Дисертації з теми "Reduced method"
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Garlapati, Revanth Reddy. "Reduced basis method for Boltzmann equation." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/39218.
Повний текст джерелаАнотація:
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006.Includes bibliographical references (p. 103-106).
The main aim of the project is to solve the BGK model of the Knudsen parameterized Boltzmann equation which is 1-d with respect to both space and velocity. In order to solve the Boltzmann equation, we first transform the original differential equation by replacing the dependent variable with another variable, weighted with function t(y); next we obtain a Petrov Galerkin weak form of this new transformed equation. To obtain a stable and accurate solution of this weak form, we perform a transformation of the velocity variable y, such that the semi-infinite domain is mapped into a finite domain; we choose the weighting function t(y), to balance contributions at infinity. Once we obtain an accurate and well defined finite element solution of the problem. The next step is to perform the reduced basis analysis of the equation using these accurate finite element solutions. We conclude the project by verifying that the orthonormal reduced Basis method based on the greedy algorithm converges rapidly over the chosen test space.
by Revanth Reddy Garlapati.
S.M.
2
Badrous, Therese, and Ebba Lund. "Reduced stress method for steel in class 4 cross-sections : Evaluation of the reduced stress method for a railway bridge." Thesis, KTH, Byggteknik och design, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-302525.
Повний текст джерелаАнотація:
The effective cross-section method, also called reduced cross-section method is generally used for steel in class 4 cross-sections in considering local buckling. This method is a bit complicated and time consuming, which often leads to engineers not using profiles in class 4 cross-sections. The reduced stress method is an alternative method for handling slender steel cross-sections. These two methods are described in the Eurocode, of which the latter is less described. The national annex states that the reduced stress method should not be used, however, without explanation to the general recommendation. This study is a comparison of the two different methods and is intended to provide a better understanding of the reduced stress method. The calculation process and design for steel profiles in class 4 cross-sections can in this way become more efficient. This is done by determining when it is most profitable to use the reduced stress method instead of the effective cross-section method. Thus, can the use of profiles in class 4 cross-sections become a more obvious choice in the industry. This study considered a simply supported I-beam in an open railway bridge exposed to bending moment where the same conditions were investigated for each method. The effective crosssection method is implemented by reducing the cross-sectional area and was calculated manually. In the reduced stress method, it is the yield stress that is reduced. The reduced stress method was analyzed both through FEM and manual calculations in this study. The result showed that the reduced stress method performed through FEM gave a similar result as the effective cross-section method, which makes it an appealing method. The reduced stress method with manual calculation, however, gave a more conservative result. These methods are relativelydifferent and recommendations for each method are presented in this report.Idag behandlas ståltvärsnitt i tvärsnittklass 4 generellt med hjälp av metoden effektivt tvärsnitt för att beakta lokal buckling. Metoden är en aning komplicerad och tidskrävande, vilket leder till att konstruktörer överlag inte använder profiler i tvärsnittsklass 4. Reducerad spänning är en alternativ metod för hantering av slanka ståltvärsnitt. Dessa två metoder beskrivs i Eurokoden varav den sist nämnda mer kortfattat. I den nationella bilagan står det att metoden reducerad spänning ej bör användas dock utan motivering till det allmänna rådet. Studien är en jämförelse av de två olika metoderna och är ämnad till att ge en bättre förståelse av metoden reducerad spänning. Således kan beräkningsgången samt projektering för stålprofiler i tvärsnittsklass 4 effektiviseras. Detta genom att avgöra när det är mest lönsamt att använda reducerad spänning framför effektivt tvärsnitt. Följaktligen kan användning av profiler i tvärsnittsklass 4 bli ett mer självklart val i branschen. Denna studie omfattade en fritt upplagd I-balk i en öppen järnvägsbro utsatt för böjande moment där samma förutsättningar har undersökts för respektive metod. Effektivt tvärsnitt går ut på att reducera en tvärsnittsarea och har utförts via handberäkningar. I metoden reducerad spänning är det sträckgränsen som reduceras. I denna studie undersöktes reducerad spänningsmetoden via FEM samt handberäkningar. Resultatet påvisade att metoden reducerad spänning utförd via FEM gav ett liknande resultat som metoden effektivt tvärsnitt, vilket gör det till en attraktiv metod. Reducerad spänning via handberäkning gav dock ett mer konservativt resultat. Metoderna är relativt olika och rekommendationer för tillämpning av respektive metod presenteras i denna rapport.
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Wahl, Jean-Baptiste. "The Reduced basis method applied to aerothermal simulations." Thesis, Strasbourg, 2018. http://www.theses.fr/2018STRAD024/document.
Повний текст джерелаАнотація:
Nous présentons dans cette thèse nos travaux sur la réduction d'ordre appliquée à des simulations d'aérothermie. Nous considérons le couplage entre les équations de Navier-Stokes et une équations d'énergie de type advection-diffusion. Les paramètres physiques considérés nous obligent à considéré l'introduction d'opérateurs de stabilisation de type SUPG ou GLS. Le but étant d'ajouter une diffusion numérique dans la direction du champs de convection, afin de supprimer les oscillations non-phyisques. Nous présentons également notre stratégie de résolution basée sur la méthode des bases réduite (RBM). Afin de retrouver une décomposition affine, essentielle pour l'application de la RBM, nous avons implémenté une version discrète de la méthode d'interpolation empirique (EIM). Cette variante permet de la construction d'approximation affine pour des opérateurs complexes. Nous utilisons notamment cette méthode pour la réduction des opérateurs de stabilisations. Cependant, la construction des bases EIM pour des problèmes non-linéaires implique un grand nombre de résolution éléments finis. Pour pallier à ce problème, nous mettons en oeuvre les récents développement de l'algorithme de coconstruction entre EIM et RBM (SER)We present in this thesis our work on model order reduction for aerothermal simulations. We consider the coupling between the incompressible Navier-Stokes equations and an advection-diffusion equation for the temperature. Since the physical parameters induce high Reynolds and Peclet numbers, we have to introduce stabilization operators in the formulation to deal with the well known numerical stability issue. The chosen stabilization, applied to both fluid and heat equations, is the usual Streamline-Upwind/Petrov-Galerkin (SUPG) which add artificial diffusivity in the direction of the convection field. We also introduce our order reduction strategy for this model, based on the Reduced Basis Method (RBM). To recover an affine decomposition for this complex model, we implemented a discrete variation of the Empirical Interpolation Method (EIM) which is a discrete version of the original EIM. This variant allows building an approximated affine decomposition for complex operators such as in the case of SUPG. We also use this method for the non-linear operators induced by the shock capturing method. The construction of an EIM basis for non-linear operators involves a potentially huge number of non-linear FEM resolutions - depending on the size of the sampling. Even if this basis is built during an offline phase, we usually can not afford such expensive computational cost. We took advantage of the recent development of the Simultaneous EIM Reduced basis algorithm (SER) to tackle this issue
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Pomplun, Jan [Verfasser]. "Reduced basis method for electromagnetic scattering problems / Jan Pomplun." Berlin : Freie Universität Berlin, 2010. http://d-nb.info/1024541436/34.
Повний текст джерела
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Pau, George Shu Heng. "Reduced basis method for quantum models of crystalline solids." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/40376.
Повний текст джерелаАнотація:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.Includes bibliographical references (p. 203-213).
Electronic structure problems in solids usually involve repetitive determination of quantities of interest, evaluation of which requires the solution of an underlying partial differential equation. We present in this thesis the application of the reduced basis method in accurate and rapid evaluations of outputs associated with some nonlinear eigenvalue problems related to electronic structure calculations. The reduced basis method provides a systematic procedure by which efficient basis sets and computational strategies can be constructed. The essential ingredients are (i) rapidly convergent global reduced basis approximation spaces; (ii) an offline-online computational procedure to decouple the generation and projection stages of the approximation process; and (iii) inexpensive a posteriori error estimation procedure for outputs of interest. We first propose two strategies by which we can construct efficient reduced basis approximations for vectorial eigensolutions - solutions consisting of several eigenvectors. The first strategy exploits the optimality of the Galerkin procedure to find a solution in the span of all eigenvectors at N judiciously chosen samples in the parameter space.
(cont.) The second strategy determines a solution in the span of N vectorial basis functions that are pre-processed to better represent the smoothness of the solution manifold induced by the parametric dependence of the solutions. We deduce from numerical results conditions in which these approximations are rapidly convergent. For linear eigenvalue problems, we construct a posteriori asymptotic error estimators for our reduced basis approximations - extensions on existing work in algebraic eigenvalue problems. We further construct efficient error estimation procedures that allow efficient construction of reduced basis spaces based on the "greedy" sampling procedure. We extend our methods to nonlinear eigenvalue problems, utilizing the empirical interpolation method. We also provide a more efficient construction procedure for the empirical interpolation method. Finally, we apply our methods to two problems in electronic structure calculations - band structure calculations and electronic ground state calculations. Band structure calculations involve approximations of linear eigenvalue problems; we demonstrate the applicability of our methods in the many query limit with several examples related to determination of spectral properties of crystalline solids.
(cont.) Electronic ground state energy calculations based on Density Functional Theory involve approximations of nonlinear eigenvalue problems; we demonstrate the potential of our methods within the context of geometry optimization.
by George Shu Heng Pau.
Ph.D.
6
Purdie, Stuart. "Magnetic ordering in systems of reduced dimensionality." Thesis, University of St Andrews, 2005. http://hdl.handle.net/10023/12927.
Повний текст джерелаАнотація:
The magnetic behaviour of thin films of (111) FCC structures and (0001) corundum structured materials were studied by the mean field analysis and some Monte Carlo simulation. These models were conditioned on a mapping from first principles calculations to the Ising model. The effect of the suggested octopolar reconstruction for the polar (111) surfaces of FCC was also examined.
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Kumar, Ashutosh. "Towards a Reduced-Scaling Method for Calculating Coupled Cluster Response Properties." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/83846.
Повний текст джерелаАнотація:
One of the central problems limiting the application of accurate {em ab initio} methods to large molecular systems is their high computational costs, i.e., their computing and storage requirements exhibit polynomial scaling with the size of the system. For example, the coupled cluster singles and doubles method with the perturbative inclusion of triples: the CCSD(T) model, which is considered to be the ``gold standard'' of quantum chemistry scales as ${cal O}(N^7)$ in its canonical formulation, where $N$ is a measure of the system size. However, the steep scaling associated with these methods is unphysical since the property of dynamic electron correlation or dispersion (for insulators) is local in nature and decays as $R^{-6}$ power of distance. Different reduced-scaling techniques which attempt to exploit this inherent sparsity in the wavefunction have been used in conjunction with the coupled cluster theory to calculate ground-state properties of molecular systems with hundreds of heavy atoms in reasonable computational time. However, efforts towards extension of these methods for describing response properties like polarizabilities, optical rotations, etc., which are related to the derivative of the wavefunction with respect to external electric or/and magnetic fields, have been fairly limited and conventional reduced-scaling algorithms have been shown to yield large and often erratic deviations from the full canonical results. Accurate simulation of response properties like optical rotation is highly desirable
as it can help the experimental chemists in understanding the structure-activity relationship
of different chiral drug candidates. In this work, we identify the reasons behind the unsatisfactory performance of the pair natural orbital (PNO) based reduced-scaling approach for calculating linear response properties at the coupled cluster level of theory and propose novel modifications, which we refer to as PNO++, (A. Kumar and T. D. Crawford. Perturbed Pair Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, {em manuscript in preparation}) that can provide the necessary accuracy at significantly lower computational costs. The motivation behind the PNO++ approach came from our works on the (frozen) virtual natural orbitals (FVNO), which can be seen as a precursor to the concept of PNOs (A. Kumar and T. D. Crawford. Frozen Virtual Natural Orbitals for Coupled-Cluster Linear-Response Theory. {em J. Phys. Chem. A}, 2017, 121(3), pp 708 716) and the improved FVNO++ method (A. Kumar and T. D. Crawford. Perturbed Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, {em manuscript in preparation}). The essence of these modified schemes (FVNO++ and PNO++) lie in finding suitable field perturbed one-electron densities to construct ``perturbation aware" virtual spaces which, by construction, are much more compact for describing response properties, making them ideal for applications on large molecular systems.Ph. D.
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Skoglund, Oskar, and Daniel Samvin. "Design of slender steel members : A comparison between the reduced stress method and the effective width method." Thesis, KTH, Bro- och stålbyggnad, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-189029.
Повний текст джерелаАнотація:
As of now, the most common way in Sweden, to address the issue of local buckling of steelstructures is through the procedure called the effective width method. A less commonprocedure for dealing with local buckling is the reduced stress method. The benefit of thelatter method is that, when combined with finite element analysis, results in a less tediousdesign process. However, this method is often labelled as a method that results in anoverconservative design. Therefore, the purpose of this report is to compare and evaluate thereduced stress method against the effective width method and nonlinear finite elementmethod. The nonlinear FE-analyses are performed with intention of simulating the realbehaviour of the structure and serve as a reference for the other two methods. The comparisonis conducted through a series of analyses, on different steel members with various loadconfigurations and slenderness in order to include the most common cases in the constructionindustry. This report resulted in recommendations for when the reduced stress method couldbe a relevant design procedure, with emphasis on providing reliable and accurate resultscompared to FE-analyses. Furthermore, the report resulted in proposed further studies, bothregarding the improvement of the reduced stress method and other structural elements thatshould be studied. The result from the report indicates that the reduced stress method can beused when the effect of patch loading is small. Furthermore, it is recommended to obtain thecritical stresses from a linear finite element analysis rather than from hand calculations, as tonot end up with over-conservative results.I Sverige behandlas problemet med lokal buckling av stålkonstruktioner vanligtvis med hjälpav den effektiva bredd metoden, vilket är en dimensionergsmetod som återfinns i Eurocode.En ytterligare dimensionerings metod för lokal buckling som presenteras i Eurocode är denreducerade spänningsmetoden. Den senare nämnda metoden är fördelaktig då den kombinerasmed linjära finita element analyser, vilket resulterar i en mindre tidskrävandedimensioneringsprocess. Dock är metoden känd för att ofta resultera i överdimensioneradekonstruktioner, vilket bidragit till att mindre antal konstruktörer använder sig av denna metod.Syftet med denna rapport blir därmed att jämföra och utvärdera den reduceradespänningsmetoden gentemot den effektiva bredd metoden och olinjär finita element metoden.De olinjära finita element analyserna genomfördes med syfte att simulera det verkligabeteendet och för att sedan jämföra dessa resultat med de två andra metoderna. Analyser harutförts på flera stålbalkar med olika lastkombinationer och slankhet för att inkludera devanligaste fallen inom byggindustrin. Dessutom har det tagits fram några rekommendationerför användningen av metoderna och dessa är presenterade med avseende på de erhållnaresultaten. Rekommendationer för den reducerade spänningsmetoden har presenterats ochytterligare studier gällande dessa metoder och andra konstruktionselement har föreslagits. Deslutsatser som kunde dras är att den reducerade spänningsmetoden kan användas förkonstruktioner som inte påverkas i allt för stor grad av intryckning. För att ge tillförliterligaresultat så rekommenderas att kritiska spänningar erhålles från linjära finita element analyser.
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Ozgur, Soner. "Reduced Complexity Sequential Monte Carlo Algorithms for Blind Receivers." Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/10518.
Повний текст джерелаАнотація:
Monte Carlo algorithms can be used to estimate the state of a system given relative observations. In this dissertation, these algorithms are applied to physical layer communications system models to estimate channel state information, to obtain soft information about transmitted symbols or multiple access interference, or to obtain estimates of all of these by joint estimation.
Initially, we develop and analyze a multiple access technique utilizing mutually orthogonal complementary sets (MOCS) of sequences. These codes deliberately introduce inter-chip interference, which is naturally eliminated during processing at the receiver. However, channel impairments can destroy their orthogonality properties and additional processing becomes necessary.
We utilize Monte Carlo algorithms to perform joint channel and symbol estimation for systems utilizing MOCS sequences as spreading codes. We apply Rao-Blackwellization to reduce the required number of particles. However, dense signaling constellations, multiuser environments, and the interchannel interference introduced by the spreading codes all increase the dimensionality of the symbol state space significantly. A full maximum likelihood solution is computationally expensive and generally not practical. However, obtaining the optimum solution is critical, and looking at only a part of the symbol space is generally not a good solution. We have sought algorithms that would guarantee that the correct transmitted symbol is considered, while only sampling a portion of the full symbol space. The performance of the proposed method is comparable to the Maximum Likelihood (ML) algorithm. While the computational complexity of ML increases exponentially with the dimensionality of the problem, the complexity of our approach increases only quadratically.
Markovian structures such as the one imposed by MOCS spreading sequences can be seen in other physical layer structures as well. We have applied this partitioning approach with some modification to blind equalization of frequency selective fading channel and to multiple-input multiple output receivers that track channel changes.
Additionally, we develop a method that obtains a metric for quantifying the convergence rate of Monte Carlo algorithms. Our approach yields an eigenvalue based method that is useful in identifying sources of slow convergence and estimation inaccuracy.
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Schiela, Anton. "The control reduced interior point method : a function space oriented algorithmic approach /." München : Hut, 2006. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=015438070&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
Повний текст джерела
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Vidal, Codina Ferran. "A reduced-basis method for input-output uncertainty propagation in stochastic PDEs." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/82417.
Повний текст джерелаАнотація:
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2013.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 123-132).
Recently there has been a growing interest in quantifying the effects of random inputs in the solution of partial differential equations that arise in a number of areas, including fluid mechanics, elasticity, and wave theory to describe phenomena such as turbulence, random vibrations, flow through porous media, and wave propagation through random media. Monte-Carlo based sampling methods, generalized polynomial chaos and stochastic collocation methods are some of the popular approaches that have been used in the analysis of such problems. This work proposes a non-intrusive reduced-basis method for the rapid and reliable evaluation of the statistics of linear functionals of stochastic PDEs. Our approach is based on constructing a reduced-basis model for the quantity of interest that enables to solve the full problem very efficiently. In particular, we apply a reduced-basis technique to the Hybridizable Discontinuous Galerkin (HDG) approximation of the underlying PDE, which allows for a rapid and accurate evaluation of the input-output relationship represented by a functional of the solution of the PDE. The method has been devised for problems where an affine parametrization of the PDE in terms of the uncertain input parameters may be obtained. This particular structure enables us to seek an offline-online computational strategy to economize the output evaluation. Indeed, the offline stage (performed once) is computationally intensive since its computational complexity depends on the dimension of the underlying high-order discontinuous finite element space. The online stage (performed many times) provides rapid output evaluation with a computational cost which is several orders of magnitude smaller than the computational cost of the HDG approximation. In addition, we incorporate two ingredients to the reduced-basis method. First, we employ the greedy algorithm to drive the sampling in the parameter space, by computing inexpensive bounds of the error in the output on the online stage. These error bounds allow us to detect which samples contribute most to the error, thereby enriching the reduced basis with high-quality basis functions. Furthermore, we develop the reduced basis for not only the primal problem, but also the adjoint problem. This allows us to compute an improved reduced basis output that is crucial in reducing the number of basis functions needed to achieve a prescribed error tolerance. Once the reduced bases have been constructed, we employ Monte-Carlo based sampling methods to perform the uncertainty propagation. The main achievement is that the forward evaluations needed for each Monte-Carlo sample are inexpensive, and therefore statistics of the output can be computed very efficiently. This combined technique renders an uncertainty propagation method that requires a small number of full forward model evaluations and thus greatly reduces the computational burden. We apply our approach to study the heat conduction of the thermal fin under uncertainty from the diffusivity coefficient and the wave propagation generated by a Gaussian source under uncertainty from the propagation medium. We shall also compare our approach to stochastic collocation methods and Monte-Carlo methods to assess the reliability of the computations.
by Ferran Vidal-Codina.
S.M.
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Glenn, Russell David. "A reduced order controller design method based on the Youla parameterization of all stabilizing controllers." Ohio : Ohio University, 1995. http://www.ohiolink.edu/etd/view.cgi?ohiou1174396903.
Повний текст джерела
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Yamazato, Takaya, Iwao Sasase, and Shinsaku Mori. "A New Viterbi Algorithm with Adaptive Path Reduction Method." IEICE, 1993. http://hdl.handle.net/2237/7839.
Повний текст джерела
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Brand, Jason M. "Biaxial Material Design Method for the ReducedAperture Waveguide Model." Wright State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=wright1421064567.
Повний текст джерела
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Lison-Pick, Mandy. "Accepting a reduced self after acute trauma." Thesis, Curtin University, 2011. http://hdl.handle.net/20.500.11937/201.
Повний текст джерелаАнотація:
Disability associated with loss of limb function following major/minor trauma is a life-changing phenomenon of global significance which poses a heavy burden on healthcare systems, communities and individuals. While there is a voluminous and growing body of knowledge on disabilities and chronic illness, little attention has been given to the short and long-term experiences of those living with loss of limb function and disability following acute major and minor trauma. The aim of this thesis is to develop a substantive theory that describes the phenomenon of living with disabilities resulting from a loss of limb function from acute minor or major trauma.Data were obtained from face-to-face interviews with 15 consenting participants aged between 18-45 years who had lost limb function from acute major/minor trauma all of whom were attending the Pain Management Centre of a major teaching hospital in Western Australia. Four clinical practitioners (who were classed as experts in their field) were also interviewed to clarify the practices the participants discussed so an all round picture could be given and analysed. Data analysis was conducted using the constant comparative technique of the Grounded Theory Method. The results indicate that the basic social problem was Loss of Self and developed from either a sudden or gradual loss of limb function as a result of acute trauma. This trauma had a biopsychosocial impact as the participant’s hospitalisations, surgical procedures, extended rehabilitation programs and resultant disability reduced the self.The basic social process experienced was recognised as Accepting a Reduced Self appearing in three stages: Floundering, Treading Water and Wading to Shore. However these stages were strongly influenced by various modifying conditions such as their persistent pain, the availability of a support crew, the type of trauma experienced and the length of time since injury. It was concluded that disabilities related to loss of limb function can occur following acute major or minor trauma. The impairment the participants experienced affected all aspects of their lives and that of their partners, family and friends as most of them continued to struggle with their disability, either biologically, psychologically or socially. The findings of this thesis point to the importance of more research into designing care and offering ongoing support services to provide long term care for this vulnerable, disabled population.
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Names, Benjamin Joseph. "An Efficient Reduced Order Modeling Method for Analyzing Composite Beams Under Aeroelastic Loading." Thesis, Virginia Tech, 2016. http://hdl.handle.net/10919/71676.
Повний текст джерелаАнотація:
Composite materials hold numerous advantages over conventional aircraft grade metals. These include high stiffness/strength-to-weight ratios and beneficial stiffness coupling typically used for aeroelastic tailoring. Due to the complexity of modeling composites, designers often select safe, simple geometry and layup schedules for their wing/blade cross-sections. An example of this might be a box-beam made up of 4 laminates, all of which are quasi-isotropic. This results in neglecting more complex designs that might yield a more effective solution, but require a greater analysis effort.
The present work aims to show that the incorporation of complex cross-sections are feasible in the early design process through the use of cross-sectional analysis in conjunction with Timoshenko beam theory. It is important to note that in general, these cross-sections can be inhomogeneous: made up of any number of various materials systems. In addition, these materials could all be anisotropic in nature. The geometry of the cross-sections can take on any shape. Through this reduced order modeling scheme, complex structures can be reduced to 1 dimensional beams. With this approach, the elastic behavior of the structure can be captured, while also allowing for accurate 3D stress and strain recovery. This efficient structural modeling would be ideal in the preliminary design optimization of a wing structure. Furthermore, in conjunction with an efficient unsteady aerodynamic model such as the doublet lattice method, the dynamic aeroelastic stability can also be efficiently captured.
This work introduces a comprehensively verified, open source python API called AeroComBAT (Aeroelastic Composite Beam Analysis Tool). By leveraging cross-sectional analysis, Timoshenko beam theory, and unsteady doublet-lattice method, this package is capable of efficiently conducting linear static structural analysis, normal mode analysis, and dynamic aeroelastic analysis. AeroComBAT can have a significant impact on the design process of a composite structure, and would be ideally implemented as part of a design optimization.Master of Science
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Gavros, Athanasios. "Use of the Reduced Precision Redundancy (RPR) method in a radix4 FFT implementation." Thesis, Monterey, California. Naval Postgraduate School, 2010. http://hdl.handle.net/10945/5162.
Повний текст джерелаАнотація:
Approved for public release; distribution is unlimitedReduced precision redundancy (RPR), as a new method for improving fault tolerance in FPGAs, appears promising in replacing triple modular redundancy (TMR) to prevent the single event effects due to radiation in arithmetic processes. As a test of this approach, the RPR technique was used to implement a Radix-4 fast Fourier transform (FFT). This design was implemented in a Xilinx Virtex 2 FPGA in order to find the possible gain in speed and power as compared to the TMR method. This thesis deals with a 64-point Radix-4 in-place FFT, based on an improved FFT algorithm. The whole FFT structure was implemented based on self-designed modules and by manipulating the embedded Virtex II FPGA's modules. The point was to create a fast and small FFT module that could be altered according to specific application requirements. The implementation of the FFT was successful, managing to handle data in real time at a speed of 134MHz. Based on this FFT design, the next challenge was the implementation of TMR and RPR modules. The first attempt was the TMR structure, implemented by creating three identical replicas of the FFT and installing a voter per FFT stage. This implementation was unsuccessful due to space limitations. The next step was the alteration of the existing FFT and the creation of a smaller 8 x 8 bit butterfly module for the RPR structure. After the successful completion of this step, implementation of a RPR module with an 8/32 degree was commenced. Ambiguities and inefficient radiation protection were identified in this implementation. Finally, adopting a new RPR approach and a higher degree of 14/32, a smooth and correct RPR module was created that could work in real time, and handle data at a speed of 163MHz. Both TMR and RPR with a degree of 14/32 methods were compared, confirming the RPR's advantage in power consumption and in occupied FPGA's resources.
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Syrén, Ludvig. "A method for introducing flexibility in rigid multibodies from reduced order elastic models." Thesis, Umeå universitet, Institutionen för fysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-160417.
Повний текст джерелаАнотація:
In multibody dynamics simulation of robots and vehicles it is common to model the systems as being composed of mainly rigid bodies with articulation joints. With the trend to more lightweight robots, however, the structural flexibility of the robots link’s needs to be considered for realistic dynamic simulations. The link’s geometries are complex and finite element models (FEM) are required to compute the deformations. However, FEM includes too many degrees of freedom for time-efficient dynamics simulation. A popular method is to generate reduced order models from the FE models, but with much fewer degrees of freedom, for fast and precise simulations. In this thesis a method for introducing reduced order models in rigid multibody systems was developed. The method is to divide a rigid body into two rigid bodies. Their relative movement is described by a six degree of freedom restoration force, determined with a reduced order model from Guyan reduction (static condensation). The method was validated for quasistatic deformation of a homogenous beam, a robot link arm with a more complex geometry and in multibody dynamics simulations. Finally the method was tested in simulation of a complete ABB robot with joint actuators, and any significant differences in the motion of the robot tool centre point due to replacing a rigid link arm by a flexible one was demonstrated.The method show good results for computing deformations of the homogenous beam, of the link arm and in the multibody simulation. The differences observed in simulation of a complete robot was expected and demonstrated the method to be applicable in robotic simulations.
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Hammerschmidt, Martin [Verfasser]. "Optical simulation of complex nanostructured solar cells with a reduced basis method / Martin Hammerschmidt." Berlin : Freie Universität Berlin, 2016. http://d-nb.info/1106250745/34.
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Tan, Yong Kwang Alex. "Reduced basis method for 2nd order wave equation : application to one-dimensional seismic problem." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/39209.
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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006.MIT Institute Archives copy: pages 93 and 94 bound in reverse order.
Includes bibliographical references (p. 93-95).
In this thesis, we solve the 2nd order wave equation, which is hyperbolic and linear in nature, to determine the pressure distribution for a one-dimensional seismic problem with smooth initial pressure and rate of pressure change with time. With Dirichlet and Neumann boundary conditions, the pressure distribution is solved for a total of 500 time steps, which is slighter more than a periodic cycle. Our focus is on the dependence of the output, the average surface pressure as it varies with time, on the system parameters ,u, which consist of the earthquake source x8 and the occurring time T. The reduced basis method, the offline-online computational procedures and the associated a posteriori error estimation are developed. We have shown that the reduced basis pressure distribution is an accurate approximation to the finite element pressure distribution. The greedy algorithm, the procedure of selecting the basis vectors which span the reduced basis space, works reasonably well although a period of slow convergence is experienced: this is because the finite element pressure distribution along the edges of the earthquake source-time space are fairly "unique" and cannot be accurately represented as a linear combination of the existing basis vectors;
(cont.) hence, the greedy algorithm has to bring these "unique" finite element pressure distribution into the reduced basis space individually, accounting for the slow convergence rate. Lastly, applying the online stage instead of the finite element method does not result in a reduction of computational cost: the dimension of the finite element space Af = 200 is comparable with the dimension of the reduced basis space N = 175; however, when the two-dimensional model problem is run, the dimension of the finite element space is A = 3.98 x .04 while the dimension of the reduced basis space is N = 267 and the online stage is around 62.2 times faster then the finite element method. The proposition for the a posteriori error estimation developed shows that the maximum effectivity. the maximum ratio of the error bound over the norm of the reduced basis error, is of magnitude O(103) and increases rapidly when the tolerance is lower. However, this high value is due to the norm of the reduced basis error having a low value and hence not a cause for concern. Furthermore, the ratio of the maximum error bound over the maximum norm of the reduced basis error has a constant magnitude of only 0(102).
(cont.) Lastly, the maximum output effectivity is significantly larger than the maximum effectivity of the pressure distribution due to a conservative bound for the dual contribution. The offline-online computational procedures work well in determining the reduced basis pressure distribution. However, during the a posteriori error estimation, heavy canceling of the various offline stage matrices results in small values for the square of the dual norm of the residuals which decreases as the tolerance is lowered. When the tolerance is of magnitude 0(10-6), the square of the dual norm of the residuals is of magnitude 0(10-14) which is very close to machine precision. Hence, precision error sets in and the offline-online computational procedures break down. Finally, the inverse problem works reasonably well, giving a "possibility region" of the set of system parameters where the actual system parameters may reside. We note that at least 9 time steps should be selected for observation to ensure that the rising and dropping region of the output is detected. Lastly, the greater the measured field error, the larger the "possibility region" we obtain.
by Tan Yong Kwang, Alex.
S.M.
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Ruchi, Sangeetika. "Computational Modeling of Laser Therapy of Port-Wine Stains- Based on Reduced Scattering Method." University of Cincinnati / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1428070493.
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Dcunha, Ruhee Lancelot. "Towards an Improved Method for the Prediction of Linear Response Properties of Small Organic Molecules." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/104677.
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Quantum chemical methods to predict experimental chiroptical properties by solving the time-dependent Schrödinger equation are useful in the assignment of absolute configurations. Chiroptical properties, being very sensitive to the electronic structure of the system, require highly-accurate methods on the one hand and on the other, need to be able to be computed with limited computational resources.
The calculation of the optical rotation in the solution phase is complicated by solvent effects. In order to capture those solvent effects, we present a study that uses conformational averaging and time-dependent density functional theory calculations that incorporate solvent molecules explicitly in the quantum mechanical region. While considering several controllable parameters along which the system's optical rotation varies, we find that the sampling of the dynamical trajectory and the density functional chosen have the largest impact on the value of the rotation.
In order to eliminate the arbitrariness of the choice of density functional, we would prefer to use coupled cluster theory, a robust and systematically improvable method. However, the high-order polynomial scaling of coupled cluster theory makes it intractable for numerous large calculations, including the conformational averaging required for optical rotation calculations in solution. We therefore attempt to reduce the scaling of a linear response coupled cluster singles and doubles (LR-CCSD) calculation via a perturbed pair natural orbital (PNO++) local correlation approach which uses an orbital space created using a perturbed density matrix. We find that by creating a "combined PNO++" space, incorporating a set of orbitals from the unperturbed pair natural orbital (PNO) space into the PNO++ space, we can obtain well-behaved convergence behavior for both CCSD correlation energies and linear response properties, including dynamic polarizabilities and optical rotations, for the small systems considered.
The PNO++ and combined PNO++ methods require aggressive truncation to keep the computational cost low, due to an expensive two-electron integral transformation at the beginning of the calculation. We apply the methods to larger systems than previously studied and refine them for more aggressive truncation by exploring an alternative form of the perturbed density and a perturbation-including weak pair approximation.Doctor of Philosophy
Theoretical chemistry attempts to provide connections between the structure of molecules and their observable properties. One such family of observables are chiroptical properties, or the effect of the medium on the light which passes through it. These properties include the scattering, absorption and change in polarization of light. Light being classically an electromagnetic field, chiroptical properties can be derived by treating molecules quantum mechanically and the light classically. The prediction of chiroptical properties on computers using the principles of quantum mechanics is still a growing field, being very sensitive to the method used, and requiring considerations of factors such as conformations and anharmonic corrections. Matching experimental properties is an important step in the creation of a reliable method of predicting properties of systems in order to provide more information than can be obtained through experimental observation. This work begins by addressing the problem of matching experimentally obtained quantities. Our results show that current time-intensive methods still fall short in the matching of experimental data. Thus, we then move on to approximating a more robust but computationally expensive method in order to be able to use a more accurate method on a larger scale than is currently possible. On obtaining positive results for small test systems, we test the new method on larger systems, and explore possible improvements to its accuracy and efficiency.
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Liu, Biheng. "Reduced order models for the analysis of offshore lattice structures." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2022.
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The lattice is a common frame applied in offshore structures benefiting from their economic construction and easily accessible, for example, the jacket platform of the offshore wind turbine. In order to accelerate the design process of a model, this thesis proposed a method to reduce the order of the offshore lattice structure models. The full order model is constructed based on the FEM. Applying the MDOF mass discrete concept lumps the structure mass on each story center. Meanwhile, apply the DSM to determine the displacement and the forces implied on the mass center for accomplishing the unitary displacement of each DOF of the mass center node. Finally, a reduced order model for the lattice structure will be obtained. That model composed of the stiffness matrix of the mass center node has the same fundamental flexural frequency as the original model. The model can be expressed by symbolic relationship as well as possible to package as a function for further quotation. All computation processes of this thesis were executed on the Python platform.
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Arkalgud, Ravi. "Vortex shedding analysis and control using reduced order modelling and viscous cell boundary element method." Thesis, University of Southampton, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.274099.
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Udoff, Geoffrey. "An Alternate Trawling Method: Reduced Bycatch and Benthic Disturbance Achieved with the Wing Trawling System." ScholarWorks@UNO, 2016. http://scholarworks.uno.edu/td/2217.
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The Wing Trawling System (WTS) was tested as an alternative to traditional shrimp capture methods in the Gulf. Compared to an otter trawl, this trawl was conceived to reduce bycatch, retain shrimp catch, and minimize seafloor disturbance. Through seventy-one paired tows, the WTS was assessed against a standard otter trawl. The WTS was found to reduce bycatch by 63-65% and reduce shrimp catch by 30-35%. Additionally, I measured the depth of the scars produced by both trawls and quantified the turbidity of the plumes behind them. The scars left by the WTS and the otter trawl were between 9.9 cm-13.6 cm. The turbidity behind the WTS was 18.6 NTU, while the turbidity behind the otter trawl was 206.8 NTU. In conclusion, the WTS offers an alternative to an otter trawl that reduces bycatch and the impact trawling has on the seafloor but results in a significant amount of shrimp loss.
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Karlsson, Fredrik, and Jan van Doorn. "Applying the Vowel Formant Dispersion (VFD) method to the study of reduced or alterered vowel productions." Umeå universitet, Institutionen för språkstudier, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-74416.
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Formant centre frequencies are regularly used as acoustic measure of vowel quality because of the well established correlation between them and properties of vowel production(Fant, 1960). While it is recognised that it is important transform formant frequencies, as measured from the spectrogram, into relevant psychoacoustic scales when addressing issues of vowel perception, production studies are still largely based on the the raw, Hz-scaled, formant measurements. As a consequence, systematic studies of vowel articulation proficiency due to clinical conditions or effects of treatment are not easily afforded. A number of derived measures have been proposed to capture whole-system effect of vowel production. Previous research has primarily used the calculated total area of formants measured from either [a], [u], [i] and [æ] or only [a], [u] and [i] productions, joined together to form a quadrilateral or a triangle (Vowel space area, VSA)(Kent & Kim, 2003). In the reduced articulatory range of hypokinetic dysarthria, VSA is expected to be reduced by the dysarthria, and increased due to successful treatment the patient’s articulatory range. However, VSA has been proposed to be not powerful enough to capture effects on vowel articulation found specifically in patients with Parkinson’s disease (PD), and therefore not able to establish treatment effects. Two alternative measures have been proposed previously that are more focused towards specifically towards finding expansion and reductions in vowel spaces, the Vowel articulation index (VAI)(Roy, Nissen, Dromey, & Sapir, 2009) or Formant Centralization Ratio (FCR)(Sapir, Ramig, Spielman, & Fox, 2010). Both VAI and FCR has been shown to be able to establish significant reductions vowel articulation due to PD. Similar to VSA, however, the VAI and FCR measures do not given any detailed insight into the nature of the change in articulation. Further, all three measures reduces all obtained vowel formant measurements into a single metric, resulting in a substantial loss of statistical power and a considerable reduction in quality of intra-speaker models of articulatory proficiency. In response to the problematic properties of previous metrics, a revised view of formant frequencies more suitable for studies of changes in vowel articulation has recently been outlined, along with a new metric (Vowel Formant Dispersion, VFD). The VFD view of vowel formants are more closely connected to properties of vowel articulation and therefore affords more more detailed interpretations to be drawn concerning speakers’ production proficiency and offers increased reliability of within speaker estimates of this proficiency. This paper presents a detailed view of how VFD may applied to clinical populations where vowel production is affected by the condition (e.g. hypokinetic dysarthria) or where production should be affected (e.g. transexual patients or in successful treatment of dysarthric patients). It will be shown that most aspects of the study of vowel articulation proficiency will be significantly enhanced by the VFD method. Fant, G. (1960). Acoustic Theory of Speech Production. Mouton and Co 's-Gravenhage. Karlsson, F. (submitted). Vowel Formant Dispersion: a revised view of vowel production. The Journal of Acoustical Society of America. Kent, R. D., & Kim, Y.-J. (2003). Toward an acoustic typology of motor speech disorders. Clinical Linguistics & Phonetics, Clinical Linguistics & Phonetics, 17(6), 427–445. Informa Allied Health. doi:10.1080/0269920031000086248 Roy, N., Nissen, S. L., Dromey, C., & Sapir, S. (2009). Articulatory changes in muscle tension dysphonia: evidence of vowel space expansion following manual circumlaryngeal therapy Journal of communication disorders, Journal of communication disorders, 42(2), 124–135. doi:10.1016/j.jcomdis.2008.10.001 Sapir, S., Ramig, L. O., Spielman, J. L., & Fox, C. (2010). Formant Centralization Ratio: A Proposal for a New Acoustic Measure of Dysarthric Speech. Journal of Speech, Language, and Hearing Research, 53(1), 114–114.
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Zhang, Zhenying Verfasser], Karen [Akademischer Betreuer] [Veroy, and Michael [Akademischer Betreuer] Herty. "Certified reduced basis method for variational inequalities / Zhenying Zhang ; Karen Paula Veroy-Grepl, Michael Matthias Herty." Aachen : Universitätsbibliothek der RWTH Aachen, 2016. http://d-nb.info/1156922216/34.
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Zhang, Zhenying [Verfasser], Karen [Akademischer Betreuer] Veroy, and Michael [Akademischer Betreuer] Herty. "Certified reduced basis method for variational inequalities / Zhenying Zhang ; Karen Paula Veroy-Grepl, Michael Matthias Herty." Aachen : Universitätsbibliothek der RWTH Aachen, 2016. http://d-nb.info/1156922216/34.
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Malik, Muhammad Haris. "Reduced order modeling for smart grids' simulation and optimization." Doctoral thesis, Universitat Politècnica de Catalunya, 2017. http://hdl.handle.net/10803/405730.
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This thesis presents the study of the model order reduction for power grids and transmission networks. The specific focus has been the transient dynamics. A mathematical viewpoint has been adopted for model reduction. Power networks are huge and complex network, simulation for power grid analysis and design require large non-linear models to be solved. In the context of developing "Smart Grids" with the distributed generation of power, real time analysis of complex systems such as these needs fast, reliable and accurate models. In the current study we propose model order reduction methods both a-priori and a-posteriori suitable for dynamic models of power grids.
The model that describes the transient dynamics of the power grids is complex non-linear swing dynamics model. The non-linearity of the swing dynamics model necessitates special attention to achieve maximum benefit from the model order reduction techniques. In the current research, POD and LATIN methods were applied initially with varying degrees of success. The method of TPWL has been proved as the best-suited model reduction method for swing dynamics model; this method combines POD with multiple linear approximations. For the transmission lines, a distributed parameters model in frequency-domain is used. PGD based reduced-order models are proposed for the DP model of transmission lines. A fully parametric problem with electrical parameters of transmission lines included as coordinates of the separated representation. The method was extended to present the solution of frequency-dependent parameters model for transmission lines.Cette these présente l'étude de la réduction de modeles pour les réseaux électriques et les réseaux de transmission. Un point de vue mathématique a été adopté pour la réduction de modeles. Les réseaux électriques sont des réseaux immenses et complexes, dont l'analyse et la conception nécessite la simulation et la résolution de grands modeles non-linéaires. Dans le cadre du développement de réseaux électriques intelligents (smart grids) avec une génération distribuée de puissance, l'analyse en temps réel de systemes complexes tels que ceux-ci nécessite des modeles rapides, fiables et précis. Dans la présente étude, nous proposons des méthodes de réduction de de modeles a la fois a priori et a posteriori, adaptées aux modeles dynamiques des réseaux électriques. Un accent particulier a été mis sur la dynamique transitoire des réseaux électriques, décrite par un modele oscillant nonlinéaire et complexe. La non-linéarité de ce modele nécessite une attention particuliere pour bénéficier du maximum d'avantages des techniques de réduction de modeles. lnitialement, des méthodes comme POD et LATIN ont été adoptées avec des degrés de succes divers. La méthode de TPWL, qui combine la POD avec des approximations linéaires multiples, a été prouvée comme étant la méthode de réduction de modeles la mieux adaptée pour le modele dynamique oscillant. Pour les lignes de transmission, un modele de parametres distribués en domaine fréquentiel est utilisé. Des modeles réduits de type PGD sont proposés pour le modele DP des lignes de transmission. Un probleme multidimensionnel entierement paramétrique a été formulé, avec les parametres électriques des lignes de transmission inclus comme coordonnées additionnelles de la représentation séparée. La méthode a été étendue pour étudier la solution du modele des lignes de transmission pour laquelle les parametres dépendent de la fréquence.
Esta tesis presenta un estudio de la reducción de modelos (MOR) para redes de transmisión y distribución de electricidad. El enfoque principal utilizado ha sido la dinámica transitoria y para la reducción de modelos se ha adoptado un punto de vista matemático. Las redes eléctricas son complejas y tienen un tamaño importante. Por lo tanto, el análisis y diseño de este tipo de redes mediante la simulación numérica, requiere la resolución de modelos no-lineales complejos. En el contexto del desarrollo de redes inteligentes, el objetivo es un análisis en tiempo real de sistemas complejos, por lo que son necesarios modelos rápidos, fiables y precisos. En el presente estudio se proponen diferentes métodos de reducción de modelos, tanto a priori como a posteriori, adecuados para modelos dinámicos de redes eléctricas. La dinámica transitoria de redes eléctricas, se describe mediante modelos dinámicos oscilatorios no-lineales. Esta no-linearidad del modelo necesita ser bien tratada para obtener el máximo beneficio de las técnicas de reducción de modelos. Métodos como la POD y la LATIN han sido inicialmente utilizados en esta problemática con diferentes grados de éxito. El método de TPWL, que combina la POD con múltiples aproximaciones lineales, ha resultado ser el mas adecuado para sistemas dinámicos oscilatorios. En el caso de las redes de transmisión eléctrica, se utiliza un modelo de parámetros distribuidos en el dominio de la frecuencia. Se propone reducir este modelo basándose en la PGD, donde los parámetros eléctricos de la red de transmisión son incluidos como coordenadas de la representación separada del modelo paramétrico. Este método es ampliado para representar la solución de modelos con parámetros dependientes de la frecuencia para las redes de transmisión eléctrica
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Nyangiwe, Nangamso Nathaniel. "Graphene based nano-coatings: synthesis and physical-chemical investigations." Thesis, UWC, 2012. http://hdl.handle.net/11394/3237.
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Magister Scientiae - MScIt is well known that a lead pencil is made of graphite, a naturally form of carbon, this is important but not very exciting. The exciting part is that graphite contains stacked layers of graphene and each and every layer is one atom thick. Scientists believed that these graphene layers could not be isolated from graphite because they were thought to be thermodynamically unstable on their own and taking them out from the parent graphite crystal will lead them to collapse and not forming a layer. The question arose, how thin one could make graphite. Two scientists from University of Manchester answered this question by peeling layers from a graphite crystal by using sticky tape and then rubbing them onto a silicon dioxide surface. They managed to isolate just one atom thick layer from graphite for the first time using a method called micromechanical cleavage or scotch tape. In this thesis chemical method also known as Hummers method has been used to fabricate graphene oxide (GO) and reduced graphene oxide. GO was synthesized through the oxidation of graphite to graphene oxide in the presence of concentrated sulphuric acid, hydrochloric acid and potassium permanganate. A strong reducing agent known as hydrazine hydrate has also been used to reduce GO to rGO by removing oxygen functional groups, but unfortunately not all oxygen functional groups have been removed, that is why the final product is named rGO. GO and rGO solutions were then deposited on silicon substrates separately. Several characterization techniques in this work have been used to investigate the optical properties, the morphology, crystallography and vibrational properties of GO and rGO.
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Song, Huimin. "Rigorous joining of advanced reduced-dimensional beam models to 3D finite element models." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/33901.
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This dissertation developed a method that can accurately and efficiently capture the response of a structure by rigorous combination of a reduced-dimensional beam finite element model with a model based on full two-dimensional (2D) or three-dimensional (3D) finite elements.
As a proof of concept, a joint 2D-beam approach is studied for planar-inplane deformation of strip-beams. This approach is developed for obtaining understanding needed to do the joint 3D-beam model. A Matlab code is developed to solve achieve this 2D-beam approach. For joint 2D-beam approach, the static response of a basic 2D-beam model is studied. The whole beam structure is divided into two parts. The root part where the boundary condition is applied is constructed as a 2D model. The free end part is constructed as a beam model. To assemble the two different dimensional model, a transformation matrix is used to achieve deflection continuity or load continuity at the interface. After the transformation matrix from deflection continuity or from load continuity is obtained, the 2D part and the beam part can be assembled together and solved as one linear system.
For a joint 3D-beam approach, the static and dynamic response of a basic 3D-beam model is studied. A Fortran program is developed to achieve this 3D-beam approach. For the uniform beam constrained at the root end, similar to the joint 2D-beam analysis, the whole beam structure is divided into two parts. The root part where the boundary condition is applied is constructed as a 3D model. The free end part is constructed as a beam model. To assemble the two different dimensional models, the approach of load continuity at the interface is used to combine the 3D model with beam model. The load continuity at the interface is achieved by stress recovery using the variational-asymptotic method. The beam properties and warping functions required for stress recovery are obtained from VABS constitutive analysis. After the transformation matrix from load continuity is obtained, the 3D part and the beam part can be assembled together and solved as one linear system. For a non-uniform beam example, the whole structure is divided into several parts, where the root end and the non-uniform parts are constructed as 3D models and the uniform parts are constructed as beams. At all the interfaces, the load continuity is used to connect 3D model with beam model. Stress recovery using the variational-asymptotic method is used to achieve the load continuity at all interfaces. For each interface, there is a transformation matrix from load continuity. After we have all the transformation matrices, the 3D parts and the beam parts are assembled together and solved as one linear system.
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Daversin, Catty Cécile. "Reduced basis method applied to large non-linear multi-physics problems : application to high field magnets design." Thesis, Strasbourg, 2016. http://www.theses.fr/2016STRAD019/document.
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Le LNCMI est un grand équipement du CNRS. Il met à la disposition de la communauté scientifique internationale des aimants produisant des champs magnétiques intenses (entre 24 et 36 Teslas pendant plusieurs heures), utilisés par les chercheurs comme un moyen d'exploration et de contrôle de la matière. Dans la thèse, nous nous intéressons à la simulation de ce type d'aimants, dans le but de les étudier, d'optimiser leur design, ou encore de faire des analyses d'incidents. Ces modèles 30 sont basés sur des équations aux dérivées partielles couplées non-linéaires. Au vu de leur complexité, nous avons développé des méthodes de réduction d'ordre, permettant de réduire considérablement les temps de calcul associés. En particulier, nous pensons avoir levé un verrou majeur de l'utilisation du cadre méthodologique de réduction d'ordre pour des problèmes multi-physiques non-linéairesThe magnetic field constitutes a powerfull tool for researchers, especially to determine the properties of the matter. This kind of applications requires magnetic fields of high intensity. The "Laboratoire National des Champs Magnetiques Intenses" (LNCMI) develops resistive magnets providing such magnetic field to scientists. The design of these magnets represents a challenge interms of design. We have developed a range of non-linear coupled models taking into account the whole involved physics, implemented through the Feel++ library. Designed for many query context, the reduced basis method applied to the multi-physics model aims to circumvent the complexity of the problem. lts efficiency allows to move towards parametric studies and sensitivity analysis in various concrete applications. Especially, the method SER we introduce in this thesis is a significant breakthrough for non-linear and non-affine problems in an industrial context
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Tonn, Timo [Verfasser]. "Reduced-Basis Method (RBM) for Non-Affine Elliptic Parametrized PDEs : (Motivated by Optimization in Hydromechanics) / Timo Tonn." Ulm : Universität Ulm. Fakultät für Mathematik und Wirtschaftswissenschaften, 2012. http://d-nb.info/1026992222/34.
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Lülf, Fritz Adrian. "An integrated method for the transient solution of reduced order models of geometrically nonlinear structural dynamic systems." Phd thesis, Conservatoire national des arts et metiers - CNAM, 2013. http://tel.archives-ouvertes.fr/tel-00957455.
Повний текст джерелаАнотація:
For repeated transient solutions of geometrically nonlinear structures the numerical effort often poses a major obstacle. Thus, the introduction of a reduced order model, which takes the nonlinear effects into account and accelerates the calculations considerably, is often necessary.This work yields a method that allows for rapid, accurate and parameterisable solutions by means of a reduced model of the original structure. The structure is discretised and its dynamic equilibrium described by a matrix equation. The projection on a reduced basis is introduced to obtain the reduced model. A comprehensive numerical study on several common reduced bases shows that the simple introduction of a constant basis is not sufficient to account for the nonlinear behaviour. Three requirements for an rapid, accurate and parameterisable solution are derived. The solution algorithm has to take into account the nonlinear evolution of the solution, the solution has to be independent of the nonlinear finite element terms and the basis has to be adapted to external parameters.Three approaches are provided, each responding to one requirement. These approaches are assembled to the integrated method. The approaches are the update and augmentation of the basis, the polynomial formulation of the nonlinear terms and the interpolation of the basis. A Newmark-type time-marching algorithm provides the frame of the integrated method. The application of the integrated method on test-cases with geometrically nonlinear finite elements confirms that this method leads to the initial aim of a rapid, accurate and parameterisable transient solution.
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Rowland, David J. Reid. "Reduced exposure time as a method of minimising the impact of vibration on electronic speckle pattern interferometry." Master's thesis, University of Cape Town, 2002. http://hdl.handle.net/11427/5475.
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May, David. "The TLC Method for Modeling Creep Deformation and Rupture." Honors in the Major Thesis, University of Central Florida, 2014. http://digital.library.ucf.edu/cdm/ref/collection/ETH/id/1620.
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This thesis describes a novel new method, termed the Tangent-Line-Chord (TLC) method, that can be used to more efficiently model creep deformation dominated by the tertiary regime. Creep deformation is a widespread mechanical mode of failure found in high-stress and temperature mechanical systems. To accurately simulate creep and its effect on structures, researchers utilize finite element analysis (FEA). General purpose FEA packages require extensive amounts of time and computer resources to simulate creep softening in components because of the large deformation rates that continuously evolve. The goal of this research is to employ multi-regime creep models, such as the Kachanov-Rabotnov model, to determine a set of equations that will allow creep to be simulated using as few iterations as possible. The key outcome is the freeing up of computational resources and the saving of time. Because both the number of equations and the value of material constants within the model change depending on the approach used, programming software will be utilized to automate this analytical process. The materials being considered in this research are mainly generic Ni-based superalloys, as they exhibit creep responses that are dominated by secondary and tertiary creep.B.S.M.E.
Bachelors
Mechanical and Aerospace Engineering
Engineering and Computer Science
Mechanical Engineering
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Di, Donfrancesco Fabrizio. "Reduced Order Models for the Navier-Stokes equations for aeroelasticity." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS603.
Повний текст джерелаАнотація:
Le coût d’une simulation numérique aéroélastique peut devenir trop onéreuse lorsque une analyse paramétrique à haut fidélité est requise. Dans ce contexte, des Modèles d'Ordre Réduit (MOR) ont été développés en vue de réduire le coût de calcul des simulations numériques en préservant un haut niveau de précision. Ce travail de thèse porte sur la construction d'un MOR pour les équations de Navier-Stokes en tenant compte d'un maillage déformable dans le cas d'une application aéroélastique. Une base modale pour l'écoulement est obtenue via la Décomposition Orthogonale aux valeurs propres et une projection Galerkin est utilisée pour réduire le système d'équations de la mécanique des fluides. Pour pouvoir prendre en compte les non-linéarités des équation de Navier-Stokes une méthode de projection masquée est mise en œuvre et évaluée pour différent cas test avec maillage fixe. Le MOR est ensuite adapté pour prendre en compte des maillages déformables. Finalement, une méthode réduite spectrale en temps (ROTSM) a été formulée afin de répondre aux problèmes de stabilité qui concernent le MORs avec projection dans le domaine de la mécanique des fluides. Une évaluation du MOR obtenu est ensuite menée sur des études paramétriques pour des applications aéroélastiquesThe numerical prediction of aeroelastic systems responses becomes unaffordable when parametric analyses with high-fidelity CFD are required. Reduced order modeling (ROM) methods have therefore been developed in view of reducing the costs of the numerical simulations while preserving a high level of accuracy. The present thesis focuses on the family of projection based methods for the compressible Navier-Stokes equations involving deforming meshes in the case of aeroelastic applications. A vector basis obtained by Proper Orthogonal Decomposition (POD) combined to a Galerkin projection of the system equations is used in order to build a ROM for fluid mechanics. Masked projection approaches are therefore implemented and assessed for different test cases with fixed boundaries in order to provide a fully nonlinear formulation for the projection-based ROMs. Then, the ROM is adapted in the case of deforming boundaries and aeroelastic applications in a parametric context. Finally, a Reduced Order Time Spectral Method (ROTSM) is formulated in order to address the stability issues which involve the projection-based ROMs for fluid mechanics applications
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Pratt, Robert L. "AFFORDABLE, ALTERNATIVE TEST METHOD FOR MEETING CIVIL AVIATION REDUCED VERTICAL SEPARATION MINIMUM (RVSM) REQUIRMENTS ON MILITARY/COMMERCIAL AIRCRAFT." International Foundation for Telemetering, 2000. http://hdl.handle.net/10150/608286.
Повний текст джерелаАнотація:
International Telemetering Conference Proceedings / October 23-26, 2000 / Town & Country Hotel and Conference Center, San Diego, CaliforniaA recent Air Traffic Management (ATM) initiative has reduced certain oceanic routes from a 2,000-foot vertical separation minimum to a 1,000-foot (300 m) separation minimum between flight levels of 29,000 feet and 41,000 feet. As a result of this initiative, an aircraft transitioning from the Continental United States (CONUS) to Europe or Asia will be required to have a validated, certified altimeter reporting system within the specified tolerances. The aging military airframes are not currently Reduced Vertical Separation Minimum (RVSM) certified. The impact on military deployment time to foreign theatres as well as high- fuel cost makes this a high-priority DoD issue. This paper describes the test and evaluation (T&E) challenge, viable solutions and test method for meeting the RVSM requirements in an approved, affordable, and least down-time (minimal aircraft modification) manner. The test method described herein utilizes a PACER aircraft in formation with the RVSM candidate aircraft. The RVSM is just one of the many Global Air Traffic Management (GATM) requirements which must be met for military aircraft to fly within premium airspace during overseas deployment. The commercial equivalent of GATM is Communications Navigation and Surveillance/Air Traffic Management (CNS/ATM). Our focus will be on meeting the RVSM certification requirements as related to the test environment.
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Clark, M. Sean. "Generalist predators in reduced-tillage corn : predation on armyworm, habitat preferences, and a method to estimate absolute densities /." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-11102009-020213/.
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Benner, P., R. Byers, and E. Barth. "HAMEV and SQRED: Fortran 77 Subroutines for Computing the Eigenvalues of Hamiltonian Matrices Using Van Loanss Square Reduced Method." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800926.
Повний текст джерелаАнотація:
This paper describes LAPACK-based Fortran 77 subroutines for the reduction of a Hamiltonian matrix to square-reduced form and the approximation of all its eigenvalues using the implicit version of Van Loan's method. The transformation of the Hamilto- nian matrix to a square-reduced Hamiltonian uses only orthogonal symplectic similarity transformations. The eigenvalues can then be determined by applying the Hessenberg QR iteration to a matrix of half the order of the Hamiltonian matrix and taking the square roots of the computed values. Using scaling strategies similar to those suggested for algebraic Riccati equations can in some cases improve the accuracy of the computed eigenvalues. We demonstrate the performance of the subroutines for several examples and show how they can be used to solve some control-theoretic problems.
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Wang, Zegao, Pingjian Li, Yuanfu Chen, Jiarui He, Wanli Zhang, Oliver G. Schmidt, and Yanrong Li. "Pure thiophene–sulfur doped reduced graphene oxide: synthesis, structure, and electrical properties." Royal Society of Chemistry, 2014. https://tud.qucosa.de/id/qucosa%3A36294.
Повний текст джерелаАнотація:
Here we propose, for the first time, a new and green ethanol-thermal reaction method to synthesize highquality and pure thiophene–sulfur doped reduced graphene oxide (rGO), which establishes an excellent platform for studying sulfur (S) doping effects on the physical/chemical properties of this material. We have quantitatively demonstrated that the conductivity enhancement of thiophene–S doped rGO is not only caused by the more effective reduction induced by S doping, but also by the doped S atoms, themselves. Furthermore, we demonstrate that the S doping is more effective in enhancing conductivity of rGO than nitrogen (N) doping due to its stronger electron donor ability. Finally, the dye-sensitized solar cell (DSCC) employing the S-doped rGO/TiO₂ photoanode exhibits much better performance than undoped rGO/TiO₂, N-doped rGO/TiO₂ and TiO₂ photoanodes. It therefore seems promising for thiophene–S doped rGO to be widely used in electronic and optoelectronic devices.
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Kasnakoglu, Cosku. "Reduced order modeling, nonlinear analysis and control methods for flow control problems." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1195629380.
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Zhao, Xiaopeng. "Modeling and Simulation of MEMS Devices." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/11227.
Повний текст джерелаАнотація:
The objective of this dissertation is to present a modeling and simulation methodology for MEMS devices and identify and understand the associated nonlinearities due to large deflections, electric actuation, impacts, and friction.
In the first part of the dissertation, we introduce a reduced-order model of flexible microplates under electric excitation. The model utilizes the von Karman plate equations to account for geometric nonlinearities due to large plate deflections. The Galerkin approach is employed to reduce the partial-differential equations of motion and associated boundary conditions into a finite dimensional system of nonlinearly coupled ordinary-differential equations. We use the reduced-order model to analyze the mechanical behavior of a simply supported microplate and a fully clamped microplate. Effect of various design parameters on both the static and dynamic characteristics of microplates is studied.
The second part of the dissertation presents comprehensive modeling and simulation tools for impact microactuators. Nonsmooth dynamics due to impacts and friction are studied, combining various approaches, including direct numerical integration, root-finding technique for periodic motions, continuation of grazing periodic orbits, and local analysis of the near grazing dynamics. The transition between nonimpacting and impacting long term motions, referred to as grazing bifurcations, indicates the transition between on and off states of an impact microactuator. Three different on-off switching mechanisms are identified for the Mita microactuator. These mechanisms also generalize to arbitrary impacting systems with a similar nonlinearity. A local map based on the concept of discontinuity mapping provides an effcient and accurate tool for the grazing bifurcation analysis. Nonlinear impacting dynamics of the microactuator are studied in detail to identify various bifurcations and parameter ranges corresponding to chaotic motions. We find that the frequency-response curves of the impacting dynamics are significantly different from those of the nonimpacting dynamics.Ph. D.
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Mummidivarapu, Satya Sri. "A Method for Determining Body Weight Replacement Load during Squat Exercise in Weightlessness." University of Cincinnati / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1447690685.
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Gao, Haotian. "POD-Galerkin based ROM for fluid flow with moving boundaries and the model adaptation in parametric space." Diss., Kansas State University, 2018. http://hdl.handle.net/2097/38776.
Повний текст джерелаАнотація:
Doctor of PhilosophyDepartment of Mechanical and Nuclear Engineering
Mingjun Wei
In this study, a global Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order model (ROM) is proposed. It is extended from usual fixed-domain problems to more general fluid-solid systems with moving boundaries/interfaces. The idea of the extension is similar to the immersed boundary method in numerical simulations which uses embedded forcing terms to represent boundary motions and domain changes. This immersed boundary method allows a globally defined fixed domain including both fluid and solid, where POD-Galerkin projection can be directly applied. However, such a modified approach cannot get away with the unsteadiness of boundary terms which appear as time-dependent coefficients in the new Galerkin model. These coefficients need to be pre-computed for prescribed periodic motion, or worse, to be computed at each time step for non-prescribed (e.g. with fluid-structure interaction) or non-periodic situations. Though computational time for each unsteady coefficient is smaller than the coefficients in a typical Galerkin model, because the associated integration is only in the close neighborhood of moving boundaries. The time cost is still much higher than a typical Galerkin model with constant coefficients. This extra expense for moving-boundary treatment eventually undermines the value of using ROMs. An aggressive approach is to decompose the moving boundary/domain to orthogonal modes and derive another low-order model with fixed coefficients for boundary motion. With this domain decomposition, an approach including two coupled low-order models both with fixed coefficients is proposed. Therefore, the new global ROM with decomposed approach is more efficient. Though the model with the domain decomposition is less accurate at the boundary, it is a fair trade-off for the benefit on saving computational cost. The study further shows, however, that the most time-consuming integration in both approaches, which come from the unsteady motion, has almost negligible impact on the overall dynamics. Dropping these time-consuming terms reduces the computation cost by at least one order while having no obvious effect on model accuracy. Based on this global POD-Galerkin based ROM with forcing term, an improved ROM which can handle the parametric variation of body motions in a certain range is also presented. This study shows that these forcing terms not only represent the moving of the boundary, but also decouple the moving parameters from the computation of model coefficients. The decoupling of control parameters provides the convenience to adapt the model for the prediction on states under variation of control parameters. An improved ROM including a shit mode seems promising in model adaptation for typical problems in a fixed domain. However, the benefit from adding a shit mode to model diminishes when the method is applied to moving-boundary problems. Instead, a combined model, which integrates data from a different set of parameters to generate the POD modes, provides a stable and accurate ROM in a certain range of parametric space for moving-boundary problems. By introducing more data from a different set of parameters, the error of the new model can be further reduced. This shows that the combined model can be trained by introducing more and more information. With the idea of the combined model, the improved global ROM with forcing terms shows impressive capability to predict problems with different unknown moving parameters, and can be used in future parametric control and optimization problems.
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Meng, Liang. "Reduced shape-space : approach to material characterization instrumented indentation test case." Thesis, Compiègne, 2017. http://www.theses.fr/2017COMP2377/document.
Повний текст джерелаАнотація:
Ce travail se situe à l’intersection des trois disciplines : méthodes numériques, techniques expérimentales et du machine learning, a pour but de proposer une famille de techniques d’identification par analyse inverse des lois de comportement en mécanique. Dans le domaine d’identification des matériaux, l’indentation instrumentée est particulièrement attractive, car elle permet de procéder à des essais non-destructifs sur l’échantillon ou sur une structure en service. L’essai d’indentation, similaire à un test de dureté, consiste à enfoncer la pointe de l’indenteur à une faible profondeur dans la matière tout en enregistrant le déplacement en fonction de la force appliquée. L’identification des propriétés élastoplastiques des matériaux est basée alors sur l’exploitation de la courbe force-déplacement (courbe P-h). Toutefois, le problème inverse est souvent mal posé et des problèmes d’unicité mènent à la notion de paires de "matériaux mystiques" produisant, dans des conditions d’essai donnés, des courbes P-h identiques, malgré des propriétés différentes. L’idée de notre travail est de compléter la procédure d’identification en faisant appel à des dispositifs expérimentaux récents, notamment à la microscopie laser, permettant de mesurer la carte 3D de l’empreinte résiduelle obtenue après le retrait de l’indenteur. Pour aborder la question de la richesse d’information de l’empreinte par rapport à la courbe P-h seule, nous proposons de construire, dans un espace affine réduit, la variété des formes d’empreinte admissibles au sens d’une loi de comportement et du modèle d’éléments finis de l’essai. La mesure de la dimension intrinsèque nous indique alors le nombre maximal de paramètres potentiellement identifiables. Cela nous permet de proposer et de valider numériquement des nouveaux procédés expérimentaux, plus représentatifs, à partir des données synthétiques, ainsi que des algorithmes d’identification associés. La prise en compte de l’erreur de modèle et de l’erreur de mesure, nous mène ensuite à proposer un ensemble d’algorithmes de projection d’empreintes expérimentales, réalisées en collaboration avec l’INSA de Rennes sur la variété synthétique. Nous abordons alors le problème d’identification des propriétés d’écrouissage de plusieurs matériaux de complexité croissante et départageons des "jumeaux mystiques" par des essais de multi-indentation, basés sur l’exploitation de l’empreinte seule ou en complément de la courbe P-hThe thesis lies at the intersection of three disciplines : numerical methods, experimental techniques, and machine learning. The primary aim of this work is to develop a group of algorithms for characterization by inverse analysis of a material’s constitutive law. In the field of material characterization, indentation test is especially attractive since it is considered non-destructive, and may be performed even on a structure in service. The test, similar to a hardness test, consists in penetrating an indenter into the surface of the material. The force exerted on the indenter is recorded against the penetration depth over a series of time instants, leading to a force-displacement (P-h) curve, which is the most frequently used source of information for the identification of material properties. However, the inverse problem based solely on this curve tends to be ill-posed, leading to nonunique identification solution, i.e., the "mystical material pair", for whom the corresponding force-displacement curves are almost identical despite the very different material properties. The basic idea is then to complete the identification process with innovative experimental measurements, such as laser microscope, which allows measuring the 3D residual imprint after the withdrawal of the indenter. To address the advantage of this measurement over P-h curve, we propose to construct, within a reduced affine space, a manifold of shapes admissible to the postulated constitutive law, experimental and simulation setups, based on synthetic data. The intrinsic dimensionality of the manifold limits the number of identifiable parameters allowing to validate numerically experimental procedures. Considering both the model and measurement errors, we develop a series of local manifold learning algorithms to solve the inverse problem iteratively for experimental results obtained in cooperation with INSA de Rennes. This approach allows us to characterize diverse metallic materials of increasing complexity, based on actual experimental measurements. For example, for the Hollomon’s law, the mystical pair is alleviated in using a single imprint, while for the Voce law, a multi-depth experimental protocol is proposed to differentiate mystical siblings
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HERATH, MUTHUKUMARA MUDIYANSELAGE Samantha Chandani. "Using EEG measures to quantify reduced daytime vigilance in patients diagnosed with obstructive sleep apnoea using a novel electroencephalogram analysis method." Thesis, The University of Sydney, 2013. http://hdl.handle.net/2123/9726.
Повний текст джерелаАнотація:
Introduction Vigilance in obstructive sleep apnoea (OSA) does not correlate well with disease severity/ symptoms: Hence the need for a simple objective test. One such method could be quantitative analysis of the awake electroencephalogram (qEEG). qEEG is conventionally analysed using Power Spectral Analysis (PSA) looking at different EEG frequencies of delta, theta, alpha and beta. A novel method of analyzing the qEEG: De-trended fluctuation analysis (DFA) provides a single value: the scaling exponent (SE), which measures the fluctuations in the EEG signal. Artefact removal from qEEG is mandatory with the gold standard being manual scoring. Another method of automated artefact removal is independent component analysis (ICA). Objective Investigate the role of PSA and DFA (SE) as an objective measure of testing vigilance and validate the use of ICA in patients diagnosed with OSA. Methodology Retrospective cross-sectional study of untreated OSA patients. Results ICA and manual artefact removal gave well-correlated results in the DFA (SE), but not PSA. EEG slowing measured by PSA and DFA did not correlate to impaired performance during a battery of 14 separate performance tests. Conclusion ICA and manual artefact removal can be interchangeably used in extracting DFA measurements with confidence. In PSA metrics the use of ICA may not be reliable.
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Capaldo, Matteo. "A new approximation framework for PGD-based nonlinear solvers." Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLN011/document.
Повний текст джерелаАнотація:
Le but de ce travail est d'introduire un cadre d'approximation, la Reference Points Method, afin de réduire la complexité de calcul des opérations algébriques lorsqu'elles concernent des approximations à variables séparées dans le cadre de la Proper Generalized Decomposition.La PGD a été introduite dans [1] dans le cadre de la méthode LaTIn pour résoudre efficacement des équations différentielles non linéaires et dépendants du temps en mécanique des structures. La technique consiste à chercher la solution d'un problème dans une base d'ordre réduit (ROB) qui est automatiquement et à la volée générée par la méthode LaTIn. La méthode LaTIn est une stratégie itérative qui génère les approximations de la solution sur l'ensemble du domaine espace-temps-paramètres par enrichissements successifs. Lors d'une itération particulière, la ROB, qui a déjà été formée, est d'abord utilisée pour calculer un nouveau modèle réduit (ROM) et, donc, pour trouver une nouvelle approximation de la solution. Si la qualité de cette approximation ne suffit pas, la ROB est enrichie avec la génération d'un nouveau produit de fonctions PGD en utilisant un algorithme de type 'greedy'.Les techniques de réduction de modèle sont particulièrement efficaces lorsque le ROM a besoin d'être construit qu'une seule fois. Ce n'est pas le cas pour les techniques de réduction de modèle quand elles concernent des problèmes non linéaires. En effet, dans un tel cas, les opérateurs qui sont impliqués dans la construction du ROM varient au cours du processus itératif et des calculs préliminaires ne peuvent pas être effectués à l'avance pour accélérer le processus 'online'.Par conséquent, la construction du ROM est un élément coûteux de la stratégie de calcul en terme de temps de calcul. Il en découle la nécessité d'évaluer, à chaque itération, la fonction non linéaire de grande dimension (et éventuellement sa jacobienne) et ensuite sa projection pour obtenir les opérateurs réduits. Cela représente un point de blocage des stratégies de réduction de modèle dans le cadre non linéaire. Le présent travail a comme but une réduction ultérieure du coût de calcul, grâce à l'introduction d'un nouveau cadre de rapprochement dédiée à la stratégie de calcul LaTIn-PGD. Il est basé sur la notion de temps, de points et de paramètres de référence et permet de définir une version compressée des données. Comparé à d'autres techniques similaires [3,4] cela ne se veut pas une technique d'interpolation, mais un cadre algébrique qui permet de donner une première approximation, peu coûteuse, de toutes les quantités sous une forme à variable séparés par des formules explicites. L'espace de données compressées présente des propriétés intéressantes qui traitent les opérations algébriques élémentaires. Le RPM est introduit dans le solveur LaTIn-PGD non linéaire pour calculer certaines opérations répétitives. Ces opérations sont liées à la résolution du problème du temps / paramètre qui implique la mise à jour de l'opérateur tangent et la projection de ce dernier sur la base réduite. La RPM permet de simplifier et de réduire le nombre d'opérations nécessaires.[1] Ladevèze P., Sur une famille d’algorithmes en mécanique des structures, Comptes Rendus Académie des Sciences. Paris. Ser. II 300, pp.41-44, 1985.[2] Chinesta, F., Ladevèze, P., and Cueto, E. A short review on model order reduction based on proper generalized decomposition. Archives of Computational Methods in Engineering, 18, pp.395-404, 2011.[3] Barrault M., Maday Y., Nguyen N., Patera A., An ’empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations, Comptes Rendus Académie des Sciences. Paris. Ser. I, 339, pp. 667-672, 2004.[4] Chaturentabut S., Sorensen D., Nonlinear model reduction via discrete empirical interpolation, Society for Industrial and Applied Mathematics 32(5), pp.2737-2764, 2010The aim of this work is to introduce an approximation framework, called Reference Points Method (RPM), in order to decrease the computational complexity of algebraic operations when dealing with separated variable approximations in the Proper Generalized Decomposition (PGD) framework.The PGD has been introduced in [1] in the context of the LATIN method to solve efficiently time dependent and/or parametrized nonlinear partial differential equations in structural mechanics (see, e.g., the review [2] for recent applications). Roughly, the PGD technique consists in seeking the solution of a problem in a relevant Reduced-Order Basis (ROB) which is generated automatically and on-the-fly by the LATIN method. This latter is an iterative strategy which generates the approximations of the solution over the entire time- space-parameter domain by successive enrichments. At a particular iteration, the ROB, which has been already formed, is at first used to compute a projected Reduced-Order Model (ROM) and find a new approximation of the solution. If the quality of this approximation is not sufficient, the ROB is enriched by determining a new functional product using a greedy algorithm.However, model reduction techniques are particularly efficient when the ROM needs one construction only. This is not the case for the model reduction techniques when they are addressed to nonlinear problems. Indeed, in such a case, the operators which are involved in the construction of the ROM change all along the iterative process and no preliminary computations can be performed in advance to speed up the online process. Hence, the construction of the ROM is an expensive part of the calculation strategy in terms of CPU. It ensues from the need to evaluate the high-dimensional nonlinear function (and eventually its Jacobian) and then to project it to get the low-dimensional operators at each computational step of a solution algorithm. This amounts to being the bottleneck of nonlinear model reduction strategies.The present work is then focused on a further reduction of the computational cost, thanks to the introduction of a new approximation framework dedicated to PGD-based nonlinear solver. It is based on the concept of reference times, points and parameters and allows to define a compressed version of the data. Compared to other similar techniques [3,4] this is not an interpolation technique but an algebraic framework allowing to give an inexpensive first approximation of all quantities in a separated variable form by explicit formulas. The space of compressed data shows interesting properties dealing the elementary algebraic operations. The RPM is introduced in the PGD-based nonlinear solver to compute some repetitive operations. These operations are related to the resolution of the time/parameter problem that involves the update of the tangent operator (for nonlinear problems) and the projection of this latter on the Reduced Order Basis. For that the RPM allows to simplify and reduce the number of operations needed.[1] Ladevèze P., Sur une famille d’algorithmes en mécanique des structures, Comptes Rendus Académie des Sciences. Paris. Ser. II 300, pp.41-44, 1985.[2] Chinesta, F., Ladevèze, P., and Cueto, E. A short review on model order reduction based on proper generalized decomposition. Archives of Computational Methods in Engineering, 18, pp.395-404, 2011.[3] Barrault M., Maday Y., Nguyen N., Patera A., An ’empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations, Comptes Rendus Académie des Sciences. Paris. Ser. I, 339, pp. 667-672, 2004.[4] Chaturentabut S., Sorensen D., Nonlinear model reduction via discrete empirical interpolation, Society for Industrial and Applied Mathematics 32(5), pp.2737-2764, 2010
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Ori, Miklós. "Local Buckling of Doubly-Symmetric I-Sections Subjected to Warping Torsion : The limitations of the Reduced Cross-Section Method under unconventional loading." Thesis, KTH, Bro- och stålbyggnad, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-251031.
Повний текст джерелаАнотація:
In regular design practice, when it comes to conventional loading, such as uniaxial compression and bending, the local buckling of thin plates is taken care of through cross section classification. The effect of warping torsion, which also gives rise to normal stresses in the section, however, is typically not considered in the process. Present work aimed to uncover the influence of warping torsion on the phenomena of local plate buckling and to investigate the limitations of the effective width method when it was applied against its intended use. In the case of varying results, a simple correction to the calculation method was to be developed to improve accuracy. The examined I-sections were tested to failure and results were obtained with two different approaches: with finite element method and a Eurocode-based hand-calculation. The finite element models were refined to closely mimic physical experiments and their results were accepted as the true resistance of the sections, while the calculation method tried to capture the structural response in a practical, easily understandable way. The calculated results showed reasonably good accuracy with that of the finite element analysis. However, what really stood out was how similar the change in resistance was when the section parameters were manipulated. Through a properly chosen function, this allowed for the creation of an exponent that could modify the calculated results to achieve an even greater accuracy. The eccentricity of the applied load on the system was also manipulated to alter the proportion of normal stresses due to the two examined effects. It became clear that the stresses from warping in the applied calculation model were underestimated and the otherwise conservative method of effective width lost much of its safety margin when its application was extended to warping as well. Consequently, the consideration of stresses from warping in the regular design process and stability control of commonly used thin walled open sections seemed to be justified. The effective width method could not reliably cover the issue with retaining its original margin of safety.
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Alvarez, Boto Roberto. "Development of the NCI method : high performance optimization and visualization." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066220/document.
Повний текст джерелаАнотація:
Les interactions non-covalentes ont une importance fondamental pour la chimique. Les interactions entre un catalyseur et le substrat, interactions entre matériaux, synthèse des enantiomers parmi autres réactions chimiques sont décrivent par interactions non-covalentes. Elles sont fondamental pour designer nouveaux matériaux. Les interactions non-covalents sont très suivant visualisées à partir de mesures de contactes atomiques qui utilisent des donnes de rayon de van de Waals. Cette type d'approximations ne sont pas très flexible pour comprendre l'interaction avec l'environnement. Aujourd'hui les approximations qui utilisent des fonctions dans l'espace réel (i.e. la densité électronique) sont très utilisent pour visualiser les interactions non-covalentes. Dans cet thèse, on analyse la méthode NCI pour visualiser interactions chimiques. On analyse les gradient réduit de la densité, ingrédient fondamental dans la méthode NCI. On montré que cette fonction est liée au la densité d'énergie cinétique et au comportement bosonique du système. On montre que la méthode NCI peut être utilisée pour analyser tous les types d'interactions; dès interactions covalentes aux non-covalentes. Finalement la méthode est appliqué à la réactivité chimiqueNon-covalent interactions are of paramount importance in chemistry. Interactions between a catalyst and its substrate, self-assembly of nanomaterials, enantiomer production and many other chemical reactions, are most of the time non-covalent in nature. They are also fundamental for crystallographic analysis, since they set up the scenario for molecular crystallization, whose guiding rules are still a fruitful filed of research. Non-covalent interactions are frequently visualized using distance dependent contacts, generally without consideration of hydrogen atoms. Most of these interactions are usually identified by the use of tabulated van der Waals radii, which are not flexible enough to reveal the interplay with the environment. New approaches, based on 3D functions that can be derived either form experiment or computation (e.g. the electro density) are now widely used to identify and visualize non-covalent interactions. In this thesis we analyse the NCI method, and namely, its main ingredient, the reduced density gradient. Its capabilities for visualizing chemical interactions are examined. This 3D function is then, connected with the kinetic energy density and a interpretation of the reduced density gradient in terms of the bosonic behaviour of the electronic system is presented. Then, the NCI method is applied to visualise and analyse chemical interactions: from covalent to non-covalent interactions. The chemical reactivity is also addressed. The NCI method is applied to rationalised the outcome of several reactions