Vehicle trajectory linearisation to enable efficient optimisation of the constant speed racing line

A driver model is presented capable of optimising the trajectory of a simple dynamic nonlinear vehicle, at constant forward speed, so that progression along a predefined track is maximised as a function of time. In doing so, the model is able to continually operate a vehicle at its lateral-handling limit, maximising vehicle performance. The technique used forms a part of the solution to the motor racing objective of minimising lap time. A new approach of formulating the minimum lap time problem is motivated by the need for a more computationally efficient and robust tool-set for understanding on-the-limit driving behaviour. This has been achieved through set point-dependent linearisation of the vehicle model and coupling the vehicle-track system using an intrinsic coordinate description. Through this, the geometric vehicle trajectory had been linearised relative to the track reference, leading to new path optimisation algorithm which can be formed as a computationally efficient convex quadratic programming problem. © 2012 Copyright Taylor and Francis Group, LLC.

An efficient approach of modelling the flexural cracking behaviour of un-notched plain concrete prisms subject to monotonic and cyclic loading

In the field of vibration-based damage detection of concrete structures efficient damage models are needed to better understand changes in the vibration properties of cracked structures. These models should quantitatively replicate the damage mechanisms in concrete and easily be used as damage detection tools. In this paper, the flexural cracking behaviour of plain concrete prisms subject to monotonic and cyclic loading regimes under displacement control is tested experimentally and modelled numerically. Four-point bending tests on simply supported un-notched prisms are conducted, where the cracking process is monitored using a digital image correlation system. A numerical model, with a single crack at midspan, is presented where the cracked zone is modelled using the fictitious crack approach and parts outside that zone are treated in a linear-elastic manner. The model considers crack initiation, growth and closure by adopting cyclic constitutive laws. A multi-variate Newton-Raphson iterative solver is used to solve the non-linear equations to ensure equilibrium and compatibility at the interface of the cracked zone. The numerical results agree well with the experiments for both loading scenarios. The model shows good predictions of the degradation of stiffness with increasing load. It also approximates the crack-mouth-opening-displacement when compared with the experimental data of the digital image correlation system. The model is found to be computationally efficient as it runs full analysis for cyclic loading in less than 2. min, and it can therefore be used within the damage detection process. © 2013 Elsevier Ltd.

An efficient method for optimal location and sizing of fixed and switched shunt capacitors in large distribution systems

This paper proposes a computationally efficient methodology for the optimal location and sizing of static and switched shunt capacitors in large distribution systems. The problem is formulated as the maximization of the savings produced by the reduction in energy losses and the avoided costs due to investment deferral in the expansion of the network. The proposed method selects the nodes to be compensated, as well as the optimal capacitor ratings and their operational characteristics, i.e. fixed or switched. After an appropriate linearization, the optimization problem was formulated as a large-scale mixed-integer linear problem, suitable for being solved by means of a widespread commercial package. Results of the proposed optimizing method are compared with another recent methodology reported in the literature using two test cases: a 15-bus and a 33-bus distribution network. For the both cases tested, the proposed methodology delivers better solutions indicated by higher loss savings, which are achieved with lower amounts of capacitive compensation. The proposed method has also been applied for compensating to an actual large distribution network served by AES-Venezuela in the metropolitan area of Caracas. A convergence time of about 4 seconds after 22298 iterations demonstrates the ability of the proposed methodology for efficiently handling large-scale compensation problems.

Efficient incorporation of channel cross-section geometry uncertainty into regional and global scale flood inundation models

This paper investigates the challenge of representing structural differences in river channel cross-section geometry for regional to global scale river hydraulic models and the effect this can have on simulations of wave dynamics. Classically, channel geometry is defined using data, yet at larger scales the necessary information and model structures do not exist to take this approach. We therefore propose a fundamentally different approach where the structural uncertainty in channel geometry is represented using a simple parameterization, which could then be estimated through calibration or data assimilation. This paper first outlines the development of a computationally efficient numerical scheme to represent generalised channel shapes using a single parameter, which is then validated using a simple straight channel test case and shown to predict wetted perimeter to within 2% for the channels tested. An application to the River Severn, UK is also presented, along with an analysis of model sensitivity to channel shape, depth and friction. The channel shape parameter was shown to improve model simulations of river level, particularly for more physically plausible channel roughness and depth parameter ranges. Calibrating channel Manning’s coefficient in a rectangular channel provided similar water level simulation accuracy in terms of Nash-Sutcliffe efficiency to a model where friction and shape or depth were calibrated. However, the calibrated Manning coefficient in the rectangular channel model was ~2/3 greater than the likely physically realistic value for this reach and this erroneously slowed wave propagation times through the reach by several hours. Therefore, for large scale models applied in data sparse areas, calibrating channel depth and/or shape may be preferable to assuming a rectangular geometry and calibrating friction alone.

Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method

The immersed boundary method is a versatile tool for the investigation of flow-structure interaction. In a large number of applications, the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well-known, severe time-step restriction for explicit discretizations. This excessive stability constraint can be removed with fully implicit or suitable semi-implicit schemes but at a seemingly prohibitive computational cost. While economical alternatives have been proposed recently for some special cases, there is a practical need for a computationally efficient approach that can be applied more broadly. In this context, we revisit a robust semi-implicit discretization introduced by Peskin in the late 1970s which has received renewed attention recently. This discretization, in which the spreading and interpolation operators are lagged. leads to a linear system of equations for the inter-face configuration at the future time, when the interfacial force is linear. However, this linear system is large and dense and thus it is challenging to streamline its solution. Moreover, while the same linear system or one of similar structure could potentially be used in Newton-type iterations, nonlinear and highly stiff immersed structures pose additional challenges to iterative methods. In this work, we address these problems and propose cost-effective computational strategies for solving Peskin`s lagged-operators type of discretization. We do this by first constructing a sufficiently accurate approximation to the system`s matrix and we obtain a rigorous estimate for this approximation. This matrix is expeditiously computed by using a combination of pre-calculated values and interpolation. The availability of a matrix allows for more efficient matrix-vector products and facilitates the design of effective iterative schemes. We propose efficient iterative approaches to deal with both linear and nonlinear interfacial forces and simple or complex immersed structures with tethered or untethered points. One of these iterative approaches employs a splitting in which we first solve a linear problem for the interfacial force and then we use a nonlinear iteration to find the interface configuration corresponding to this force. We demonstrate that the proposed approach is several orders of magnitude more efficient than the standard explicit method. In addition to considering the standard elliptical drop test case, we show both the robustness and efficacy of the proposed methodology with a 2D model of a heart valve. (C) 2009 Elsevier Inc. All rights reserved.

Efficient certification of feasibility and objective value of linear programs and its applications

The use of linear programming in various areas has increased with the significant improvement of specialized solvers. Linear programs are used as such to model practical problems, or as subroutines in algorithms such as formal proofs or branch-and-cut frameworks. In many situations a certified answer is needed, for example the guarantee that the linear program is feasible or infeasible, or a provably safe bound on its objective value. Most of the available solvers work with floating-point arithmetic and are thus subject to its shortcomings such as rounding errors or underflow, therefore they can deliver incorrect answers. While adequate for some applications, this is unacceptable for critical applications like flight controlling or nuclear plant management due to the potential catastrophic consequences. We propose a method that gives a certified answer whether a linear program is feasible or infeasible, or returns unknown'. The advantage of our method is that it is reasonably fast and rarely answers unknown'. It works by computing a safe solution that is in some way the best possible in the relative interior of the feasible set. To certify the relative interior, we employ exact arithmetic, whose use is nevertheless limited in general to critical places, allowing us to rnremain computationally efficient. Moreover, when certain conditions are fulfilled, our method is able to deliver a provable bound on the objective value of the linear program. We test our algorithm on typical benchmark sets and obtain higher rates of success compared to previous approaches for this problem, while keeping the running times acceptably small. The computed objective value bounds are in most of the cases very close to the known exact objective values. We prove the usability of the method we developed by additionally employing a variant of it in a different scenario, namely to improve the results of a Satisfiability Modulo Theories solver. Our method is used as a black box in the nodes of a branch-and-bound tree to implement conflict learning based on the certificate of infeasibility for linear programs consisting of subsets of linear constraints. The generated conflict clauses are in general small and give good rnprospects for reducing the search space. Compared to other methods we obtain significant improvements in the running time, especially on the large instances.

DYPTOP: a cost-efficient TOPMODEL implementation to simulate sub-grid spatio-temporal dynamics of global wetlands and peatlands

Simulating the spatio-temporal dynamics of inundation is key to understanding the role of wetlands under past and future climate change. Earlier modelling studies have mostly relied on fixed prescribed peatland maps and inundation time series of limited temporal coverage. Here, we describe and assess the the Dynamical Peatland Model Based on TOPMODEL (DYPTOP), which predicts the extent of inundation based on a computationally efficient TOPMODEL implementation. This approach rests on an empirical, grid-cell-specific relationship between the mean soil water balance and the flooded area. DYPTOP combines the simulated inundation extent and its temporal persistency with criteria for the ecosystem water balance and the modelled peatland-specific soil carbon balance to predict the global distribution of peatlands. We apply DYPTOP in combination with the LPX-Bern DGVM and benchmark the global-scale distribution, extent, and seasonality of inundation against satellite data. DYPTOP successfully predicts the spatial distribution and extent of wetlands and major boreal and tropical peatland complexes and reveals the governing limitations to peatland occurrence across the globe. Peatlands covering large boreal lowlands are reproduced only when accounting for a positive feedback induced by the enhanced mean soil water holding capacity in peatland-dominated regions. DYPTOP is designed to minimize input data requirements, optimizes computational efficiency and allows for a modular adoption in Earth system models.

Efficient optimisation of per-channel pre-compensation in WDM 20-Gbit/s RZ-DPSK transmission in non-slope matched submarine links

We propose a computationally efficient method to the per-channel dispersion optimisation applied to 50 GHz-spaced N × 20-Gbit/s wavelength division multiplexing return-to-zero differential phase shift keying transmission in non-zero dispersion-shifted fibre based submarine systems. Crown Copyright © 2010.

Efficient optimisation of per-channel pre-compensation in WDM 20-Gbit/s RZ-DPSK transmission in non-slope matched submarine links

We propose a computationally efficient method to the per-channel dispersion optimisation applied to 50 GHz-spaced N × 20-Gbit/s wavelength division multiplexing return-to-zero differential phase shift keying transmission in non-zero dispersion-shifted fibre based submarine systems. Crown Copyright © 2010.

Efficient Learning of Bayesian Networks with Bounded Tree-width

Learning Bayesian networks with bounded tree-width has attracted much attention recently, because low tree-width allows exact inference to be performed efficiently. Some existing methods \cite{korhonen2exact, nie2014advances} tackle the problem by using $k$-trees to learn the optimal Bayesian network with tree-width up to $k$. Finding the best $k$-tree, however, is computationally intractable. In this paper, we propose a sampling method to efficiently find representative $k$-trees by introducing an informative score function to characterize the quality of a $k$-tree. To further improve the quality of the $k$-trees, we propose a probabilistic hill climbing approach that locally refines the sampled $k$-trees. The proposed algorithm can efficiently learn a quality Bayesian network with tree-width at most $k$. Experimental results demonstrate that our approach is more computationally efficient than the exact methods with comparable accuracy, and outperforms most existing approximate methods.

Rough set-based reasoning and pattern mining for information filtering

An information filtering (IF) system monitors an incoming document stream to find the documents that match the information needs specified by the user profiles. To learn to use the user profiles effectively is one of the most challenging tasks when developing an IF system. With the document selection criteria better defined based on the users’ needs, filtering large streams of information can be more efficient and effective. To learn the user profiles, term-based approaches have been widely used in the IF community because of their simplicity and directness. Term-based approaches are relatively well established. However, these approaches have problems when dealing with polysemy and synonymy, which often lead to an information overload problem. Recently, pattern-based approaches (or Pattern Taxonomy Models (PTM) [160]) have been proposed for IF by the data mining community. These approaches are better at capturing sematic information and have shown encouraging results for improving the effectiveness of the IF system. On the other hand, pattern discovery from large data streams is not computationally efficient. Also, these approaches had to deal with low frequency pattern issues. The measures used by the data mining technique (for example, “support” and “confidences”) to learn the profile have turned out to be not suitable for filtering. They can lead to a mismatch problem. This thesis uses the rough set-based reasoning (term-based) and pattern mining approach as a unified framework for information filtering to overcome the aforementioned problems. This system consists of two stages - topic filtering and pattern mining stages. The topic filtering stage is intended to minimize information overloading by filtering out the most likely irrelevant information based on the user profiles. A novel user-profiles learning method and a theoretical model of the threshold setting have been developed by using rough set decision theory. The second stage (pattern mining) aims at solving the problem of the information mismatch. This stage is precision-oriented. A new document-ranking function has been derived by exploiting the patterns in the pattern taxonomy. The most likely relevant documents were assigned higher scores by the ranking function. Because there is a relatively small amount of documents left after the first stage, the computational cost is markedly reduced; at the same time, pattern discoveries yield more accurate results. The overall performance of the system was improved significantly. The new two-stage information filtering model has been evaluated by extensive experiments. Tests were based on the well-known IR bench-marking processes, using the latest version of the Reuters dataset, namely, the Reuters Corpus Volume 1 (RCV1). The performance of the new two-stage model was compared with both the term-based and data mining-based IF models. The results demonstrate that the proposed information filtering system outperforms significantly the other IF systems, such as the traditional Rocchio IF model, the state-of-the-art term-based models, including the BM25, Support Vector Machines (SVM), and Pattern Taxonomy Model (PTM).

Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

Theoretical investigation of thermal tweezers for parallel manipulation of atoms and nanoparticles on surfaces

A major focus of research in nanotechnology is the development of novel, high throughput techniques for fabrication of arbitrarily shaped surface nanostructures of sub 100 nm to atomic scale. A related pursuit is the development of simple and efficient means for parallel manipulation and redistribution of adsorbed atoms, molecules and nanoparticles on surfaces – adparticle manipulation. These techniques will be used for the manufacture of nanoscale surface supported functional devices in nanotechnologies such as quantum computing, molecular electronics and lab-on-achip, as well as for modifying surfaces to obtain novel optical, electronic, chemical, or mechanical properties. A favourable approach to formation of surface nanostructures is self-assembly. In self-assembly, nanostructures are grown by aggregation of individual adparticles that diffuse by thermally activated processes on the surface. The passive nature of this process means it is generally not suited to formation of arbitrarily shaped structures. The self-assembly of nanostructures at arbitrary positions has been demonstrated, though these have typically required a pre-patterning treatment of the surface using sophisticated techniques such as electron beam lithography. On the other hand, a parallel adparticle manipulation technique would be suited for directing the selfassembly process to occur at arbitrary positions, without the need for pre-patterning the surface. There is at present a lack of techniques for parallel manipulation and redistribution of adparticles to arbitrary positions on the surface. This is an issue that needs to be addressed since these techniques can play an important role in nanotechnology. In this thesis, we propose such a technique – thermal tweezers. In thermal tweezers, adparticles are redistributed by localised heating of the surface. This locally enhances surface diffusion of adparticles so that they rapidly diffuse away from the heated regions. Using this technique, the redistribution of adparticles to form a desired pattern is achieved by heating the surface at specific regions. In this project, we have focussed on the holographic implementation of this approach, where the surface is heated by holographic patterns of interfering pulsed laser beams. This implementation is suitable for the formation of arbitrarily shaped structures; the only condition is that the shape can be produced by holographic means. In the simplest case, the laser pulses are linearly polarised and intersect to form an interference pattern that is a modulation of intensity along a single direction. Strong optical absorption at the intensity maxima of the interference pattern results in approximately a sinusoidal variation of the surface temperature along one direction. The main aim of this research project is to investigate the feasibility of the holographic implementation of thermal tweezers as an adparticle manipulation technique. Firstly, we investigate theoretically the surface diffusion of adparticles in the presence of sinusoidal modulation of the surface temperature. Very strong redistribution of adparticles is predicted when there is strong interaction between the adparticle and the surface, and the amplitude of the temperature modulation is ~100 K. We have proposed a thin metallic film deposited on a glass substrate heated by interfering laser beams (optical wavelengths) as a means of generating very large amplitude of surface temperature modulation. Indeed, we predict theoretically by numerical solution of the thermal conduction equation that amplitude of the temperature modulation on the metallic film can be much greater than 100 K when heated by nanosecond pulses with an energy ~1 mJ. The formation of surface nanostructures of less than 100 nm in width is predicted at optical wavelengths in this implementation of thermal tweezers. Furthermore, we propose a simple extension to this technique where spatial phase shift of the temperature modulation effectively doubles or triples the resolution. At the same time, increased resolution is predicted by reducing the wavelength of the laser pulses. In addition, we present two distinctly different, computationally efficient numerical approaches for theoretical investigation of surface diffusion of interacting adparticles – the Monte Carlo Interaction Method (MCIM) and the random potential well method (RPWM). Using each of these approaches we have investigated thermal tweezers for redistribution of both strongly and weakly interacting adparticles. We have predicted that strong interactions between adparticles can increase the effectiveness of thermal tweezers, by demonstrating practically complete adparticle redistribution into the low temperature regions of the surface. This is promising from the point of view of thermal tweezers applied to directed self-assembly of nanostructures. Finally, we present a new and more efficient numerical approach to theoretical investigation of thermal tweezers of non-interacting adparticles. In this approach, the local diffusion coefficient is determined from solution of the Fokker-Planck equation. The diffusion equation is then solved numerically using the finite volume method (FVM) to directly obtain the probability density of adparticle position. We compare predictions of this approach to those of the Ermak algorithm solution of the Langevin equation, and relatively good agreement is shown at intermediate and high friction. In the low friction regime, we predict and investigate the phenomenon of ‘optimal’ friction and describe its occurrence due to very long jumps of adparticles as they diffuse from the hot regions of the surface. Future research directions, both theoretical and experimental are also discussed.

Multi-objective mission flight planning in civil unmanned aerial systems

Unmanned Aerial Vehicles (UAVs) are emerging as an ideal platform for a wide range of civil applications such as disaster monitoring, atmospheric observation and outback delivery. However, the operation of UAVs is currently restricted to specially segregated regions of airspace outside of the National Airspace System (NAS). Mission Flight Planning (MFP) is an integral part of UAV operation that addresses some of the requirements (such as safety and the rules of the air) of integrating UAVs in the NAS. Automated MFP is a key enabler for a number of UAV operating scenarios as it aids in increasing the level of onboard autonomy. For example, onboard MFP is required to ensure continued conformance with the NAS integration requirements when there is an outage in the communications link. MFP is a motion planning task concerned with finding a path between a designated start waypoint and goal waypoint. This path is described with a sequence of 4 Dimensional (4D) waypoints (three spatial and one time dimension) or equivalently with a sequence of trajectory segments (or tracks). It is necessary to consider the time dimension as the UAV operates in a dynamic environment. Existing methods for generic motion planning, UAV motion planning and general vehicle motion planning cannot adequately address the requirements of MFP. The flight plan needs to optimise for multiple decision objectives including mission safety objectives, the rules of the air and mission efficiency objectives. Online (in-flight) replanning capability is needed as the UAV operates in a large, dynamic and uncertain outdoor environment. This thesis derives a multi-objective 4D search algorithm entitled Multi- Step A* (MSA*) based on the seminal A* search algorithm. MSA* is proven to find the optimal (least cost) path given a variable successor operator (which enables arbitrary track angle and track velocity resolution). Furthermore, it is shown to be of comparable complexity to multi-objective, vector neighbourhood based A* (Vector A*, an extension of A*). A variable successor operator enables the imposition of a multi-resolution lattice structure on the search space (which results in fewer search nodes). Unlike cell decomposition based methods, soundness is guaranteed with multi-resolution MSA*. MSA* is demonstrated through Monte Carlo simulations to be computationally efficient. It is shown that multi-resolution, lattice based MSA* finds paths of equivalent cost (less than 0.5% difference) to Vector A* (the benchmark) in a third of the computation time (on average). This is the first contribution of the research. The second contribution is the discovery of the additive consistency property for planning with multiple decision objectives. Additive consistency ensures that the planner is not biased (which results in a suboptimal path) by ensuring that the cost of traversing a track using one step equals that of traversing the same track using multiple steps. MSA* mitigates uncertainty through online replanning, Multi-Criteria Decision Making (MCDM) and tolerance. Each trajectory segment is modeled with a cell sequence that completely encloses the trajectory segment. The tolerance, measured as the minimum distance between the track and cell boundaries, is the third major contribution. Even though MSA* is demonstrated for UAV MFP, it is extensible to other 4D vehicle motion planning applications. Finally, the research proposes a self-scheduling replanning architecture for MFP. This architecture replicates the decision strategies of human experts to meet the time constraints of online replanning. Based on a feedback loop, the proposed architecture switches between fast, near-optimal planning and optimal planning to minimise the need for hold manoeuvres. The derived MFP framework is original and shown, through extensive verification and validation, to satisfy the requirements of UAV MFP. As MFP is an enabling factor for operation of UAVs in the NAS, the presented work is both original and significant.