THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

A method, called the Eigensystem Realization Algorithm (ERA), is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system modes and noise modes. For illustration of the algorithm, examples are shown using simulation data and experimental data for a rectangular grid structure.

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An eigensystem realization algorithm for modal parameter identification and model reduction

Aircraft wings are a compromise that allows the aircraft to fly at a range of flight conditions, but the performance at each condition is sub-optimal. The ability of a wing surface to change its geometry during flight has interested researchers and designers over the years as this reduces the design compromises required. Morphing is the short form for metamorphose; however, there is neither an exact definition nor an agreement between the researchers about the type or the extent of the geometrical changes necessary to qualify an aircraft for the title ‘shape morphing.’ Geometrical parameters that can be affected by morphing solutions can be categorized into: planform alteration (span, sweep, and chord), out-of-plane transformation (twist, dihedral/gull, and span-wise bending), and airfoil adjustment (camber and thickness). Changing the wing shape or geometry is not new. Historically, morphing solutions always led to penalties in terms of cost, complexity, or weight, although in certain circumstances, thes...

A Review of Morphing Aircraft

Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time series for which the measurement dimension is much larger than the number of measurements taken. We present a theoretical framework in which we define DMD as the eigendecomposition of an approximating linear operator. This generalizes DMD to a larger class of datasets, including nonsequential time series. We demonstrate the utility of this approach by presenting novel sampling strategies that increase computational efficiency and mitigate the effects of noise, respectively. We also introduce the concept of linear consistency, which helps explain the potential pitfalls of applying DMD to rank-deficient datasets, illustrating with examples. Such computations are not considered in the existing literature, but can be understood using our more general framework. In addition, we show that our theory strengthens the connections between DMD and Koopman operator theory. It also establishes connections between DMD and other techniques, including the eigensystem realization algorithm (ERA), a system identification method, and linear inverse modeling (LIM), a method from climate science. We show that under certain conditions, DMD is equivalent to LIM.

On Dynamic Mode Decomposition: Theory and Applications

We develop a new method which extends dynamic mode decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear analysis to nonlinear operator theory, and provides an equation-free architecture which is compatible with compressive sensing. In actuated systems, DMD is incapable of producing an input-output model; moreover, the dynamics and the modes will be corrupted by external forcing. Our new method, dynamic mode decomposition with control (DMDc), capitalizes on all of the advantages of DMD and provides the additional innovation of being able to disambiguate between the underlying dynamics and the effects of actuation, resulting in accurate input-output models. The method is data-driven in that it does not require knowledge of the underlying governing equations---only snapshots in time of observables and actuation data from historical, experimental, or black-box simulations. W...

https://epubs.siam.org/doi/pdf/10.1137/15M1013857

Dynamic Mode Decomposition with Control

Control system design and closed-loop test results for the Mini-Mast truss structure located at the NASA Langley Research Center are presented. The simplicity and effectiveness of a classical control approach to the active structural control design are demonstrated by ground experiments. The concepts of robust non-minimum phase compensation and periodic disturbance rejection are also experimentally validated. The practicality of a sensor output decoupling approach is demonstrated for the inherent, multivariable control problem of the Mini-Mast.

Active Structural Control Design and Experiment for the Mini-Mast

The International Space Station (ISS) relies on sixteen solar-voltaic blankets to provide electrical power to the station Each pair of blankets is supported by a deployable boom called the Folding Articulated Square Truss Mast (FAST Mast) At certain ISS attitudes, the solar arrays can be positioned in such a way that shadowing of either one or three longerons causes an unexpected asymmetric thermal loading that if unchecked can exceed the operational stability limits of the mast Work in this paper documents part of an independent NASA Engineering and Safety Center effort to assess the existing operational limits Because of the complexity of the system, the problem is being worked using a building-block progression from components (longerons), to units (single or multiple bays), to assembly (full mast) The paper presents results from efforts to calibrate the longeron components The work includes experimental testing of two types of longerons (straight and tapered), development of Finite Element (FE) models, development of parameter uncertainty models, and the establishment of a calibration and validation process to demonstrate adequacy of the models Models in the context of this paper refer to both FE model and probabilistic parameter models Results from model calibration of the straight longerons show that the model is capable of predicting the mean load, axial strain, and bending strain For validation, parameter values obtained from calibration of straight longerons are used to validate experimental results for the tapered longerons

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Model Calibration Efforts for the International Space Station's Solar Array Mast

Acceptance of new deployable structures architectures and concepts requires validated design methods to minimize the expense involved with technology validation flight testing. Deployable concepts for large lightweight spacecraft include booms, antennae, and masts. This paper explores the implementation of probabilistic methods in the design process for the deployment of a strain-energy mechanism, specifically a simple tape-spring hinge. Strain-energy mechanisms are attractive for deployment in very lightweight systems because they do not require the added mass and complexity associated with motors and controllers. However, designers are hesitant to include free deployment, strain-energy mechanisms because of the potential for uncontrolled behavior. In the example presented here, the tapespring cross-sectional dimensions have been varied and a target displacement during deployment has been selected as the design metric. Specifically, the tape-spring should reach the final position in the shortest time with the minimal amount of overshoot and oscillations. Surrogate models have been used to reduce computational expense. Parameter values to achieve the target response have been computed and used to demonstrate the approach. Based on these results, the application of probabilistic methods for design of a tape-spring hinge has shown promise as a means of designing strain-energy components for more complex space concepts.

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Deployment Analysis of a Simple Tape-Spring Hinge Using Probabilistic Methods

The conceptual and preliminary design processes for aircraft with large shape changes are generally difficult and time-consuming, and the processes are often customized for a specific shape change concept to streamline the vehicle design effort. Accordingly, several existing reports show excellent results of assessing a particular shape change concept or perturbations of a concept. The goal of the current effort was to develop a multidisciplinary analysis tool and process that would enable an aircraft designer to assess several very different morphing concepts early in the design phase and yet obtain second-order performance results so that design decisions can be made with better confidence. The approach uses an efficient parametric model formulation that allows automatic model generation for systems undergoing radical shape changes as a function of aerodynamic parameters, geometry parameters, and shape change parameters. In contrast to other more self-contained approaches, the approach utilizes off-the-shelf analysis modules to reduce development time and to make it accessible to many users. Because the analysis is loosely coupled, discipline modules like a multibody code can be easily swapped for other modules with similar capabilities. One of the advantages of this loosely coupled system is the ability to use the medium- to high-fidelity tools early in the design stages when the information can significantly influence and improve overall vehicle design. Data transfer among the analysis modules are based on an accurate and automated general purpose data transfer tool. In general, setup time for the integrated system presented in this paper is 2-4 days for simple shape change concepts and 1-2 weeks for more mechanically complicated concepts. Some of the key elements briefly described in the paper include parametric model development, aerodynamic database generation, multibody analysis, and the required software modules as well as examples for a telescoping wing, a folding wing, and a bat-like wing. The paper also includes the verification of a medium-fidelity aerodynamic tool used for the aerodynamic database generation with a steady and unsteady high-fidelity CFD analysis tool for a folding wing example.

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Lucas G. Horta

Papers

Active Structural Control Design and Experiment for the Mini-Mast

Model Calibration Efforts for the International Space Station's Solar Array Mast

Deployment Analysis of a Simple Tape-Spring Hinge Using Probabilistic Methods

Efficient Multidisciplinary Analysis Approach for Conceptual Design of Aircraft with Large Shape Change

Uncertainty quantification of an inflatable/rigidizable torus