Abstract: The Boundary Representation of a 3D manifold contains
FACES (connected subsets of a parametric surface S : R2 -!
R3). In many science and engineering applications it is cumbersome
and algebraically difficult to deal with the polynomial set and
constraints (LOOPs) representing the FACE. Because of this reason, a
Piecewise Linear (PL) approximation of the FACE is needed, which is
usually represented in terms of triangles (i.e. 2-simplices). Solving the
problem of FACE triangulation requires producing quality triangles
which are: (i) independent of the arguments of S, (ii) sensitive to the
local curvatures, and (iii) compliant with the boundaries of the FACE
and (iv) topologically compatible with the triangles of the neighboring
FACEs. In the existing literature there are no guarantees for the point
(iii). This article contributes to the topic of triangulations conforming
to the boundaries of the FACE by applying the concept of parameterindependent
Gabriel complex, which improves the correctness of the
triangulation regarding aspects (iii) and (iv). In addition, the article
applies the geometric concept of tangent ball to a surface at a point to
address points (i) and (ii). Additional research is needed in algorithms
that (i) take advantage of the concepts presented in the heuristic
algorithm proposed and (ii) can be proved correct.
Abstract: This paper is concerned with an improved algorithm
based on the piecewise-smooth Mumford and Shah (MS) functional
for an efficient and reliable segmentation. In order to speed up
convergence, an additional force, at each time step, is introduced
further to drive the evolution of the curves instead of only driven by
the extensions of the complementary functions u + and u - . In our
scheme, furthermore, the piecewise-constant MS functional is
integrated to generate the extra force based on a temporary image that
is dynamically created by computing the union of u + and u - during
segmenting. Therefore, some drawbacks of the original algorithm,
such as smaller objects generated by noise and local minimal problem
also are eliminated or improved. The resulting algorithm has been
implemented in Matlab and Visual Cµ, and demonstrated efficiently
by several cases.
Abstract: The complex hybrid and nonlinear nature of many processes that are met in practice causes problems with both structure modelling and parameter identification; therefore, obtaining a model that is suitable for MPC is often a difficult task. The basic idea of this paper is to present an identification method for a piecewise affine (PWA) model based on a fuzzy clustering algorithm. First we introduce the PWA model. Next, we tackle the identification method. We treat the fuzzy clustering algorithm, deal with the projections of the fuzzy clusters into the input space of the PWA model and explain the estimation of the parameters of the PWA model by means of a modified least-squares method. Furthermore, we verify the usability of the proposed identification approach on a hybrid nonlinear batch reactor example. The result suggest that the batch reactor can be efficiently identified and thus formulated as a PWA model, which can eventually be used for model predictive control purposes.
Abstract: This paper presents a generalized formulation for the
problem of buckling optimization of anisotropic, radially graded,
thin-walled, long cylinders subject to external hydrostatic pressure.
The main structure to be analyzed is built of multi-angle fibrous
laminated composite lay-ups having different volume fractions of the
constituent materials within the individual plies. This yield to a
piecewise grading of the material in the radial direction; that is the
physical and mechanical properties of the composite material are
allowed to vary radially. The objective function is measured by
maximizing the critical buckling pressure while preserving the total
structural mass at a constant value equals to that of a baseline
reference design. In the selection of the significant optimization
variables, the fiber volume fractions adjoin the standard design
variables including fiber orientation angles and ply thicknesses. The
mathematical formulation employs the classical lamination theory,
where an analytical solution that accounts for the effective axial and
flexural stiffness separately as well as the inclusion of the coupling
stiffness terms is presented. The proposed model deals with
dimensionless quantities in order to be valid for thin shells having
arbitrary thickness-to-radius ratios. The critical buckling pressure
level curves augmented with the mass equality constraint are given
for several types of cylinders showing the functional dependence of
the constrained objective function on the selected design variables. It
was shown that material grading can have significant contribution to
the whole optimization process in achieving the required structural
designs with enhanced stability limits.