Unknown Amplitude Research Articles

Design of prescribed-precision controllers of multivariable systems by root-mean-square criterion on the basis of LQ-optimization procedures

A problem of designing the continuous controllers of multivariable linear systems ensuring in the root-mean-square their desired precision in the controlled variables under the action of nonmeasurable, power-bounded polyharmonic determinate exogenous disturbances having unknown amplitudes, frequencies, and number of frequencies was formulated. Conditions were established for solvability of the problem with state controllers (in this case, the disturbances and controls must be applied to the same point) and measurable output controllers (the plant must be minimum phase with the same number of controls and controlled variables) on the basis of the LQ-optimization procedures by selecting the weight coefficients of the quadratic optimization functional.

Detection of a signal with unknown amplitude and duration

We synthesize a maximum-likely algorithm for detecting an arbitrary-shaped signal with unknown duration and amplitude, which is observed against the background of additive Gaussian white noise. The synthesized algorithm is analyzed on the assumption of sufficiently large signal-to-noise ratios. Asymptotically accurate expressions for the detection-error probabilities are found. The efficiency of the synthesized algorithm is estimated by numerical simulation and the applicability limits of the asymptotic expressions are determined.

Synthesizing H ∞-controllers for multidimensional systems with given accuracy and degree of stability

We consider linear multidimensional systems with output controllers subject to external perturbances from the class of polyharmonic functions with unknown amplitudes and bounded powers. We formulate the synthesis problem for continuous and discrete output controllers that guarantee a given accuracy with respect to the object's controlled variables. We introduce the notion of a stabilized state radius of the closed system with respect to controlled variables and reformulate the problem of guaranteeing a given accuracy as a problem of guaranteeing the necessary or minimal possible stabilized state radius. Controller synthesis reduces to a standard H∞-problem of suppressing external perturbances, and its numerical solution is based on the linear matrix inequalities (LMI) approach implemented in the MATLAB package LMI Control Toolbox. We show a way to take into account a given degree of stability of the closed system which determines control time. We show a sample controller synthesis for an interconnected electric drive.

Synthesis of digital H ∞-controllers for multidimensional systems with given accuracy with the mean squared criterion

We consider linear multidimensional objects subject to power bounded polyharmonic perturbances and measurement noise that contains an arbitrary number of harmonics with unknown amplitudes and frequencies. For such objects, we propose a synthesis method for digital state controllers and controllers with respect to measurable output. The problem of guaranteeing a desired accuracy is formulated as the problem of guaranteeing a given mean squared radius of the stabilized state [1]; our solution of this problem is based on the choice of weight matrices in the minimal quadratic functional of a discrete H∞-optimization problem. We give a synthesis algorithm for a digital controller in the LMI Control Toolbox package and a numerical example for an interconnected electric drive.

Maximum A Posteriori Probability Multiple-Pitch Tracking Using the Harmonic Model

In this paper, a new method for multiple fundamental frequency estimation for speech and music signals is proposed. Applications of audio and speech processing include many well-reviewed algorithms for estimating the fundamental frequency of monophonic speech and music signals. In the case of polyphonic signals, it is more difficult to successfully estimate each of the fundamental frequencies, as reflected by the dearth of existing methods addressing this problem. In this paper, a new method based on the combination of the maximum likelihood and maximum a posteriori probability criteria is derived for fundamental frequencies tracking where each one of the fundamental frequencies is modeled by a first-order Markov process. The dominant signal is modeled as a harmonic source with unknown deterministic amplitudes, while the remaining signals, including other harmonic signals, are modeled as Gaussian interference sources with an unknown covariance matrix. After estimation of the dominant source, it is removed from the signal by projection of the signal into the null subspace spanned by the estimated signal. This procedure is iterated for all the harmonic sources in the data. The algorithm is tested with speech, music, and synthetic signals where in each case, two harmonic sources of the same kind were mixed. The performance of the proposed algorithm is evaluated and compared to an existing reference method in terms of gross-error-rate as a function of signal-to-interference ratio.

The use of the virtual source technique in computing scattering from periodic ocean surfaces

In this paper the virtual source technique is used to compute scattering of a plane wave from a periodic ocean surface. The virtual source technique is a method of imposing boundary conditions using virtual sources, with initially unknown complex amplitudes. These amplitudes are then determined by applying the boundary conditions. The fields due to these virtual sources are given by the environment Green's function. In principle, satisfying boundary conditions on an infinite surface requires an infinite number of sources. In this paper, the periodic nature of the surface is employed to populate a single period of the surface with virtual sources and m surface periods are added to obtain scattering from the entire surface. The use of an accelerated sum formula makes it possible to obtain a convergent sum with relatively small number of terms (∼40). The accuracy of the technique is verified by comparing its results with those obtained using the integral equation technique.

Finite-state Markov channel modelling under jointly varying amplitude and phase in time-varying flat fading channels

In this study, the authors investigate the first-order finite-state Markov chain modelling of time-varying flat fading channels. The scope of this work is to consider the joint effects of unknown channel phase and amplitude on the received signal. Performance measures such as level crossing rate, steady-state probability, state transition probability and state time duration of the fading models are derived, plotted and analysed. Comparison of the performance measures are made for Rician, Lognormal and Weibull fading distributions.

Phase estimation characteristics of ultra-wideband quasi-radio signal

Synthesis and analysis of the maximum likelihood algorithm for estimating the phase of ultra-wideband quasi-radio signal with unknown amplitude and phase are performed. Duration of the specified signal may amount to several periods or a fraction of the period of harmonic oscillation. Characteristics of the classical maximum likelihood phase estimate of a narrow-band radio signal are found when receiving an ultra-wideband quasi-radio signal. Applicability conditions of narrow-band radio signal model are defined for solving the problem of phase estimation with the specified accuracy.

Vertex Diffracted Edge Waves on a Perfectly Conducting Plane Angular Sector

Numerical diffraction coefficients are presented for vertex-diffracted edge waves induced on an infinitely-thin, perfectly conducting, semi-infinite plane angular sector. The current density on the surface of the plane angular sector is modeled using the physical theory of diffraction (PTD). The vertex-diffracted currents are defined as the difference between the exact and the PTD currents. The difference current is then modeled as a wave traveling away from the corner with unknown amplitude and phase factors. The unknown coefficients for the vertex-diffracted currents are calculated by using a least squares fit approximation. The vertex-diffracted currents are successfully modeled even for narrow angular sectors. The vertex-diffracted currents provide a substantial improvement to the accuracy of RCS patterns in off-specular directions.

Damage-Based Design Earthquake Loads for Single-Degree-Of-Freedom Inelastic Structures

This paper develops a new framework for modeling design earthquake loads for inelastic structures. Limited information on strong ground motions is assumed to be available only at the given site. The design earthquake acceleration is expressed as a Fourier series, with unknown amplitude and phase angle, modulated by an envelope function. The design ground acceleration is estimated by solving an inverse dynamic problem, using nonlinear programming techniques, so that the structure performance is minimized. At the same time, the design earthquake is constrained to the available information on past recorded ground motions. New measures of the structure performance based on energy concepts and damage indexes are introduced in this paper. Specifically, the structural performance is quantified in terms of Park and Ang damage indexes. Damage indexes imply that the structure is damaged by a combination of repeated stress reversals and high-stress excursions. Furthermore, the use of damage indexes provides a measure on the structure damage level, and making a decision on necessary repair possible. The material stress-strain relationship is modeled as either bilinear or elastic-plastic. The formulation is demonstrated by deriving the design earthquake loads for inelastic frame structures at a firm soil site. The damage spectra for the site are also established, to provide upper bounds of damage under possible future earthquakes. DOI: 10.1061/(ASCE)ST.1943-541X .0000074. © 2011 American Society of Civil Engineers. CE Database subject headings: Ductility; Damage; Optimization; Earthquake loads; Seismic design; Inelasticity; Earthquake resistant structures. Author keywords: Design earthquake loads; Input energy; Inelastic structures; Ductility ratio; Hysteretic energy; Damage indexes; Damage spectra; Nonlinear optimization.

Noise Benefits in Quantizer-Array Correlation Detection and Watermark Decoding

Quantizer noise can improve statistical signal detection in array-based nonlinear correlators in Neyman-Pearson and maximum-likelihood (ML) detection. This holds even for infinite-variance symmetric alpha-stable channel noise and for generalized-Gaussian channel noise. Noise-enhanced correlation detection leads to noise-enhanced watermark extraction based on such nonlinear detection at the pixel or bit level. This yields a noise-based algorithm for digital watermark decoding using two new noise-benefit theorems. The first theorem gives a necessary and sufficient condition for quantizer noise to increase the detection probability of a constant signal for a fixed false-alarm probability if the channel noise is symmetric and if the sample size is large. The second theorem shows that the array must contain more than one quantizer for such a stochastic-resonance noise benefit if the symmetric channel noise is unimodal. It also shows that the noise-benefit rate improves in the small-quantizer noise limit as the number of array quantizers increases. The second theorem further shows that symmetric uniform quantizer noise gives the optimal rate for an initial noise benefit among all finite-variance symmetric scale-family noise. Two corollaries give similar results for stochastic-resonance noise benefits in ML detection of a signal sequence with known shape but unknown amplitude.

Stability of circumferentially corrugated shells under hydrostatic pressure

A method to solve stability problems for corrugated shells with dished ends subject to hydrostatic pressure is outlined. Critical loads are determined by solving a boundary-value problem with unknown amplitude of nonaxisymmetric perturbation. It is shown that the shells are highly sensitive to the axial component of hydrostatic pressure

Transient responses of Timoshenko beams subject to a moving mass

The dynamic behavior of beam structures subject to a moving mass is a topic of practical importance in many research fields. In this study, the method of reverberation-ray matrix is presented to investigate the dynamic responses of an undamped Timoshenko beam subject to a moving mass. Based on Inglis’s assumption, the moving mass is simplified into a moving force and a concentrated mass fixed at the mid-span of the beam. Two dual local coordinates are introduced. Based on the theory of elastodynamics, the general wave solutions with two sets of unknown amplitude coefficients are derived in the transformed domain by the dual integral transform. From continuity conditions of forces and displacements at each joint and the compatibility conditions with respect to the dual coordinates, the unknown amplitude coefficients can be determined exactly. The transient dynamic motions for a Timoshenko beam under a moving mass are then determined numerically by inverse integral transform in which the Neumann series expansion is employed to avoid the integral singularities. Two simple numerical examples are presented and the results so obtained are compared with both the experimental and theoretical ones. It is shown that the present method can be a simple alternative for determining dynamic responses of bridges subject to a moving vehicle.

Light-scattering experiments in dye-doped liquid crystals both to determine crystal parameters and to construct consistent neural network empirical physical formulas for scattering amplitudes

The aim of this paper is two-fold. Firstly, static laser light-scattering amplitude measurements in azo-dye doped nematic liquid crystals (NLCs) were made versus scattering angle, temperature and applied bias voltage. Three NLC parameters were determined: the elastic constant ratios K11/K22 by regression, phase transition temperatures, and Freedericksz voltages from the graphs. They were all doping ratio dependent. Secondly, as a novel approach, by a nonlinear universal function approximator layered feedforward neural network (LFNN) we constructed an explicit form of empirical physical formulas (EPFs) for theoretically unknown nonlinear azo-dye doped NLC scattering amplitude functions. Excellent LFNN test set (i.e. yet-to-be measured experimental data) predictions prove that the constructed LFNN-EPPs estimate unknown amplitude functions consistently. The LFFN-EPFs, too, confirmed the doping-ratio dependency. Also, comparing LFNN and regression amplitude fits, the LFNN fits were significantly better. In conclusion, physical laws embedded in the physical data can be consistently extracted by LFNN. One major potential application in the nonlinear optics domain is that these LFNN-EPFs, by differentiation, integration, minimization, etc., can be used to obtain further NLC scattering amplitude related molecular structural physical quantities. This could in turn help us to develop new nonlinear optical materials.

Fault Detection and Isolation in Large-Scale IP Network

AbstractThis paper adresses the problem of fault detection and isolation by using a noisy measurement vector corrupted by some linear unknown nuisance parameters. An invariant constrained asymptotically uniformly minimax test is proposed. It minimizes the maximum false isolation probability as the signal-to-noise ratio becomes arbitrary large, uniformly with respect to the unknown fault amplitude and independently on the nuisance parameters. The theoretical statistical performances of this algorithm are established. To illustrate the practical interest of this test, it is applied to the problem of fault detection and isolation in network origin-destination traffic demands from simple link load measurements. The test performances are evaluated by using real traffic data from a backbone network.

A Structurally Stable Globally Adaptive Internal Model Regulator for MIMO Linear Systems

The problem of compensating an uncertain disturbance and/or tracking some reference signals for a general linear MIMO system is studied in this work using the robust regulation theory frame. The disturbances are assumed to be composed by a known number of distinct sinusoidal signals with unknown phases, amplitude and frequencies. Under suitable assumptions, an exponentially convergent estimator of the unknown disturbance parameters is proposed and introduced into the classical robust regulator design to obtain an adaptive controller. This controller guarantees that the closed-loop robust regulation is attained in some neighborhood of the nominal values of the parameters of system. A simulated example shows the validity of the proposed approach.

Expansions for the distribution ofM-estimates with applications to the Multi-Tone problem

We give a stochastic expansion for estimates that minimise the arithmetic mean of (typically independent) random functions of a known parameter θ . Examples include least squares estimates, maximum likelihood estimates and more generally M -estimates. This is used to obtain leading cumulant coefficients of needed for the Edgeworth expansions for the distribution and density n 1/2 ( of − θ 0 ) to magnitude n −3/2 (or to n −2 for the symmetric case), where θ 0 is the true parameter value and n is typically the sample size. Applications are given to least squares estimates for both real and complex models. An alternative approach is given when the linear parameters of the model are nuisance parameters. The methods are illustrated with the problem of estimating the frequencies when the signal consists of the sum of sinusoids of unknown amplitudes.

Asynchronous Classification of Digital Amplitude-Phase Modulated Signals in Flat-Fading Channels

This paper presents a new asynchronous modulation classifier for digital amplitude-phase modulated signals in flat-fading channels when the channel state is assumed unknown. In the design of this classifier, we propose new estimators for the unknown amplitude, time offset, and noise power that are blind to the modulation scheme of the received signal. It is shown that the proposed classifier performs well compared to the optimal classifier with perfect channel knowledge for an adequate estimation interval.

Robust control of a submarine snorkel system

AbstractThis paper illustrates a control strategy for a submarine snorkel able to assure that the water surface profile can be tracked by the extremity of the device, called “fluctuating head”. The proposed solution is based on adaptive output regulation theory. More precisely, it is assumed that wave profile can be approximated as a linear combination of a number of harmonics of unknown amplitude, phase and frequency and we look for an internal model-based adaptive regulator able to enforce the top of the mast to track the reference profile. The effectiveness of the proposed adaptive scheme is shown through simulations.

Stability Analysis of Normalized Frequency Adaptive Comb Filter

A normalized frequency adaptive comb filter composed of a number of normalized frequency estimators in parallel is proposed to track unknown frequency and unknown amplitude of each component of an almost periodic signal. The filter consists of two coupled nonlinear differential equations respectively for updating frequencies and estimating state variables. A nonlinear autonomous equation for frequency estimation is deduced after average method is applied to the almost periodic dynamic system resulting from system decoupling by slow integral manifold. Three kinds of local stability of the autonomous system:the exponential stability of isolated equilibrium point,the semistability on center manifold,and the robustness under unknown periodic disturbance are proved. The convergence and the boundedness of amplitude estimation and signal tracking as well as the effect of parameters on the transient and steady-state performance of frequency and amplitude are investigated. Each sinusoidal component and its amplitude are accurately tracked on the condition of given intervals instead of the values of frequencies. The response speed is independent of the component amplitude. Simulation results reveal the validity of the proposed algorithm.