93,266 research outputs found
Parameter Identification in a Probabilistic Setting
Parameter identification problems are formulated in a probabilistic language,
where the randomness reflects the uncertainty about the knowledge of the true
values. This setting allows conceptually easily to incorporate new information,
e.g. through a measurement, by connecting it to Bayes's theorem. The unknown
quantity is modelled as a (may be high-dimensional) random variable. Such a
description has two constituents, the measurable function and the measure. One
group of methods is identified as updating the measure, the other group changes
the measurable function. We connect both groups with the relatively recent
methods of functional approximation of stochastic problems, and introduce
especially in combination with the second group of methods a new procedure
which does not need any sampling, hence works completely deterministically. It
also seems to be the fastest and more reliable when compared with other
methods. We show by example that it also works for highly nonlinear non-smooth
problems with non-Gaussian measures.Comment: 29 pages, 16 figure
Characterization of random stress fields obtained from polycrystalline aggregate calculations using multi-scale stochastic finite elements
The spatial variability of stress fields resulting from polycrystalline
aggregate calculations involving random grain geometry and crystal orientations
is investigated. A periodogram-based method is proposed to identify the
properties of homogeneous Gaussian random fields (power spectral density and
related covariance structure). Based on a set of finite element polycrystalline
aggregate calculations the properties of the maximal principal stress field are
identified. Two cases are considered, using either a fixed or random grain
geometry. The stability of the method w.r.t the number of samples and the load
level (up to 3.5 % macroscopic deformation) is investigated
Gradient-Based Estimation of Uncertain Parameters for Elliptic Partial Differential Equations
This paper addresses the estimation of uncertain distributed diffusion
coefficients in elliptic systems based on noisy measurements of the model
output. We formulate the parameter identification problem as an infinite
dimensional constrained optimization problem for which we establish existence
of minimizers as well as first order necessary conditions. A spectral
approximation of the uncertain observations allows us to estimate the infinite
dimensional problem by a smooth, albeit high dimensional, deterministic
optimization problem, the so-called finite noise problem in the space of
functions with bounded mixed derivatives. We prove convergence of finite noise
minimizers to the appropriate infinite dimensional ones, and devise a
stochastic augmented Lagrangian method for locating these numerically. Lastly,
we illustrate our method with three numerical examples
Bayesian Identification of Elastic Constants in Multi-Directional Laminate from Moir\'e Interferometry Displacement Fields
The ply elastic constants needed for classical lamination theory analysis of
multi-directional laminates may differ from those obtained from unidirectional
laminates because of three dimensional effects. In addition, the unidirectional
laminates may not be available for testing. In such cases, full-field
displacement measurements offer the potential of identifying several material
properties simultaneously. For that, it is desirable to create complex
displacement fields that are strongly influenced by all the elastic constants.
In this work, we explore the potential of using a laminated plate with an
open-hole under traction loading to achieve that and identify all four ply
elastic constants (E 1, E 2, 12, G 12) at once. However, the accuracy of the
identified properties may not be as good as properties measured from individual
tests due to the complexity of the experiment, the relative insensitivity of
the measured quantities to some of the properties and the various possible
sources of uncertainty. It is thus important to quantify the uncertainty (or
confidence) with which these properties are identified. Here, Bayesian
identification is used for this purpose, because it can readily model all the
uncertainties in the analysis and measurements, and because it provides the
full coupled probability distribution of the identified material properties. In
addition, it offers the potential to combine properties identified based on
substantially different experiments. The full-field measurement is obtained by
moir\'e interferometry. For computational efficiency the Bayesian approach was
applied to a proper orthogonal decomposition (POD) of the displacement fields.
The analysis showed that the four orthotropic elastic constants are determined
with quite different confidence levels as well as with significant correlation.
Comparison with manufacturing specifications showed substantial difference in
one constant, and this conclusion agreed with earlier measurement of that
constant by a traditional four-point bending test. It is possible that the POD
approach did not take full advantage of the copious data provided by the full
field measurements, and for that reason that data is provided for others to use
(as on line material attached to the article)
Cumulative reports and publications through December 31, 1990
This document contains a complete list of ICASE reports. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available
System Identification of Constructed Facilities: Challenges and Opportunities Across Hazards
The motivation, success and prevalence of full-scale monitoring of constructed buildings vary
considerably across the hazard of concern (earthquakes, strong winds, etc.), due in part to various
fiscal and life safety motivators. Yet while the challenges of successful deployment and
operation of large-scale monitoring initiatives are significant, they are perhaps dwarfed by the
challenges of data management, interrogation and ultimately system identification. Practical
constraints on everything from sensor density to the availability of measured input has driven the
development of a wide array of system identification and damage detection techniques, which in
many cases become hazard-specific. In this study, the authors share their experiences in fullscale monitoring of buildings across hazards and the associated challenges of system
identification. The study will conclude with a brief agenda for next generation research in the
area of system identification of constructed facilities
Energy-based trajectory tracking and vibration control for multilink highly flexible manipulators
In this paper, a discrete model is adopted, as proposed by Hencky for elastica based on rigid bars and lumped rotational springs, to design the control of a lightweight planar manipulator with multiple highly flexible links. This model is particularly suited to deal with nonlinear equations of motion as those associated with multilink robot arms, because it does not include any simplification due to linearization, as in the assumed modes method. The aim of the control is to track a trajectory of the end effector of the robot arm, without the onset of vibrations. To this end, an energy-based method is proposed. Numerical simulations show the effectiveness of the presented approach
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