665 research outputs found
Flexible Tools for Specifying Design Variation
This paper describes flexible tools for specifying design variations that are based on nonuniform profile tolerance definitions. These tools specify bounds of design performance that can be used for negotiation among engineers in a collaborative design process. These specification methods allow for the capture of many different design functions that are not easily described with current tool designs. In addition, these specification methods lend themselves to efficient verification methods. Profile tolerance definitions provide the most general variation controls for complex mechanical surfaces. Common design practices and engineering standards for profile tolerances exhibit many weaknesses and limitations. We present a rationale for a complete specification approach using B-splines [1, 2] for profile tolerances, and illustrate the approach with examples. B-splines can be used to specify both uniform and nonuniform profile tolerance boundaries. Subsequently, algorithms for the evaluation of actual feature deviations and reporting methodologies for such tolerance zones are presented
Representation and Analysis of Multi-Modal, Nonuniform Time Series Data: An Application to Survival Prognosis of Oncology Patients in an Outpatient Setting
The representation of nonuniform, multi-modal, time-limited time series data is complex and explored through the use of discrete representation, dimensionality reduction with segmentation based techniques, and with behavioral representation approaches. These explorations are done with a focus on an outpatient oncology setting with the classification and regression analysis being used for length of survival prognosis. Each decision of representation and analysis is not independent, with implications of each decision in method for how the data is represented and then which analysis technique is used. One unique aspect of the work is the use of outpatient clinical data for patients, which was explored initially through discrete sampling and behavioral representation. The length of survival was evaluated with both classification and regression methods initially. The first conclusion determined that including more discrete samples in the model showed no statistical benefit and the addition of behavioral approaches did improve the prognostic accuracy.
From this result, the adaption of Piecewise Aggregate Approximation was made to accommodate the multi-modal time series data of the outpatient clinical data, and evaluated with the regression methodologies. This representation approach demonstrated promise due to the simplicity but had decreased performance in the length of survival prognosis compared with behavioral representation and discrete samples approach. A solution was a new representation approach made which incorporates a genetic algorithm to select the window boundaries of the Piecewise Aggregate Approximation method. This selection is based on the fraction of the Piecewise Aggregate Approximation windows that contain values other than zero. The new representation improved the performance in some cases by a 20% reduction in median relative error
Estimates for the spectral condition number of cardinal B-spline collocation matrices
The famous de Boor conjecture states that the condition of the polynomial B-spline collocation matrix at the knot averages is bounded independently of the knot sequence, i.e., it depends only on the spline degree.
For highly nonuniform knot meshes, like geometric meshes, the conjecture is known to be false. As an effort towards finding an answer for uniform meshes, we investigate the spectral condition number of cardinal B-spline collocation matrices. Numerical testing strongly suggests that the conjecture is true for cardinal B-splines
Fast Isogeometric Boundary Element Method based on Independent Field Approximation
An isogeometric boundary element method for problems in elasticity is
presented, which is based on an independent approximation for the geometry,
traction and displacement field. This enables a flexible choice of refinement
strategies, permits an efficient evaluation of geometry related information, a
mixed collocation scheme which deals with discontinuous tractions along
non-smooth boundaries and a significant reduction of the right hand side of the
system of equations for common boundary conditions. All these benefits are
achieved without any loss of accuracy compared to conventional isogeometric
formulations. The system matrices are approximated by means of hierarchical
matrices to reduce the computational complexity for large scale analysis. For
the required geometrical bisection of the domain, a strategy for the evaluation
of bounding boxes containing the supports of NURBS basis functions is
presented. The versatility and accuracy of the proposed methodology is
demonstrated by convergence studies showing optimal rates and real world
examples in two and three dimensions.Comment: 32 pages, 27 figure
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