Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.

Combination of Kalman filter and least error square techniques in power system

An algorithm based on the concept of combining Kalman filter and Least Error Square (LES) techniques is proposed in this paper. The algorithm is intended to estimate signal attributes like amplitude, frequency and phase angle in the online mode. This technique can be used in protection relays, digital AVRs, DGs, DSTATCOMs, FACTS and other power electronics applications. The Kalman filter is modified to operate on a fictitious input signal and provides precise estimation results insensitive to noise and other disturbances. At the same time, the LES system has been arranged to operate in critical transient cases to compensate the delay and inaccuracy identified because of the response of the standard Kalman filter. Practical considerations such as the effect of noise, higher order harmonics, and computational issues of the algorithm are considered and tested in the paper. Several computer simulations and a laboratory test are presented to highlight the usefulness of the proposed method. Simulation results show that the proposed technique can simultaneously estimate the signal attributes, even if it is highly distorted due to the presence of non-linear loads and noise.

Non-linear oscillations assessment of the distribution static compensator operating in voltage control mode

This article deals with the non-linear oscillations assessment of a distribution static comensator ooperating in voltage control mode using the bifurcation theory. A mathematical model of the distribution static compensator in the voltage control mode to carry out the bifurcation analysis is derived. The stabiity regions in the Thevein equivalent plane are computed. In addition, the stability regions in the control gains space, as well as the contour lines for different Floquet multipliers are computed. The AC and DC capacitor impacts on the stability are analyzed through the bifurcation theory. The observations are verified through simulaation studies. The computation of the stability region allows the assessment of the stable operating zones for a power system that includes a distribution static compensator operating in the voltage mode.

Regulation of train service by coasting control in metro railway system

To maximise the capacity of the rail lineand provide a reliable service for pas-sengers throughout the day, regulation of train service to maintain steady service headway is es-sential. In most current metro systems, train usually starts coasting at a fixed distance from the departed station to achieve service regulation. However, this approach is only effective with re-spect to a nominal operational condition of train schedule but not necessarily the current service demand. Moreover, it is not simply to identify the necessary starting point for coasting under the run time constraints of current service conditions since train movement is attributed by a large number of factors, most of which are non-linear and inter-dependent. This paper presents an ap-plication of classical measures to search for the appropriate coasting point to meet a specified inter-station run time and they can be integrated in the on-board Automatic Train Operation (ATO) system and have the potential for on-line implementation in making a set of coasting command decisions.

Parallel solution for railway power network simulation

The Streaming SIMD extension (SSE) is a special feature that is available in the Intel Pentium III and P4 classes of microprocessors. As its name implies, SSE enables the execution of SIMD (Single Instruction Multiple Data) operations upon 32-bit floating-point data therefore, performance of floating-point algorithms can be improved. In electrified railway system simulation, the computation involves the solving of a huge set of simultaneous linear equations, which represent the electrical characteristic of the railway network at a particular time-step and a fast solution for the equations is desirable in order to simulate the system in real-time. In this paper, we present how SSE is being applied to the railway network simulation.

A regional construction R&D evaluation system for China

Expenditure on R&D in the China construction industry has been relatively low in comparison with many developed countries for a number of years – a situation considered to be a major barrier to the industry’s competitiveness in general and unsatisfactory industry development of the 31 regions involved. A major problem with this is the lack of a sufficiently sophisticated method of objectively evaluating R&D activity in what are quite complex circumstances considering the size and regional differences that exist in this part of the world. A regional construction R&D evaluation system (RCRES) is presented aimed at rectifying the situation. This is based on 12 indicators drawn from the Chinese Government’s R&D Inventory of Resources in consultation with a small group of experts in the field, and further factor analysed into three groups. From this, the required evaluation is obtained by a simple formula. Examination of the results provides a ranking list of the R&D performance of each of the 31 regions, indicating a general disproportion between coastal and inland regions and highlighting regions receiving special emphasis or currently lacking in development. The understanding on this is vital for the future of China’s construction industry.

Crossing boundaries to explore sustainable architecture by open system design

This paper argues a model of open system design for sustainable architecture, based on a thermodynamics framework of entropy as an evolutionary paradigm. The framework can be simplified to stating that an open system evolves in a non-linear pattern from a far-from-equilibrium state towards a non-equilibrium state of entropy balance, which is a highly ordered organization of the system when order comes out of chaos. This paper is work in progress on a PhD research project which aims to propose building information modelling for optimization and adaptation of buildings environmental performance as an alternative sustainable design program in architecture. It will be used for efficient distribution and consumption of energy and material resource in life-cycle buildings, with the active involvement of the end-users and the physical constraints of the natural environment.

Semi-supervised intelligent surveillance system for secure environments

This paper proposes a semi-supervised intelligent visual surveillance system to exploit the information from multi-camera networks for the monitoring of people and vehicles. Modules are proposed to perform critical surveillance tasks including: the management and calibration of cameras within a multi-camera network; tracking of objects across multiple views; recognition of people utilising biometrics and in particular soft-biometrics; the monitoring of crowds; and activity recognition. Recent advances in these computer vision modules and capability gaps in surveillance technology are also highlighted.

Exploiting system fluctuations. Differential training in physical prevention and rehabilitation programs for health and exercise

Background: Traditional causal modeling of health interventions tends to be linear in nature and lacks multidisciplinarity. Consequently, strategies for exercise prescription in health maintenance are typically group based and focused on the role of a common optimal health status template toward which all individuals should aspire. ----- ----- Materials and methods: In this paper, we discuss inherent weaknesses of traditional methods and introduce an approach exercise training based on neurobiological system variability. The significance of neurobiological system variability in differential learning and training was highlighted.----- ----- Results: Our theoretical analysis revealed differential training as a method by which neurobiological system variability could be harnessed to facilitate health benefits of exercise training. It was observed that this approach emphasizes the importance of using individualized programs in rehabilitation and exercise, rather than group-based strategies to exercise prescription.----- ----- Conclusion: Research is needed on potential benefits of differential training as an approach to physical rehabilitation and exercise prescription that could counteract psychological and physical effects of disease and illness in subelite populations. For example, enhancing the complexity and variability of movement patterns in exercise prescription programs might alleviate effects of depression in nonathletic populations and physical effects of repetitive strain injuries experienced by athletes in elite and developing sport programs.

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.

The constraints-based approach to motor learning : Implications for a non-linear pedagogy in sport and physical education

Recently, a constraints- led approach has been promoted as a framework for understanding how children and adults acquire movement skills for sport and exercise (see Davids, Button & Bennett, 2008; Araújo et al., 2004). The aim of a constraints- led approach is to identify the nature of interacting constraints that influence skill acquisition in learners. In this chapter the main theoretical ideas behind a constraints- led approach are outlined to assist practical applications by sports practitioners and physical educators in a non- linear pedagogy (see Chow et al., 2006, 2007). To achieve this goal, this chapter examines implications for some of the typical challenges facing sport pedagogists and physical educators in the design of learning programmes.

Development of a high-level gene expression system for the production of bioplastics in sugarcane

Despite various approaches, the production of biodegradable plastics such as polyhydroxybutyrate (PHB) in transgenic plants has met with limited success due largely to low expression levels. Even in the few instances where high levels of protein expression have been reported, the transgenic plants have been stunted indicating PHB is phytotoxic (Poirier 2002). This PhD describes the application of a novel virus-based gene expression technology, termed InPAct („In Plant Activation.), for the production of PHB in tobacco and sugarcane. InPAct is based on the rolling circle replication mechanism by which circular ssDNA viruses replicate and provides a system for controlled, high-level gene expression. Based on these features, InPAct was thought to represent an ideal system to enable the controlled, high-level expression of the three phb genes (phbA, phbB and phbC) required for PHB production in sugarcane at a preferred stage of plant growth. A Tobacco yellow dwarf virus (TbYDV)-based InPAct-phbA vector, as well as linear vectors constitutively expressing phbB and phbC were constructed and different combinations were used to transform tobacco leaf discs. A total of four, eight, three and three phenotypically normal tobacco lines were generated from discs transformed with InPAct-phbA, InPAct-phbA + p1300-TaBV P-phbB/phbC- 35S T, p1300-35S P-phbA-NOS T + p1300-TaBV P-phbB/phbC-35S T and InPAct-GUS, respectively. To determine whether the InPAct cassette could be activated in the presence of the TbYDV Rep, leaf samples from the eight InPActphbA + p1300-TaBV P-phbB/phbC-35S T plants were agroinfiltrated with p1300- TbYDV-Rep/RepA. Three days later, successful activation was indicated by the detection of episomes using both PCR and Southern analysis. Leaf discs from the eight InPAct-phbA + p1300-TaBV P-phbB/phbC-35S T transgenic plant lines were agroinfiltrated with p1300-TbYDV-Rep/RepA and leaf tissue was collected ten days post-infiltration and examined for the presence of PHB granules. Confocal microscopy and TEM revealed the presence of typical PHB granules in five of the eight lines, thus demonstrating the functionality of InPActbased PHB production in tobacco. However, analysis of leaf extracts by HPLC failed to detect the presence of PHB suggesting only very low level expression levels. Subsequent molecular analysis of three lines revealed low levels of correctly processed mRNA from the catalase intron contained within the InPAct cassette and also the presence of cryptic splice sites within the intron. In an attempt to increase expression levels, new InPAct-phb cassettes were generated in which the castorbean catalase intron was replaced with a synthetic intron (syntron). Further, in an attempt to both increase and better control Rep/RepA-mediated activation of InPAct cassettes, Rep/RepA expression was placed under the control of a stably integrated alc switch. Leaf discs from a transgenic tobacco line (Alc ML) containing 35S P-AlcR-AlcA P-Rep/RepA were supertransformed with InPAct-phbAsyn or InPAct-GUSsyn using Agrobacterium and three plants (lines) were regenerated for each construct. Analysis of the RNA processing of the InPAct-phbAsyn cassette revealed highly efficient and correct splicing of the syntron, thus supporting its inclusion within the InPAct system. To determine the efficiency of the alc switch to activate InPAct, leaf material from the three Alc ML + InPAct-phbAsyn lines was either agroinfiltrated with 35S P-Rep/RepA or treated with ethanol. Unexpectedly, episomes were detected not only in the infiltrated and ethanol treated samples, but also in non-treated samples. Subsequent analysis of transgenic Alc ML + InPAct-GUS lines, confirmed that the alc switch was leaky in tissue culture. Although this was shown to be reversible once plants were removed from the tissue culture environment, it made the regeneration of Alc ML + InPAct-phbsyn plant lines extremely difficult, due to unintentional Rep expression and therefore high levels of phb expression and phytotoxic PHB production. Two Alc ML + InPAct-phbAsyn + p1300-TaBV P-phbB/phbC-35S T transgenic lines were able to be regenerated, and these were acclimatised, alcohol-treated and analysed. Although episome formation was detected as late as 21 days post activation, no PHB was detected in the leaves of any plants using either microscopy or HPLC, suggesting the presence of a corrupt InPAct-phbA cassette in both lines. The final component of this thesis involved the application of both the alc switch and the InPAct systems to sugarcane in an attempt to produce PHB. Initial experiments using transgenic Alc ML + InPAct-GUS lines indicated that the alc system was not functional in sugarcane under the conditions tested. The functionality of the InPAct system, independent of the alc gene switch, was subsequently examined by bombarding the 35S Rep/RepA cassette into leaf and immature leaf whorl cells derived from InPAct-GUS transgenic sugarcane plants. No GUS expression was observed in leaf tissue, whereas weak and irregular GUS expression was observed in immature leaf whorl tissue derived from two InPAct- GUS lines and two InPAct-GUS + 35S P-AlcR-AlcA P-GUS lines. The most plausible reason to explain the inconsistent and low levels of GUS expression in leaf whorls is a combination of low numbers of sugarcane cells in the DNA replication-conducive S-phase and the irregular and random nature of sugarcane cells bombarded with Rep/RepA. This study details the first report to develop a TbYDV-based InPAct system under control of the alc switch to produce PHB in tobacco and sugarcane. Despite the inability to detect quantifiable levels of PHB levels in either tobacco or sugarcane, the findings of this study should nevertheless assist in the further development of both the InPAct system and the alc system, particularly for sugarcane and ultimately lead to an ethanol-inducible InPAct gene expression system for the production of bioplastics and other proteins of commercial value in plants.

Renewal decision support for linear assets

Linear (or continuous) assets are engineering infrastructure that usually spans long distances and can be divided into different segments, all of which perform the same function but may be subject to different loads and environmental factors. Typical linear assets include railway lines, roads, pipelines and cables. How and when to renew such assets are critical decisions for asset owners as they normally involves significant capital investment. Through investigating the characteristics of linear asset renewal decisions and identifying the critical requirements that are associated with renewal decisions, we present a multi-criteria decision support method to help optimise renewal decisions. A case study that concerns renewal of an economiser's tubing system is a coal-fired power station is adopted to demonstrate the application of this method. Although the paper concerns a particular linear asset decision type, the approach has broad applicability for linear asset management.

An estimation of crash risks using a log-linear model and the induced exposure technique

Prevention and safety promotion programmes. Traditionally, in-depth investigations of crash risks are conducted using exposure controlled study or case-control methodology. However, these studies need either observational data for control cases or exogenous exposure data like vehicle-kilometres travel, entry flow or product of conflicting flow for a particular traffic location, or a traffic site. These data are not readily available and often require extensive data collection effort on a system-wide basis. Aim: The objective of this research is to propose an alternative methodology to investigate crash risks of a road user group in different circumstances using readily available traffic police crash data. Methods: This study employs a combination of a log-linear model and the quasi-induced exposure technique to estimate crash risks of a road user group. While the log-linear model reveals the significant interactions and thus the prevalence of crashes of a road user group under various sets of traffic, environmental and roadway factors, the quasi-induced exposure technique estimates relative exposure of that road user in the same set of explanatory variables. Therefore, the combination of these two techniques provides relative measures of crash risks under various influences of roadway, environmental and traffic conditions. The proposed methodology has been illustrated using Brisbane motorcycle crash data of five years. Results: Interpretations of results on different combination of interactive factors show that the poor conspicuity of motorcycles is a predominant cause of motorcycle crashes. Inability of other drivers to correctly judge the speed and distance of an oncoming motorcyclist is also evident in right-of-way violation motorcycle crashes at intersections. Discussion and Conclusions: The combination of a log-linear model and the induced exposure technique is a promising methodology and can be applied to better estimate crash risks of other road users. This study also highlights the importance of considering interaction effects to better understand hazardous situations. A further study on the comparison between the proposed methodology and case-control method would be useful.

Solving tri-diagonal linear systems using field programmable gate arrays

In this paper, we present the outcomes of a project on the exploration of the use of Field Programmable Gate Arrays(FPGAs) as co-processors for scientific computation. We designed a custom circuit for the pipelined solving of multiple tri-diagonal linear systems. The design is well suited for applications that require many independent tri diagonal system solves, such as finite difference methods for solving PDEs or applications utilising cubic spline interpolation. The selected solver algorithm was the Tri Diagonal Matrix Algorithm (TDMA or Thomas Algorithm). Our solver supports user specified precision thought the use of a custom floating point VHDL library supporting addition, subtraction, multiplication and division. The variable precision TDMA solver was tested for correctness in simulation mode. The TDMA pipeline was tested successfully in hardware using a simplified solver model. The details of implementation, the limitations, and future work are also discussed.