Interocular corneal symmetry in refractive error groups

Purpose: To examine between eye differences in corneal higher order aberrations and topographical characteristics in a range of refractive error groups. Methods: One hundred and seventy subjects were recruited including; 50 emmetropic isometropes, 48 myopic isometropes (spherical equivalent anisometropia ≤ 0.75 D), 50 myopic anisometropes (spherical equivalent anisometropia ≥ 1.00 D) and 22 keratoconics. The corneal topography of each eye was captured using the E300 videokeratoscope (Medmont, Victoria, Australia) and analyzed using custom written software. All left eye data were rotated about the vertical midline to account for enantiomorphism. Corneal height data were used to calculate the corneal wavefront error using a ray tracing procedure and fit with Zernike polynomials (up to and including the eighth radial order). The wavefront was centred on the line of sight by using the pupil offset value from the pupil detection function in the videokeratoscope. Refractive power maps were analysed to assess corneal sphero-cylindrical power vectors. Differences between the more myopic (or more advanced eye for keratoconics) and the less myopic (advanced) eye were examined. Results: Over a 6 mm diameter, the cornea of the more myopic eye was significantly steeper (refractive power vector M) compared to the fellow eye in both anisometropes (0.10 ± 0.27 D steeper, p = 0.01) and keratoconics (2.54 ± 2.32 D steeper, p < 0.001) while no significant interocular difference was observed for isometropic emmetropes (-0.03 ± 0.32 D) or isometropic myopes (0.02 ± 0.30 D) (both p > 0.05). In keratoconic eyes, the between eye difference in corneal refractive power was greatest inferiorly (associated with cone location). Similarly, in myopic anisometropes, the more myopic eye displayed a central region of significant inferior corneal steepening (0.15 ± 0.42 D steeper) relative to the fellow eye (p = 0.01). Significant interocular differences in higher order aberrations were only observed in the keratoconic group for; vertical trefoil C(3,-3), horizontal coma C(3,1) secondary astigmatism along 45 C(4, -2) (p < 0.05) and vertical coma C(3,-1) (p < 0.001). The interocular difference in vertical pupil decentration (relative to the corneal vertex normal) increased with between eye asymmetry in refraction (isometropia 0.00 ± 0.09, anisometropia 0.03 ± 0.15 and keratoconus 0.08 ± 0.16 mm) as did the interocular difference in corneal vertical coma C (3,-1) (isometropia -0.006 ± 0.142, anisometropia -0.037 ± 0.195 and keratoconus -1.243 ± 0.936 μm) but only reached statistical significance for pair-wise comparisons between the isometropic and keratoconic groups. Conclusions: There is a high degree of corneal symmetry between the fellow eyes of myopic and emmetropic isometropes. Interocular differences in corneal topography and higher order aberrations are more apparent in myopic anisometropes and keratoconics due to regional (primarily inferior) differences in topography and between eye differences in vertical pupil decentration relative to the corneal vertex normal. Interocular asymmetries in corneal optics appear to be associated with anisometropic refractive development.

Identification and elimination of a matrix-induced systematic error in LA–ICP–MS 206Pb/238U dating of zircon

Black et al. (2004) identified a systematic difference between LA–ICP–MS and TIMS measurements of 206Pb/238U in zircons, which they correlated with the incompatible trace element content of the zircon. We show that the offset between the LA–ICP–MS and TIMS measured 206Pb/238U correlates more strongly with the total radiogenic Pb than with any incompatible trace element. This suggests that the cause of the 206Pb/238U offset is related to differences in the radiation damage (alpha dose) between the reference and unknowns. We test this hypothesis in two ways. First, we show that there is a strong correlation between the difference in the LA–ICP–MS and TIMS measured 206Pb/238U and the difference in the alpha dose received by unknown and reference zircons. The LA–ICP–MS ages for the zircons we have dated can be as much as 5.1% younger than their TIMS age to 2.1% older, depending on whether the unknown or reference received the higher alpha dose. Second, we show that by annealing both reference and unknown zircons at 850 °C for 48 h in air we can eliminate the alpha-dose-induced differences in measured 206Pb/238U. This was achieved by analyzing six reference zircons a minimum of 16 times in two round robin experiments: the first consisting of unannealed zircons and the second of annealed grains. The maximum offset between the LA–ICP–MS and TIMS measured 206Pb/238U for the unannealed zircons was 2.3%, which reduced to 0.5% for the annealed grains, as predicted by within-session precision based on counting statistics. Annealing unknown zircons and references to the same state prior to analysis holds the promise of reducing the 3% external error for the measurement of 206Pb/238U of zircon by LA–ICP–MS, indicated by Klötzli et al. (2009), to better than 1%, but more analyses of annealed zircons by other laboratories are required to evaluate the true potential of the annealing method.

Locally weighted learning model predictive control for nonlinear and time varying dynamics

This paper proposes an online learning control system that uses the strategy of Model Predictive Control (MPC) in a model based locally weighted learning framework. The new approach, named Locally Weighted Learning Model Predictive Control (LWL-MPC), is proposed as a solution to learn to control robotic systems with nonlinear and time varying dynamics. This paper demonstrates the capability of LWL-MPC to perform online learning while controlling the joint trajectories of a low cost, three degree of freedom elastic joint robot. The learning performance is investigated in both an initial learning phase, and when the system dynamics change due to a heavy object added to the tool point. The experiment on the real elastic joint robot is presented and LWL-MPC is shown to successfully learn to control the system with and without the object. The results highlight the capability of the learning control system to accommodate the lack of mechanical consistency and linearity in a low cost robot arm.

Nonlinear pre-fire and post-fire analysis of steel frames

A numerical procedure based on the plastic hinge concept for study of the structural behaviour of steel framed structures exposed to fire is described. Most previous research on fire analysis considered the structural performance due to rising temperature. When strain reversal occurs during the cooling phase, the stress–strain curve is different. The plastic deformation is incorporated into the stress–strain curve to model the strain reversal effect in which unloading under elastic behaviour is allowed. This unloading response is traced by the incremental–iterative Newton–Raphson method. The mechanical properties of the steel member in the present fire analysis follows both Eurocode 3 Part 1.2 and BS5950 Part 8, which implicitly allow for thermal creep deformation. This paper presents an efficient fire analysis procedure for predicting thermal and cooling effects on an isolated element and a multi-storey frame. Several numerical and experimental examples related to structural behaviour in cooling phase are studied and compared with results obtained by other researchers. The proposed method is effective in the fire safety design and analysis of a building in a real fire scenario. The scope of investigation is of great significance since a large number of rescuers would normally enter a fire site as soon as the fire is extinguished and during the cooling phase, so a structural collapse can be catastrophic.

Model-predictive control and closed-loop stability considerations for nonlinear plants described by local ARX-type models

In this paper, a model-predictive control (MPC) method is detailed for the control of nonlinear systems with stability considerations. It will be assumed that the plant is described by a local input/output ARX-type model, with the control potentially included in the premise variables, which enables the control of systems that are nonlinear in both the state and control input. Additionally, for the case of set point regulation, a suboptimal controller is derived which has the dual purpose of ensuring stability and enabling finite-iteration termination of the iterative procedure used to solve the nonlinear optimization problem that is used to determine the control signal.

Error modeling and calibration of exteroceptive sensors for accurate mapping applications

Reliable robotic perception and planning are critical to performing autonomous actions in uncertain, unstructured environments. In field robotic systems, automation is achieved by interpreting exteroceptive sensor information to infer something about the world. This is then mapped to provide a consistent spatial context, so that actions can be planned around the predicted future interaction of the robot and the world. The whole system is as reliable as the weakest link in this chain. In this paper, the term mapping is used broadly to describe the transformation of range-based exteroceptive sensor data (such as LIDAR or stereo vision) to a fixed navigation frame, so that it can be used to form an internal representation of the environment. The coordinate transformation from the sensor frame to the navigation frame is analyzed to produce a spatial error model that captures the dominant geometric and temporal sources of mapping error. This allows the mapping accuracy to be calculated at run time. A generic extrinsic calibration method for exteroceptive range-based sensors is then presented to determine the sensor location and orientation. This allows systematic errors in individual sensors to be minimized, and when multiple sensors are used, it minimizes the systematic contradiction between them to enable reliable multisensor data fusion. The mathematical derivations at the core of this model are not particularly novel or complicated, but the rigorous analysis and application to field robotics seems to be largely absent from the literature to date. The techniques in this paper are simple to implement, and they offer a significant improvement to the accuracy, precision, and integrity of mapped information. Consequently, they should be employed whenever maps are formed from range-based exteroceptive sensor data. © 2009 Wiley Periodicals, Inc.

Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns

The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear algebraic equations that enforce a singular integro-differential equation at each midpoint on a two-dimensional mesh. Our contribution is to solve the system of equations with a Jacobian-free Newton-Krylov method together with a banded preconditioner that is carefully constructed with entries taken from the Jacobian of the linearised problem. Further, we are able to utilise graphics processing unit acceleration to significantly increase the grid refinement and decrease the run-time of our solutions in comparison to schemes that are presently employed in the literature. Our approach provides opportunities to explore the nonlinear features of three-dimensional ship wave patterns, such as the shape of steep waves close to their limiting configuration, in a manner that has been possible in the two-dimensional analogue for some time.

Using pulse transit delay in Z-scan to discriminate between excited-state absorption and other nonlinear processes in ZnO nanocones

We report a new approach that uses the single beam Z-scan technique, to discriminate between excited state absorption (ESA) and two and three photon nonlinear absorption. By measuring the apparent delay or advance of the pulse in reaching the detector, the nonlinear absorption can be unambiguously identified as either instantaneous or transient. The simple method does not require a large range of input fluences or sophisticated pulse-probe experimental apparatus. The technique is easily extended to any absorption process dependent on pulse width and to nonlinear refraction measurements. We demonstrate in particular, that the large nonlinear absorption in ZnO nanocones when exposed to nanosecond 532 nm pulses, is due mostly to ESA, not pure two-photon absorption.

Nonlinear analysis of plastic ball grid array solder joints

A nonlinear finite element analysis was carried out to investigate the viscoplastic deformation of solder joints in a ball grid array (BGA) package under temperature cycle. The effects of constraint on print circuit board (PCB) and stiffness of substrate on the deformation behaviour of the solder joints were also studied. A relative damage stress was adopted to analyze the potential failure sites in the solder joints. The results indicated that high inelastic strain and strain energy density were developed in the joints close to the package center. On the other hand, high constraint and high relative damage stress were associated with the joint closest to the edge of the silicon chip. The joint closest to the edge of the silicon chip was regarded as the most susceptible failure site if cavitation instability is the dominant failure mechanism. Increase the external constraint on the print circuit board (PCB) causes a slight increase in stress triaxiality (m/eq) and relative damage stress in the joint closest to the edge of silicon die. The relative damage stress is not sensitive to the Young’s modulus of the substrate.

Nonlinear container ship model for the study of parametric roll resonance

Parametric roll is a critical phenomenon for ships, whose onset may cause roll oscillations up to +-40 degrees, leading to very dangerous situations and possibly capsizing. Container ships have been shown to be particularly prone to parametric roll resonance when they are sailing in moderate to heavy head seas. A Matlab/Simulink parametric roll benchmark model for a large container ship has been implemented and validated against a wide set of experimental data. The model is a part of a Matlab/Simulink Toolbox (MSS, 2007). The benchmark implements a 3rd-order nonlinear model where the dynamics of roll is strongly coupled with the heave and pitch dynamics. The implemented model has shown good accuracy in predicting the container ship motions, both in the vertical plane and in the transversal one. Parametric roll has been reproduced for all the data sets in which it happened, and the model provides realistic results which are in good agreement with the model tank experiments.

Energy-based nonlinear control of ship roll gyro-stabiliser with precession angle constraints

In this paper, we consider a passivity-based approach for the design of a control law of multiple ship-roll gyro-stabiliser units. We extend previous work on control of ship roll gyro-stabilisation by considering the problem within a nonlinear framework. In particular, we derive an energy-based model using the port-Hamiltonian theory and then design an active precession controller using passivity-based control interconnection and damping assignment. The design considers the possibility of having multiple gyro-stabiliser units, and the desired potential energy of the system (in closed loop) is chosen to behave like a barrier function, which allows us to enforce constraints on the precession angle of the gyros.

A nonlinear observer for estimating transverse stability parameters of marine surface vessels

This paper presents a nonlinear observer for estimating parameters associated with the restoring term of a roll motion model of a marine vessel in longitudinal waves. Changes in restoring, also referred to as transverse stability, can be the result of changes in the vessel's centre of gravity due to, for example, water on deck and also in changes in the buoyancy triggered by variations in the water-plane area produced by longitudinal waves -- propagating along the fore-aft direction along the hull. These variations in the restoring can change dramatically the dynamics of the roll motion leading to dangerous resonance. Therefore, it is of interest to estimate and detect such changes.

Damping structure selection in nonlinear ship manoeuvring models

This paper presents the application of a statistical method for model structure selection of lift-drag and viscous damping components in ship manoeuvring models. The damping model is posed as a family of linear stochastic models, which is postulated based on previous work in the literature. Then a nested test of hypothesis problem is considered. The testing reduces to a recursive comparison of two competing models, for which optimal tests in the Neyman sense exist. The method yields a preferred model structure and its initial parameter estimates. Alternatively, the method can give a reduced set of likely models. Using simulated data we study how the selection method performs when there is both uncorrelated and correlated noise in the measurements. The first case is related to instrumentation noise, whereas the second case is related to spurious wave-induced motion often present during sea trials. We then consider the model structure selection of a modern high-speed trimaran ferry from full scale trial data.