typically 11-feet. </p> <p> </p> <p>The final connected vehicle data set evaluated was pavement roughness and compared with traditional dedicated vehicles collecting international roughness index (IRI) data. The study evaluated a 20-mile segment in 2022, and showed a linear regression between these data sets had an R2 of over 0.7, suggesting that connected vehicle roughness data can be utilized for network level monitoring of pavement quality. Scalability of these techniques is also illustrated with graphics characterizing IRI values obtained from almost 6 million records to evaluate improvements in Indiana construction zones and over 5,800 miles of I-80 in April of 2022 and October 2022.</p> <p><br></p> <p>Although connected vehicle data for infrastructure assessment is still in its infancy, these case studies demonstrate significant opportunities for public agencies to collect selected system wide infrastructure condition in near real-time, and in many cases at a lower cost than traditional techniques. </p>

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This paper deals with the symmetric approximation numbers as well as the other types of s-numbers. Concerning the s-numbers in the Banach spaces, namely the app- roximation numbers the Kolmogorov numbers and the Gelfand numbers, we present a few of possible definitions and some of their properties. We present the symmetric approximation numbers and their relation to the other s-numbers. We also focus on the s-numbers in the quasi-Banach spaces. The situation is a bit different, as we can not use the Hahn-Banach Theorem. Therefore some of the previous definitions and properties can not be retained. Moreover we define the symmetric approximation num- bers in the quasi-Banach spaces and discuss the problematics of this definition. Finally, we deal with the Carl's inequality regarding the entropy numbers and the s-numbers. We derive the proof for the symmetric approximation numbers in both Banach and quasi-Banach case. 1

Orientadores: Alexander Kushpel, Sergio Antonio Tozoni / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T06:22:45Z (GMT). No. of bitstreams: 1 Stabile_RegisLeandroBraguim_M.pdf: 861507 bytes, checksum: 9a902b95c3b1523df6cf1e1e230b9505 (MD5) Previous issue date: 2009 / Resumo: O objetivo principal da dissertação é realizar um estudo sobre estimativas de n-larguras de conjuntos de funções suaves sobre a esfera unitária d-dimensional real. Esses conjuntos são gerados por operadores multiplicadores. Outro objetivo é desenvolver um texto em português sobre as n-larguras mais importantes, suas propriedades e suas relações. Este objetivo é realizado no primeiro capítulo. No segundo capítulo é realizado um estudo rápido e com poucas demonstrações sobre Análise Harmônica na esfera d-dimensional real. No terceiro capítulo são estudadas estimativas de médias de Levy para uma classe de normas especiais e em seguida esses resultados são aplicados no estudo de estimativas inferiores para as n-larguras de Kolmogorov e Gel'fand e superiores para a de Kolmogorov, para operadores multiplicadores gerais. No quarto e último capítulo são estudadas estimativas para n-larguras de conjuntos de funções suaves, finitamente e infinitamente diferenciáveis sobre a esfera. Várias dessas estimativas são assintoticamente exatas em termos de ordem e as constantes que determinam a ordem dessas estimativas são determinadas explicitamente. / Abstract: The purpose of this work is to study estimates of n-widths of sets of smooth functions on the d-dimensional real unitary sphere. These sets are generated by multipliers operator. Another aim is to develop a text in portuguese about the most important n-widths, your properties and relations. We do this in the first chapter. In the second chapter, we develop a brief and proof-less study about Harmonic Analysis on the d-dimensional real unitary sphere. In the third chapter, the Levy means for a class of special norms are studied and applied in the study of lower estimates for the Kolmorogov and Gel'fand's n-widths, and upper estimates for the Kolmorogov's, for general multipliers operators. In the fourth and last chapter, the estimates for the n-widths of sets of smooth functions, finitely and infinitely differentiables on the sphere are studied. Several of these estimates are asymptotically exacts in terms of order and the constants that determine the order of these estimatives are given in a explicit form. / Mestrado / Mestre em Matemática

Orientador: Sergio Antonio Tozoni / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-25T19:58:00Z (GMT). No. of bitstreams: 1 Stabile_RegisLeandroBraguim_D.pdf: 1552111 bytes, checksum: af2b74d1076ee2c6dd825049748fd3fd (MD5) Previous issue date: 2014 / Resumo: As teorias de n-larguras e de entropia foram introduzidas por Kolmogorov na década de 1930. Desde então, muitos trabalhos têm visado obter estimativas assintóticas para n-larguras e números de entropia de diferentes classes de conjuntos. Neste trabalho, investigamos n-larguras e números de entropia de operadores multiplicadores definidos sobre o toro d-dimensional. Na primeira parte, estabelecemos estimativas inferiores e superiores para n-larguras e números de entropia de operadores multiplicadores gerais. Na segunda parte, aplicamos estes resultados para operadores multiplicadores específicos, associados a conjuntos de funções finitamente e infinitamente diferenciáveis sobre o toro. Em particular, demonstramos que as estimativas obtidas são exatas em termos de ordem em diversas situações / Abstract: The theories of n-widths and entropy were introduced by Kolmogorov in the 1930s. Since then, many works aims to find estimates for n-widths and entropy numbers of different classes of sets. In this work, we investigate n-widths and entropy numbers of multiplier operators defined on the d-dimensional torus. In the first part, upper and lower bounds are established for n-widths and entropy numbers of general multiplier operators. In the second part, we apply these results to specific multiplier operators, associated with sets of finitely and infinitely differentiable functions on the torus. In particular, we prove that, the estimates obtained are order sharp in various situations / Doutorado / Matematica / Doutor em Matemática

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<p>NR 20140805</p>

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Thesis (MScEng (Civil Engineering))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: Strain Hardening Cement-based Composite (SHCC) is part of the High Performance Fibre Reinforced Cement-based Composite (HPFRCC) family and is a relative new concrete composite. This Fibre Reinforced Cement-based Composite (FRCC) contains randomly distributed short fibres and when subjected to a uni-axial tensile load multiple cracking occurs. The multiple cracking generates fine cracks which are normally smaller than 100 μm and achieve a strain capacity of more than 5 %. There are limited publications regarding the research of sustained tensile tests on SHCC and especially the cracking behaviour of SHCC under quasi-static uni-axial as well as sustained tensile loads. The cracking behaviour is described as the average crack width, number of cracks and descriptive statistical properties which could be used to represent the distribution of the multiple fine cracks under uni-axial tension. There are two types of tests that were under consideration to determine the cracking behaviour of SHCC. The first is quasi-static uniaxial tensile tests and the second is sustained tensile tests. The latter was dependant on the uni-axial tensile tests in terms of the sustained load applied. The sustained loads ranged from 40 % to 80 % of the ultimate tensile resistance recorded from the uni-axial tensile tests that correspond with a strain rate of 0.001 /s. Different strain rates were used for the uni-axial tensile tests to determine the effect on the cracking behaviour. The cracking behaviour was determined with the aid of a non-contact optical 3D digital deformation measuring device called ARAMIS. The content of this thesis gives a background study of the cracking behaviour and relevant research performed on SHCC under certain loads as well as some literature about the timedependant effects of a cement-based composite. The functioning of the device called ARAMIS is explained as well as the resulting effects of this device on the preparation of the test specimens. The experimental framework for the uni-axial and sustained tensile tests is discussed. Thereafter, the experimental results of the tests are depicted and discussed. The results shed some light on the basic material properties such as the average ultimate stress and average ultimate strain, Young’s modulus, etc. for the quasi-static tensile tests as well as shrinkage and creep of SHCC. The cracking behaviour such as the average crack width, number of cracks, the variance and skewness of the distribution of the crack widths in the test specimens for the quasi-static uni-axial and sustained tensile tests are depicted and discussed. The cracking behaviour when subjected to uni-axial tensile tests with different strain rates is significantly governed by the formation of new cracks and the average crack width remains small with increase in strain. There is no significant difference for the cracking behaviour found when subjected to different strain rates. However, when SHCC is subjected to a sustained load then the average crack width is dependant on the number of cracks that form over time as well as the load level. The formation of fewer and wider cracks was observed for specimens loaded at average 40 % of the ultimate tensile resistance stress, however at loading percentages of higher than 65 % more cracks developed which resulted in a smaller average crack width. / AFRIKAANSE OPSOMMING: Vervorming Verharding Sement gebaseerde samestelling “Strain Hardening Cement-based Composite” (SHCC) is deel van die familie van “High Performance Fibre Reinforced Cement-based Composite” (HPFRCC) en is ʼn relatiewe nuwe beton samestelling. Hierdie vesel versterkte sement gebaseerde beton bevat willekeurig verspreide kort vesels en veelvoudige klein krake vorm onder monotoniese trekkragte. Hierdie veelvoudige klein krake is minder as 100 μm wyd en lei tot ʼn vervorming van meer as 5 %. Daar is ʼn tekort aan navorsing oor die kruip van SHCC sowel as die kraak gedrag van hierdie sement gebaseerde samestelling onderhewig aan trek. Die kraak gedrag word beskryf as die gemiddelde kraakwydte, aantal krake en ʼn paar beskrywende statistiese parameters. Hierdie kraak gedrag parameters kan gebruik word om ʼn verdeling te kan weergee van die veelvoudige klein krake onder ʼn trek belasting. Twee tipes toetse was uitgevoer om die kraak gedrag te beskryf. Die eerste tipe toets was monotoniese trek toetse en die tweede tipe was kruip toetse. Die tweede toets was afhanklik van die monotoniese trek toetse in terme van die belasting wat gebruik was vir die kruip toetse. Die belasting was gevarieer vanaf 40 % tot 80 % van die breekbelasting wat bepaal is met die monotoniese trektoetse wat ooreenstem met ʼn vervorming tempo van 0.001 /s. Verskillende vervorming tempo’s vir die monotoniese trektoetse was uitgevoer om te bepaal wat die effek is op die kraak gedrag. Die kraak gedrag was bepaal met behulp van ʼn geen-kontak optiese 3D digitale deformasie meet instrument genoem ARAMIS. Die inhoud van die tesis bevat ʼn kort opsoming oor ʼn agtergrond studie van die kraak gedrag en relevante navorsing oor vesel versterkte sement gebaseerde beton, sowel as literatuur oor die tydafhanklike effekte van ʼn sement gebaseerde samestelling. Die beheer en gebruik van die meet instrument ARAMIS word verduidelik, sowel as die effek van hierdie masjien op die voorbereiding vir die eksperimente. Die eksperimentele uiteensetting vir die monotoniese en kruip toetse word beskryf. Daarvolgens is die resultate van die eksperimentele toetse getoon en verduidelik. Die resultate verduidelik die basiese materiaal eienskappe, byvoorbeeld die gemiddelde breekspanning met die ooreenkomstige breekvervorming, Young’s modulus en so voorts vir die monotoniese trektoetse, sowel as eienskappe met betrekking tot krimp en kruip van SHCC. Die kraak gedrag naamlik die gemiddelde kraakwydte, aantal krake per meter, variansie en die skuinsheid van die ontwikkelde krake met die toets proefstukke vir die monotoniese en kruip trek toetse word weergegee en verduidelik. Die kraak gedrag van SHCC wanneer getoets word met verskillende monotoniese trektoets tempo’s word beheer deur die ontwikkeling van nuwe krake en die gemiddelde kraakwydte is beduidend laag met toenemende vervorming. Daar is geen beduidende verskil in die kraak gedrag ten opsigte van die verskillende monotoniese trek tempo’s nie. In teendeel, wanneer SHCC belas word met ʼn konstante las oor tyd word die gemiddelde kraakwydte beheer deur die ontwikkeling van nuwe krake sowel as die belasting wat aangewend is. Onder ʼn belasting van so laag as 40 % van die breekbelasting vorm daar minder krake, maar met ʼn groter gemiddelde kraakwydte. Wanneer belas word met meer as 65 % van die breekbelasting vorm meer krake wat lei tot ʼn kleiner gemiddelde kraakwydte.