Identification of damping: Part 4, error analysis

In previous papers (S. Adhikari and J. Woodhouse 2001 Journal of Sound and Vibration 243, 43-61; 63-88; S. Adhikari and J. Woodhouse 2002 Journal of Sound and Vibration 251, 477-490) methods were proposed to obtain the coefficient matrix for a viscous damping model or a non-viscous damping model with an exponential relaxation function, from measured complex natural frequencies and modes. In all these works, it has been assumed that exact complex natural frequencies and complex modes are known. In reality, this will not be the case. The purpose of this paper is to analyze the sensitivity of the identified damping matrices to measurement errors. By using numerical and analytical studies it is shown that the proposed methods can indeed be expected to give useful results from moderately noisy data provided a correct damping model is selected for fitting. Indications are also given of what level of noise in the measured modal properties is needed to mask the true physical behaviour.

Investigation of damping effects on statistical energy analysis of coupled structures

The effects of damping on energy sharing in coupled systems are investigated. The approach taken is to compute the forced response patterns of various idealised systems, and from these to calculate the parameters of Statistical Energy Analysis model for the systems using the matrix inversion approach [1]. It is shown that when SEA models are fitted by this procedure, the values of the coupling loss factors are significantly dependent on damping except when it is sufficiently high. For very lightly damped coupled systems, varying the damping causes the values of the coupling loss factor to vary in direct proportion to the internal loss factor. In the limit of zero damping, the coupling loss factors tend to zero. This is a view which contrasts strongly with 'classical' SEA, in which coupling loss factors are determined by the nature of the coupling between subsystems, independent of subsystem damping. One implication of the strong damping dependency is that equipartition of modal energy under low damping does not in general occur. This is contrary to the classical SEA prediction that equipartition of modal energy always occurs if the damping can be reduced to a sufficiently small value. It is demonstrated that the use of this classical assumption can lead to gross overestimates of subsystem energy ratios, especially in multi-subsystem structures. © 1996 Academic Press Limited.

Characterization of the temperature sensitivity of gain and recombination mechanisms in 1.3-μm AlGaInAs MQW lasers

The potential of 1.3-μm AlGaInAs multiple quantum-well (MQW) laser diodes for uncooled operation in high-speed optical communication systems is experimentally evaluated by characterizing the temperature dependence of key parameters such as the threshold current, transparency current density, optical gain and carrier lifetime. Detailed measurements performed in the 20°C-100°C temperature range indicate a localized T0 value of 68 K at 98°C for a device with a 2.8μm ridge width and 700-μm cavity length. The transparency current density is measured for temperatures from 20°C to 60°C and found to increase at a rate of 7.7 A·cm -2 · °C-1. Optical gain characterizations show that the peak modal gain at threshold is independent of temperature, whereas the differential gain decreases linearly with temperature at a rate of 3 × 10-4 A-1·°C-1. The differential carrier lifetime is determined from electrical impedance measurements and found to decrease with temperature. From the measured carrier lifetime we derive the monomolecular (A), radiative (B), and nonradiative Auger (C) recombination coefficients and determine their temperature dependence in the 20 °C-80 °C range. Our study shows that A is temperature independent, B decreases with temperature, and C exhibits a less pronounced increase with temperature. The experimental observations are discussed and compared with theoretical predictions and measurements performed on other material systems. © 2005 IEEE.

Probabilistic fault identification using vibration data and neural networks

Bayesian formulated neural networks are implemented using hybrid Monte Carlo method for probabilistic fault identification in cylindrical shells. Each of the 20 nominally identical cylindrical shells is divided into three substructures. Holes of (12±2) mm in diameter are introduced in each of the substructures and vibration data are measured. Modal properties and the Coordinate Modal Assurance Criterion (COMAC) are utilized to train the two modal-property-neural-networks. These COMAC are calculated by taking the natural-frequency-vector to be an additional mode. Modal energies are calculated by determining the integrals of the real and imaginary components of the frequency response functions over bandwidths of 12% of the natural frequencies. The modal energies and the Coordinate Modal Energy Assurance Criterion (COMEAC) are used to train the two frequency-response-function-neural-networks. The averages of the two sets of trained-networks (COMAC and COMEAC as well as modal properties and modal energies) form two committees of networks. The COMEAC and the COMAC are found to be better identification data than using modal properties and modal energies directly. The committee approach is observed to give lower standard deviations than the individual methods. The main advantage of the Bayesian formulation is that it gives identities of damage and their respective confidence intervals.

Feasibility of damage detection using vibration data in a population of cylinders

The feasibility of vibration data to identify damage in a population of cylindrical shells is assessed. Vibration data from a population of cylinders were measured and modal analysis was employed to obtain natural frequencies and mode shapes. The mode shapes were transformed into the Coordinate Modal Assurance Criterion (COMAC). The natural frequencies and the COMAC before and after damage for a population of structures show that modal analysis is a viable route to damage identification in a population of nominally identical cylinders. Modal energies, which are defined as the integrals of the real and imaginary components of the frequency response functions over various frequency ranges, were extracted and transformed into the Coordinate Modal Energy Assurance Criterion (COMEAC). The COMEAC before and after damage show that using modal energies is a viable approach to damage identification in a population of cylinders.

Online multiple classifier boosting for object tracking

This paper presents a new online multi-classifier boosting algorithm for learning object appearance models. In many cases the appearance model is multi-modal, which we capture by training and updating multiple strong classifiers. The proposed algorithm jointly learns the classifiers and a soft partitioning of the input space, defining an area of expertise for each classifier. We show how this formulation improves the specificity of the strong classifiers, allowing simultaneous location and pose estimation in a tracking task. The proposed online scheme iteratively adapts the classifiers during tracking. Experiments show that the algorithm successfully learns multi-modal appearance models during a short initial training phase, subsequently updating them for tracking an object under rapid appearance changes. © 2010 IEEE.

Predicting shock response in uncertain structures using the Hybrid method

Using the Hybrid method (FE + SEA) it is possible to estimate the frequency response of an uncertain structure. The current work develops the Hybrid method to allow for time domain analysis of the shock response of a structure. Problems to be overcome when taking Hybrid method results into the time domain are a) the Hybrid method frequency response has no phase information, and b) the Hybrid method frequency response is smoothed in frequency and shows no modal peaks. In this paper the first problem has been overcome, using minimum phase reconstruction. Explanation of minimum phase reconstruction and its limitations are described, and application to shock problems described. © 2009 IOP Publishing Ltd.

Fluid-structure interaction with mean flow: Over-scattering and unstable resonance growth

It is known theoretically [1-3] that infinitely long fluid loaded plates in mean flow exhibit a range of unusual phenomena in the 'long time' limit. These include convective instability, absolute instability and negative energy waves which are destabilized by dissipation. However, structures are necessarily of finite length and may have discontinuities. Moreover, linear instability waves can only grow over a limited number of cycles before non-linear effects become dominant. We have undertaken an analytical and computational study to investigate the response of finite, discontinuous plates to ascertain if these unusual effects might be realized in practice. Analytically, we take a "wave scattering" [2,4] - as opposed to a "modal superposition" [5] - view of the fluttering plate problem. First, we solve for the scattering coefficients of localized plate discontinuities and identify a range of parameter space, well outside the convective instability regime, where over-scattering or amplified reflection/transmission occurs. These are scattering processes that draw energy from the mean flow into the plate. Next, we use the Wiener-Hopf technique to solve for the scattering coefficients from the leading and trailing edges of a baffled plate. Finally, we construct the response of a finite, baffled plate by a superposition of infinite plate propagating waves continuously scattering off the plate ends and solve for the unstable resonance frequencies and temporal growth rates for long plates. We present a comparison between our computational results and the infinite plate theory. In particular, the resonance response of a moderately sized plate is shown to be in excellent agreement with our long plate analytical predictions. Copyright © 2010 by ASME.

Eccentricity effects on acoustic radiation from a spherical source suspended within a thermoviscous fluid sphere.

Acoustic radiation from a spherical source undergoing angularly periodic axisymmetric harmonic surface vibrations while eccentrically suspended within a thermoviscous fluid sphere, which is immersed in a viscous thermally conducting unbounded fluid medium, is analyzed in an exact fashion. The formulation uses the appropriate wave-harmonic field expansions along with the translational addition theorem for spherical wave functions and the relevant boundary conditions to develop a closed-form solution in form of infinite series. The analytical results are illustrated with a numerical example in which the vibrating source is eccentrically positioned within a chemical fluid sphere submerged in water. The modal acoustic radiation impedance load on the source and the radiated far-field pressure are evaluated and discussed for representative values of the parameters characterizing the system. The proposed model can lead to a better understanding of dynamic response of an underwater acoustic lens. It is equally applicable in miniature transducer analysis and design with applications in medical ultrasonics.

Optical design of liquid crystal lenses: Off-axis modelling

We report on our work on producing liquid crystal switchable modal lenses and their use in a compound lens system in order to produce variable focus/zoom lenses. We describe work on producing a high power lens, and present theoretical work on off-axis phase modulation in a liquid crystal lens which is important in order to be able to carry out a complete optical design of a liquid crystal lens.

Adaptive modally addressed liquid crystal lenses

An adaptive lens, which has variable focus and is rapidly controllable with simple low-power electronics, has numerous applications in optical telecommunications devices, 3D display systems, miniature cameras and adaptive optics. The University of Durham is developing a range of adaptive liquid crystal lenses, and here we describe work on construction of modal liquid crystal lenses. This type of lens was first described by Naumov [1] and further developed by others [24]. In this system, a spatially varying and circularly symmetric voltage profile can be generated across a liquid-crystal cell, generating a lens-like refractive index profile. Such devices are simple in design, and do not require a pixellated structure. The shape and focussing power of the lens can be controlled by the variation of applied electric field and frequency. Results show adaptive lenses operating at optical wavelengths with continuously variable focal lengths from infinity to 70 cm. Switching speeds are of the order of 1 second between focal positions. Manufacturing methods of our adaptive lenses are presented, together with the latest results to the performance of these devices.

Stability enhancement by casing grooves: The importance of stall inception mechanism and solidity

This paper concerns the optimisation of casing grooves and the important influence of stall inception mechanism on groove performance. Installing casing grooves is a well known technique for improving the stable operating range of a compressor, but the wide-spread use of grooves is restricted by the loss of efficiency and flow capacity. In this paper, laboratory tests are used to examine the conditions under which casing treatment can be used to greatest effect. The use of a single casing groove was investigated in a recently published companion paper. The current work extends this to multiple-groove treatments and considers their performance in relation to stall inception mechanisms. Here it is shown that the stall margin gain from multiple grooves is less than the sum of the gains if the grooves were used individually. By contrast, the loss of efficiency is additive as the number of grooves increases. It is then shown that casing grooves give the greatest stall margin improvement when used in a compressor which exhibits spike-type stall inception, while modal activity before stall can dramatically reduce the effectiveness of the grooves. This finding highlights the importance of being able to predict the stall inception mechanism which might occur in a given compressor before and after grooves are added. Some published prediction techniques are therefore examined, but found wanting. Lastly, it is shown that casing grooves can, in some cases, be used to remove rotor blades and produce a more efficient, stable and light-weight rotor. © 2010 by ASME.

Initial modelling and controller design for active control of spacecraft microvibrations

Microvibrations, at frequencies between 1 and 1000 Hz, generated by on board equipment, propagate throughout a spacecraft structure affecting the performance of sensitive payloads. The purpose of this work is to investigate strategies to model and reduce these dynamic disturbances by active control. Initial studies were performed by considering a mass loaded panel where the disturbance excitation source consisted of point forces, the objective being to minimise the displacement at an arbitrary output location. Piezoelectric patches acting as sensors and actuators were used. The equations of motion are derived by using Lagrange's equation with modal shapes as Ritz functions. The number of sensors/actuators and their location is variable. The set of equations obtained is then transformed into state variables and some initial controller design studies have been undertaken. These are based on feedback control implemented using a full state feedback and an observer which reconstructs the state vector from the available sensor signal. Here, the basics behind the structural modelling and controller design will be described. This preliminary analysis will also be used to identify short to medium term further work.

Moderate energy impact analysis combining phenomenological contact law with localised damage and integral equation method

A computational impact analysis methodology has been developed, based on modal analysis and a local contact force-deflection model. The contact law is based on Hertz contact theory while contact stresses are elastic, defines a modified contact theory to take account of local permanent indentation, and considers elastic recovery during unloading. The model was validated experimentally through impact testing of glass-carbon hybrid braided composite panels. Specimens were mounted in a support frame and the contact force was inferred from the deceleration of the impactor, measured by high-speed photography. A Finite Element analysis of the panel and support frame assembly was performed to compute the modal responses. The new contact model performed well in predicting the peak forces and impact durations for moderate energy impacts (15 J), where contact stresses locally exceed the linear elastic limit and damage may be deemed to have occurred. C-scan measurements revealed substantial damage for impact energies in the range of 30-50 J. For this regime the new model predictions might be improved by characterisation of the contact law hysteresis during the unloading phase, and a modification of the elastic vibration response in line with damage levels acquired during the impact. © 2011 Elsevier Ltd. All rights reserved.