Critical timescales and time intervals for coupled linear processes

In 1991, McNabb introduced the concept of mean action time (MAT) as a finite measure of the time required for a diffusive process to effectively reach steady state. Although this concept was initially adopted by others within the Australian and New Zealand applied mathematics community, it appears to have had little use outside this region until very recently, when in 2010 Berezhkovskii and coworkers rediscovered the concept of MAT in their study of morphogen gradient formation. All previous work in this area has been limited to studying single–species differential equations, such as the linear advection–diffusion–reaction equation. Here we generalise the concept of MAT by showing how the theory can be applied to coupled linear processes. We begin by studying coupled ordinary differential equations and extend our approach to coupled partial differential equations. Our new results have broad applications including the analysis of models describing coupled chemical decay and cell differentiation processes, amongst others.

A non-linear dynamic analysis of heavy haul track line sleepers under wheel flat

Significant wheel-rail dynamic forces occur because of imperfections in the wheels and/or rail. One of the key responses to the transmission of these forces down through the track is impact force on the sleepers. Dynamic analysis of nonlinear systems is very complicated and does not lend itself easily to a classical solution of multiple equations. Trying to deduce the behaviour of track components from experimental data is very difficult because such data is hard to obtain and applies to only the particular conditions of the track being tested. The finite element method can be the best solution to this dilemma. This paper describes a finite element model using the software package ANSYS for various sized flat defects in the tread of a wheel rolling at a typical speed on heavy haul track. The paper explores the dynamic response of a prestressed concrete sleeper to these defects.

Hybrid game evolutionary algorithm for mission path planning of aerial survey tasks

The aim of this paper is to implement a Game-Theory based offline mission path planner for aerial inspection tasks of large linear infrastructures. Like most real-world optimisation problems, mission path planning involves a number of objectives which ideally should be minimised simultaneously. The goal of this work is then to develop a Multi-Objective (MO) optimisation tool able to provide a set of optimal solutions for the inspection task, given the environment data, the mission requirements and the definition of the objectives to minimise. Results indicate the robustness and capability of the method to find the trade-off between the Pareto-optimal solutions.

RcppArmadillo : accelerating R with high-performance C++ linear algebra

The R statistical environment and language has demonstrated particular strengths for interactive development of statistical algorithms, as well as data modelling and visualisation. Its current implementation has an interpreter at its core which may result in a performance penalty in comparison to directly executing user algorithms in the native machine code of the host CPU. In contrast, the C++ language has no built-in visualisation capabilities, handling of linear algebra or even basic statistical algorithms; however, user programs are converted to high-performance machine code, ahead of execution. A new method avoids possible speed penalties in R by using the Rcpp extension package in conjunction with the Armadillo C++ matrix library. In addition to the inherent performance advantages of compiled code, Armadillo provides an easy-to-use template-based meta-programming framework, allowing the automatic pooling of several linear algebra operations into one, which in turn can lead to further speedups. With the aid of Rcpp and Armadillo, conversion of linear algebra centered algorithms from R to C++ becomes straightforward. The algorithms retains the overall structure as well as readability, all while maintaining a bidirectional link with the host R environment. Empirical timing comparisons of R and C++ implementations of a Kalman filtering algorithm indicate a speedup of several orders of magnitude.

Optimal distribution network reinforcement considering load growth, line loss, and reliability

In this paper, a new comprehensive planning methodology is proposed for implementing distribution network reinforcement. The load growth, voltage profile, distribution line loss, and reliability are considered in this procedure. A time-segmentation technique is employed to reduce the computational load. Options considered range from supporting the load growth using the traditional approach of upgrading the conventional equipment in the distribution network, through to the use of dispatchable distributed generators (DDG). The objective function is composed of the construction cost, loss cost and reliability cost. As constraints, the bus voltages and the feeder currents should be maintained within the standard level. The DDG output power should not be less than a ratio of its rated power because of efficiency. A hybrid optimization method, called modified discrete particle swarm optimization, is employed to solve this nonlinear and discrete optimization problem. A comparison is performed between the optimized solution based on planning of capacitors along with tap-changing transformer and line upgrading and when DDGs are included in the optimization.

Glider path-planning for optimal sampling of mesocale eddies

Ocean gliders constitute an important advance in the highly demanding ocean monitoring scenario. Their effciency, endurance and increasing robustness make these vehicles an ideal observing platform for many long term oceanographic applications. However, they have proved to be also useful in the opportunis-tic short term characterization of dynamic structures. Among these, mesoscale eddies are of particular interest due to the relevance they have in many oceano-graphic processes.

Optimal power system stabilizer tuning in multi-machine system via an improved differential evolution

Power system stabilizer (PSS) is one of the most important controllers in modern power systems for damping low frequency oscillations. Many efforts have been dedicated to design the tuning methodologies and allocation techniques to obtain optimal damping behaviors of the system. Traditionally, it is tuned mostly for local damping performance, however, in order to obtain a globally optimal performance, the tuning of PSS needs to be done considering more variables. Furthermore, with the enhancement of system interconnection and the increase of system complexity, new tools are required to achieve global tuning and coordination of PSS to achieve optimal solution in a global meaning. Differential evolution (DE) is a recognized as a simple and powerful global optimum technique, which can gain fast convergence speed as well as high computational efficiency. However, as many other evolutionary algorithms (EA), the premature of population restricts optimization capacity of DE. In this paper, a modified DE is proposed and applied for optimal PSS tuning of 39-Bus New-England system. New operators are introduced to reduce the probability of getting premature. To investigate the impact of system conditions on PSS tuning, multiple operating points will be studied. Simulation result is compared with standard DE and particle swarm optimization (PSO).

An optimal under-frequency load shedding strategy considering distributed generators and load static characteristics

The well-established under-frequency load shedding (UFLS) is deemed to be the last of effective remedial measures against a severe frequency decline of a power system. With the ever-increasing size of power systems and the extensive penetration of distributed generators (DGs) in power systems, the problem of developing an optimal UFLS strategy is facing some new challenges. Given this background, an optimal UFLS strategy for a distribution system with DGs and load static characteristics taken into consideration is developed. Based on the frequency and the rate of change of frequency, the presented strategy consists of several basic rounds and a special round. In the basic round, the frequency emergency can be alleviated by quickly shedding some loads. In the special round, the frequency security can be maintained, and the operating parameters of the distribution system can be optimized by adjusting the output powers of DGs and some loads. The modified IEEE 37-node test feeder is employed to demonstrate the essential features of the developed optimal UFLS strategy in the MATLAB/SIMULINK environment.

Analytical Solution of a Walters’ Liquid B Flow Over a Linear Stretching Sheet in a Porous Medium

This chapter represents the analytical solution of two-dimensional linear stretching sheet problem involving a non-Newtonian liquid and suction by (a) invoking the boundary layer approximation and (b) using this result to solve the stretching sheet problem without using boundary layer approximation. The basic boundary layer equations for momentum, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The results reveal a new analytical procedure for solving the boundary layer equations arising in a linear stretching sheet problem involving a non-Newtonian liquid (Walters’ liquid B). The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem.

On the statistical determination of optimal camera configurations in large scale surveillance networks

The selection of optimal camera configurations (camera locations, orientations etc.) for multi-camera networks remains an unsolved problem. Previous approaches largely focus on proposing various objective functions to achieve different tasks. Most of them, however, do not generalize well to large scale networks. To tackle this, we introduce a statistical formulation of the optimal selection of camera configurations as well as propose a Trans-Dimensional Simulated Annealing (TDSA) algorithm to effectively solve the problem. We compare our approach with a state-of-the-art method based on Binary Integer Programming (BIP) and show that our approach offers similar performance on small scale problems. However, we also demonstrate the capability of our approach in dealing with large scale problems and show that our approach produces better results than 2 alternative heuristics designed to deal with the scalability issue of BIP.

Heteroscedastic probabilistic linear discriminant analysis for manifold learning in video-based face recognition

To recognize faces in video, face appearances have been widely modeled as piece-wise local linear models which linearly approximate the smooth yet non-linear low dimensional face appearance manifolds. The choice of representations of the local models is crucial. Most of the existing methods learn each local model individually meaning that they only anticipate variations within each class. In this work, we propose to represent local models as Gaussian distributions which are learned simultaneously using the heteroscedastic probabilistic linear discriminant analysis (PLDA). Each gallery video is therefore represented as a collection of such distributions. With the PLDA, not only the within-class variations are estimated during the training, the separability between classes is also maximized leading to an improved discrimination. The heteroscedastic PLDA itself is adapted from the standard PLDA to approximate face appearance manifolds more accurately. Instead of assuming a single global within-class covariance, the heteroscedastic PLDA learns different within-class covariances specific to each local model. In the recognition phase, a probe video is matched against gallery samples through the fusion of point-to-model distances. Experiments on the Honda and MoBo datasets have shown the merit of the proposed method which achieves better performance than the state-of-the-art technique.

Image based visual servo control for fixed wing UAVs tracking linear infrastructure in wind

This paper presents an Image Based Visual Servo control design for Fixed Wing Unmanned Aerial Vehicles tracking locally linear infrastructure in the presence of wind using a body fixed imaging sensor. Visual servoing offers improved data collection by posing the tracking task as one of controlling a feature as viewed by the inspection sensor, although is complicated by the introduction of wind as aircraft heading and course angle no longer align. In this work it is shown that the effects of wind alter the desired line angle required for continuous tracking to equal the wind correction angle as would be calculated to set a desired course. A control solution is then sort by linearizing the interaction matrix about the new feature pose such that kinematics of the feature can be augmented with the lateral dynamics of the aircraft, from which a state feedback control design is developed. Simulation results are presented comparing no compensation, integral control and the proposed controller using the wind correction angle, followed by an assessment of response to atmospheric disturbances in the form of turbulence and wind gusts

Board age and gender diversity : a test of competing linear and curvilinear predictions

We test competing linear and curvilinear predictions between board diversity and performance. The predictions were tested using archival data on 288 organizations listed on the Australian Securities Exchange. The findings provide additional evidence on the business case for board gender diversity and refine the business case for board age diversity.

Coordinated probabilistic optimal decision-making model for multi-area ATC with risk control

In the decision-making of multi-area ATC (Available Transfer Capacity) in electricity market environment, the existing resources of transmission network should be optimally dispatched and coordinately employed on the premise that the secure system operation is maintained and risk associated is controllable. The non-sequential Monte Carlo simulation is used to determine the ATC probability density distribution of specified areas under the influence of several uncertainty factors, based on which, a coordinated probabilistic optimal decision-making model with the maximal risk benefit as its objective is developed for multi-area ATC. The NSGA-II is applied to calculate the ATC of each area, which considers the risk cost caused by relevant uncertainty factors and the synchronous coordination among areas. The essential characteristics of the developed model and the employed algorithm are illustrated by the example of IEEE 118-bus test system. Simulative result shows that, the risk of multi-area ATC decision-making is influenced by the uncertainties in power system operation and the relative importance degrees of different areas.