| 1. |
- Berglund, Tomas, et al.
(författare)
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Epi-convergence of minimum curvature variation B-splines
- 2003
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We study the curvature variation functional, i.e., the integral over the square of arc-length derivative of curvature, along a planar curve. With no other constraints than prescribed position, slope angle, and curvature at the endpoints of the curve, the minimizer of this functional is known as a cubic spiral. It remains a challenge to effectively compute minimizers or approximations to minimizers of this functional subject to additional constraints such as, for example, for the curve to avoid obstacles such as other curves. In this paper, we consider the set of smooth curves that can be written as graphs of three times continuously differentiable functions on an interval, and, in particular, we consider approximations using quartic uniform B- spline functions. We show that if quartic uniform B-spline minimizers of the curvature variation functional converge to a curve, as the number of B-spline basis functions tends to infinity, then this curve is in fact a minimizer of the curvature variation functional. In order to illustrate this result, we present an example of sequences of B-spline minimizers that converge to a cubic spiral.
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| 2. |
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| 3. |
- Eriksson, J, et al.
(författare)
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Regularization methods for uniformly rank-deficient nonlinear least-squares problems
- 2005
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Ingår i: Journal of Optimization Theory and Applications. - : Springer Science and Business Media LLC. - 0022-3239 .- 1573-2878. ; 127:1, s. 1-26
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Tidskriftsartikel (refereegranskat)abstract
- In solving the nonlinear least-squares problem of minimizing ||f(x)||22, difficulties arise with standard approaches, such as the Levenberg-Marquardt approach, when the Jacobian of f is rank-deficient or very ill-conditioned at the solution. To handle this difficulty, we study a special class of least-squares problems that are uniformly rank-deficient, i.e., the Jacobian of f has the same deficient rank in the neighborhood of a solution. For such problems, the solution is not locally unique. We present two solution tecniques: (i) finding a minimum-norm solution to the basic problem, (ii) using a Tikhonov regularization. Optimality conditions and algorithms are given for both of these strategies. Asymptotical convergence properties of the algorithms are derived and confirmed by numerical experiments. Extensions of the presented ideas make it possible to solve more general nonlinear least-squares problems in which the Jacobian of f at the solution is rank-deficient or ill-conditioned.
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| 4. |
- Gulliksson, Mårten, et al.
(författare)
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Implicit surface fitting using directional constraints
- 2001
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Ingår i: BIT Numerical Mathematics. - 0006-3835 .- 1572-9125. ; 41:1, s. 308-321
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Tidskriftsartikel (refereegranskat)abstract
- A commonly used technique for fitting curves and surfaces to measured data is that known as orthogonal distance regression, where the sum of squares of orthogonal distances from the data points to the surface is minimized. An alternative has recently been proposed for curves and surfaces which are parametrically defined, which minimizes the sum of squares in given directions which depend on the measuring process. In addition to taking account of that process, it is claimed that this technique has the advantage of complying with traditional fixed-regressor assumptions, enabling standard inference theory to apply. Here we consider extending this idea to curves and surfaces where the only assumption made is that there is an implicit formulation. Numerical results are given to illustrate the algorithmic performance.
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| 5. |
- Larsson, Torbjörn, et al.
(författare)
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A generic column generation principle: derivation and convergence analysis
- 2015
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Ingår i: Operational Research. - : Springer Science and Business Media LLC. - 1109-2858 .- 1866-1505. ; 15:2, s. 163-198
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Tidskriftsartikel (refereegranskat)abstract
- Given a non-empty, compact and convex set, and an a priori definedcondition which each element either satisfies or not, we want to find an elementbelonging to the former category. This is a fundamental problem of mathematicalprogramming which encompasses nonlinear programs, variational inequalities,saddle-point problems. We present a conceptual column generation scheme, whichalternates between solving a restriction of the original problem and a columngeneration phase which is used to augment the restricted problems. We establishgeneral applicability of the conceptual method, as well as to the three problemclasses mentioned. We also establish a version of the conceptual method in whichthe restricted and column generation problems are allowed to be solvedproximately, and of a version allowing for the dropping of columns. We showsome solution methods (e.g., Dantzig–Wolfe decomposition and simplicialcomposition) are special instances, and present new convergent column generationmethods in nonlinear programming, such as a sequential linear programming typemethod. Along the way, we also relate our quite general scheme in nonlinearprogramming presented in this paper with several other classic, and more recent,iterative methods in nonlinear optimization.
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| 6. |
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| 7. |
- Grip, Niklas, 1970-, et al.
(författare)
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Vibrationsanalys för tillståndsbedömning av byggkonstruktioner : Tillämpningsexempel : (Main results and summary in Swedish. Detailed results in English Appendices.)
- 2017
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- I projektet beskrivs och tillämpasnågra metoder för tillståndsbedömningav olika typer av konstruktioner med och utan skador.Tillståndsbedömningen skermed hjälp av vibrationsanalys.Detektering av skador av olika typ och storlekdiskuteras. Randvillkorens betydelse undersöks för att få överensstämmelse mellan förutspådda och uppmätta egenmoder och egenfrekvenser.Med den programvara som utvecklats är det möjligt att detektera sprickor i enkla betongplattor med hjälp av vibrationsmätningar. För mer avancerade konstruktioner finns en potential att vidareutveckla programvaran.Mätningar och analyser presenterasför femkonstruktioner: (1) En betongplatta –Sprickor har kunnat identifieras utifrån vibrationsmätningar och en successivt uppdaterad finit element modell (FEM).(2) En bågbro av betong över Långforsen i Kalix älv–Okända randvillkor har kunnat bestämmasför t ex undergrundens styvhetmedhjälp avuppmätta vibrationer. Detekteringav specifika skadorhar ännu inte kunnat genomföras.(3) En fackverksbro av stålöver Åby älv–Enviss skadedetektering har kunnat genomföras med vibrationsmätningar. Brons sårbarhet för korrosion och lokala mekaniska skador har studerats.(4) En förspänd betongbrotill gruvan i Kiruna–Modeller av bron har arbetats framför obelastatoch brottbelastat tillståndoch jämförts med uppmätta vibrationer med gott resultat.(5) Ett betonghus med nio våningar i Luleå –En FEM-modell av huseti bruksstadiethar tagits fram och resultat från den har jämförts med uppmätta vibrationer med gott resultat.Metoder och resultatpresenteras översiktligti rapportens huvudtext. Detaljerade beskrivningar gesi appendix.I appendix presenterasäven en programvaramed färdiga moduler för de undersökta konstruktionerna. Programmet kan laddas ner och användasfritt
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| 8. |
- Kjellmert, Bo, et al.
(författare)
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Time-dependent electromagnetic waves in a cavity
- 2009
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Ingår i: Applications of Mathematics. - : Institute of Mathematics, Czech Academy of Sciences. - 0862-7940 .- 1572-9109. ; 54:1, s. 17-45
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Tidskriftsartikel (refereegranskat)abstract
- The electromagnetic initial-boundary value problem for a cavity enclosed by perfectly conducting walls is considered. The cavity medium is defined by its permittivity and permeability which vary continuously in space. The electromagnetic field comes from a source in the cavity. The field is described by a magnetic vector potential A satisfying a wave equation with initial-boundary conditions. This description through A is rigorously shown to give a unique solution of the problem and is the starting point for numerical computations. A Chebyshev collocation solver has been implemented for a cubic cavity, and it has been compared to a standard finite element solver. The results obtained are consistent while the collocation solver performs substantially faster. Some time histories and spectra are computed.
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| 9. |
- Vanhatalo, Erik, et al.
(författare)
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Towards improved analysis methods for two-level factorial experiments with time series responses
- 2013
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Ingår i: Quality and Reliability Engineering International. - : Wiley. - 0748-8017 .- 1099-1638. ; 29:5, s. 725-741
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Tidskriftsartikel (refereegranskat)abstract
- Dynamic processes exhibit a time delay between the disturbances and the resulting process response. Therefore, one has to acknowledge process dynamics, such as transition times, when planning and analyzing experiments in dynamic processes. In this article, we explore, discuss, and compare different methods to estimate location effects for two-level factorial experiments where the responses are represented by time series. Particularly, we outline the use of intervention-noise modeling to estimate the effects and to compare this method by using the averages of the response observations in each run as the single response. The comparisons are made by simulated experiments using a dynamic continuous process model. The results show that the effect estimates for the different analysis methods are similar. Using the average of the response in each run, but removing the transition time, is found to be a competitive, robust, and straightforward method, whereas intervention-noise models are found to be more comprehensive, render slightly fewer spurious effects, find more of the active effects for unreplicated experiments and provide the possibility to model effect dynamics. Copyright © 2012 John Wiley & Sons, Ltd. Copyright © 2012 John Wiley & Sons, Ltd.
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| 10. |
- Bergström, Per, et al.
(författare)
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Efficient computation of the Gauss-Newton direction when fitting NURBS using ODR
- 2012
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Ingår i: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 52:3, s. 571-588
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Tidskriftsartikel (refereegranskat)abstract
- We consider a subproblem in parameter estimation using the Gauss-Newton algorithm with regularization for NURBS curve fitting. The NURBS curve is fitted to a set of data points in least-squares sense, where the sum of squared orthogonal distances is minimized. Control-points and weights are estimated. The knot-vector and the degree of the NURBS curve are kept constant. In the Gauss-Newton algorithm, a search direction is obtained from a linear overdetermined system with a Jacobian and a residual vector. Because of the properties of our problem, the Jacobian has a particular sparse structure which is suitable for performing a splitting of variables. We are handling the computational problems and report the obtained accuracy using different methods, and the elapsed real computational time. The splitting of variables is a two times faster method than using plain normal equations.
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