1,363 research outputs found
Good measures on locally compact Cantor sets
We study the set M(X) of full non-atomic Borel (finite or infinite) measures
on a non-compact locally compact Cantor set X. For an infinite measure in
M(X), the set is called defective. We call
non-defective if . The class
consists of probability measures and infinite non-defective measures. We
classify measures from with respect to a homeomorphism. The
notions of goodness and compact open values set are defined. A
criterion when two good measures from are homeomorphic is given. For
any group-like we find a good probability measure on X
such that . For any group-like and any
locally compact, zero-dimensional, metric space A we find a good non-defective
measure on X such that and is
homeomorphic to A. We consider compactifications cX of X and give a criterion
when a good measure can be extended to a good measure on cX.Comment: 21 page
Multi-disciplinary optimization of aeroservoelastic systems
Efficient analytical and computational tools for simultaneous optimal design of the structural and control components of aeroservoelastic systems are presented. The optimization objective is to achieve aircraft performance requirements and sufficient flutter and control stability margins with a minimal weight penalty and without violating the design constraints. Analytical sensitivity derivatives facilitate an efficient optimization process which allows a relatively large number of design variables. Standard finite element and unsteady aerodynamic routines are used to construct a modal data base. Minimum State aerodynamic approximations and dynamic residualization methods are used to construct a high accuracy, low order aeroservoelastic model. Sensitivity derivatives of flutter dynamic pressure, control stability margins and control effectiveness with respect to structural and control design variables are presented. The performance requirements are utilized by equality constraints which affect the sensitivity derivatives. A gradient-based optimization algorithm is used to minimize an overall cost function. A realistic numerical example of a composite wing with four controls is used to demonstrate the modeling technique, the optimization process, and their accuracy and efficiency
Multi-disciplinary optimization of aeroservoelastic systems
New methods were developed for efficient aeroservoelastic analysis and optimization. The main target was to develop a method for investigating large structural variations using a single set of modal coordinates. This task was accomplished by basing the structural modal coordinates on normal modes calculated with a set of fictitious masses loading the locations of anticipated structural changes. The following subject areas are covered: (1) modal coordinates for aeroelastic analysis with large local structural variations; and (2) time simulation of flutter with large stiffness changes
Homeomorphic measures on stationary Bratteli diagrams
We study the set S of ergodic probability Borel measures on stationary
non-simple Bratteli diagrams which are invariant with respect to the tail
equivalence relation. Equivalently, the set S is formed by ergodic probability
measures invariant with respect to aperiodic substitution dynamical systems.
The paper is devoted to the classification of measures from S with
respect to a homeomorphism. The properties of these measures related to the
clopen values set are studied. It is shown that for every measure
in S there exists a subgroup G of such that is the
intersection of G with [0,1], i.e. is group-like. A criterion of
goodness is proved for such measures. This result is used to classify the
measures from S up to a homeomorphism. It is proved that for every good measure
in S there exist countably many measures
from S such that and are homeomorphic measures but the tail
equivalence relations on corresponding Bratteli diagrams are not orbit
equivalent.Comment: 36 pages, references added, typos fixe
Subdiagrams of Bratteli diagrams supporting finite invariant measures
We study finite measures on Bratteli diagrams invariant with respect to the
tail equivalence relation. Amongst the proved results on finiteness of measure
extension, we characterize the vertices of a Bratteli diagram that support an
ergodic finite invariant measure.Comment: 9 page
Aeroservoelastic modeling and applications using minimum-state approximations of the unsteady aerodynamics
Various control analysis, design, and simulation techniques for aeroelastic applications require the equations of motion to be cast in a linear time-invariant state-space form. Unsteady aerodynamics forces have to be approximated as rational functions of the Laplace variable in order to put them in this framework. For the minimum-state method, the number of denominator roots in the rational approximation. Results are shown of applying various approximation enhancements (including optimization, frequency dependent weighting of the tabular data, and constraint selection) with the minimum-state formulation to the active flexible wing wind-tunnel model. The results demonstrate that good models can be developed which have an order of magnitude fewer augmenting aerodynamic equations more than traditional approaches. This reduction facilitates the design of lower order control systems, analysis of control system performance, and near real-time simulation of aeroservoelastic phenomena
Physically weighted approximations of unsteady aerodynamic forces using the minimum-state method
The Minimum-State Method for rational approximation of unsteady aerodynamic force coefficient matrices, modified to allow physical weighting of the tabulated aerodynamic data, is presented. The approximation formula and the associated time-domain, state-space, open-loop equations of motion are given, and the numerical procedure for calculating the approximation matrices, with weighted data and with various equality constraints are described. Two data weighting options are presented. The first weighting is for normalizing the aerodynamic data to maximum unit value of each aerodynamic coefficient. The second weighting is one in which each tabulated coefficient, at each reduced frequency value, is weighted according to the effect of an incremental error of this coefficient on aeroelastic characteristics of the system. This weighting yields a better fit of the more important terms, at the expense of less important ones. The resulting approximate yields a relatively low number of aerodynamic lag states in the subsequent state-space model. The formulation forms the basis of the MIST computer program which is written in FORTRAN for use on the MicroVAX computer and interfaces with NASA's Interaction of Structures, Aerodynamics and Controls (ISAC) computer program. The program structure, capabilities and interfaces are outlined in the appendices, and a numerical example which utilizes Rockwell's Active Flexible Wing (AFW) model is given and discussed
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