NASA Scientific and Technical Aerospace Reports

little from one frequency to the next. This suggests that an iterative method using the solution at one frequency could be used
to obtain the next frequency solution. In this report, the matrix inverse at the first frequency serves as the preconditioner for
the preconditioned conjugate gradient method to obtain subsequent frequencies. For the problem examined in this report, in
which the matrix comes from the finite-element analysis of a cube, the iterative method is more than an order of magnitude
faster than Gaussian elimination.
DTIC
Frequency Response; Linear Equations; Sound Waves
20040073804 North Carolina Agricultural and Technical State Univ., Greensboro, NC
Language Analysis and Generation in Algebra Tutorial Dialogues for Language-Based Intelligent Tutoring Systems
Kim, Jung Hee; May 10, 2004; 18 pp.; In English
Contract(s)/Grant(s): N00014-02-1-0164
Report No.(s): AD-A422821; FRS-4-41204; No Copyright; Avail: CASI; A03, Hardcopy
The North Carolina A&T State University algebra tutoring dialogue project collects and analyzes algebra tutoring
dialogues with the aim of describing tutoring strategies and language with enough rigor that they may be evaluated and
incorporated in machine tutoring. The tutoring is computer-mediated chat-style, with the tutor and student collaboratively
solving a problem and editing equations. Transcripts of these dialogues are annotated for tutorial intentions. language, and
behaviors. Comparison of tutoring by more and less expert tutors allows us to focus on the strategies that are most effective.
The most prominent we observe is a metacognitive strategy where the tutor tries to elicit from the student a categorization of
the problem under discussion and to name a solution method. We combine these strategies into a structured set of tutorial
goals, with example sentences for each. In subsequent tutoring the computer then suggests these goals and sentences to the
- human tutor, who can pick use them in the dialogue. Measuring how much the tutors follow the computer-assistance, as well
as student learning gains, allows to evaluate the validity of our structural analysis of tutoring.
DTIC
Algebra; Computer Assisted Instruction
20040073825 Air Force Inst. of Tech., Wright-Patterson AFB, OH
Age Replacement and Service Rate Control of Stochastically Degrading Queues
Chapin, Patrick S.; Mar. 2004; 101 pp.; In English
Report No.(s): AD-A422880; AFIT/GOR/ENS/04-02; No Copyright; Avail: CASI; A06, Hardcopy
This thesis considers the problem of optimally selecting a periodic replacement time for a multiserver queueing system
in which each server is subject to degradation as a function of the mean service rate and a stochastic and dynamic environment.
Also considered is the problem of optimal service rate selection for such a system. In both cases, the performance metric is
the long-run average cost rate. Analytical expressions are obtained, in terms of Laplace transforms, for the nonlinear objective
functions, necessitating the use of numerical Laplace transform inversion to evaluate candidate solutions in conjunction with
standard numerical algorithms. Due to the convexity of the objective function, the optimal replacement time is computed using
a hybrid bisection-secant method which yields globally optimal solutions. The optimal service rates are obtained via gradient
search methods but are only guaranteed to provide locally optimal solutions. The analytical results are implemented on three
notional examples that demonstrate the benefits of dynamically adjusting service rates under the described maintenance policy.
DTIC
Aging (Materials); Degradation; Economic Factors; Replacing; Stochastic Processes
20040074229 NASA Langley Research Center, Hampton, VA, USA, National Inst. of Aerospace, Hampton, VA, USA
Stochastic Control Synthesis of Systems with Structured Uncertainty
Padula, Sharon L., Technical Monitor; Crespo, Luis G.; December 2003; 31 pp.; In English; Original contains black and white
illustrations
Contract(s)/Grant(s): NCC-1-02043; WU 762-20-61-01; 23-762-45-G6
Report No.(s): NASA/CR-2003-212167; NIA-2003-01; No Copyright; Avail: CASI; A03, Hardcopy
This paper presents a study on the design of robust controllers by using random variables to model structured uncertainty
for both SISO and MIMO feedback systems. Once the parameter uncertainty is prescribed with probability density functions,
its effects are propagated through the analysis leading to stochastic metrics for the system’s output. Control designs that aim
for satisfactory performances while guaranteeing robust closed loop stability are attained by solving constrained non-linear
optimization problems in the frequency domain. This approach permits not only to quantify the probability of having unstable
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