VTechWorks Repository :: Browsing by Author "Cliff, Eugene M."

Browsing by Author "Cliff, Eugene M."

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Acceleration techniques for the radiative analysis of general computational fluid dynamics solutions using reverse Monte-Carlo ray tracing
Turk, Jeffrey A. (Virginia Tech, 1994)
A reverse Monte-Carlo ray trace capable of performing a radiative analysis on arbitrary multiple overlapping structured computational fluid dynamics solution sets is developed. In order to make effective use of time, a method based on a set of simplifying assumptions but using the same calculation procedures is developed for comparison and study purposes. Three acceleration techniques are tried. One acceleration technique reduces the grid dimensions to reduce the number of volumes intersected. The second acceleration technique develops a version of the code for execution in a parallel processing environment. The third acceleration technique mixes an orthogonal, evenly spaced grid with the computational fluid dynamics grids to obtain fast ray traversal of low variance areas while retaining the higher resolution of the computational fluid dynamics grids in the high variance areas. Two experimental data sets are used for comparison and as test cases during these studies: an exhaust plume from an auxiliary power unit, and a Boeing 747 in flight. Timing for the baseline and accelerated analyses is provided as well as numerical comparisons for a selected subset.
An active-constraint logic for nonlinear programming
Das, Alok (Virginia Polytechnic Institute and State University, 1982)
The choice of active-constraint logic for screening inequalities has a major impact on the performance of gradient-projection method. It has been found that least-constrained strategies, which keep the number of constraints in the active set as small as possible, are computationally most efficient. However, these strategies are often prone to cycling of constraints between active and inactive status. This occurs mainly due to the violation of some of the constraints, taken as inactive, by the resulting step. This research develops methods for choosing an active set such that constraints in the active set satisfy the Kuhn-Tucker conditions and the resulting step does not violate the linear approximations to any of the constraints satisfied as equalities but considered inactive. Some of the existing active-constraint logics, specifically the dual-violator rule, yield the desired active set when two constraints are satisfied as equalities. However, when three or more constraints are satisfied as equalities, none of the existing logics give the desired active set. A number of general results, which help in the selection of the active set, have been developed in this research. An active-constraint logic has been developed for the case of three constraints. This logic gives the desired active-set. For the general case, when more than three constraints are satisfied as equalities, a separate active-set logic is suggested. This guarantees the nonviolation of the linear approximations to any of the constraints, taken as inactive, by the resulting step. The resulting active-set may not, however, satisfy the Kuhn-Tucker conditions. The efficiency of the proposed logic was tested computationally using quadratic programming problems. Three existing active-set strategies were used for comparision. The proposed logic almost always performed as well or better than the best among the three existing active-set strategies.
Aerodynamic Modeling Using Computational Fluid Dynamics and Sensitivity Equations
Limache, Alejandro Cesar (Virginia Tech, 2000-04-10)
A mathematical model for the determination of the aerodynamic forces acting on an aircraft is presented. The mathematical model is based on the generalization of the idea of aerodynamically steady motions. One important use of these results is the determination of steady (time-invariant) aerodynamic forces and moments. Such aerodynamic forces can be determined using computer simulation by determining numerically the associated steady flows around the aircraft when it is moving along such generalized steady trajectories. The method required the extension of standard (inertial) CFD formulations to general non-inertial reference frames. Generalized Navier-Stokes and Euler equations have been derived. The formulation is valid for all ranges of Mach numbers including transonic flow. The method was implemented numerically for the planar case using the generalized Euler equations. The developed computer codes can be used to obtain numerical flow solutions for airfoils moving in general steady motions (i.e. circular motions). From these numerical solutions it is possible to determine the variation of the lift, drag and pitching moment with respect to the pitch rate at different Mach numbers and angles of attack. One of the advantages of the mathematical model developed here is that the aerodynamic forces become well-defined functions of the motion variables (including angular rates). In particular, the stability derivatives are associated with partial derivatives of these functions. These stability derivatives can be computed using finite differences or the sensitivity equation method.
Aircraft cruise performance optimization using chattering controls
Bhardwaj, Pradeep (Virginia Tech, 1986-07-05)
Aircraft Cruise Performance is examined by using energy-state modelling to investigate fuel-range optimal trajectories. Chattering controls are considered appropriate when the hodograph is non-convex. Classical steady-state cruise, simple chattering-cruise and the extended chattering-cruise models are studied as constrained parameter-optimization problems. The term "extended chattering" refers to vehicle system modelling extended to maintain vertical equilibrium only on the average. Numerical solution is obtained using a variable-metric gradient-protection algorithm and computational results are presented for three different aircraft. This study shows that simple chattering cruise for certain specific energies can result in substantial fuel savings over classical steady-state cruise. However extended chattering cruise results in only marginal fuel savings when compared to simple chattering cruise.
Aircraft Multidisciplinary Design Optimization using Design of Experiments Theory and Response Surface Modeling Methods
Giunta, Anthony A. (Virginia Tech, 1997-05-01)
Design engineers often employ numerical optimization techniques to assist in the evaluation and comparison of new aircraft configurations. While the use of numerical optimization methods is largely successful, the presence of numerical noise in realistic engineering optimization problems often inhibits the use of many gradient-based optimization techniques. Numerical noise causes inaccurate gradient calculations which in turn slows or prevents convergence during optimization. The problems created by numerical noise are particularly acute in aircraft design applications where a single aerodynamic or structural analysis of a realistic aircraft configuration may require tens of CPU hours on a supercomputer. The computational expense of the analyses coupled with the convergence difficulties created by numerical noise are significant obstacles to performing aircraft multidisciplinary design optimization. To address these issues, a procedure has been developed to create two types of noise-free mathematical models for use in aircraft optimization studies. These two methods use elements of statistical analysis and the overall procedure for using the methods is made computationally affordable by the application of parallel computing techniques. The first modeling method, which has been the primary focus of this work, employs classical statistical techniques in response surface modeling and least squares surface fitting to yield polynomial approximation models. The second method, in which only a preliminary investigation has been performed, uses Bayesian statistics and an adaptation of the Kriging process in Geostatistics to create exponential function-based interpolating models. The particular application of this research involves modeling the subsonic and supersonic aerodynamic performance of high-speed civil transport (HSCT) aircraft configurations. The aerodynamic models created using the two methods outlined above are employed in HSCT optimization studies so that the detrimental effects of numerical noise are reduced or eliminated during optimization. Results from sample HSCT optimization studies involving five and ten variables are presented here to demonstrate the utility of the two modeling methods.
An alternating direction search algorithm for low dimensional optimization: an application to power flow
Burrell, Tinal R. (Virginia Tech, 1993-05-05)
Presented in this paper is a scheme for minimizing the cost function of a three-source technique to arrive at an approximation point (I,J) that is within one unit of the true minimum. The Line-Step algorithm is applied to several systems and is also compared to other minimization techniques, including the Equal Incremental Loss Algorithm. Variations are made on the Line-Step Algorithm for faster convergence and also to handle inequality constraints.
Analysis and Approximation of Viscoelastic and Thermoelastic Joint-Beam Systems
Fulton, Brian I. (Virginia Tech, 2006-07-21)
Rigidizable/Inflatable space structures have been the focus of renewed interest in recent years due to efficient packaging for transport. In this work, we examine new mathematical systems used to model small-scale joint dynamics for inflatable space truss structures. We investigate the regularity and asymptotic behavior of systems resulting from various damping models, including Kelvin-Voigt, Boltzmann, and thermoelastic damping. Approximation schemes will also be introduced. Finally, we look at optimal control for the Kelvin-Voigt model using a linear feedback regulator.
Analysis and numerical approximations of exact controllability problems for systems governed by parabolic differential equations
Cao, Yanzhao (Virginia Tech, 1996-06-16)
The exact controllability problems for systems modeled by linear parabolic differential equations and the Burger's equations are considered. A condition on the exact controllability of linear parabolic equations is obtained using the optimal control approach. We also prove that the exact control is the limit of appropriate optimal controls. A numerical scheme of computing exact controls for linear parabolic equations is constructed based on this result. To obtain numerical approximation of the exact control for the Burger's equation, we first construct another numerical scheme of computing exact controls for linear parabolic equations by reducing the problem to a hypoelliptic equation problem. A numerical scheme for the exact zero control of the Burger's equation is then constructed, based on the simple iteration of the corresponding linearized problem. The efficiency of the computational methods are illustrated by a variety of numerical experiments.
Analysis of flutter and flutter suppression via an energy method
York, Darrell L. (Virginia Tech, 1980-05-01)
The design of modern high-performance aircraft is toward increased aerodynamic efficiency, decreased structural weight, and higher flight speeds. Preliminary designs often exhibit a flutter instability within the desired operating envelope of the aircraft. Passive methods which have been used to solve the flutter problem include added structural stiffness, mass balancing, and speed restrictions. These methods may result in significant weight penalties. Studies by Boeing (ref. 1) show that weight penalties as high as 2 to 4% of the total structural weight may be required to solve the flutter problem passively by increasing the structural stiffness. Therefore, there is considerable interest in alternative methods of increasing the flutter speed beyond the original unaided value.
Analysis of the dynamic stability derivatives for high angle of attack aircraft
Ko, Joon Soo (Virginia Polytechnic Institute and State University, 1985)
Modern, high performance aircraft are required to be able to fly and be controlled over a wide variety of flight conditions. In order to predict the aircraft behavior and control requirements over the entire flight regime it is necessary to have a proper aerodynamic model. Flight conditions at high angles of attack lead to separated flows making the aerodynamic model more difficult to obtain. In this research wind tunnel experiments are performed on an F-5 air-craft model at high angles of attack, with small oscillations about the body oriented roll axis. In addition the free stream environment can be configured in one of three ways: l) straight uniform flow, 2) curved flow to simulated a horizontal turn, and 3) rolling flow to simulated a roll motion about the relative Velocity vector.
Analysis, finite element approximation, and computation of optimal and feedback flow control problems
Lee, Hyung-Chun (Virginia Tech, 1994-07-05)
The analysis, finite element approximation, and numerical simulation of some control problems associated with fluid flows are considered. First, we consider a coupled solid/fluid temperature control problem. This optimization problem is motivated by the desire to remove temperature peaks, i.e., "hot spots", along the bounding surface of containers of fluid flows. The heat equation of the solid container is coupled to the energy equation for the fluid. Control is effected by adjustments to the temperature of the fluid at the inflow boundary. We give a precise statement of the mathematical model, prove the existence and uniqueness of optimal solutions, and derive an optimality system. We study a finite element approximation and provide rigorous error estimates for the error in the approximate solution of the optimality system. We then develop and implement an iterative algorithm to compute the approximate solution. Second, a computational study of the feedback control of the magnitude of the lift in flow around a cylinder is presented. The uncontrolled flow exhibits an unsymmetric Karman vortex street and a periodic lift coefficient. The size of the oscillations in the lift is reduced through an active feedback control system. The control used is the injection and suction of fluid through orifices on the cylinder; the amount of fluid injected or sucked is determined, through a simple feedback law, from pressure measurements at stations along the surface of the cylinder. The results of some computational experiments are given; these indicate that the simple feedback law used is effective in reducing the size of the oscillations in the lift. Finally, some boundary value problems which arise from a feedback control problem are considered. We give a precise statement of the mathematical problems and then prove the existence and uniqueness of solutions to the boundary value problems for the Laplace and Stokes equations by studying the boundary integral equation method.
Analytical and experimental comparison of deterministic and probabilistic optimization
Ponslet, Eric (Virginia Tech, 1994)
The probabilistic approach to design optimization has received increased attention in the last two decades. It is widely recognized that such an approach should lead to designs that make better use of the resources than designs obtained with the classical deterministic approach by distributing safety onto the different components and/or failure modes of a system in an optimal manner. However, probabilistic models rely on a number of assumptions regarding the magnitude of the uncertainties, their distributions, correlations, etc. In addition, modelling errors and approximate reliability calculations (first order methods for example) introduce uncertainty in the predicted system reliability. Because of these inaccuracies, it is not clear if a design obtained from probabilistic optimization will really be more reliable than a design based on deterministic optimization. The objective of this work is to provide a partial answer to this question through laboratory experiments — such experimental validation is not currently available in the literature. A cantilevered truss structure is used as a test case. First, the uncertainties in stiffness and mass properties of the truss elements are evaluated from a large number of measurements. The transmitted scatter in the natural frequencies of the truss is computed and compared to experimental estimates obtained from measurements on 6 realizations of the structure. The experimental results are in reasonable agreement with the predictions, although the magnitude of the transmitted scatter is extremely small. The truss is then equipped with passive viscoelastic tuned dampers for vibration control. The controlled structure is optimized by selecting locations for the dampers and for tuning masses added to the truss. The objective is to satisfy upper limits on the acceleration at given points on the truss for a specified excitation. The properties of the dampers are the primary sources of uncertainties. Two optimal designs are obtained from deterministic and probabilistic optimizations; the deterministic approach maximizes safety margins while the probability of failure (i.e. exceeding the acceleration limit) is minimized in the probabilistic approach. The optimizations are performed with genetic algorithms. The predicted probability of failure of the optimum probabilistic design is less than half that of the deterministic optimum. Finally, optimal deterministic and probabilistic designs are compared in the laboratory. Because small differences in failure rates between two designs are not measurable with a reasonable number of tests, we use anti-optimization to identify a design problem that maximizes the contrast in probability of failure between the two approaches. The anti-optimization is also performed with a genetic algorithm. For the problem identified by the anti-optimization, the probability of failure of the optimum probabilistic design is 25 times smaller than that of the deterministic design. The rates of failure are then measured by testing 29 realizations of each optimum design. The results agree well with the predictions and confirm the larger reliability of the probabilistic design. However, the probabilistic optimum is shown to be very sensitive to modelling errors. This sensitivity can be reduced by including the modelling errors as additional uncertainties in the probabilistic formulation.
Analytical and Numerical Optimal Motion Planning for an Underwater Glider
Kraus, Robert J. (Virginia Tech, 2010-03-30)
The use of autonomous underwater vehicles (AUVs) for oceanic observation and research is becoming more common. Underwater gliders are a specific class of AUV that do not use conventional propulsion. Instead they change their buoyancy and center of mass location to control attitude and trajectory. The vehicles spend most of their time in long, steady glides, so even minor improvements in glide range can be magnified over multiple dives. This dissertation presents a rigid-body dynamic system for a generic vehicle operating in a moving fluid (ocean current or wind). The model is then reduced to apply to underwater gliders. A reduced-order point-mass model is analyzed for optimal gliding in the presence of a current. Different numerical method solutions are compared while attempting to achieve maximum glide range. The result, although approximate, provides good insight into how the vehicles may be operated more effectively. At the end of each dive, the gliders must change their buoyancy and pitch to transition to a climb. Improper scheduling of the buoyancy and pitch change may cause the vehicle to stall and lose directional stability. Optimal control theory is applied to the buoyancy and angle of attack scheduling of a point-mass model. A rigid-body model is analyzed on a singular arc steady glide. An analytical solution for the control required to stay on the arc is calculated. The model is linearized to calculate possible perturbation directions while remaining on the arc. The nonlinear model is then propagated in forward and reverse time with the perturbations and analyzed. Lastly, one of the numerical solutions is analyzed using the singular arc equations for verification. This work received support from the Office of Naval Research under Grant Number N00014-08-1-0012.
Application of Control Allocation Methods to Linear Systems with Four or More Objectives
Beck, Roger Ezekiel (Virginia Tech, 2002-06-11)
Methods for allocating redundant controls for systems with four or more objectives are studied. Previous research into aircraft control allocation has focused on allocating control effectors to provide commands for three rotational degrees of freedom. Redundant control systems have the capability to allocate commands for a larger number of objectives. For aircraft, direct force commands can be applied in addition to moment commands. When controls are limited, constraints must be placed on the objectives which can be achieved. Methods for meeting commands in the entire set of of achievable objectives have been developed. The Bisecting Edge Search Algorithm has been presented as a computationally efficient method for allocating controls in the three objective problem. Linear programming techniques are also frequently presented. This research focuses on an effort to extend the Bisecting Edge Search Algorithm to handle higher numbers of objectives. A recursive algorithm for allocating controls for four or more objectives is proposed. The recursive algorithm is designed to be similar to the three objective allocator and to require computational effort which scales linearly with the controls. The control allocation problem can be formulated as a linear program. Some background on linear programming is presented. Methods based on five formulations are presented. The recursive allocator and linear programming solutions are implemented. Numerical results illustrate how the average and worst case performance scales with the problem size. The recursive allocator is found to scale linearly with the number of controls. As the number of objectives increases, the computational time grows much faster. The linear programming solutions are also seen to scale linearly in the controls for problems with many more controls than objectives. In online applications, computational resources are limited. Even if an allocator performs well in the average case, there still may not be sufficient time to find the worst case solution. If the optimal solution cannot be guaranteed within the available time, some method for early termination should be provided. Estimation of solutions from current information in the allocators is discussed. For the recursive implementation, this estimation is seen to provide nearly optimal performance.
Approximation and control of a thermoviscoelastic system
Liu, Zhuangyi (Virginia Polytechnic Institute and State University, 1989)
In this paper consider the problem of controlling a thermoviscoelastic system. We present a semigroup setting for this system, and prove the well-posedness by applying a general theorem which is given in this paper. We also study the stability of the system. We give a finite element/averaging scheme to approximate the linear quadratic regulator problem governed by the system. We prove that yields faster convergence. We give a proof of convergence of the simulation problem for singular kernels and of the control problem for L2 kernels. We carry on the numerical computation to investigate the effect of heat transfer on damping and the closed-loop system.
Approximation and Control of the Boussinesq Equations with Application to Control of Energy Efficient Building Systems
Hu, Weiwei (Virginia Tech, 2012-05-21)
In this thesis we present theoretical and numerical results for a feedback control problem defined by a thermal fluid. The problem is motivated by recent interest in designing and controlling energy efficient building systems. In particular, we show that it is possible to locally exponentially stabilize the nonlinear Boussinesq Equations by applying Neumann/Robin type boundary control on a bounded and connected domain. The feedback controller is obtained by solving a Linear Quadratic Regulator problem for the linearized Boussinesq equations. Applying classical results for semilinear equations where the linear term generates an analytic semigroup, we establish that this Riccati-based optimal boundary feedback control provides a local stabilizing controller for the full nonlinear Boussinesq equations. In addition, we present a finite element Galerkin approximation. Finally, we provide numerical results based on standard Taylor-Hood elements to illustrate the theory.
Approximation of integro-partial differential equations of hyperbolic type
Fabiano, Richard H. (Virginia Polytechnic Institute and State University, 1986)
A state space model is developed for a class of integro-partial differential equations of hyperbolic type which arise in viscoelasticity. An approximation scheme is developed based on a spline approximation in the spatial variable and an averaging approximation in the de1ay variable. Techniques from linear semigroup theory are used to discuss the well-posedness of the state space model and the convergence properties of the approximation scheme. We give numerical results for a sample problem to illustrate some properties of the approximation scheme.
Approximation of the LQR control problem for systems governed by partial functional differential equations
Miller, Robert Edwin (Virginia Polytechnic Institute and State University, 1988)
We present an abstract framework for state space formulation and a generalized theorem on well-posedness which can be applied to a class of partial functional differential equations which arise in the modeling of viscoelastic and certain thermo-viscoelastic systems. Examples to which the theory applies include both second- and fourth-order equations with a variety of boundary conditions. The theory presented here allows for singular kernels as well as flexibility in the choice of state space. We discuss an approximation scheme using spline in the spatial variable and an averaging scheme in the delay variable. We compare a uniform mesh to a nonuniform mesh and give numerical results which indicate that the non-uniform mesh, which gives a better approximation of the kernel near the singularity, yields faster convergence. We give a proof of convergence of the simulation problem for singular kernels and of the control problem for bounded kernels. We use techniques of semigroup theory to establish the results on well-posedness and convergence.
Approximations and Object-Oriented Implementation for a Parabolic Partial Differential Equation
Camphouse, Russell C. (Virginia Tech, 1999-01-27)
This work is a numerical study of the 2-D heat equation with Dirichlet boundary conditions over a polygonal domain. The motivation for this study is a chemical vapor deposition (CVD) reactor in which a substrate is heated while being exposed to a gas containing precursor molecules. The interaction between the gas and the substrate results in the deposition of a compound thin film on the substrate. Two different numerical approximations are implemented to produce numerical solutions describing the conduction of thermal energy in the reactor. The first method used is a Crank-Nicholson finite difference technique which tranforms the 2-D heat equation into an algebraic system of equations. For the second method, a semi-discrete method is used which transforms the partial differential equation into a system of ordinary differential equations. The goal of this work is to investigate the influence of boundary conditions, domain geometry, and initial condition on thermal conduction throughout the reactor. Once insight is gained with respect to the aforementioned conditions, optimal design and control can be investigated. This work represents a first step in our long term goal of developing optimal design and control of such CVD systems. This work has been funded through Partnerships in Research Excellence and Transition (PRET) grant number F49620-96-1-0329.
Aspect ratio effects on wings at low Reynolds numbers
Abtahi, Ali A. (Virginia Polytechnic Institute and State University, 1985)
In this study the primary objective was to determine the effect of aspect ratio in particular and in general the effect of three dimensionality on the flow around wings at low Reynolds numbers. It was seen that the effects observed at high Reynolds number are also present in this Re range. There is the usual increase in lift slope and this increase can even be predicted with reasonable accuracy using Prandtl's lifting line theory. In addition to the change in lift slope the zero lift angle of attack was also influenced by the aspect ratio. Through flow visualization it was ascertained that the wingtips have a rather restricted effect on the laminar separation bubble. The disappearance of the bubble extends only for a small distance inboard from the tips. The size of the hysteresis loop and the Reynolds number at which hysteresis starts was found to be influenced by the aspect ratio. The momentum deficit method was used to validate the data obtained by the strain gauge method and there was adequate agreement between the values found through the two methods. From the measurements of pressure done around the airfoil contour one could determine both the location of the laminar separation bubble and the regions were flow is separated. The pressure taps themselves were found to influence measurements somewhat in certain regions of angle of attack and Reynolds number. In the future it would be beneficial to continue strain gauge measurements on this airfoil with flaps and control surfaces to determine their effect on the formation of the laminar separation bubble. Also measurements on other shapes would give more insight into the phenomena occurring here. The effects of turbulence and noise will have to be investigated in detail to determine what performance to expect from an actual aircraft. Finally detailed measurements on boundary layer stability and its effect on the occurrence of reattachment should be studied in detail to gain insight into the reasons for the presence of a hysteresis loop in stall at these Reynolds numbers.

Browsing by Author "Cliff, Eugene M."

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