Unknown Amplitude Research Articles

Experimental verification of a global exponential stable nonlinear wave encounter frequency estimator

This paper presents a global exponential stability (GES) proof for a signal-based nonlinear wave encounter frequency estimator. The estimator under consideration is a second-order nonlinear observer designed to estimate the frequency of a sinusoid with unknown frequency, amplitude and phase. The GES proof extends previous results that only guarantee global K-exponential stability. Typical applications are control and decision-support systems for marine craft, where it is important to know the sea state and wave frequency. The theoretical results are verified experimentally by analyzing data from towing tank experiments using a container ship scale model. The estimates for both regular and irregular waves confirm the results. Finally, the estimator is applied to full-scale data gathered from a container ship operating in the Atlantic Ocean during a storm. Again the theoretical results are confirmed.

Design of H∞ Controllers under Parametric Uncertainty and Power-Bounded External Disturbances

We consider robust stabilization of linear MIMO systems, whose physical parameters are allowed to deviate from the nominal ones within known bounds, and the control plant is subjected to unknown power-bounded polyharmonic external disturbances (with unknown amplitudes and frequencies). The problem is to design a robustly stabilizing controller such that the prespecified errors for the controlled variables in steady state are guaranteed. The solution is based on the “loop-breaking technique” of the plant-controller system with respect to the physical parameters, e.g. Chestnov (1999); it reduces to the standard H∞-optimization procedure by properly choosing the weighting matrix at the controlled variables. This approach is implemented numerically in the MATLAB-based Robust Control Toolbox (RCT).

Dynamic calibration of higher eigenmode parameters of a cantilever in atomic force microscopy by using tip-surface interactions.

We present a theoretical framework for the dynamic calibration of the higher eigenmode parameters (stiffness and optical lever inverse responsivity) of a cantilever. The method is based on the tip–surface force reconstruction technique and does not require any prior knowledge of the eigenmode shape or the particular form of the tip–surface interaction. The calibration method proposed requires a single-point force measurement by using a multimodal drive and its accuracy is independent of the unknown physical amplitude of a higher eigenmode.

Harmonic tonal detectors based on the BOGA

Tonals generated by machineries with rotating elements typically have a harmonic structure with unknown fundamental frequencies, amplitude, harmonic order and phase. Detecting this type of signals is of great importance to numerous engineering applications. In the frequency domain, tonals are represented by a few harmonic frequencies, which appear in blocks, related to one or more fundamental frequencies. This block-sparsity property of the frequency content suggests alternative ways to recover and detect tonals by using sparse signal processing techniques. Motivated by the success of the block orthonormal greedy algorithm (BOGA), new detection architectures, which require no prior information about the number of the fundamental frequencies, are proposed for robust tonal detection in low signal to noise ratio (SNR) environments. The distributions of the test statistics of detection architectures are firstly analyzed theoretically and comprehensively based on the theory of order statistics. Detection performances are also analyzed and compared theoretically and experimentally. Significant improvements on detection performance in low SNR environments are shown over the conventional detectors that do not consider the harmonic structure and the sparsity of the tonals.

KANTBP 3.0: New version of a program for computing energy levels, reflection and transmission matrices, and corresponding wave functions in the coupled-channel adiabatic approach

A FORTRAN program for calculating energy values, reflection and transmission matrices, and corresponding wave functions in a coupled-channel approximation of the adiabatic approach is presented. In this approach, a multidimensional Schrodinger equation is reduced to a system of the coupled second-order ordinary differential equations on a finite interval with the homogeneous boundary conditions of the third type at the left- and right-boundary points for continuous spectrum problem. The resulting system of these equations containing the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite element method. As a test desk, the program is applied to the calculation of the reflection and transmission matrices and corresponding wave functions for the two-dimensional problem with different barrier potentials.

Adaptive Radar Detection Algorithm Based on an Autoregressive GARCH-2D Clutter Model

We propose a model for radar clutter that combines an autoregressive (AR) process with a two-dimensional generalized autoregressive conditional heteroscedastic (GARCH-2D) process. Based on this model, we derive an adaptive detection test, called AR-GARCH-2D detector, for a target with known Doppler frequency and unknown complex amplitude. Using real radar data, we evaluate its performance for different model orders, and we use a model selection criteria to choose the best fit to the data. The resulting detector is not the constant false alarm rate (CFAR) with respect to the process coefficients, but we show that in practical situations it is very robust. Finally, we compare the AR-GARCH-2D detector performance with the performance of the generalized likelihood ratio test (GLRT), the adaptive linear-quadratic (ALQ), and the autoregressive generalized likelihood ratio (ARGLR) detectors by processing the real radar data. We show that the proposed detector offers a higher probability of detection than the other tests, for a given probability of false alarm.

Robust adaptive model tracking for distributed parameter control of linear infinite-dimensional systems in Hilbert space

This paper is focused on adaptively controlling a linear infinite-dimensional system to track a finite-dimensional reference model. Given a linear continuous-time infinite-dimensional plant on a Hilbert space with disturbances of known waveform but unknown amplitude and phase, we show that there exists a stabilizing direct model reference adaptive control law with the properties of certain disturbance rejection and robustness. The plant is described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. The central result will show that all errors will converge to a prescribed neighborhood of zero in an infinite-dimensional Hilbert space. The result will not require the use of the standard Barbalat's lemma which requires certain signals to be uniformly continuous. This result is used to determine conditions under which a linear infinite-dimensional system can be directly adaptively controlled to follow a reference model. In particular, we examine conditions for a set of ideal trajectories to exist for the tracking problem. Our results are applied to adaptive control of general linear diffusion systems described by self-adjoint operators with compact resolvent.

Optimal invariant detection of a monochromatic plane wave with unknown amplitude, frequency, phase, direction of arrival and noise variance

This study deals with the problem of detecting a monochromatic plane wave with unknown amplitude, phase, temporal frequency and direction of arrival in complex white Gaussian noise with unknown variance. Depending on the natural invariance in scale, temporal modulation and spatial modulation of the problem, the uniformly most powerful invariant (UMPI) test is derived by using the statistical invariance principles. However, the UMPI test does not apply unless the signal-to-noise ratio (SNR) is known. However, it provides us with performance bound to evaluate any invariant test's performance when the SNR is unknown. Typically, the generalised likelihood ratio test (GLRT) and locally most powerful invariant (LMPI) test are derived as realisable suboptimal invariant tests with their performance comparison in different SNR through theoretical analysis. Computer simulation examples corroborate the authors analysis and indicate that the GLRT is close to the UMPI bound especially in the low probability-of-false-alarm (P FA) region of the receiver operating characteristic curve while the performance of the LMPI test is close to that of the UMPI test in the low SNR region.

Robust Helicopter Stabilization with Wind Disturbance Elimination

When a helicopter is required to hover with minimum deviations from a desired position without measurements of a persistent wind disturbance, a robustly stabilizing control action is vital. In this paper, the stabilization of the position and translational velocity of a nonlinear helicopter model affected by a wind disturbance is addressed. An estimate of the disturbance is introduced to be adapted using state measurements for control purposes. A nonlinear controller is then designed based on nonlinear adaptive output regulation and robust stabilization of a chain of integrators by a saturated feedback. While in the control synthesis the wind disturbance is assumed to be a sum of a fixed number of sinusoids with unknown amplitudes, frequencies and phases, a practical turbulence model is presented to the helicopter model in the control test. Simulation results show the effectiveness of the control design in the stabilization of helicopter motion and the built-in robustness of the controller in handling parameter and model uncertainties.

A non-linear one-dimensional model of cross-deformable tubular beam

A direct non-linear one-dimensional model of an elastic, thin-walled, planar beam is formulated. The model accounts for changes in shape of the cross-section, in particular the ovalization (or flattening) occurring in tubular beams. The deformation of the cross-section is described in the spirit of the Generalized Beam Theory, as a linear combination of known deformation modes and unknown amplitude functions, said to be distortions. Kinematics calls for introducing distortional and bi-distortional strains, in addition to the usual strain measures of rigid cross-section beams. The balance equations are derived through the Virtual Power Principle, in which distortional and bi-distortional stresses, as well as distortional forces, are defined as conjugate quantities of distortional strain-rates and velocities, respectively. A non-linear, fully coupled, hyperelastic law is assumed. All the distortional quantities and the constitutive law are identified, via energy equalities, from a three-dimensional fiber-model of thin-walled beam where, for simplicity, just a distortion mode is considered. The model is specialized to a Euler–Bernoulli tubular beam, in which only constitutive non-linearities are retained, while kinematics is linearized. The relevant non-linear equations are solved, via a perturbation method, for several static loadings and for large-amplitude free vibrations. The interaction occurring between global bending and cross-section distortion is analyzed.

Dyadic Green’s function of an eccentrically stratified sphere

The electric dyadic Green's function (dGf) of an eccentrically stratified sphere is built by use of the superposition principle, dyadic algebra, and the addition theorem of vector spherical harmonics. The end result of the analytical formulation is a set of linear equations for the unknown vector wave amplitudes of the dGf. The unknowns are calculated by truncation of the infinite sums and matrix inversion. The theory is exact, as no simplifying assumptions are required in any one of the analytical steps leading to the dGf, and it is general in the sense that any number, position, size, and electrical properties can be considered for the layers of the sphere. The point source can be placed outside of or in any lossless part of the sphere. Energy conservation, reciprocity, and other checks verify that the dGf is correct. A numerical application is made to a stratified sphere made of gold and glass, which operates as a lens.

T(2)-relaxometry for myelin water fraction extraction using wald distribution and extended phase graph.

Quantitative assessment of myelin density in the white matter is an emerging tool for neurodegenerative disease related studies such as multiple sclerosis and Schizophrenia. For the last two decades, T2 relaxometry based on multi-exponential fitting to a single slice multi-echo sequence has been the most common MRI technique for myelin water fraction (MWF) mapping, where the short T2 is associated with myelin water. However, modeling the spectrum of the relaxations as the sum of large number of impulse functions with unknown amplitudes makes the accuracy and robustness of the estimated MWF's questionable. In this paper, we introduce a novel model with small number of parameters to simultaneously characterize transverse relaxation rate spectrum and B1 inhomogeneity at each voxel. We use mixture of three Wald distributions with unknown mixture weights, mean and shape parameters to represent the distribution of the relative amount of water in between myelin sheets, tissue water, and cerebrospinal fluid. The parameters of the model are estimated using the variable projection method and are used to extract the MWF at each voxel. In addition, we use Extended Phase Graph (EPG) method to compensate for the stimulated echoes caused by B1 inhomogeneity. To validate our model, synthetic and real brain experiments were conducted where we have compared our novel algorithm with the non-negative least squares (NNLS) as the state-of-the-art technique in the literature. Our results indicate that we can estimate MWF map with substantially higher accuracy as compared to the NNLS method.

Applying the variational method to the problem of estimating signal parameters in passive radar with external illumination

A passive bistatic radar comprising an illumination source and two antennas for receiving the direct signal from the illumination source and a mixture of signals scattered by moving objects is considered. The problem of estimating the amplitudes, delays, and Doppler shifts of scattered signals is formulated as the problem of minimizing the residual of an overdetermined system of linear algebraic equations. An additional condition is imposed on the unknown amplitude to provide sparsity of the desired signal amplitudes in the delay-Doppler shift coordinates. The problem is solved by the variational method. The method was successfully tested using real data.

A plane wave method for modeling acoustic variables in cavities

The pressure field within a cavity that contains a homogeneous fluid is modeled in the frequency domain as a superposition of N plane waves with arbitrary orientations and unknown complex amplitudes. Specifying the pressure, the normal velocity, or the specific impedance at N locations produces a system of N linear equations with N unknowns. Then, solving for the complex amplitudes yields an approximation of the pressure and velocity fields inside the cavity. Preliminary comparisons to analytic results are presented.

Channelized model observer for the detection and estimation of signals with unknown amplitude, orientation, and size

As a task-based approach for medical image quality assessment, model observers (MOs) have been proposed as surrogates for human observers. While most MOs treat only signal-known-exactly tasks, there are few studies on signal-known-statistically (SKS) MOs, which are clinically more relevant. In this paper, we present a new SKS MO named channelized joint detection and estimation observer (CJO), capable of detecting and estimating signals with unknown amplitude, orientation, and size. We evaluate its estimation and detection performance using both synthesized (correlated Gaussian) backgrounds and real clinical (magnetic resonance) backgrounds. The results suggest that the CJO has good performance in the SKS detection-estimation task.

Adaptive Regulation Against Unknown Narrow Band Disturbances Applied to the Flying Height Control in Data Storage Systems

AbstractThis paper presents an adaptive regulation approach in linear systems against exogenous narrow band inputs such as disturbances or reference signals consisting of a linear combination of biased sinusoids with unknown amplitudes, frequencies, and phases. The design of the regulator is based on considering a Q‐parameterized set of stabilizing controllers for the linear system, where an adaptive FIR filter with fixed IIR filtering is adopted as the Q parameter. The goal of the adaptation is to search within the set of stabilizing controllers for a controller, or equivalently a Q parameter, that yields regulation in the closed loop system. The proposed adaptive regulation algorithm is applied to an active suspension beam system, which is motivated by the flying height control problem in data storage systems. The experimental result of the closed loop system shows the effectiveness of the proposed adaptive regulator in achieving the desired tracking performance under unknown exogenous disturbances.

Probing vector mesons in deuteron breakup reactions

We study vector meson photoproduction from the deuteron at high momentum transfer, accompanied by break-up of the deuteron into a proton and neutron. The large $-t$ involved allows one of the nucleons to be identified as struck, and the other as a spectator to the $\gamma N\rightarrow VN$ subprocess. Corrections to the plane wave impulse approximation involve final state interactions (FSIs) between the struck nucleon or the vector meson, either of which is energetic, with the slow spectator nucleon. In this regime, the eikonal approximation is valid, so is employed to calculate the cross-section for the reaction. Due to the high-energy nature of the FSIs, the maxima of the rescatterings are located at nearly transverse directions of the fast hadrons. This results in two peaks in the angular distribution of the spectator nucleon, each corresponding to either the $V$-$N$ or the $p$-$n$ rescattering. The $V$-$N$ peak provides a new means of probing the $V$-$N$ interaction. This is checked for near-threshold $\phi$ and $J/\Psi$ photoproduction reactions which demonstrate that the $V$-$N$ peak can be used to extract the largely unknown amplitudes of $\phi$-$N$ and $J/\Psi$-$N$ interactions. Two additional phenomena are observed when extending the calculation of $J/\Psi$ photoproduction to the sub-threshold and high-energy domains. In the first case we observe overall suppression of FSI effects due to a restricted phase space for sub-threshold production in the rescattering amplitude. In the second, we observe cancellation of the $V$-$N$ rescattering amplitudes for vector mesons produced off of different nucleons in the deuteron.

Youla parameterized adaptive regulation against unknown multiple narrow-band disturbances

An adaptive regulation approach in linear systems against exogenous inputs consisting of a linear combination of sinusoids with unknown amplitudes, frequencies and phases is proposed within the framework of Youla parameterized stabilizing controllers. The goal of the developed adaptation algorithm is to search, within the set of weighted Ritz-type Youla parameters, for a controller that yields regulation in the closed-loop system. The proposed approach is applied to an active vibration control problem, and the performance of the developed regulator is illustrated by considering the vibration cancellation against exogenous inputs represented as a linear combination of unknown stationary as well as time-varying sinusoidal disturbances.

Nonparametric Estimation of Power Quantities in the Frequency Domain Using Rife-Vincent Windows

This paper presents algorithms for fast measurement and the nonparametric estimation of the unknown changing frequency, amplitude, and phase difference of the signals from two channels with the same frequency, as well as other power quantities, such as the apparent, the active, and the reactive power. The possibilities for systematic error reduction through use of the interpolated discrete Fourier transform using the Rife-Vincent windows class I (RV-I) are described. RV-I windows are designed for maximization of the window spectrum side-lobes fall-off and owing to their minimal leakage, minimal systematic bias curves can be evaluated as a function of the measurement interval duration expressed in signal cycles. Parameters are calculated from the discrete Fourier transform coefficients around the component peaks by summation to reduce the leakage effects. The optimum for reducing the time of measurement and for reducing systematic errors under non-coherent conditions of sampling real noisy signals could be the estimation with the three cycles window using the three-point interpolation and the RV-I window order 3.

Direct model reference adaptive control of linear systems with input/output delays

In this paper, we develop a Direct Model Reference Adaptive Tracking Controller for linear systems with unknown time varying input delays. This controller can also reject bounded disturbances of known waveform but unknown amplitude, e.g. steps or sinusoids. In this paper a robustness result is developed for DMRAC of linear systems with unknown small constant or time varying input delays using the concept of un-delayed ideal trajectories. We will show that the adaptively controlled system is globally stable, but the adaptive tracking error is no longer guaranteed to approach the origin. However, exponential convergence to a neighborhood can be achieved as a result of the control design. A simple example will be provided to illustrate this adaptive control method.