7,728 research outputs found
Low-order coupled map lattices for estimation of wake patterns behind vibrating flexible cables
Fluid-structure interaction arises in a wide array of technological applications including naval and marine hydrodynamics, civil and wind engineering and flight vehicle aerodynamics. When a fluid flows over a bluff body such as a circular cylinder, the periodic vortex shedding in the wake causes fluctuating lift and drag forces on the body. This phenomenon can lead to fatigue damage of the structure due to large amplitude vibration. It is widely believed that the wake structures behind the structure determine the hydrodynamic forces acting on the structure and control of wake structures can lead to vibration control of the structure. Modeling this complex non-linear interaction requires coupling of the dynamics of the fluid and the structure. In this thesis, however, the vibration of the flexible cylinder is prescribed, and the focus is on modeling the fluid dynamics in its wake. Low-dimensional iterative circle maps have been found to predict the universal dynamics of a two-oscillator system such as the rigid cylinder wake. Coupled map lattice (CML)models that combine a series of low-dimensional circle maps with a diffusion model have previously predicted qualitative features of wake patterns behind freely vibrating cables at low Reynolds number. However, the simple nature of the CML models implies that there will always be unmodelled wake dynamics if a detailed, quantitative comparison is made with laboratory or simulated wake flows. Motivated by a desire to develop an improved CML model, we incorporate self-learning features into a new CML that is trained to precisely estimate wake patterns from target numerical simulations and experimental wake flows. The eventual goal is to have the CML learn from a laboratory flow in real time. A real-time self-learning CML capable of estimating experimental wake patterns could serve as a wake model in a future anticipated feedback control system designed to produce desired wake patterns. A new convective-diffusive map that includes additional wake dynamics is developed. Two different self-learning CML models, each capable of precisely estimating complex wake patterns, have been developed by considering additional dynamics from the convective-diffusive map. The new self-learning CML models use adaptive estimation schemes which seek to precisely estimate target wake patterns from numerical simulations and experiments. In the first self-learning CML, the estimator scheme uses a multi-variable least-squares algorithm to adaptively vary the spanwise velocity distribution in order to minimize the state error (difference between modeled and target wake patterns). The second self-learning model uses radial basis function neural networks as online approximators of the unmodelled dynamics. Additional unmodelled dynamics not present in the first self-learning CML model are considered here. The estimator model uses a combination of a multi-variable normalized least squares scheme and a projection algorithm to adaptively vary the neural network weights. Studies of this approach are conducted using wake patterns from spectral element based NEKTAR simulations of freely vibrating cable wakes at low Reynolds numbers on the order of 100. It is shown that the self-learning models accurately and efficiently estimate the simulated wake patterns within several shedding cycles. Next, experimental wake patterns behind different configurations of rigid cylinders were obtained. The self-learning CML models were then used for off-line estimation of the stored wake patterns. With the eventual goal of incorporating low-order CML models into a wake pattern control system in mind, in a related study control terms were added to the simple CML model in order to drive the wake to the desired target pattern of shedding. Proportional, adaptive proportional and non-linear control techniques were developed and their control efficiencies compared
An EnKF-Based Flow State Estimator for Aerodynamic Flows
Regardless of plant model, robust flow estimation based on limited measurements remains a major obstacle to successful flow control applications. Aiming to combine the robustness of a high-dimensional representation of the dynamics with the cost efficiency of a low-order approximation of the state covariance matrix, a flow state estimator based on the Ensemble Kalman Filter (EnKF) is applied to two-dimensional flow past a cylinder and an airfoil at high angle of attack and low Reynolds number. For the development purposes, we use the numerical algorithm as both the estimator and as a surrogate for the measurements. Estimation is successful using a reduced number of either pressure sensors on the surface of the body or sparsely placed velocity probes in the wake. Because the most relevant features of these flows is restricted to a low-dimensional subspace/manifold of the state space, asymptotic behavior of the estimator is shown to be achieved with a small ensemble size. The relative importance of each sensor location is evaluated by analyzing how they influence the estimated flow field. Covariance inflation is used to enhance the estimator performance in the presence of unmodeled free stream perturbations. A combination of parametric modeling and augmented state methodology is used to successfully estimate the forces on immersed bodies
Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators
We present an estimator-based control design procedure for flow control,
using reduced-order models of the governing equations, linearized about a
possibly unstable steady state. The reduced models are obtained using an
approximate balanced truncation method that retains the most controllable and
observable modes of the system. The original method is valid only for stable
linear systems, and we present an extension to unstable linear systems. The
dynamics on the unstable subspace are represented by projecting the original
equations onto the global unstable eigenmodes, assumed to be small in number. A
snapshot-based algorithm is developed, using approximate balanced truncation,
for obtaining a reduced-order model of the dynamics on the stable subspace. The
proposed algorithm is used to study feedback control of 2-D flow over a flat
plate at a low Reynolds number and at large angles of attack, where the natural
flow is vortex shedding, though there also exists an unstable steady state. For
control design, we derive reduced-order models valid in the neighborhood of
this unstable steady state. The actuation is modeled as a localized body force
near the leading edge of the flat plate, and the sensors are two velocity
measurements in the near-wake of the plate. A reduced-order Kalman filter is
developed based on these models and is shown to accurately reconstruct the flow
field from the sensor measurements, and the resulting estimator-based control
is shown to stabilize the unstable steady state. For small perturbations of the
steady state, the model accurately predicts the response of the full
simulation. Furthermore, the resulting controller is even able to suppress the
stable periodic vortex shedding, where the nonlinear effects are strong, thus
implying a large domain of attraction of the stabilized steady state.Comment: 36 pages, 17 figure
Sum-of-Squares approach to feedback control of laminar wake flows
A novel nonlinear feedback control design methodology for incompressible
fluid flows aiming at the optimisation of long-time averages of flow quantities
is presented. It applies to reduced-order finite-dimensional models of fluid
flows, expressed as a set of first-order nonlinear ordinary differential
equations with the right-hand side being a polynomial function in the state
variables and in the controls. The key idea, first discussed in Chernyshenko et
al. 2014, Philos. T. Roy. Soc. 372(2020), is that the difficulties of treating
and optimising long-time averages of a cost are relaxed by using the
upper/lower bounds of such averages as the objective function. In this setting,
control design reduces to finding a feedback controller that optimises the
bound, subject to a polynomial inequality constraint involving the cost
function, the nonlinear system, the controller itself and a tunable polynomial
function. A numerically tractable approach to the solution of such optimisation
problems, based on Sum-of-Squares techniques and semidefinite programming, is
proposed.
To showcase the methodology, the mitigation of the fluctuation kinetic energy
in the unsteady wake behind a circular cylinder in the laminar regime at
Re=100, via controlled angular motions of the surface, is numerically
investigated. A compact reduced-order model that resolves the long-term
behaviour of the fluid flow and the effects of actuation, is derived using
Proper Orthogonal Decomposition and Galerkin projection. In a full-information
setting, feedback controllers are then designed to reduce the long-time average
of the kinetic energy associated with the limit cycle. These controllers are
then implemented in direct numerical simulations of the actuated flow. Control
performance, energy efficiency, and physical control mechanisms identified are
analysed. Key elements, implications and future work are discussed
Rough clustering for web transactions
Grouping web transactions into clusters is important in order to obtain better
understanding of user's behavior. Currently, the rough approximation-based
clustering technique has been used to group web transactions into clusters. It is based
on the similarity of upper approximations of transactions by given threshold.
However, the processing time is still an issue due to the high complexity for finding
the similarity of upper approximations of a transaction which used to merge between
two or more clusters. In this study, an alternative technique for grouping web
transactions using rough set theory is proposed. It is based on the two similarity
classes which is nonvoid intersection. The technique is implemented in MATLAB
®
version 7.6.0.324 (R2008a). The two UCI benchmark datasets taken from:
http:/kdd.ics.uci.edu/ databases/msnbc/msnbc.html and
http:/kdd.ics.uci.edu/databases/ Microsoft / microsoft.html are opted in the
simulation processes. The simulation reveals that the proposed technique
significantly requires lower response time up to 62.69 % and 66.82 % as compared to
the rough approximation-based clustering, severally. Meanwhile, for cluster purity it
performs better until 2.5 % and 14.47%, respectively
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