Engineering topics

Banks, H. T.

Publications and source records attributed to Banks, H. T..

At least 37 records · Page 2

NASA NTRS1991

Active noise control - Piezoceramic actuators in fluid/structure interaction models

A model for a 2-D acoustic cavity with a flexible boundary (a beam) controlled via piezoceramic patches producing bending moments in the beam is considered. The associated control problem for this fluid/structure interaction system to reduce the acoustic pressure in the cavity involves unbounded control inputs. Approximation methods in the context of an LQR state space formulation are discussed, and numerical results are presented to demonstrate the effectiveness of this approach in computing feedback controls for noise reduction.

Banks, H. T.↗

NASA NTRS1991

Input-output stability for accelerometer control systems

It is shown that, although accelerometer control systems are not well-posed in the sense of Salamon, a well-defined input-output relation exists. It is established that the output of an accelerometer control system can be described by the convolution of the input and a distribution. This distribution is Laplace transformable, and the Laplace transform of the distribution is the transfer function of the system.

Banks, H. T.↗

NASA NTRS1990

Analytic semigroups: Applications to inverse problems for flexible structures

Convergence and stability results for least squares inverse problems involving systems described by analytic semigroups are presented. The practical importance of these results is demonstrated by application to several examples from problems of estimation of material parameters in flexible structures using accelerometer data.

Banks, H. T.↗

NASA NTRS1990

An approximation theory for the identification of nonlinear distributed parameter systems

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato appproximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

Banks, H. T.↗

NASA NTRS1989

Boundary estimation problems arising in thermal tomography

Problems on the identification of two-dimensional spatial domains arising in the detection and characterization of structural flaws in materials are considered. For a thermal diffusion system with external boundary input, observations of the temperature on the surface are used in a output least squares approach. Parameter estimation techniques based on the method of mappings are discussed and approximation schemes are developed based on a finite element Galerkin approach. Theoretical convergence results for computational techniques are given and the results are applied to experimental data for the identification of flaws in the thermal testing of materials.

Banks, H. T.↗

NASA NTRS1989

On damping mechanisms in beams

A partial differential equation model of a cantilevered beam with a tip mass at its free end is used to study damping in a composite. Four separate damping mechanisms consisting of air damping, strain rate damping, spatial hysteresis and time hysteresis are considered experimentally. Dynamic tests were performed to produce time histories. The time history data is then used along with an approximate model to form a sequence of least squares problems. The solution of the least squares problem yields the estimated damping coefficients. The resulting experimentally determined analytical model is compared with the time histories via numerical simulation of the dynamic response. The procedure suggested here is compared with a standard modal damping ratio model commonly used in experimental modal analysis.

Banks, H. T.↗

NASA NTRS1989

Optimal feedback control of infinite-dimensional parabolic evolution systems - Approximation techniques

A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

Banks, H. T.↗

NASA NTRS1989

Estimation on nonlinear damping in second order distributed parameter systems

An approximation and convergence theory for the identification of nonlinear damping in abstract wave equations is developed. It is assumed that the unknown dissipation mechanism to be identified can be described by a maximal monotone operator acting on the generalized velocity. The stiffness is assumed to be linear and symmetric. Functional analytic techniques are used to establish that solutions to a sequence of finite dimensional (Galerkin) approximating identification problems in some sense approximate a solution to the original infinite dimensional inverse problem.

Banks, H. T.↗

NASA NTRS1989

Boundary shape identification problems in two-dimensional domains related to thermal testing of materials

The identification of the geometrical structure of the system boundary for a two-dimensional diffusion system is reported. The domain identification problem treated here is converted into an optimization problem based on a fit-to-data criterion and theoretical convergence results for approximate identification techniques are discussed. Ressults of numerical experiments to demonstrate the efficacy of the theoretical ideas are reported.

Banks, H. T.↗

NASA NTRS1989

Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

Banks, H. T.↗

NASA NTRS1989

Numerical studies of identification in nonlinear distributed parameter systems

An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.

Banks, H. T.↗

NASA NTRS1989

Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

Banks, H. T.↗

NASA NTRS1989

Tau approximation techniques for identification of coefficients in parabolic PDE

A variant of the Tau method, called the weak Tau method, is developed on the basis of the weak form of the PDE for use in least-squares parameter estimation; also presented is a suitable abstract convergence framework. The emphasis is on the theoretical framework that allows treatment of the weak Tau method when it is applied to a wide class of inverse problems, including those for diffusion-advection equations, the Fokker-Planck model for population dynamics, and damped beam equations. Extensive numerical testing of the weak Tau method has demonstrated that it compares quite favorably with existing methods.

Banks, H. T.↗

NASA NTRS1989

Bending rate damping in elastic systems

Preliminary results of an investigation of the bending rate damping model for elastic structures are presented. A model for which the internal damping term is physically plausible and which can accomodate cantilevered boundary conditions is discussed. The model formulation and mathematical foundations are given, and numerical results are discussed.

Banks, H. T.↗

NASA NTRS1988

The identification of a distributed parameter model for a flexible structure

A computational method is developed for the estimation of parameters in a distributed model for a flexible structure. The structure we consider (part of the RPL experiment) consists of a cantilevered beam with a thruster and linear accelerometer at the free end. The thruster is fed by a pressurized hose whose horizontal motion effects the transverse vibration of the beam. The Euler-Bernoulli theory is used to model the vibration of the beam and treat the hose thruster assembly as a lumped or point mass dashpot spring system at the tip. Measurements of linear acceleration at the tip are used to estimate the hose parameters (mass, stiffness, damping) and a Voigt-Kelvin viscoelastic structural damping parameter for the beam using a least squares fit to the data. Spline based approximations are considered to the hybrid (coupled ordinary and partial differential equations) systems; theoretical convergence results and numerical studies with both simulation and actual experimental data obtained from the structure are presented and discussed.

Banks, H. T.↗

NASA NTRS1988

Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems

An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.

Banks, H. T.↗

NASA NTRS1988

An approximation theory for the identification of nonlinear distributed parameter systems

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

Banks, H. T.↗

NASA NTRS1988

Boundary shape identification problems in two-dimensional domains related to thermal testing of materials

The identification of the geometrical structure of the system boundary for a two-dimensional diffusion system is reported. The domain identification problem treated here is converted into an optimization problem based on a fit-to-data criterion and theoretical convergence results for approximate identification techniques are discussed. Results of numerical experiments to demonstrate the efficacy of the theoretical ideas are reported.

Banks, H. T.↗