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This paper describes the formulation and experimental testing of an estimation of submanifold models of animal motion. It is assumed that the animal motion is supported on a configuration manifold, Q, and that the manifold is homeomorphic to a known smooth, Riemannian manifold, S. Estimation of the configuration submanifold is achieved by finding an unknown mapping, γ , from S to Q. The overall problem is cast as a distribution-free learning problem over the manifold of measurements. This paper defines sufficient conditions that show that the rates of convergence in L μ 2 (S) of approximations of γ correspond to those known for classical distribution-free learning theory over Euclidean space. This paper concludes with a study and discussion of the performance of the proposed method using samples from recent reptile motion studies. [ABSTRACT FROM AUTHOR]

A switched feedback control law is derived for an autonomous pursuing agent that attempts to intercept an evading agent whose dynamics are initially unknown. The model of the pursuer's dynamics is known perfectly, and the evader is modeled as a disturbance. A new method is presented to efficiently update the pursuer's control law as measurements of the parameters that govern the evader's dynamics are received. Using a graph theoretical approach, the control law updates are limited to specific partitions of the state space, which eliminate many unneeded calculations. Results show increases in the time efficiency of the update calculations compared to traditional control law generation methods with a minimal loss in accuracy. An 11.6% overall decrease in calculation time over traditional methods and a 1% error rate compared to the true solution is achieved when solving the homicidal chauffeur game. We show how actual gains in time efficiency depend on the specific application of the controller and the size of the state space grid approximation. Both the theoretical development and implementation of the switched feedback controller are discussed. [ABSTRACT FROM AUTHOR]

We develop a family of reduced-order models for the modeling and control of a flow system operating under varying fluid and actuation parameters. The parametric subspaces of the reduced-order models are formed by considering the angle between the reduced-order subspaces that span the velocity fields. This grouping is combined with a discrete switching law to form a switched dynamic system composed of a set of reduced-order models. This methodology is applied to the modeling of a lid-driven cavity under varying translation velocities and phase differentials between the upper and lower walls. It is shown that the subspace angle metric successfully partitions the parametric space and provides insight on the dominant parameters that characterize the flowfields. An open-loop simulation of the resulting switched dynamic system demonstrates its ability to capture the evolution of the flow and input parameters as it occurs in the full-order model. [ABSTRACT FROM AUTHOR]

Recently, scanning laser Doppler vibrometry experiments have been conducted in order to identify structural faults in frescoes at the US Capitol. In these experiments, the artwork is subjected to force excitations over a range of frequencies and a laser vibrometer is used to measure the velocity response of the structure over an array of spatial locations. At each frequency, a two-dimensional spatial image of the force–velocity transfer function is obtained. Spatial locations that consistently exhibit large responses are indicative of potential regions of delamination. In this paper the use of proper orthogonal decomposition, also known as principle component analysis, to identify coherent features in the structural response and obtain a succinct representation of the data is described. It is shown that, for the fresco studied in this paper, the response can be characterized in terms of only a few proper orthogonal decomposition modes. Unfortunately, these modes are corrupted by spatially varying noise. This noise is a result of surface irregularities that affect the direction in which the incident laser beam is reflected, which in turn corrupts the measured response at those locations. Therefore, the use of spatial filtering techniques is also explored for removing this “speckle noise” from the measured force–velocity transfer functions prior to performing the proper orthogonal decomposition analysis. Wavelets are particularly well suited for this application because they decompose images into functions that are localized in the spatial and frequency domains. In this paper, several wavelet bases with differing properties are used to filter the scanning laser Doppler vibrometry images. In addition, wavenumber filters, which essentially act as low-pass filters, are also employed. While the results do not definitively show which filtering technique is most effective for this application, it is clear that both wavelet processing and wavenumber filtering can reduce speckle noise while retaining the salient physical features in the image data. Therefore, it is demonstrated that proper orthogonal decomposition analysis coupled with spatial filtering is an effective tool for analyzing scanning laser Doppler vibrometry data in fault detection applications. [Copyright &y& Elsevier]

This paper defines a modal scheduling method for obtaining reduced order systems. In contrast to most order reduction schemes for linear structural systems, the methodology in this paper introduces a switched system to achieve order reduction. The switched system model is based on modal participation factors calculated from an input forcing function and the initial conditions at each switching time. Stability of the reduced order model is discussed, and necessary conditions for stability of the proposed switched model are derived. A numerical example that considers a flexible beam provides a testbed for the study of mode switching. The transient response in the testbed example is constructed such that it oscillates between two distinct subspaces. Numerical experiments show that an error indicator based on modal participation factors provides an effective switching strategy. [ABSTRACT FROM AUTHOR]

The Volterra series provides a convenient framework for the representation of nonlinear dynamical systems. One of the main drawbacks of this approach, however, is the large number of terms that are often needed to represent Volterra kernels. In this paper we present an approach whereby wavelets are used to obtain low-order estimates of first-order and second-order Volterra kernels. Several constructions of tensor-product wavelets have been employed for some Volterra kernel approximations. In this paper, a triangular wavelet basis is constructed for the representation of the triangular form of the second-order kernel. These wavelets are piecewise-constant, orthonormal, and are supported over the triangular domain over which the second-order kernel is defined. The well-known Haar wavelet is used concurrently for the identification of the first-order kernel. This kernel identification algorithm is demonstrated on a prototypical nonlinear oscillator. It is shown that accurate kernel estimates can be obtained in terms of a relatively small number of wavelet coefficients. It is also demonstrated that, for this particular system, the derived Volterra model is valid for input amplitudes below a specified bound. When the input amplitude exceeds this threshold, higher-order kernels are needed to adequately describe the system dynamics. Thus, the approach taken in this paper is applicable to a large class of nonlinear systems provided that the input excitation is sufficiently bounded. [ABSTRACT FROM AUTHOR]

While piezoelectric (PZT) actuators exhibit only mild nonlinear response at low voltage levels, it is well known that the response can be profoundly nonlinear at high field strengths. Moreover, the use of mechanical linkages and structural design to amplify the stroke of PZT-based actuation likewise induces sources of mechanical hysteresis (friction, backlash, etc.) that can couple with this material nonlinearity to yield a structural scale nonlinearity that is nonnegligible. These two sources of hysteresis, due to mechanism response and nonlinear material response, are not easily decoupled. In this paper, we investigate such a nonlinear response in a PZT actuated trailing edge flap attached to a scaled helicopter rotor blade. While the example studied in this paper is quite specific, the methodology derived is generally applicable. We extend the results of previous papers for the derivation of closed loop control for active material actuated devices. The goal is to derive a control methodology that accounts for the overall, total hysteresis due to material nonlinearities and mechanism response. In this technique, a compensator derived from an offline identification of a Krasnoselskii-Pokrovskii hysteresis operator is cascaded with the plant. We show that the methodology is well posed for the class of problems under consideration; we describe relevant closed loop stability and robustness conditions that can be associated with the prediction error in the identified hysteresis operator. We study the performance of our methodology in numerical examples and discuss relevant experimental results. [ABSTRACT FROM AUTHOR]

Presents a study which proposed a novel method for the analysis of flowfields obtained from either particle image velocimetry or computational fluid dynamics. Problem framework; Application of zero mass flux actuators to experimental flow diagnostics; Results and discussion.

Presents information on the study which provides a novel analytical and image processing methods derived as part of the development of a digital particle image velocimetry system, based on multiresolution wavelet analysis. Presentation of a novel particle image cross-correlation algorithms based on wavelet theory; Description of imaging hardware and experimental setup used to generate the data in the study; Conclusions.

The paper investigates the accuracy and numerical stability of a class of wavelet Galerkin formulations on irregular domains. The method of numerical boundary measures is based upon a domain embedding strategy in which the irregular domain of interest is embedded in a larger domain having regular geometry. One advantage of the domain embedding method is that the boundary conditions on the larger, regular domain can be enforced in a straightforward manner, and the solution procedure can exploit the highly structured form of the resulting governing equations. The defining characteristic of this method is that the calculation of integrals along the irregular boundary are carried out using recently derived numerical boundary measures. In addition, the coercive bilinear forms characterizing the boundary value problem of interest must be calculated when restricted to the actual domain. In the case of wavelet Galerkin formulations, this calculation is accomplished with the three term connection coefficients that characterize the numerical boundary measure. The numerical stability and accuracy of the domain embedding procedure is compared to a newly developed wavelet-based finite element formulation. [ABSTRACT FROM AUTHOR]

Summary: This article studies the distributed parameter system that governs adaptive estimation by mobile sensor networks of external fields in a reproducing kernel Hilbert space (RKHS). The article begins with the derivation of conditions that guarantee the well‐posedness of the ideal, infinite dimensional governing equations of evolution for the centralized estimation scheme. Subsequently, convergence of finite dimensional approximations is studied. Rates of convergence in all formulations are established using history‐dependent bases defined from translates of the RKHS kernel that are centered at sample points along the agent trajectories. Sufficient conditions are derived that ensure that the finite dimensional approximations of the ideal estimator equations converge at a rate that is bounded by the fill distance of samples in the agents' assigned subdomains. The article concludes with examples of simulations and experiments that illustrate the qualitative performance of the introduced algorithms. [ABSTRACT FROM AUTHOR]

The frequency response of an oscillating structure can be tailored by attaching one or more subordinate oscillators. This paper shows how the magnitude and phase of the frequency response can be deliberately shaped by prescribing the distributions of the dynamic properties in an array of such subordinate oscillators. Exact analytic governing equations of motion are derived for the coupled system composed of the primary system and the subordinate array. For a relatively small number (<100) of attached oscillators whose total mass is small (<1%) relative to the primary structure, it is possible to engineer frequency-response functions of the primary oscillator to have, for example, nearly linear phase or constant amplitude over a frequency band of interest. The frequency range over which response shaping is achieved is determined by the band of the attached oscillators. It is shown that the common analytic methodology for designing a dynamic vibration absorber represents the limiting case of a single oscillator in the subordinate set. Moreover, increasing the number of subordinate oscillators (without increasing the total added mass) offers a number of advantages in reshaping the dominant system’s frequency response. [ABSTRACT FROM AUTHOR]

This paper extends a conventional, general framework for online adaptive estimation problems for systems governed by unknown or uncertain nonlinear ordinary differential equations. The central feature of the theory introduced in this paper represents the unknown function as a member of a reproducing kernel Hilbert space (RKHS) and defines a distributed parameter system (DPS) that governs state estimates and estimates of the unknown function. Under the assumption that full state measurements are available, this paper (1) derives sufficient conditions for the existence and stability of the infinite dimensional online estimation problem, (2) derives existence and stability of finite dimensional approximations of the infinite dimensional approximations, and (3) determines sufficient conditions for the convergence of finite dimensional approximations to the infinite dimensional online estimates. A new condition for persistency of excitation in a RKHS in terms of its evaluation functionals is introduced in the paper that enables proof of convergence of the finite dimensional approximations of the unknown function in the RKHS. This paper studies two particular choices of the RKHS, those that are generated by exponential functions and those that are generated by multiscale kernels defined from a multiresolution analysis. [ABSTRACT FROM AUTHOR]

This paper investigates the modeling of parameter-varying nonlinear aeroelastic systems using Volterra theory. With this approach, the system dynamics are expressed in terms of a set of Volterra kernels. It is well known that the parameters of aeroelastic systems, such as natural frequencies and damping ratios, change with flight condition. Therefore, a system is characterized by a different set of Volterra kernels at each flight condition. These kernels must be extracted from the flight data at each flight condition of interest: a relatively costly procedure. This paper presents a kernel extrapolation method designed to model first- and second-order kernels as functions of a single varying parameter, such as altitude or Mach number. First, using a multiwavelet-based algorithm, a set of Volterra kernels is identified from the input/output data at a number of flight conditions. In this manner, each kernel is represented in terms of a set of multiwavelet basis functions. Anextrapolation model is then obtained by using a polynomial curve-fit to express the magnitude of each basis coefficient as a function of the varying parameter. The performance of this kernel extrapolation method is studied in detail for a simulated nonlinear aeroelastic system, demonstrating the validity of the approach. Then, the algorithm is applied to flight data from the F/A-18 Active Aeroelastic Wing. This example illustrates some of the difficulties associated with extrapolating kernels from noisy flight data. [ABSTRACT FROM AUTHOR]

Focuses on study which utilized the structured model reference adaptive control (SMARC) method for the active suppression of limit cycle oscillations for a typical wing section with a structural nonlinearity. Investigation on nonlinear aeroelastic control; Steps in adaptive feedback linearization; Advantages of SMARC over conventional adaptive methods.

• Designing an array of linear oscillators, also referred to as Subordinate Oscillator Arrays using dry fettuccine pasta. • Accounting for unknown material properties of structural elements. • Testing multi-DOF structure with Subordinate Oscillator Arrays. • A practical demonstration of vibration attenuation using mundane pasta. • Extending the teaching of vibration attenuation to broadband attenuation. Dynamic vibration absorbers (DVAs) and tuned mass-dampers (TVAs) have wide-spread applications in the aerospace industry, the automotive sector, and in civil engineering structures. There are numerous designs of active and passive vibration attenuators or absorbers that isolate structural vibrations at or around the desired frequency. All these design approaches are fundamentally different ways to modify and tune the placement of the resonant frequencies of the host structure. The current work presents a novel method to passively attenuate vibration over a broad frequency bandwidth in the presence of uncertainty. An array of linear oscillators, also referred to as subordinate oscillator arrays (SOAs), are attached to a two-degrees-of-freedom structure to produce an attenuated broadband frequency response around a target frequency. SOAs can also be interpreted as an array of DVAs and in some categories, they can be considered as an approach to meta-structures. Another objective of the current work is to develop a hands-on approach to extend classroom teaching of vibration-attenuation using SOAs made out of fettuccine strands and modeling clay. The frequencies of the oscillators in the array are tuned by varying the length of each strand and the mass of the modeling clay attached to its tip. Uncertainty in dynamic properties of such oscillators often results in mistuned SOAs with non-uniform frequency response function. Therefore, designing and testing fettuccine-based SOAs allows students to handle cases when structural uncertainties arise in engineering systems. Additionally, some of the work in the field of meta-structures can be modeled and represented by SOAs and this will provide a straight forward way to teach students some of these contemporary concepts. [ABSTRACT FROM AUTHOR]