Unknown Amplitude Research Articles

Cooperative control of leader–follower ships with prescribed performance

With consideration of prescribed performance, the robust cooperative control of leader–follower ships with the existence of ocean disturbances and model uncertainties is studied. The environmental disturbances are modeled as the harmonics disturbances with unknown amplitude and frequency, which are evaluated using an adaptive disturbance observer(ADO). Meanwhile, the model uncertainties is approximated utilizing the neural network, and the prescribed performance method is employed so that the tracking errors can be limited to the predefined set. Then the anti-disturbance cooperative control strategy is presented such that the system states are uniformly ultimately bounded, in addition, the collaborative motion among the leader–follower formation ships are achieved. Eventually, comparative simulations are employed to validate the cooperative control method.

Quasi-likelihood estimation of the arrival time of an ultra-wideband quasi-radio signal with unknown amplitude and initial phase

The problem of estimating the time of arrival of a signal is relevant in the fields of radio and hydrolocation, radio astronomy, remote observation and sensing, etc. The useful signal is often described by a quasi-deterministic function of time, which can be regular or discontinuous. In recent years, problems of processing ultra-wideband signals have been of significant interest. Among the many UWB signals, it is customary to distinguish a separate class of ultra-wideband quasi-radio signals, the structure of which is similar to the structure of narrowband radio signals, but the condition of relative narrowband for which may not be met. Algorithms for estimating the arrival time of regular ultra-wideband quasi-radio signals have been studied in the existing literature. In this case, the synthesis and analysis of an algorithm for quasi-plausible estimation of the arrival time of a discontinuous signal of finite duration and arbitrary shape is of practical interest. The purpose of the work is to synthesize and analyze a quasi-likelihood algorithm for estimating the time of arrival of a discontinuous ultra-wideband quasi-radio signal with an unknown amplitude and initial phase against a background of white Gaussian noise. In this work, closed asymptotically exact expressions for the bias and scattering of the estimate are obtained, which make it possible to study the effectiveness of the synthesized algorithm, as well as compare its effectiveness with special cases of signal models - narrowband and wideband radio and video signals. The results of the study make it possible to determine losses in the accuracy of estimation the signal arrival time due to a priori ignorance of the initial phase and shape of the modulating function of the signal. Depending on the required accuracy of estimate the time of arrival of an ultra-wideband quasi-radio signal, it is possible to optimize the parameters of the transmitted signals and determine the limits of applicability of the designed radio system.

A hybrid fractional order LMS algorithm for power system harmonic estimation

This article proposes a novel multi-innovation fractional order least mean square algorithm for estimating harmonic parameters in power systems with unknown amplitudes and phases. The algorithm incorporates fractional order calculus with variable initial values, which, in contrast to the fixed initial value approach, overcomes the non-locality issue, and converges to its true extreme value. In addition, by extending scalar innovation term to a vector form, the algorithm fully utilizes innovation within a fixed window to improve computational accuracy. The convex combination between integer order and novel fractional order ensures that the performance of the algorithm will not change significantly with the fractional order. Finally, the effectiveness is verified by numerical simulations and comparisons.

Detection of phase modulation disorder when processing a sequence of ultra-wideband quasi-radio signals against a background of white Gaussian noise

In conditions of a complex electromagnetic environment in communication and data transmission systems, a change in the type of modulation occurs when one or more signal parameters change abruptly, therefore the task of determining the type of signal modulation can be reduced to the task of detecting a disorder, that is, detecting the fact of a change in the type of modulation of the signal and estimation of the disorder time. The purpose of the work is to synthesize an algorithm for detecting phase modulation disorder when processing a sequence of ultra-wideband quasi-radio signals with unknown amplitude and initial phase against a background of white Gaussian noise and to analyze the effectiveness of the resulting algorithm based on the results of statistical modeling. The work synthesizes an algorithm for detecting a phase modulation disorder of a received sequence of ultra-wideband quasi-radio signals against a background of white Gaussian noise. To analyze the effectiveness of the resulting algorithm, statistical modeling of algorithm for detecting a phase modulation disorder is carried out. The dependences of the probability of detection of a disorder on the signal-to-noise ratio and the length of the sequence of received signals at a fixed moment of disorder are obtained. A comparison of the detection characteristics of phase modulation disorder of ultra-wideband quasi-radio signals and narrowband radio signals is made. It is shown that when a low-order phase modulation disorder is detected, the required values of the probability of detection are achieved at low signal-to-noise ratios, while with an increase in the modulation order and the use of its modifications, the efficiency indicators of the algorithm will deteriorate. The introduction of algorithms for detecting a disorder in radio engineering applications will allow optimizing synchronization algorithms and adaptation to interference conditions with a concomitant change in the type of modulation, as well as reducing the amount of transmitted service information in telecommunication systems.

Probing the galactic and extragalactic gravitational wave backgrounds with space-based interferometers

We employ the formalism developed in [1] and [2] to study the prospect of detecting an anisotropic Stochastic Gravitational Wave Background (SGWB) with the Laser Interferometer Space Antenna (LISA) alone, and combined with the proposed space-based interferometer Taiji. Previous analyses have been performed in the frequency domain only. Here, we study the detectability of the individual coefficients of the expansion of the SGWB in spherical harmonics, by taking into account the specific motion of the satellites. This requires the use of time-dependent response functions, which we include in our analysis to obtain an optimal estimate of the anisotropic signal. We focus on two applications. Firstly, the reconstruction of the anisotropic galactic signal without assuming any prior knowledge of its spatial distribution. We find that both LISA and LISA with Taiji cannot put tight constraints on the harmonic coefficients for realistic models of the galactic SGWB. We then focus on the discrimination between a galactic signal of known morphology but unknown overall amplitude and an isotropic extragalactic SGWB component of astrophysical origin. In this case, we find that the two surveys can confirm, at a confidence level ≳ 3σ, the existence of both the galactic and extragalactic background if both have amplitudes as predicted in standard models. We also find that, in the LISA-only case, the analysis in the frequency domain (under the assumption of a time average of data taken homogeneously across the year) provides a nearly identical determination of the two amplitudes as compared to the optimal analysis.

Adaptive observer based controls for a flexible wing system under unknown output disturbances

This paper considers a wing system under unknown output disturbances, references, distributed disturbances and boundary disturbances. These signals have unknown frequencies, amplitudes and phases, and are then supposed to be from an exosystem with an unknown matrix. In this sense, we firstly find the wing system merely under the references and output disturbances, for which the PDE observer can be easily designed based on the measurable outputs. Then, an adaptive observer is designed for a detectable exosystem so that the references have known coefficients and approximately known states. Adaptive observer based controls are then proposed for the closed-loop system so that the convergence of tracking error and the boundedness of the states are guaranteed. Two simulation examples are compared to show the robustness of the designed controls.

Fault diagnosis of virtually‐coupled trains by adaptive observer with pattern‐matched detection and reinforced identification

SummaryVirtual coupling is gaining in popularity as a promising development direction to maximize the rail‐line efficiency by minimizing the headway distance among trains in the presence of potentially encountered traction engines' faults with unknown amplitude, happening time and probability, which would be huge threat to the safety of trains without proper sensing and handling. This paper considers the fault diagnosis problem for virtually‐coupled multiple trains using adaptive observer design. In order to generate false‐free and timely fault alarming and relieving signals, an adaptive threshold function design is firstly given using a novel pattern‐matched gain technique with explicit consideration of model uncertainty. Then, reinforced regressor‐based fault identification algorithm is proposed to generate precise estimation of unknown fault values, activated and powered‐off by the fault alarming and relieving signals output by fault detection observer, with globally Lipschitz property and fast convergence performance. Finally, comparative and simulation results are given to demonstrate the effectiveness and advantages of proposed fault diagnosis algorithms.

Generating a 4-photon tetrahedron state: toward simultaneous super-sensitivity to non-commuting rotations

It is often thought that the super-sensitivity of a quantum state to an observable comes at the cost of a decreased sensitivity to other non-commuting observables. For example, a squeezed state squeezed in position quadrature is super-sensitive to position displacements, but very insensitive to momentum displacements. This misconception was cleared with the introduction of the compass state [Nature 412, 712 (2001)10.1038/35089017], a quantum state equally super-sensitive to displacements in position and momentum. When looking at quantum states used to measure spin rotations, N00N states are known to be more advantageous than classical methods as long as they are aligned to the rotation axis. When considering the estimation of a rotation with unknown direction and amplitude, a certain class of states stands out with interesting properties. These states are equally sensitive to rotations around any axis, are second-order unpolarized, and can possess the rotational properties of Platonic solids in particular dimensions. Importantly, these states are optimal for simultaneously estimating the three parameters describing a rotation. In the asymptotic limit, estimating all d parameters describing a transformation simultaneously rather than sequentially can lead to a reduction of the appropriately weighted sum of the measured parameters’ variances by a factor of d. We report the experimental creation and characterization of the lowest-dimensional such state, which we call the “tetrahedron state” due to its tetrahedral symmetry. This tetrahedron state is created in the symmetric subspace of four optical photons’ polarization in a single spatial and temporal mode, which behaves as a spin-2 particle. While imperfections due to the hardware limited the performance of our method, ongoing technological advances will enable this method to generate states which out-perform any other existing strategy in per-photon comparisons.

Rejection of Sinusoidal Disturbances With Unknown Slowly Time-Varying Frequencies for Linear Time-Varying Systems

Abstract Recently, a class of adaptive schemes has been developed for rejecting sinusoidal output disturbances with unknown frequencies, phases, and amplitudes. These adaptive schemes require an accurate model of the affected system's dynamics to function, and the controller performance degrades as the modeling error increases. While linear time-invariant (LTI) dynamics can adequately model the dynamics of some systems, a time-varying model of the system dynamics is more appropriate in certain scenarios. This paper proposes a robust adaptive scheme for rejecting disturbances that affect the output of a system described by a known linear time-varying model. The disturbances are described by an unknown number of sinusoidal terms with unknown time-varying frequencies. Analysis is done in ideal case where the disturbance frequencies are perfectly known to provide conditions guaranteeing the existence of a controller and a corresponding set of parameters which reject the disturbance. Analysis is then done in the more realistic adaptive scenario where the disturbance frequencies are unknown, and a robust adaptive scheme for selecting controller parameters which reject the disturbance is proposed. Performance of the controller with respect to the speed of variation in the plant model parameters is assessed via simulation.

Power based adaptive compensator of output oscillations

Power-based output feedback compensator for oscillatory systems is proposed. The average input-output power of an oscillatory signal serves as an equivalent control effort, while the unknown amplitude and frequency of oscillations are detected at each half-period. This makes the compensator adaptive and discrete, while the measured oscillatory output is the single available signal in use. The resulting discrete control scheme enables a drastic reduction of communication efforts in the control loop. The compensator is designed for 2nd order systems, while an extension to higher-order dynamics, like e.g. in case of two-inertia systems, is also provided. Illustrative experimental case study of the 5th order oscillatory system is provided.

ASYMPTOTICALLY OPTIMAL ALGORITHM FOR PROCESSING SIDE RADIATION SIGNALS FROM MONITOR SCREENS ON LIQUID CRYSTAL STRUCTURES

An asymptotically optimal compatible algorithm for detecting side radiation signals from the monitor screen on liquid crystal structures and estimating the duration of image immutability on the monitor screen is found, which will better intercept information from monitor screens. The structure of a special technical intelligence tool is justified as a maximum likelihood algorithm for a finite number of unknown quadrature amplitudes of the information leakage signal from the monitor screen on liquid crystal structures.

Distributed sub-Nyquist sampling and parameters measurement of common frequency support MEDS signals

Parameters measurement of multiple exponentially damped sinusoids (MEDS) signals is of great significance in many areas. However, recent technologies are most based on Nyquist sampling theory and thus require very high sampling rate for wide band signals. In this paper, a distributed sub-Nyquist sampling and parameters measurement method is proposed for common frequency support MEDS signals. The proposed method can measure the parameters of P common frequency support MEDS signals by P+1 distributed sub-Nyquist sampling channels. A subspace based parameters estimation algorithm is proposed to estimate the unknown amplitudes, frequencies and damping factors of the measured MEDS signals. It can be determined that K(P+1)+P⌈K/P⌉ samples are sufficient for parameters measuring of P MEDS signals with K common frequency components, which is much smaller than previous works. Finally, we design a hardware prototype to verify the effectiveness of the proposed method. Simulation and hardware experiments have demonstrated the effectiveness and noise robustness of the proposed method.

Semi-analytical solution for the 3D response of a tunnel embedded in an elastic half-space subject to seismic waves

This paper presents a semi-analytical solution for the 3D problem of a cylindrical tunnel embedded in an elastic half-space subject to plane harmonic compressional and shear waves. Both the tunnel and soil are modelled as an elastic continuum. Conformal mapping is employed to transform the original physical domain with boundary surfaces of two different types onto an image domain with surfaces of the same type, which makes the problem easier to solve. The total wave field in the half-space consists of incident and reflected (from the half-space surface) plane waves, as well as directly and secondary scattered cylindrical waves, while the total wave field in the tunnel consists of refracted cylindrical waves. The secondary scattered waves, generated when the cylindrical waves directly scattered from the tunnel meet the half-space surface, are represented by cylindrical waves that originate from an image source, which is in line with the spirit of the method of images. The unknown amplitude coefficients of the cylindrical waves are determined from the boundary and continuity conditions of the tunnel–soil system by projecting those onto the set of circumferential modes, which results in a set of algebraic equations. Results show that the present method converges for a small number of circumferential modes. We observe very good agreement between the obtained results and those in literature. In a systematic evaluation, we demonstrate that the method works well for the frequency band of seismic waves, as well as for the complete considered ranges of the tunnel/soil stiffness ratio, the embedded depth of the tunnel, the vertical incident angle and the tunnel thickness. However, the results obtained for a moderate tunnel–soil stiffness contrast under the incident compressional wave are inaccurate when Hankel functions are used to represent the cylindrical waves in the tunnel, which is due to the refracted shear waves in the tunnel transitioning from propagating to evanescent (in the 3D case). These inaccuracies can be perfectly overcome by representing the waves in the tunnel by Bessel functions. We also find that the present method generally works better for the incident compressional wave than for the incident shear wave, as the condition number of the matrix (related to the mentioned algebraic equations) is often larger in the latter case. In view of engineering practice, we conclude that the tunnel is safer when the surrounding soil is stiffer, the tunnel is thicker and the vertical incident angle is larger. Finally, the present method, which is in general fast, elegant and accurate, can be used in preliminary design so as to avoid pronounced resonances, and to assess stress distributions and ground vibrations.

Оценка длительности сверхширокополосного квазирадиосигнала при неуверенности в его наличии

We synthesize a quasi-likelihood algorithm for estimation of the duration of an arbitrary shape ultra-wideband quasi-radio signal with unknown amplitude and initial phase, which observed against the background of additive Gaussian white noise. Among the ultra-wideband signals, a separate class is distinguished – ultra-wideband quasi-radio signals, which structure is similar to narrowband radio signals, but the condition of relative narrowband is not satisfied. We suggest that its duration can be equal to several periods or a fraction of the period of a harmonic oscillation. We consider the model of a signal which may be absent in the received realization, while the structure of the receiver does not take into account the disappearance of the signal. Statistical characteristics of the synthesized duration estimates are conditional bias and dispersions. The obtained results can be used for estimation of the decrease in efficiency in evaluation of the duration of a signal, when such a signal may disappear in the received realization.

Analysis of Arbitrary EM Field Exposure to a Multilayer Spherical Head Model Using Spherical Vector Wave Functions

A semi-analytical method is presented for the assessment of induced electromagnetic field inside a multilayer head model exposed to radiated field of an arbitrary source antenna. First the source antenna is simulated by a full-wave software in the absence of the head model to evaluate its radiating characteristics. Then, by sampling of the source radiated fields, its spherical vector wave function (SVWF) amplitudes are evaluated. The well-known translation addition theorem for spherical vector wave functions (SVWFs) is implemented to translate radiating field SVWFs to the local coordinates system of head model. Neglecting the reaction of model on source fields, using boundary conditions on the interfaces of adjacent layers, the unknown SVWF amplitudes of the fields inside each layer as well as those of the scattered field outside the head model are evaluated. Some numerical examples are presented for the verification of the proposed method. The acceptable consistency between the results obtained by the proposed method and full-wave simulations of the problem verifies the authenticity of the proposed method. In comparison to a full-wave numerical method, the proposed method provides an efficient repeatable simulation approach due to the independency of the source and head model analyses.

Numerical simulation of wave propagation in ice-covered ocean environments based on the equivalent-source method

Accurate modeling of sound propagation in ice-covered ocean environments can help with interpreting discrepancies between predictions and experimental observations in the changing Arctic Ocean; this is advantageous for environmental conservation, resource exploration, and naval applications. Building on the recent development of the equivalent-source (ES) method (ESM), herein, an ESM-based sub-ice model (ESM-SUBICE) is presented for wave propagation in an ice-covered ocean acoustic environment. The presented model solves exact governing equations for acoustic–elastic propagation in an ice-covered waveguide by expressing the wave solution in terms of a field superposition produced by several sets of ESs. Their unknown amplitudes are solved by strictly enforcing additional ice-layer boundary conditions. ESM-SUBICE achieves high efficiency using a water–seabed Green's function to automatically satisfy the boundary conditions at this interface. By further dividing the ocean environment into layers, ESM-SUBICE is extended for more general situations including stratified sound-speed structures and seabed range dependencies. ESM-SUBICE is benchmarked against a finite-element model, and it is found to produce high-quality solutions with high efficiency. Transmission-loss predictions for elastic, fluid, and free-surface ice representations in different ocean environments are compared to examine the effect of ice elasticity on propagation and scattering. The results suggest that the fluid representation is adequate for deep-water environments where the seabed is soft and the surface duct effect is insignificant; otherwise, for accurate predictions, the ice elasticity should be considered.

Leaderless Consensus of Heterogeneous Multiple Euler–Lagrange Systems With Unknown Disturbance

This paper studies the leaderless consensus problem of heterogeneous multiple networked Euler-Lagrange systems subject to persistent disturbances with unknown constant biases, amplitudes, initial phases and frequencies. The main characteristic of this study is that none of the agents has information of a common reference model or of a common reference trajectory. Therefore, the agents must simultaneously and in a distributed way: achieve consensus to a common reference model (group model); achieve consensus to a common reference trajectory; and reject the unknown disturbances. We show that this is possible via a suitable combination of techniques of distributed observers, internal model principle and adaptive regulation. The proposed design generalizes recent results on group model learning, which have been studied for linear agents over undirected networks. In this work, group model learning is achieved for Euler-Lagrange dynamics over directed networks in the presence of persistent unknown disturbances.

Method for identification of sinusoidal signal parameters with variable unknown amplitude

A new method proposed for identifying the parameters of sinusoidal signal with unknown variable amplitude. The problem of estimating the parameters of sinusoidal signals is relevant in the problems of dynamic positioning and disturbance compensation, for the synthesis of control laws that take into account external disturbances. In the proposed method, the restriction on the signal amplitude is removed. In contrast to known approaches, where the amplitude must be fixed, in the proposed method the signal amplitude can be variable. To implement the proposed identification algorithm, the Jordan matrix form and delay operators are used. During parameterization, a regression model is formed containing unknown stationary parameters. To search for unknown parameters, the method of dynamic expansion of the regressor and mixing is used. The results of computer simulation demonstrate the efficiency of the proposed algorithm. The simulation results confirmed the convergence of parameter estimation to the true values. The proposed approach can be applied to a wide class of applied problems related to disturbance compensation in vibration protection systems, monitoring systems in determining the parameters of high-rise or large-span building structures, and in robotic object control systems.

Add-on Harmonic Disturbance Cancellation Control in Continuous Hot-Dip Galvanizing Lines

In continuous hot-dip galvanizing of steel strips, unwanted vibrations of the processed strip can significantly degrade the coating uniformity and quality. Thus, an increasing number of hot-dip galvanizing lines are equipped with electromagnetic strip stabilization devices to enable active strip-shape and vibration control. Typically, commercial strip stabilizers achieve adequate broad-band vibration attenuation. However, their disturbance rejection capabilities are usually insufficient in case of persistently exciting harmonic disturbances. This work proposes a new multivariable harmonic disturbance cancellation control strategy which can be used as add-on to the position control loop of an existing strip stabilization device. The unknown amplitude, phase angle, and disturbance frequency are estimated during online operation. The systematic consideration of controller-output and estimator constraints in the design guarantees a reliable and safe operation in the challenging industrial environment. The devised control system works well even in the case of non-persistently exciting harmonic disturbances. The effectiveness of the proposed control scheme is demonstrated by short- and long-term measurement results from an industrial hot-dip galvanizing line.

Variational Bayesian-Based Moving Horizon Estimation of Toolface for Rotary Steerable Drilling Tool Systems

This article is concerned with the estimation problem of Toolface for dynamic point-the-bit rotary steerable drilling tool systems. First, considering the unknown frequency and amplitude of vibration during the drilling process, the Toolface system is modeled as a time-varying stochastic system with unknown and time-varying noise covariance matrices. Under the assumption that the noises and their covariance matrices, respectively, obey the Gaussian distribution and the inverse Wishart distribution, the variational Bayesian-based moving horizon estimation algorithm is proposed. Then, the state and the noise covariance matrices are inferred by iteratively updating their approximate posterior probability distributions. Finally, simulations and experiments are provided to demonstrate the effectiveness and superiority of the developed estimation scheme.