794 research outputs found
Acceleration of Uncertainty Updating in the Description of Transport Processes in Heterogeneous Materials
The prediction of thermo-mechanical behaviour of heterogeneous materials such
as heat and moisture transport is strongly influenced by the uncertainty in
parameters. Such materials occur e.g. in historic buildings, and the durability
assessment of these therefore needs a reliable and probabilistic simulation of
transport processes, which is related to the suitable identification of
material parameters. In order to include expert knowledge as well as
experimental results, one can employ an updating procedure such as Bayesian
inference. The classical probabilistic setting of the identification process in
Bayes's form requires the solution of a stochastic forward problem via
computationally expensive sampling techniques, which makes the method almost
impractical. In this paper novel stochastic computational techniques such as
the stochastic Galerkin method are applied in order to accelerate the updating
procedure. The idea is to replace the computationally expensive forward
simulation via the conventional finite element (FE) method by the evaluation of
a polynomial chaos expansion (PCE). Such an approximation of the FE model for
the forward simulation perfectly suits the Bayesian updating. The presented
uncertainty updating techniques are applied to the numerical model of coupled
heat and moisture transport in heterogeneous materials with spatially varying
coefficients defined by random fields
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
Inverse Problems in a Bayesian Setting
In a Bayesian setting, inverse problems and uncertainty quantification (UQ)
--- the propagation of uncertainty through a computational (forward) model ---
are strongly connected. In the form of conditional expectation the Bayesian
update becomes computationally attractive. We give a detailed account of this
approach via conditional approximation, various approximations, and the
construction of filters. Together with a functional or spectral approach for
the forward UQ there is no need for time-consuming and slowly convergent Monte
Carlo sampling. The developed sampling-free non-linear Bayesian update in form
of a filter is derived from the variational problem associated with conditional
expectation. This formulation in general calls for further discretisation to
make the computation possible, and we choose a polynomial approximation. After
giving details on the actual computation in the framework of functional or
spectral approximations, we demonstrate the workings of the algorithm on a
number of examples of increasing complexity. At last, we compare the linear and
nonlinear Bayesian update in form of a filter on some examples.Comment: arXiv admin note: substantial text overlap with arXiv:1312.504
Multiphysics modelling and experimental validation of microelectromechanical resonator dynamics
The modelling of microelectromechanical systems provides a very challenging task in microsystems engineering. This field of research is inherently multiphysics of nature, since different physical phenomena are tightly intertwined at microscale. Typically, up to four different physical domains are usually considered in the analysis of microsystems: mechanical, electrical, thermal and fluidic. For each of these separate domains, well-established modelling and analysis techniques are available. However, one of the main challenges in the field of microsystems engineering is to connect models for the behavior of the device in each of these domains to equivalent lumped or reduced-order models without making unacceptably inaccurate assumptions and simplifications and to couple these domains correctly and efficiently. Such a so-called multiphysics modelling framework is very important for simulation of microdevices, since fast and accurate computational prototyping may greatly shorten the design cycle and thus the time-to-market of new products. This research will focus on a specific class of microsystems: microelectromechanical resonators. MEMS resonators provide a promising alternative for quartz crystals in time reference oscillators, due to their small size and on-chip integrability. However, because of their small size, they have to be driven into nonlinear regimes in order to store enough energy for obtaining an acceptable signal-to-noise ratio in the oscillator. Since these resonators are to be used as a frequency reference in the oscillator circuits, their steady-state (nonlinear) dynamic vibration behaviour is of special interest. A heuristic modelling approach is investigated for two different MEMS resonators, a clamped-clamped beam resonator and a dog-bone resonator. For the clamped-clamped beam resonator, the simulations with the proposed model shows a good agreement with experimental results, but the model is limited in its predictive capabilities. For the dogbone resonator, the proposed heuristic modelling approach does not lead to a match between simulations and experiments. Shortcomings of the heuristic modelling approach serve as a motivation for a first-principles based approach. The main objective of this research is to derive a multiphysics modelling framework for MEMS resonators that is based on first-principles formulations. The framework is intended for fast and accurate simulation of the steady-state nonlinear dynamic behaviour of MEMS resonators. Moreover, the proposed approach is validated by means of experiments. Although the multiphysics modelling framework is proposed for MEMS resonators, it is not restricted to this application field within microsystems engineering. Other fields, such as (resonant) sensors, switches and variable capacitors, allow for a similar modelling approach. In the proposed framework, themechanical, electrical and thermal domains are included. Since the resonators considered are operated in vacuum, the fluidic domain (squeeze film damping) is not included. Starting from a first-principles description, founded on partial differential equations (PDEs), characteristic nonlinear effects from each of the included domains are incorporated. Both flexural and bulk resonators can be considered. Next, Galerkin discretization of the coupled PDEs takes place, to construct reduced-order models while retaining the nonlinear effects. The multiphysics model consists of the combined reduced-order models from the different domains. Designated numerical tools are used to solve for the steady-state nonlinear dynamic behaviour of the combined model. The proposed semi-analytical (i.e. analytical-numerical) multiphysics modeling framework is illustrated for a full case study of an electrostatically actuated single-crystal silicon clamped-clamped beam MEMS resonator. By means of the modelling framework, multiphysics models of varying complexity have been derived for this resonator, including effects like electrostatic actuation, fringing fields, shear deformation, rotary inertia, thermoelastic damping and nonlinear material behaviour. The first-principles based approach allows for addressing the relevance of individual effects in a straightforward way, such that the models can be used as a (pre-)design tool for dynamic response analysis. The method can be considered complementary to conventional finite element simulations. The multiphysics model for the clamped-clamped beam resonator is validated by means of experiments. A good match between the simulations and experiments is obtained, thereby giving confidence in the proposed modelling framework. Finally, next to themodelling approach for MEMS resonators, a technique for using these nonlinear resonators in an oscillator circuit setting is presented. This approach, called phase feedback, allows for operation of the resonator in its nonlinear regime. The closedloop technique enables control of both the frequency of oscillation and the output power of the signal. Additionally, optimal operation points for oscillator circuits incorporating a nonlinear resonator can be defined
Inverse problems and uncertainty quantification
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) -
the propagation of uncertainty through a computational (forward) model - are
strongly connected. In the form of conditional expectation the Bayesian update
becomes computationally attractive. This is especially the case as together
with a functional or spectral approach for the forward UQ there is no need for
time-consuming and slowly convergent Monte Carlo sampling. The developed
sampling-free non-linear Bayesian update is derived from the variational
problem associated with conditional expectation. This formulation in general
calls for further discretisation to make the computation possible, and we
choose a polynomial approximation. After giving details on the actual
computation in the framework of functional or spectral approximations, we
demonstrate the workings of the algorithm on a number of examples of increasing
complexity. At last, we compare the linear and quadratic Bayesian update on the
small but taxing example of the chaotic Lorenz 84 model, where we experiment
with the influence of different observation or measurement operators on the
update.Comment: 25 pages, 17 figures. arXiv admin note: text overlap with
arXiv:1201.404
Optimal control of wave energy converters
Wave Energy Converters (WECs) are devices designed to absorb energy from ocean waves.
The particular type of Wave Energy Converter (WEC) considered in this thesis is an oscillating
body; energy conversion is carried out by means of a structure immersed in water which
oscillates under forces exerted by waves. This thesis addresses the control of oscillating body
WECs and the objective of the control system is to optimise the motion of the devices that maximises
the energy absorption. In particular, this thesis presents the formulation of the optimal
control problem for WECs in the framework of direct transcription methods, known as spectral
and pseudospectral optimal control. Direct transcription methods transform continuous time
optimal control problems into Non Linear Programming (NLP) problems, for which the literature
(and the market) offer a large number of standard algorithms (and software packages). It
is shown, in this thesis, that direct transcription gives the possibility of formulating complex
control problems where realistic scenarios can be taken into account, such as physical limitations
and nonlinearities in the behaviour of the devices. Additionally, by means of spectral and
pseudospectral methods, it is possible to find an approximation of the optimal solution directly
from sampled frequency and impulse response models of the radiation forces, obviating the
need for finite order approximate models. By implementing a spectral method, convexity of
the NLP problem, associated with the optimal control problem for a single body WEC described
by a linear model, is demonstrated analytically. The solution to a nonlinear optimal control
problem is approximated by means of pseudospectral optimal control. In the nonlinear case,
simulation results show a significant difference in the optimal behaviour of the device, both in
the motion and in the energy absorption, when the quadratic term describing the viscous forces
are dominant, compared to the linear case. This thesis also considers the comparison of two
control strategies for arrays of WECs. A Global Control strategy computes the optimal motion
by taking into account the complete model of the array and it provides the global optimum for
the absorbed energy. In contrast, an Independent Control strategy implements a control system
on each device which is independent from all the other devices. The final part of the thesis illustrates
an approach for the study of the effects of constraints on the total absorbed energy. The
procedure allows the feasibility of the constrained energy maximisation problem to be studied,
and it provides an intuitive framework for the design of WECs relating to the power take-off
operating envelope, thanks to the geometrical interpretation of the functions describing both
the total absorbed energy and the constraints
Statistical extraction of process zones and representative subspaces in fracture of random composite
We propose to identify process zones in heterogeneous materials by tailored
statistical tools. The process zone is redefined as the part of the structure
where the random process cannot be correctly approximated in a low-dimensional
deterministic space. Such a low-dimensional space is obtained by a spectral
analysis performed on pre-computed solution samples. A greedy algorithm is
proposed to identify both process zone and low-dimensional representative
subspace for the solution in the complementary region. In addition to the
novelty of the tools proposed in this paper for the analysis of localised
phenomena, we show that the reduced space generated by the method is a valid
basis for the construction of a reduced order model.Comment: Submitted for publication in International Journal for Multiscale
Computational Engineerin
Optimal control of wave energy converters
Wave Energy Converters (WECs) are devices designed to absorb energy from ocean waves.
The particular type of Wave Energy Converter (WEC) considered in this thesis is an oscillating
body; energy conversion is carried out by means of a structure immersed in water which
oscillates under forces exerted by waves. This thesis addresses the control of oscillating body
WECs and the objective of the control system is to optimise the motion of the devices that maximises
the energy absorption. In particular, this thesis presents the formulation of the optimal
control problem for WECs in the framework of direct transcription methods, known as spectral
and pseudospectral optimal control. Direct transcription methods transform continuous time
optimal control problems into Non Linear Programming (NLP) problems, for which the literature
(and the market) offer a large number of standard algorithms (and software packages). It
is shown, in this thesis, that direct transcription gives the possibility of formulating complex
control problems where realistic scenarios can be taken into account, such as physical limitations
and nonlinearities in the behaviour of the devices. Additionally, by means of spectral and
pseudospectral methods, it is possible to find an approximation of the optimal solution directly
from sampled frequency and impulse response models of the radiation forces, obviating the
need for finite order approximate models. By implementing a spectral method, convexity of
the NLP problem, associated with the optimal control problem for a single body WEC described
by a linear model, is demonstrated analytically. The solution to a nonlinear optimal control
problem is approximated by means of pseudospectral optimal control. In the nonlinear case,
simulation results show a significant difference in the optimal behaviour of the device, both in
the motion and in the energy absorption, when the quadratic term describing the viscous forces
are dominant, compared to the linear case. This thesis also considers the comparison of two
control strategies for arrays of WECs. A Global Control strategy computes the optimal motion
by taking into account the complete model of the array and it provides the global optimum for
the absorbed energy. In contrast, an Independent Control strategy implements a control system
on each device which is independent from all the other devices. The final part of the thesis illustrates
an approach for the study of the effects of constraints on the total absorbed energy. The
procedure allows the feasibility of the constrained energy maximisation problem to be studied,
and it provides an intuitive framework for the design of WECs relating to the power take-off
operating envelope, thanks to the geometrical interpretation of the functions describing both
the total absorbed energy and the constraints
- …