Tracking control of a class of Hamiltonian mechanical systems with disturbances

This paper presents a trajectory-tracking control strategy for a class of mechanical systems in Hamiltonian form. The class is characterised by a simplectic interconnection arising from the use of generalised coordinates and full actuation. The tracking error dynamic is modelled as a port-Hamiltonian Systems (PHS). The control action is designed to take the error dynamics into a desired closed-loop PHS characterised by a constant mass matrix and a potential energy with a minimum at the origin. A transformation of the momentum and a feedback control is exploited to obtain a constant generalised mass matrix in closed loop. The stability of the close-loop system is shown using the close-loop Hamiltonian as a Lyapunov function. The paper also considers the addition of integral action to design a robust controller that ensures tracking in spite of disturbances. As a case study, the proposed control design methodology is applied to a fully actuated robotic manipulator.

Novel non-linear elastic structural analysis with generalised transverse element loads using a refined finite element

In the finite element modelling of structural frames, external loads such as wind loads, dead loads and imposed loads usually act along the elements rather than at the nodes only. Conventionally, when an element is subjected to these general transverse element loads, they are usually converted to nodal forces acting at the ends of the elements by either lumping or consistent load approaches. In addition, it is especially important for an element subjected to the first- and second-order elastic behaviour, to which the steel structure is critically prone to; in particular the thin-walled steel structures, when the stocky element section may be generally critical to the inelastic behaviour. In this sense, the accurate first- and second-order elastic displacement solutions of element load effect along an element is vitally crucial, but cannot be simulated using neither numerical nodal nor consistent load methods alone, as long as no equilibrium condition is enforced in the finite element formulation, which can inevitably impair the structural safety of the steel structure particularly. It can be therefore regarded as a unique element load method to account for the element load nonlinearly. If accurate displacement solution is targeted for simulating the first- and second-order elastic behaviour on an element on the basis of sophisticated non-linear element stiffness formulation, the numerous prescribed stiffness matrices must indispensably be used for the plethora of specific transverse element loading patterns encountered. In order to circumvent this shortcoming, the present paper proposes a numerical technique to include the transverse element loading in the non-linear stiffness formulation without numerous prescribed stiffness matrices, and which is able to predict structural responses involving the effect of first-order element loads as well as the second-order coupling effect between the transverse load and axial force in the element. This paper shows that the principle of superposition can be applied to derive the generalized stiffness formulation for element load effect, so that the form of the stiffness matrix remains unchanged with respect to the specific loading patterns, but with only the magnitude of the loading (element load coefficients) being needed to be adjusted in the stiffness formulation, and subsequently the non-linear effect on element loadings can be commensurate by updating the magnitude of element load coefficients through the non-linear solution procedures. In principle, the element loading distribution is converted into a single loading magnitude at mid-span in order to provide the initial perturbation for triggering the member bowing effect due to its transverse element loads. This approach in turn sacrifices the effect of element loading distribution except at mid-span. Therefore, it can be foreseen that the load-deflection behaviour may not be as accurate as those at mid-span, but its discrepancy is still trivial as proved. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. Moreover, another significance of this paper is placed on shifting the nodal response (system analysis) to both nodal and element response (sophisticated element formulation). For the conventional finite element method, such as the cubic element, all accurate solutions can be only found at node. It means no accurate and reliable structural safety can be ensured within an element, and as a result, it hinders the engineering applications. The results of the paper are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple frames.

Reliability and criterion-related validity with a smartphone used in timed-up-and-go test

Background The capacity to diagnosys, quantify and evaluate movement beyond the general confines of a clinical environment under effectiveness conditions may alleviate rampant strain on limited, expensive and highly specialized medical resources. An iPhone 4® mounted a three dimensional accelerometer subsystem with highly robust software applications. The present study aimed to evaluate the reliability and concurrent criterion-related validity of the accelerations with an iPhone 4® in an Extended Timed Get Up and Go test. Extended Timed Get Up and Go is a clinical test with that the patient get up from the chair and walking ten meters, turn and coming back to the chair. Methods A repeated measure, cross-sectional, analytical study. Test-retest reliability of the kinematic measurements of the iPhone 4® compared with a standard validated laboratory device. We calculated the Coefficient of Multiple Correlation between the two sensors acceleration signal of each subject, in each sub-stage, in each of the three Extended Timed Get Up and Go test trials. To investigate statistical agreement between the two sensors we used the Bland-Altman method. Results With respect to the analysis of the correlation data in the present work, the Coefficient of Multiple Correlation of the five subjects in their triplicated trials were as follows: in sub-phase Sit to Stand the ranged between r = 0.991 to 0.842; in Gait Go, r = 0.967 to 0.852; in Turn, 0.979 to 0.798; in Gait Come, 0.964 to 0.887; and in Turn to Stand to Sit, 0.992 to 0.877. All the correlations between the sensors were significant (p < 0.001). The Bland-Altman plots obtained showed a solid tendency to stay at close to zero, especially on the y and x-axes, during the five phases of the Extended Timed Get Up and Go test. Conclusions The inertial sensor mounted in the iPhone 4® is sufficiently reliable and accurate to evaluate and identify the kinematic patterns in an Extended Timed Get and Go test. While analysis and interpretation of 3D kinematics data continue to be dauntingly complex, the iPhone 4® makes the task of acquiring the data relatively inexpensive and easy to use.

Two-dimensional bow and stern flows in a finite-depth fluid with constant vorticity

This thesis is concerned with two-dimensional free surface flows past semi-infinite surface-piercing bodies in a fluid of finite-depth. Throughout the study, it is assumed that the fluid in question is incompressible, and that the effects of viscosity and surface tension are negligible. The problems considered are physically important, since they can be used to model the flow of water near the bow or stern of a wide, blunt ship. Alternatively, the solutions can be interpreted as describing the flow into, or out of, a horizontal slot. In the past, all research conducted on this topic has been dedicated to the situation where the flow is irrotational. The results from such studies are extended here, by allowing the fluid to have constant vorticity throughout the flow domain. In addition, new results for irrotational flow are also presented. When studying the flow of a fluid past a surface-piercing body, it is important to stipulate in advance the nature of the free surface as it intersects the body. Three different possibilities are considered in this thesis. In the first of these possibilities, it is assumed that the free surface rises up and meets the body at a stagnation point. For this configuration, the nonlinear problem is solved numerically with the use of a boundary integral method in the physical plane. Here the semi-infinite body is assumed to be rectangular in shape, with a rounded corner. Supercritical solutions which satisfy the radiation condition are found for various values of the Froude number and the dimensionless vorticity. Subcritical solutions are also found; however these solutions violate the radiation condition and are characterised by a train of waves upstream. In the limit that the height of the body above the horizontal bottom vanishes, the flow approaches that due to a submerged line sink in a $90^\circ$ corner. This limiting problem is also examined as a special case. The second configuration considered in this thesis involves the free surface attaching smoothly to the front face of the rectangular shaped body. For this configuration, nonlinear solutions are computed using a similar numerical scheme to that used in the stagnant attachment case. It is found that these solution exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a corner is also considered. Finally, the flow of a fluid emerging from beneath a semi-infinite flat plate is examined. Here the free surface is assumed to detach from the trailing edge of the plate horizontally. A linear problem is formulated under the assumption that the elevation of the plate is close to the undisturbed free surface level. This problem is solved exactly using the Wiener-Hopf technique, and subcritical solutions are found which are characterised by a train of sinusoidal waves in the far field. The nonlinear problem is also considered. Exact relations between certain parameters for supercritical flow are derived using conservation of mass and momentum arguments, and these are confirmed numerically. Nonlinear subcritical solutions are computed, and the results are compared to those predicted by the linear theory.

Generalised features for bird vocalisation retrieval in acoustic recordings

Bioacoustic monitoring has become a significant research topic for species diversity conservation. Due to the development of sensing techniques, acoustic sensors are widely deployed in the field to record animal sounds over a large spatial and temporal scale. With large volumes of collected audio data, it is essential to develop semi-automatic or automatic techniques to analyse the data. This can help ecologists make decisions on how to protect and promote the species diversity. This paper presents generic features to characterize a range of bird species for vocalisation retrieval. In the implementation, audio recordings are first converted to spectrograms using short-time Fourier transform, then a ridge detection method is applied to the spectrogram for detecting points of interest. Based on the detected points, a new region representation are explored for describing various bird vocalisations and a local descriptor including temporal entropy, frequency bin entropy and histogram of counts of four ridge directions is calculated for each sub-region. To speed up the retrieval process, indexing is carried out and the retrieved results are ranked according to similarity scores. The experiment results show that our proposed feature set can achieve 0.71 in term of retrieval success rate which outperforms spectral ridge features alone (0.55) and Mel frequency cepstral coefficients (0.36).

From “somatic scandals” to “a constant potential for violence”? The culture of dissection, brain-based learning, and the rewriting/rewiring of “the child”

This article analyzes the “messy and numberless beginnings” of the hope placed upon neurological foundationalism to provide a solution to the “problem” of differences between students and to the achievement of educational goals. Rather than arguing for or against educational neuroscience, the article moves through five levels to examine the conditions of possibility for subscribing to the brain as a causal organological locus of learning.

An eigenproblem approach to classical screw theory

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general two-, three-systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. We also present novel methods for the determination of the principal screws for four-, five-systems which do not require the explicit computation of the reciprocal systems. Principal screws of the systems of different orders are identified from one uniform criterion, namely that the pitches of the principal screws are the extreme values of the pitch.The classical results of screw theory, namely the equations for the cylindroid and the pitch-hyperboloid associated with the two-and three-systems, respectively have been derived within the proposed framework. Algebraic conditions have been derived for some of the special screw systems. The formulation is also illustrated with several examples including two spatial manipulators of serial and parallel architecture, respectively.

In vivo mri-based estimation of time-dependent elastic modulus in healthy arteries

The elastic properties of the arterial wall have been the subject of physiological, clinical and biomedical research for many years. There is convincing evidence that the elastic properties of the large arteries are seriously impaired in the presence of cardiovascular disease (CVD), due to alterations in the intrinsic structural and functional characteristics of vessels [1]. Early detection of changes in the elastic modulus of arteries would provide a powerful tool for both monitoring patients at high cardiovascular risk and testing the effects of pharmaceuticals aimed at stabilizing existing plaques by stiffening them or lowering the lipids.

In vivo non-invasive high resolution MR-based method for the determination of the elastic modulus of arterial vessels

The mechanical properties of arterial walls have long been recognized to play an essential role in the development and progression of cardiovascular disease (CVD). Early detection of variations in the elastic modulus of arteries would help in monitoring patients at high cardiovascular risk stratifying them according to risk. An in vivo, non-invasive, high resolution MR-phase-contrast based method for the estimation of the time-dependent elastic modulus of healthy arteries was developed, validated in vitro by means of a thin walled silicon rubber tube integrated into an existing MR-compatible flow simulator and used on healthy volunteers. A comparison of the elastic modulus of the silicon tube measured from the MRI-based technique with direct measurements confirmed the method's capability. The repeatability of the method was assessed. Viscoelastic and inertial effects characterizing the dynamic response of arteries in vivo emerged from the comparison of the pressure waveform and the area variation curve over a period. For all the volunteers who took part in the study the elastic modulus was found to be in the range 50-250 kPa, to increase during the rising part of the cycle, and to decrease with decreasing pressure during the downstroke of systole and subsequent diastole.

Phase transitions and gravity

Einstein's gravitational field is non-minimally coupled to a self-interacting scalar field in the presence of radiation. Such a theory can give rise to a phase transition associated with a change of sign of the gravitational “constant”. In our approach, the criterion for stability is formulated in terms of an effective potential, the phase-transition takes place due to temperature dependence of the scalar self-interaction coupling constant.

Stability Of Large Damped Flexible Spacecraft With Stored Angular Momentum

Vibrational stability of large flexible structurally damped spacecraft carrying internal angular momentum and undergoing large rigid body rotations is analysed modeling the systems as elastic continua. Initially, analytical solutions to the motion of rigid gyrostats under torque-free conditions are developed. The solutions to the gyrostats modeled as axisymmetric and triaxial spacecraft carrying three and two constant speed momentum wheels, respectively, with spin axes aligned with body principal axes are shown to be complicated. These represent extensions of solutions for simpler cases existing in the literature. Using these solutions and modal analysis, the vibrational equations are reduced to linear ordinary differential equations. Equations with periodically varying coefficients are analysed applying Floquet theory. Study of a few typical beam- and plate-like spacecraft configurations indicate that the introduction of a single reaction wheel into an axisymmetric satellite does not alter the stability criterion. However, introduction of constant speed rotors deteriorates vibrational stability. Effects of structural damping and vehicle inertia ratio are also studied.

Generalised growth models for aquatic species with an application to blacklip abalone (Haliotis rubra)

This paper presents a maximum likelihood method for estimating growth parameters for an aquatic species that incorporates growth covariates, and takes into consideration multiple tag-recapture data. Individual variability in asymptotic length, age-at-tagging, and measurement error are also considered in the model structure. Using distribution theory, the log-likelihood function is derived under a generalised framework for the von Bertalanffy and Gompertz growth models. Due to the generality of the derivation, covariate effects can be included for both models with seasonality and tagging effects investigated. Method robustness is established via comparison with the Fabens, improved Fabens, James and a non-linear mixed-effects growth models, with the maximum likelihood method performing the best. The method is illustrated further with an application to blacklip abalone (Haliotis rubra) for which a strong growth-retarding tagging effect that persisted for several months was detected

Analysing commercial catch and effort data from a penaeid trawl fishery: A comparison of linear models, mixed models, and generalised estimating equations approaches

Statistical methods are often used to analyse commercial catch and effort data to provide standardised fishing effort and/or a relative index of fish abundance for input into stock assessment models. Achieving reliable results has proved difficult in Australia's Northern Prawn Fishery (NPF), due to a combination of such factors as the biological characteristics of the animals, some aspects of the fleet dynamics, and the changes in fishing technology. For this set of data, we compared four modelling approaches (linear models, mixed models, generalised estimating equations, and generalised linear models) with respect to the outcomes of the standardised fishing effort or the relative index of abundance. We also varied the number and form of vessel covariates in the models. Within a subset of data from this fishery, modelling correlation structures did not alter the conclusions from simpler statistical models. The random-effects models also yielded similar results. This is because the estimators are all consistent even if the correlation structure is mis-specified, and the data set is very large. However, the standard errors from different models differed, suggesting that different methods have different statistical efficiency. We suggest that there is value in modelling the variance function and the correlation structure, to make valid and efficient statistical inferences and gain insight into the data. We found that fishing power was separable from the indices of prawn abundance only when we offset the impact of vessel characteristics at assumed values from external sources. This may be due to the large degree of confounding within the data, and the extreme temporal changes in certain aspects of individual vessels, the fleet and the fleet dynamics.

Working correlation structure misspecification, estimation and covariate design: Implications for generalised estimating equations performance

The method of generalised estimating equations for regression modelling of clustered outcomes allows for specification of a working matrix that is intended to approximate the true correlation matrix of the observations. We investigate the asymptotic relative efficiency of the generalised estimating equation for the mean parameters when the correlation parameters are estimated by various methods. The asymptotic relative efficiency depends on three-features of the analysis, namely (i) the discrepancy between the working correlation structure and the unobservable true correlation structure, (ii) the method by which the correlation parameters are estimated and (iii) the 'design', by which we refer to both the structures of the predictor matrices within clusters and distribution of cluster sizes. Analytical and numerical studies of realistic data-analysis scenarios show that choice of working covariance model has a substantial impact on regression estimator efficiency. Protection against avoidable loss of efficiency associated with covariance misspecification is obtained when a 'Gaussian estimation' pseudolikelihood procedure is used with an AR(1) structure.