In the dissertation, a monotone spline-based nonparametric estimation method is proposed for analyzing longitudinal data with mixture distributions. The innovative and efficient algorithm combining the concept of projected Newton-Raphson algorithm with linear mixed model estimation method is developed to obtain the nonparametric estimation of monotone B-spline functions. This algorithm provides an efficient and flexible approach for modeling longitudinal data monotonically. An iterative 'one-step-forward' algorithm based on the K-means clustering is then proposed to classify mixture distributions of longitudinal data. This algorithm is computationally efficient, especially for data with a large number of underlying distributions. To quantify the disparity of underlying distributions of longitudinal data, we also propose an index measure on the basis of the aggregated areas under the curve (AAUC), which makes no distributional assumptions and fits the theme of nonparametric analysis. An extensive simulation study is conducted to assess the empirical performance of our method under different AAUC values, covariance structures, and sample sizes. Finally, we apply the new approach in the PREDICT-HD study, a multi-site observational study of Huntington Disease (HD), to explore and assess clinical markers in motor and cognitive domains for the purpose of distinguishing participants at risk of HD from healthy subjects.

An evolutionary geometry parametrization is established to represent aerodynamic configurations. This geometry parametrization technique is constructed by integrating the classical B-spline formulation with the knot insertion algorithm. It is capable of inserting control points to a given parametrization without modifying its geometry. Taking advantage of this technique, a shape design problem can be solved as a sequence of optimizations from the basic parametrization to more refined parametrizations. Owing to the nature of the B-spline formulation, feasible parametrization refinements are not unique; guidelines based on sensitivity analysis and geometry constraints are developed to assist the automation of the proposed optimization sequence. Test cases involving airfoil optimization and induced drag minimization are solved adopting this method. Its effectiveness is demonstrated through comparisons with optimizations using uniform refined parametrizations.

An evolutionary geometry parametrization is established to represent aerodynamic configurations. This geometry parametrization technique is constructed by integrating the classical B-spline formulation with the knot insertion algorithm. It is capable of inserting control points to a given parametrization without modifying its geometry. Taking advantage of this technique, a shape design problem can be solved as a sequence of optimizations from the basic parametrization to more refined parametrizations. Owing to the nature of the B-spline formulation, feasible parametrization refinements are not unique; guidelines based on sensitivity analysis and geometry constraints are developed to assist the automation of the proposed optimization sequence. Test cases involving airfoil optimization and induced drag minimization are solved adopting this method. Its effectiveness is demonstrated through comparisons with optimizations using uniform refined parametrizations.

For modelling curves, B-splines [3] are among the most versatile control schemes. However, scaling this technique to surface patches has proven to be a non-trivial endeavor. While a suitable scheme exists for rectangular patches in the form of tensor product B-splines, techniques involving the triangular domain are much less spectacular. The current cutting edge in triangular B-splines [2] is the DMS-spline. While the resulting surfaces possess high degrees of continuity, the control scheme is awkward and the evaluation is computationally expensive. A more fundamental problem is the construction bears little resemblance to the construction used for the B-Spline. This deficiency leads to the central idea of the thesis; what happens if the simple blending functions found at the heart of the B-Spline construction are used over higher dimension domains? In this thesis I develop a geometric generalization of B-Spline curves over the triangular domain. This construction mimics the control point blending that occurs with uniform B-Splines. The construction preserves the simple control scheme and evaluation of B-Splines, without the immense computational requirements of DMS-splines. The result is a new patch control scheme, the G-Patch, possessing <i>C</i>0 continuity between adjacent patches.

For modelling curves, B-splines [3] are among the most versatile control schemes. However, scaling this technique to surface patches has proven to be a non-trivial endeavor. While a suitable scheme exists for rectangular patches in the form of tensor product B-splines, techniques involving the triangular domain are much less spectacular. The current cutting edge in triangular B-splines [2] is the DMS-spline. While the resulting surfaces possess high degrees of continuity, the control scheme is awkward and the evaluation is computationally expensive. A more fundamental problem is the construction bears little resemblance to the construction used for the B-Spline. This deficiency leads to the central idea of the thesis; what happens if the simple blending functions found at the heart of the B-Spline construction are used over higher dimension domains? In this thesis I develop a geometric generalization of B-Spline curves over the triangular domain. This construction mimics the control point blending that occurs with uniform B-Splines. The construction preserves the simple control scheme and evaluation of B-Splines, without the immense computational requirements of DMS-splines. The result is a new patch control scheme, the G-Patch, possessing <i>C</i>0 continuity between adjacent patches.

This dissertation presents a synthesis of methods for structural optimization of aircraft wing boxes. The optimization problem considered herein is the minimization of structural weight with respect to component sizes, subject to stress constraints. Different aspects of structural optimization methods representing the current state-of-the-art are discussed, including sequential quadratic programming, sensitivity analysis, parameterization of design variables, constraint handling, and multiple load treatment. Shortcomings of the current techniques are identified and a B-spline parameterization representing the structural sizes is proposed to address them. A new configurable B-spline parameterization method for structural optimization of wing boxes is developed that makes it possible to flexibly explore design spaces. An automatic scheme using different levels of B-spline parameterization configurations is also proposed, along with a constraint aggregation method in order to reduce the computational effort. Numerical results are compared to evaluate the effectiveness of the B-spline approach and the constraint aggregation method. To evaluate the new formulations and explore design spaces, the wing box of an airliner is optimized for the minimum weight subject to stress constraints under multiple load conditions. The new approaches are shown to significantly reduce the computational time required to perform structural optimization and to yield designs that are more realistic than existing methods.

Chemnitz, Techn. Univ., Diss., 2006.

Zugl.: Braunschweig, Techn. Univ., Diss., 2009

Universiẗat, Diss., 2000--Kassel. / Lizenzpflichtig.

University, Diss., 2005--Bonn.