R. Chris Camphouse

A Framework for Assessing the Resilience of Infrastructure and Economic Systems

Recent U.S. national mandates are shifting the country’s homeland security policy from one of asset-level critical infrastructure protection (CIP) to allhazards critical infrastructure resilience, creating the need for a unifying framework for assessing the resilience of critical infrastructure systems and the economies that rely on them. Resilience has been defined and applied in many disciplines; consequently, many disparate approaches exist. We propose a general framework for assessing the resilience of infrastructure and economic systems. The framework consists of three primary components: (1) a definition of resilience that is specific to infrastructure systems; (2) a quantitative model for measuring the resilience of systems to disruptive events through the evaluation of both impacts to system performance and the cost of recovery; and (3) a qualitative method for assessing the system properties that inherently determine system resilience, providing insight and direction for potential improvements in these systems.

Infrastructure resilience assessment through control design

Infrastructure resilience is a priority for homeland security in many nations around the globe. This paper describes a new approach for quantitatively assessing the resilience of critical infrastructure systems. The mathematics of optimal control design provides the theoretical foundation for this methodology. This foundation enables the inclusion of recovery costs within the resilience assessment approach, a unique capability for quantitative resilience assessment techniques. This paper describes the formulation of the optimal control problem for a set of representative infrastructure models. This example demonstrates the importance of recovery costs in quantitative resilience analysis, and the increased capability provided by this approachs ability to discern between varying levels of resilience.

Boundary Feedback Flow Control: Proportional Control with Potential Application to Aero-Optics

A large percentage of the losses in performance and effectiveness of airborne optical systems are caused by turbulence. In an effort to reduce these adverse effects in airborne optical systems, we are exploring the use of both openand closed-loop flow control over a cylindrical turret. A series of experiments were performed at a Reynolds number of 2 10, based on the turret’s diameter and freestream velocity, which corresponds to aMach number of 0.3. The three-dimensional turret contained an actuation system that consists of 17 synthetic jets placed upstream from the leading edge of the aperture. Initially, a large database containing no control and open-loop control was obtained. These data sets provide a rich ensemble for the development and application of a simple proportional closed-loop control with the use of proper orthogonal decomposition. Surface pressuremeasurements were acquired across the aperture region for all cases studied. Results from the open-loop test demonstrate a reduction of 19.6% in the root-mean-square values when compared to the baseline case. The closed-loop flow control results show that the root-mean-square pressure fluctuations are reduced by 25.7%, the integral scales are significantly reduced, and the flow is driven toward homogeneity.

Reduced Order Modelling and Boundary Feedback Control of Nonlinear Convection

A distributed parameter model of a nonlinear two-dimensional convective system is formulated. Proper orthogonal decomposition is used to construct a reduced order state-space model of the system. Open-loop simulations of the full and reduced models are compared to demonstrate the validity of the reduced model. A linear quadratic regulator control problem is formulated for the system under boundary control. Control efiectiveness is demonstrated in reduced and full order simulations.

Empirical reduced-order modeling for boundary feedback flow control

This paper deals with the practical and theoretical implications of model reduction for aerodynamic flow-based control problems. Various aspects of model reduction are discussed that apply to partial differential equation-(PDE-) based models in general. Specifically, the proper orthogonal decomposition (POD) of a high dimension system as well as frequency domain identification methods are discussed for initial model construction. Projections on the POD basis give a nonlinear Galerkin model. Then, a model reduction method based on empirical balanced truncation is developed and applied to the Galerkin model. The rationale for doing so is that linear subspace approximations to exact submanifolds associated with nonlinear controllability and observability require only standard matrix manipulations utilizing simulation/experimental data. The proposed method uses a chirp signal as input to produce the output in the eigensystem realization algorithm (ERA). This method estimates the systems Markov parameters that accurately reproduce the output. Balanced truncation is used to show that model reduction is still effective on ERA produced approximated systems. The method is applied to a prototype convective flow on obstacle geometry. An H∞ feedback flow controller is designed based on the reduced model to achieve tracking and then applied to the full-order model with excellent performance.

Feedback Control for a Two-Dimensional Burgers' Equation System Model

In this paper, we consider the problem of controlling a system governed by a two-dimensional nonlinear partial differential equation. Motivation for the problem is the development of control methodologies for fluid flow, where the dynamics of the system are governed by the nonlinear Navier-Stokes equations. An initial boundary value problem described by the twodimensional Burgers’ equation is formulated to model a right-travelling shock over an obstacle. We focus on implementing feedback control via Dirichlet boundary conditions on the obstacle. We formulate a control problem for the system model, and examine two different methods of finding the control. The first method involves obtaining the solution of an algebraic Riccati equation. The second method involves obtaining a steady-state solution of the Chandrasekhar equations. Numerical approximations are developed to numerically simulate solutions of the problem with and without control. Numerical examples are presented to illustrate the efficacy, as well as the shortcomings, of the control method. Additionally, the influence of boundary condition on the functional gains, and the resulting controls, is demonstrated through numerical examples. Avenues of future work are presented.

Flow and aero-optics around a turret. Part 1. Open loop flow control

A large percentage of the losses in performance and eectiveness of airborne optical systems are caused by turbulence. In particular, separated turbulent flow phenomena is present in several aero-optics applications. In an eort to reduce the adverse eects of turbulence in airborne optical systems, we are exploring the use of both open and closedloop flow control over a cylindrical turret. A series of experiments were performed at Reynolds number of 2;000;000 that corresponds to a Mach number of 0:3 using a half scale test model. The 3D turret contained an actuation system that consists of 17 synthetic jets placed upstream from the leading edge of the aperture. Multiple actuation cases were tested to evaluate the eects of active flow control over the aperture area and their control authority. Simultaneous surface pressure and velocity measurements were acquired in the separated region for both with and without flow control. Pressure results from the open loop test presents reduction of 10 percent in the root-mean-square values when compare to the baseline case. Two-point statistics showed that the forcing is driving the flow towards homogeneity across the surface of turret.

Rotation implementation of a circular cylinder in incompressible flow via staggered grid approach

In this paper, we present a finite difference method for the implementation of the rotation of a circular cylinder in the incompressible flow field by solving the two-dimensional unsteady Navier-Stokes equations. The approach is to use staggered grid method so that the accuracy and order of convergence of the associated algorithms can be maintained. The proposed method is easy to be implemented and is effective. A set of simulations for the flow dynamics is provided to show the computational results.