Linear stern waves in finite depth channels

This paper formulates an analytically tractable problem for the wake generated by a long flat bottom ship by considering the steady free surface flow of an inviscid, incompressible fluid emerging from beneath a semi-infinite rigid plate. The flow is considered to be irrotational and two-dimensional so that classical potential flow methods can be exploited. In addition, it is assumed that the draft of the plate is small compared to the depth of the channel. The linearised problem is solved exactly using a Fourier transform and the Wiener-Hopf technique, and it is shown that there is a family of subcritical solutions characterised by a train of sinusoidal waves on the downstream free surface. The amplitude of these waves decreases as the Froude number increases. Supercritical solutions are also obtained, but, in general, these have infinite vertical velocities at the trailing edge of the plate. Consideration of further terms in the expansions suggests a way of canceling the singularity for certain values of the Froude number.

Multi-objective four-dimensional vehicle motion planning in large dynamic environments

This paper presents Multi-Step A* (MSA*), a search algorithm based on A* for multi-objective 4D vehicle motion planning (three spatial and one time dimension). The research is principally motivated by the need for offline and online motion planning for autonomous Unmanned Aerial Vehicles (UAVs). For UAVs operating in large, dynamic and uncertain 4D environments, the motion plan consists of a sequence of connected linear tracks (or trajectory segments). The track angle and velocity are important parameters that are often restricted by assumptions and grid geometry in conventional motion planners. Many existing planners also fail to incorporate multiple decision criteria and constraints such as wind, fuel, dynamic obstacles and the rules of the air. It is shown that MSA* finds a cost optimal solution using variable length, angle and velocity trajectory segments. These segments are approximated with a grid based cell sequence that provides an inherent tolerance to uncertainty. Computational efficiency is achieved by using variable successor operators to create a multi-resolution, memory efficient lattice sampling structure. Simulation studies on the UAV flight planning problem show that MSA* meets the time constraints of online replanning and finds paths of equivalent cost but in a quarter of the time (on average) of vector neighbourhood based A*.

Processing load and the use of concrete representations and strategies for solving linear equations

This paper is a report of students' responses to instruction which was based on the use of concrete representations to solve linear equations. The sample consisted of 21 Grade 8 students from a middle-class suburban state secondary school with a reputation for high academic standards and innovative mathematics teaching. The students were interviewed before and after instruction. Interviews and classroom interactions were observed and videotaped. A qualitative analysis of the responses revealed that students did not use the materials in solving problems. The increased processing load caused by concrete representations is hypothesised as a reason.

Person-independent facial expression detection using constrained local models

In automatic facial expression detection, very accurate registration is desired which can be achieved via a deformable model approach where a dense mesh of 60-70 points on the face is used, such as an active appearance model (AAM). However, for applications where manually labeling frames is prohibitive, AAMs do not work well as they do not generalize well to unseen subjects. As such, a more coarse approach is taken for person-independent facial expression detection, where just a couple of key features (such as face and eyes) are tracked using a Viola-Jones type approach. The tracked image is normally post-processed to encode for shift and illumination invariance using a linear bank of filters. Recently, it was shown that this preprocessing step is of no benefit when close to ideal registration has been obtained. In this paper, we present a system based on the Constrained Local Model (CLM) which is a generic or person-independent face alignment algorithm which gains high accuracy. We show these results against the LBP feature extraction on the CK+ and GEMEP datasets.

meso-Porphyrinylphosphine Oxides: Mono- and Bidentate Ligands for Supramolecular Chemistry and the Crystal Structures of Monomeric [10,20-Diphenylporphyrinatonickel(II)-5,15-diyl]-bis-[P(O)Ph2] and Polymeric Self-Coordinated ([10,20-Diphenylporphyrinatozinc(II)-5,15-diyl]-bis-[P(O)Ph2])

A series of porphyrins substituted in one or two meso-positions by diphenylphosphine oxide groups has been prepared by the palladium catalysed reaction of diphenylphosphine or its oxide with the corresponding bromoporphyrins. Compounds {MDPP-[P(O)Ph2]n} (M = H2, Ni, Zn; H2DPP = 5,15-diphenylporphyrin; n = 1, 2) were isolated in yields of 60-95%. The reaction is believed to proceed via the conventional oxidative addition, phosphination and reductive elimination steps, as the stoichiometric reaction of η1-palladio(II) porphyrin [PdBr(H2DPP)(dppe)] (H2DPP = 5,15-diphenylporphyrin; dppe = 1,2-bis(diphenylphosphino)ethane) with diphenylphosphine oxide also results in the desired mono-porphyrinylphosphine oxide [H2DPP-P(O)Ph2]. Attempts to isolate the tertiary phosphines failed due to their extreme air-sensitivity. Variable temperature 1H NMR studies of [H2DPP-P(O)Ph2] revealed an intrinsic lack of symmetry, while fluorescence spectroscopy showed that the phosphine oxide group does not behave as a "heavy atom" quencher. The electron withdrawing effect of the phosphine oxide group was confirmed by voltammetry. The ligands were characterised by multinuclear NMR and UV-visible spectroscopy as well as mass spectrometry. Single crystal X-ray crystallography showed that the bis(phosphine oxide) nickel(II) complex {[NiDPP-[P(O)Ph2]2} is monomeric in the solid state, with a ruffled porphyrin core and the two P=O fragments on the same side of the average plane of the molecule. On the other hand, the corresponding zinc(II) complex formed infinite chains through coordination of one Ph2PO substituent to the neighbouring zinc porphyrin through an almost linear P=O---Zn unit, leaving the other Ph2PO group facing into a parallel channel filled with disordered water molecules. These new phosphine oxides are attractive ligands for supramolecular porphyrin chemistry.

Validation Gating for Non-Linear Non-Gaussian Target Tracking

This paper develops a general theory of validation gating for non-linear non-Gaussian mod- els. Validation gates are used in target tracking to cull very unlikely measurement-to-track associa- tions, before remaining association ambiguities are handled by a more comprehensive (and expensive) data association scheme. The essential property of a gate is to accept a high percentage of correct associ- ations, thus maximising track accuracy, but provide a su±ciently tight bound to minimise the number of ambiguous associations. For linear Gaussian systems, the ellipsoidal vali- dation gate is standard, and possesses the statistical property whereby a given threshold will accept a cer- tain percentage of true associations. This property does not hold for non-linear non-Gaussian models. As a system departs from linear-Gaussian, the ellip- soid gate tends to reject a higher than expected pro- portion of correct associations and permit an excess of false ones. In this paper, the concept of the ellip- soidal gate is extended to permit correct statistics for the non-linear non-Gaussian case. The new gate is demonstrated by a bearing-only tracking example.

Asset life prediction and maintenance decision-making using a non-linear non-Gaussian state space model

Estimating and predicting degradation processes of engineering assets is crucial for reducing the cost and insuring the productivity of enterprises. Assisted by modern condition monitoring (CM) technologies, most asset degradation processes can be revealed by various degradation indicators extracted from CM data. Maintenance strategies developed using these degradation indicators (i.e. condition-based maintenance) are more cost-effective, because unnecessary maintenance activities are avoided when an asset is still in a decent health state. A practical difficulty in condition-based maintenance (CBM) is that degradation indicators extracted from CM data can only partially reveal asset health states in most situations. Underestimating this uncertainty in relationships between degradation indicators and health states can cause excessive false alarms or failures without pre-alarms. The state space model provides an efficient approach to describe a degradation process using these indicators that can only partially reveal health states. However, existing state space models that describe asset degradation processes largely depend on assumptions such as, discrete time, discrete state, linearity, and Gaussianity. The discrete time assumption requires that failures and inspections only happen at fixed intervals. The discrete state assumption entails discretising continuous degradation indicators, which requires expert knowledge and often introduces additional errors. The linear and Gaussian assumptions are not consistent with nonlinear and irreversible degradation processes in most engineering assets. This research proposes a Gamma-based state space model that does not have discrete time, discrete state, linear and Gaussian assumptions to model partially observable degradation processes. Monte Carlo-based algorithms are developed to estimate model parameters and asset remaining useful lives. In addition, this research also develops a continuous state partially observable semi-Markov decision process (POSMDP) to model a degradation process that follows the Gamma-based state space model and is under various maintenance strategies. Optimal maintenance strategies are obtained by solving the POSMDP. Simulation studies through the MATLAB are performed; case studies using the data from an accelerated life test of a gearbox and a liquefied natural gas industry are also conducted. The results show that the proposed Monte Carlo-based EM algorithm can estimate model parameters accurately. The results also show that the proposed Gamma-based state space model have better fitness result than linear and Gaussian state space models when used to process monotonically increasing degradation data in the accelerated life test of a gear box. Furthermore, both simulation studies and case studies show that the prediction algorithm based on the Gamma-based state space model can identify the mean value and confidence interval of asset remaining useful lives accurately. In addition, the simulation study shows that the proposed maintenance strategy optimisation method based on the POSMDP is more flexible than that assumes a predetermined strategy structure and uses the renewal theory. Moreover, the simulation study also shows that the proposed maintenance optimisation method can obtain more cost-effective strategies than a recently published maintenance strategy optimisation method by optimising the next maintenance activity and the waiting time till the next maintenance activity simultaneously.

Variable structure control for power systems stabilization

The application of variable structure control (VSC) for power systems stabilization is studied in this paper. It is the application, aspects and constraints of VSC which are of particular interest. A variable structure control methodology has been proposed for power systems stabilization. The method is implemented using thyristor controlled series compensators. A three machine power system is stabilized using a switching line control for large disturbances which becomes a sliding control as the disturbance becomes smaller. The results demonstrate the effectiveness of the methodology proposed as an useful tool to suppress the oscillations in power systems.

Calibration and operational analysis of variable speed limits for high flow condition

Variable Speed Limits (VSL) is a control tool of Intelligent Transportation Systems (ITS) which can enhance traffic safety and which has the potential to contribute to traffic efficiency. This study presents the results of a calibration and operational analysis of a candidate VSL algorithm for high flow conditions on an urban motorway of Queensland, Australia. The analysis was done using a framework consisting of a microscopic simulation model combined with runtime API and a proposed efficiency index. The operational analysis includes impacts on speed-flow curve, travel time, speed deviation, fuel consumption and emission.

Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy

Design of experiments for bivariate binary responses modelled by Copula functions

Optimal design for generalized linear models has primarily focused on univariate data. Often experiments are performed that have multiple dependent responses described by regression type models, and it is of interest and of value to design the experiment for all these responses. This requires a multivariate distribution underlying a pre-chosen model for the data. Here, we consider the design of experiments for bivariate binary data which are dependent. We explore Copula functions which provide a rich and flexible class of structures to derive joint distributions for bivariate binary data. We present methods for deriving optimal experimental designs for dependent bivariate binary data using Copulas, and demonstrate that, by including the dependence between responses in the design process, more efficient parameter estimates are obtained than by the usual practice of simply designing for a single variable only. Further, we investigate the robustness of designs with respect to initial parameter estimates and Copula function, and also show the performance of compound criteria within this bivariate binary setting.