Unknown Amplitude Research Articles

Multiple fault-based FDI and reconfiguration for aircraft engine sensors

PurposeCondition monitoring and health management of an aircraft engine is of importance due to engine’s critical position in aircraft. Missions require uninterrupted and safer conditions during the flight or taxi operations. Hence, the deviations, abnormal situations or failures have to be under control. This paper aims to propose a cascade connected approach for an aircraft engine fault tolerant control.Design/methodology/approachThe cascade connected structure includes a full-order unknown input observer for fault detection and eliminating the unknown disturbance effect on system, a generalized observer scheme for fault isolation and a Boolean logic mechanism for decision-making in reconfiguration process, respectively. This combination is simulated on a linear turbojet engine model in case of unknown input disturbance and under various sensor failure scenarios.FindingsThe simulation results show that the suggested fault detection isolation reconfiguration (FDIR) approach works effectively for multiple sensor failures with various amplitudes.Originality/valueDifferent from other studies, the proposed model is sensitive to unknown input disturbance and failures that have unknown amplitudes. One another notable feature of suggested FDIR approach is adaptability of structure against multiple sensor failures. Here, it is assumed that only a single fault is to be detected and isolated at a time. The simulation results show that the proposed structure can be suggested for linear models especially for physical redundancy-based real-time applications easily, quickly and effectively.

Cooperative composite sequential detection and its application in spectrum sensing

In this study, the authors present a method to derive sequential detector (SD) for a general class of composite hypothesis problems. The authors first explain how the SD is constructed by employing a `weight function'. Then, the authors employ this method in the cooperative spectrum sensing (SS) in cognitive radio networks where the primary user transmits a phase shift keying (PSK) signal with unknown complex amplitude in additive white Gaussian noise. The noise power is assumed known in the first scenario and unknown in the second one. To evaluate the performance of the resulting SDs, the authors obtain the required average sample number (ASN) function to meet the bounds of false alarm and missed detection probabilities through some numerical evaluations. The results illustrate that the average sensing delay of the proposed SDs are less than the required number of observations in the traditional fixed sample size detectors. In the proposed SDs, the authors also demonstrate that the increase of signal-to-noise ratio leads to decrease of ASN.

Determination of amplitude levels of the piecewise constant signal by using polynomial approximation

A new approach to determining the amplitude levels of piecewise constant signal has been proposed that is based on using its multiplicative model and solving the problem of polynomial approximation. In case of the absence of noise, the statement of polynomial approximation problem is based on the requirement of exact match of the current signal value with the amplitude value of one of its levels. In case of the presence of ordinary additive noise, the problem statement is based on the least squares criterion, while the solution of problem is presented in the analytical form. For the case of the presence of pulse-type noise, the problem statement is based on the minimum duration criterion, while the problem solution is achieved numerically by an appropriate functional minimization in unknown amplitudes of levels. The case of binary piecewise constant signal is considered in detail. The results of numerical simulation are presented for the cases, where the binary signal is distorted by ordinary additive noise with Gaussian distribution law and the pulse-type noise with the Cauchy distribution law.

Extended PCJO for the Detection-Localization of Hypersignals and Hyposignals in CT Images

The anthropomorphic model observer (MO) plays an important role in the assessment and optimization of medical imaging systems. The MO is a task-based approach; while the abnormality can appear as a hypersignal or a hyposignal for different imaging modalities, sequences, or organs, no MO has been proposed for the hyposignals detection-localization task in the literature. To improve the clinical relevance of the existing MOs, we propose an anthropomorphic MO that can also deal with hyposignals in this paper. In a previous study, we reported a perceptually relevant channelized joint observer (PCJO) for detecting and localizing multiple signals with unknown amplitude, orientation, size, and location. Here, we extend it mathematically to hyposignals task. A free-response study (close to the real-diagnostic procedure) for both hypersignals and hyposignals in cerebral and abdominal CT images was conducted with four radiologists. The equally weighted alternative free-response operating characteristic was used as the figure of merit. Statistical analyses show that the extended PCJO approaches the experts’ performances with no significant difference in the studied tasks. The results demonstrate that the extended PCJO is an alternative to replace radiologists for the evaluation and comparison of different medical image processing algorithms. The PCJO has been originally proposed on magnetic resonance imaging but tested on computerized tomography (CT) here; the coherent results show that the PCJO can be generalized to another modality-CT. We also provide in this paper, the reference values of all the parameters in the PCJO to facilitate its future application on magnetic resonance (MR) or CT images.

Adaptive and compressive matched field processing.

Matched field processing is a generalized beamforming method that matches received array data to a dictionary of replica vectors in order to locate one or more sources. Its solution set is sparse since there are considerably fewer sources than replicas. Using compressive sensing (CS) implemented using basis pursuit, the matched field problem is reformulated as an underdetermined, convex optimization problem. CS estimates the unknown source amplitudes using the replica dictionary to best explain the data, subject to a row-sparsity constraint. This constraint selects the best matching replicas within the dictionary when using multiple observations and/or frequencies. For a single source, theory and simulations show that the performance of CS and the Bartlett processor are equivalent for any number of snapshots. Contrary to most adaptive processors, CS also can accommodate coherent sources. For a single and multiple incoherent sources, simulations indicate that CS offers modest localization performance improvement over the adaptive white noise constraint processor. SWellEx-96 experiment data results show comparable performance for both processors when localizing a weaker source in the presence of a stronger source. Moreover, CS often displays less ambiguity, demonstrating it is robust to data-replica mismatch.

Order tracking usingH∞estimator and polynomial approximation

This paper presents the H ∞ estimator for discrete-time varying linear system combined with the polynomial approximation for order tracking of non-stationary signals. The proposed approach is applied to the gearbox diagnosis under variable speed condition. In this instance, it is well known that the occurrence of a fault on a gear tooth leads to an amplitude and a phase modulation in the vibration signal. The purpose is to estimate this unknown amplitude and phase modulation by tracking orders. To estimate these modulations, the vibration signal is described in state space model. Then, the H ∞ criterion is used to minimize the worst possible amplification of the estimation error related to both the process and the measurement noises. Such an approach doesn't require any assumption on the statistic properties of the noises unlike the Kalman estimator. A numerical example is given in order to evaluate the performance of the H ∞ estimator regarding the conventional Kalman estimator.

Completion of metric reconstruction for a particle orbiting a Kerr black hole

Vacuum perturbations of the Kerr metric can be reconstructed from the corresponding perturbation in either of the two Weyl scalars $\psi_0$ or $\psi_4$, using a procedure described by Chrzanowski and others in the 1970s. More recent work, motivated within the context of self-force physics, extends the procedure to metric perturbations sourced by a particle in a bound geodesic orbit. However, the existing procedure leaves undetermined a certain stationary, axially-symmetric piece of the metric perturbation. In the vacuum region away from the particle, this "completion" piece corresponds simply to mass and angular-momentum perturbations of the Kerr background, with amplitudes that are, however, a priori unknown. Here we present and implement a rigorous method for finding the completion piece. The key idea is to impose continuity, off the particle, of certain gauge-invariant fields constructed from the full (completed) perturbation, in order to determine the unknown amplitude parameters of the completion piece. We implement this method in full for bound (eccentric) geodesic orbits in the equatorial plane of the Kerr black hole. Our results provide a rigorous underpinning of recent results by Friedman {\it et al.}\ for circular orbits, and extend them to non-circular orbits.

Coordinated control with multiple dynamic leaders for uncertain Lagrangian systems via self‐tuning adaptive distributed observer

SummaryThis paper studies coordinated control of multiple Lagrangian systems with parametric uncertainties subject to external disturbances by proposing a fully distributed continuous control law based on the improved self‐tuning adaptive observer inspired by non‐identifier‐based high‐gain adaptive control technique. Under this distributed continuous control law, a group of Lagrangian systems are driven to the convex hull spanned by multiple heterogenous dynamic leaders, which can be any combination of step signals of arbitrary unknown magnitudes, ramp signals of arbitrary unknown slopes, and sinusoidal signals of arbitrary unknown amplitudes, initial phases, and any unknown frequencies. It is also worth to mention that this control law we propose, depending neither on any information of leader systems for uninformed followers, nor on external disturbances, even independent of neighbors' velocity, can achieve asymptotic tracking of multiple leaders without any additional condition instead of ensuring the ultimate boundedness of the containment error as in the literature. Copyright © 2016 John Wiley & Sons, Ltd.

Wave Finite Element Formulation of the Acoustic Transmission Through Complex Infinite Plates

A finite element-based derivation of the transmission loss (TL) of anisotropic layered infinite plates is presented in this paper. The wave-finite element method (WFE) is used to represent the plate with a finite element model of a single unit cell. The incident acoustic field is a known plane wave, and the reflected and transmitted pressures are supposed to be plane waves with unknown amplitudes and phases. The periodicity conditions on the unit cell allow to find a simple matrix equation linking the amplitudes of the transmitted and reflected fields as a function of the incident one. This approach is validated for several cases against classical analytical models for thin plates and sandwich constructions, where the results agree perfectly for a reasonable mesh size. The method is then used to study the effect of stacking order in a laminated composite plate. The main interest of the method is the use of finite elements, which enables a relative easy modelling since most packages readily include different formulations, compared to analytical models, where different formulations have to be implemented for every kind of material.

Rigorous theory for transient capillary imbibition in channels of arbitrary cross section

This article addresses a classical fluid mechanics problem where the effect of capillary action on a column of viscous liquid is analyzed by quantifying its time-dependent penetrated length in a narrow channel. Despite several past studies, a rigorous mathematical formulation of this inherently unsteady process is still unavailable, because these existing works resort to a crucial assumption only valid for mildly transient systems. The approximate theories use an integral approach where the penetration is described by equating total force acting on the domain to rate of change of total momentum. However, while doing so, the viscous resistance under temporally varying condition is assumed to be same as the resistance created by a quasi-steady velocity profile. Thus, leading order error appears due to such approximation which can only be true when the variation in time is not strong enough causing negligible transient deviation in the hydrodynamic quantities. The present paper proposes a new way to solve this problem by considering the unsteady field itself as an unknown variable. Accordingly, the analysis applies an eigenfunction expansion of the flow with unknown time-dependent amplitudes which along with the unsteady intrusion length are calculated from a system of ordinary differential equations. A comparative exploration identifies the situation for which the integral approach and the rigorous technique based on eigenfunction expansion deviate from each other. It also reveals that the two methods differ substantially in short-time dynamics at the initial stage. Then, an asymptotic perturbation shows how the two sets of results should coincide in their long-time behavior. In this way, the findings will provide a comprehensive understanding of the physics behind the transport phenomenon.

Robust multi-frequency sparse Bayesian learning: Theory and simulations

Compressive sensing based techniques have recently been applied successfully to underwater acoustics problems such as beamforming and matched field processing. Sparse Bayesian Learning (SBL) is one of the fast compressive sensing methods and is formulated using Bayesian statistics. In the SBL framework, source amplitudes are modeled as complex Gaussian random variables with unknown variance. Evidence maximization is performed to estimate the unknown source amplitude variance and source position. A major advantage of SBL over more commonly used methods such as basis pursuit is that it is computationally faster. In this work, we develop a robust sparse Bayesian learning algorithm that can account for model mismatch leading to errors in the replica vector dictionary. Specifically, the likelihood function is modified so that it takes into account the covariance matrix of error in replica vectors. We also extend the SBL algorithm to process observations from multiple frequencies. The derived update rule combines observations from all the frequencies in a holistic manner. We demonstrate the robust SBL algorithm with simulations. A comparison is done with other compressed sensing methods including basis pursuit and orthogonal matching pursuit.

Complex modes expansion with vector projection using power flow to simulate Lamb waves scattering from horizontal cracks and disbonds.

This paper presents an inexpensive but accurate analytical method to calculate the scattering of straight-crested Lamb waves from cracks parallel to the plate surface. The same method is applicable for the disbond problem. In this method, the scatter field is expanded in terms of complex Lamb wave modes with unknown amplitudes. These unknown amplitudes are obtained from the boundary conditions using vector projection utilizing the power expression. The process works by projecting the stress conditions onto the displacement eigen-spaces of complex Lamb wave modes and vice versa. The authors call this technique "complex modes expansion with vector projection" (CMEP). The CMEP approach is versatile and can be readily applied to corrosion, cracks, or disbonds. In this paper, the CMEP method is applied to a horizontal crack in a plate. For verification of the results the authors compared them with the results obtained by using the finite element method (FEM) and literature. The FEM analysis was conducted in the frequency domain with non-reflecting boundaries. It was found that CMEP results correspond very well with FEM results over a wide frequency-thickness range up to 1.5 MHz mm with CMEP being orders of magnitude faster than FEM.

Estimation of the number of orthogonal signals with unknown parameters

Algorithms for estimation of the number of signals with unknown amplitudes and several non-energy parameters are synthesized on the basis of the modified maximum likelihood method. Asymptotic values of the probabilities of the error in estimation of the signal number are determined. The effect of a reduced volume of the a priori domain of possible values and the dimensionality of the vector of unknown non-energy parameters on the quality of operation of the algorithms for estimation of the number of signals is investigated.

From adaptive control to variable structure systems – seeking harmony

From adaptive control to variable structure systems – seeking harmony

The leader-following rendezvous with connectivity preservation via a self-tuning adaptive distributed observer

ABSTRACTThis paper studies the leader-following rendezvous with connectivity preservation problem for multiple double-integrator systems subject to external disturbances via a self-tuning adaptive distributed observer approach. This approach offers two advantages over the existing approach. First, it removes the existing assumption that all the followers know the system matrix of the leader system. Second, the difficult task of calculating the observer gain is avoided by the employment of the dynamic observer gain. A rigorous analysis shows that our control law is capable of maintaining the connectivity of any initial connected communication network, and achieving the asymptotic tracking and disturbance rejection for a class of leader's signals and external disturbances, which can be the algebraic sum or multiplication of any polynomial functions with any unknown coefficients and sinusoidal functions with arbitrary unknown amplitudes, initial phases, and any frequencies.

Leader-following attitude consensus of multiple uncertain spacecraft systems subject to external disturbance

Summary The attitude consensus problem of multiple rigid spacecraft systems is one of the key issues in spacecraft formation flying and has been extensively studied. In this paper, we further consider the leader-following attitude consensus problem of multiple rigid uncertain spacecraft systems subject to a class of multi-tone sinusoidal disturbances with arbitrarily unknown amplitudes, initial phases, frequencies, and constant biases. In contrast to the existing results, in order to achieve asymptotic reference tracking and disturbance rejection by smooth control, we have integrated the distributed observer approach with internal model and adaptive control techniques. Simulation results are shown to validate the effectiveness of the proposed control law. Copyright © 2016 John Wiley & Sons, Ltd.

Observation and output adaptive tracking for a class of nonlinear non-minimum phase systems

ABSTRACTIn this paper, the output tracking problem for a class of systems with unstable zero dynamics is addressed. The state is assumed not measurable. The output of the dynamical system to be controlled has to track a signal, which is the sum of a known number of sinusoids with unknown frequencies, amplitudes and phases. The non-minimum phase nature of the considered systems prevents the direct tracking by standard sliding mode methods, which are known to generate unstable behaviours of the internal dynamics. The proposed method relies on the availability of a flat output and its time derivatives which are functions of the unavailable state; therefore, a nonlinear observer is needed. Due to the uncertainty in the frequencies and in the parameters defining the relationship between the output of the system and the flat states, adaptive indirect methods are applied.

Extending the method of fundamental solutions to non-homogeneous elastic wave problems

Two meshfree methods are developed for the numerical solution of the non-homogeneous Cauchy–Navier equations of elastodynamics in an isotropic material. The two approaches differ upon the choice of the basis functions used for the approximation of the unknown wave amplitude. In the first case, the solution is approximated in terms of a linear combination of fundamental solutions of the Navier differential operator with different source points and test frequencies. In the second method the solution is approximated by superposition of acoustic waves, i.e. fundamental solutions of the Helmholtz operator, with different source points and test frequencies. The applicability of the two methods is justified in terms of density results and a convergence result is proven. The accuracy of the methods is illustrated through 2D numerical examples. Applications to interior elastic wave scattering problems are also presented.

Output‐based disturbance rejection control for non‐linear uncertain systems with unknown frequency disturbances using an observer backstepping approach

This paper is concerned with the output feedback control design for a class of nonlinear uncertain systems subject to multiple sources of disturbances including model uncertainties, unknown constant disturbances, harmonic disturbances with unknown frequency and amplitude. The total disturbances and uncertainties are delicately represented by a compact exogenous model first. By incorporating the adaptive internal model principle, a set of dynamic estimators are developed for both state and disturbance observations. By means of observer backstepping technique, a composite output feedback controller is constructed based on the disturbance and state estimations. The stability of the closed-loop system is rigorously established based on Lyapunov stability criterion. A missile roll stabilization example is finally investigated to validate the effectiveness of the proposed control approach.

Scattering of Lamb waves from a discontinuity: An improved ​ analytical approach

This paper presents an efficient and accurate analytical method to calculate the scattering of straight-crested Lamb waves from geometric discontinuities. In this method, the scattered field is expanded in terms of complex Lamb wave modes with unknown amplitudes. These unknown amplitudes are obtained from the boundary conditions using a vector projection utilizing the power expression. The process works by projecting the stress conditions onto the displacement eigen-spaces of complex Lamb wave modes and vice-versa. We call this technique “complex modes expansion with vector projection” (CMEP). Unlike other methods, the CMEP approach is versatile and can be readily applied to notches, cracks, or disbonds. In this paper, the methodology is illustrated by applying the CMEP method to a benchmark problem — the geometric discontinuity created by a step in the thickness of a plate. For method verification, the finite element method (FEM) and the axial–flexural analytical model were used. The FEM analysis was conducted in the frequency domain with non-reflecting boundaries. It was found that the CMEP results correspond very well with the FEM results over a wide frequency–thickness range up to 1.5 MHz-mm. The axial–flexural model was used to verify only the CMEP asymptotic behavior toward zero frequency where frequency-domain FEM encounters difficulties. Our study shows that the computational efficiency of CMEP is orders of magnitude higher than FEM. The paper ends with a discussion of how the CMEP method may be extended to the fast and accurate analysis of realistic damage situations.