Applying data mining to assess crash risk on curves

The wide range of contributing factors and circumstances surrounding crashes on road curves suggest that no single intervention can prevent these crashes. This paper presents a novel methodology, based on data mining techniques, to identify contributing factors and the relationship between them. It identifies contributing factors that influence the risk of a crash. Incident records, described using free text, from a large insurance company were analysed with rough set theory. Rough set theory was used to discover dependencies among data, and reasons using the vague, uncertain and imprecise information that characterised the insurance dataset. The results show that male drivers, who are between 50 and 59 years old, driving during evening peak hours are involved with a collision, had a lowest crash risk. Drivers between 25 and 29 years old, driving from around midnight to 6 am and in a new car has the highest risk. The analysis of the most significant contributing factors on curves suggests that drivers with driving experience of 25 to 42 years, who are driving a new vehicle have the highest crash cost risk, characterised by the vehicle running off the road and hitting a tree. This research complements existing statistically based tools approach to analyse road crashes. Our data mining approach is supported with proven theory and will allow road safety practitioners to effectively understand the dependencies between contributing factors and the crash type with the view to designing tailored countermeasures.

Mining patterns and factors contributing to crash severity on road curves

Road curves are an important feature of road infrastructure and many serious crashes occur on road curves. In Queensland, the number of fatalities is twice as many on curves as that on straight roads. Therefore, there is a need to reduce drivers’ exposure to crash risk on road curves. Road crashes in Australia and in the Organisation for Economic Co-operation and Development(OECD) have plateaued in the last five years (2004 to 2008) and the road safety community is desperately seeking innovative interventions to reduce the number of crashes. However, designing an innovative and effective intervention may prove to be difficult as it relies on providing theoretical foundation, coherence, understanding, and structure to both the design and validation of the efficiency of the new intervention. Researchers from multiple disciplines have developed various models to determine the contributing factors for crashes on road curves with a view towards reducing the crash rate. However, most of the existing methods are based on statistical analysis of contributing factors described in government crash reports. In order to further explore the contributing factors related to crashes on road curves, this thesis designs a novel method to analyse and validate these contributing factors. The use of crash claim reports from an insurance company is proposed for analysis using data mining techniques. To the best of our knowledge, this is the first attempt to use data mining techniques to analyse crashes on road curves. Text mining technique is employed as the reports consist of thousands of textual descriptions and hence, text mining is able to identify the contributing factors. Besides identifying the contributing factors, limited studies to date have investigated the relationships between these factors, especially for crashes on road curves. Thus, this study proposed the use of the rough set analysis technique to determine these relationships. The results from this analysis are used to assess the effect of these contributing factors on crash severity. The findings obtained through the use of data mining techniques presented in this thesis, have been found to be consistent with existing identified contributing factors. Furthermore, this thesis has identified new contributing factors towards crashes and the relationships between them. A significant pattern related with crash severity is the time of the day where severe road crashes occur more frequently in the evening or night time. Tree collision is another common pattern where crashes that occur in the morning and involves hitting a tree are likely to have a higher crash severity. Another factor that influences crash severity is the age of the driver. Most age groups face a high crash severity except for drivers between 60 and 100 years old, who have the lowest crash severity. The significant relationship identified between contributing factors consists of the time of the crash, the manufactured year of the vehicle, the age of the driver and hitting a tree. Having identified new contributing factors and relationships, a validation process is carried out using a traffic simulator in order to determine their accuracy. The validation process indicates that the results are accurate. This demonstrates that data mining techniques are a powerful tool in road safety research, and can be usefully applied within the Intelligent Transport System (ITS) domain. The research presented in this thesis provides an insight into the complexity of crashes on road curves. The findings of this research have important implications for both practitioners and academics. For road safety practitioners, the results from this research illustrate practical benefits for the design of interventions for road curves that will potentially help in decreasing related injuries and fatalities. For academics, this research opens up a new research methodology to assess crash severity, related to road crashes on curves.

Elliptic curves, group law, and efficient computation

This thesis is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law. The outcomes of this research guarantee practical speedups in higher level operations which depend on point additions. In particular, the contributions immediately find applications in cryptology. Mastered by the 19th century mathematicians, the study of the theory of elliptic curves has been active for decades. Elliptic curves over finite fields made their way into public key cryptography in late 1980’s with independent proposals by Miller [Mil86] and Koblitz [Kob87]. Elliptic Curve Cryptography (ECC), following Miller’s and Koblitz’s proposals, employs the group of rational points on an elliptic curve in building discrete logarithm based public key cryptosystems. Starting from late 1990’s, the emergence of the ECC market has boosted the research in computational aspects of elliptic curves. This thesis falls into this same area of research where the main aim is to speed up the additions of rational points on an arbitrary elliptic curve (over a field of large characteristic). The outcomes of this work can be used to speed up applications which are based on elliptic curves, including cryptographic applications in ECC. The aforementioned goals of this thesis are achieved in five main steps. As the first step, this thesis brings together several algebraic tools in order to derive the unique group law of an elliptic curve. This step also includes an investigation of recent computer algebra packages relating to their capabilities. Although the group law is unique, its evaluation can be performed using abundant (in fact infinitely many) formulae. As the second step, this thesis progresses the finding of the best formulae for efficient addition of points. In the third step, the group law is stated explicitly by handling all possible summands. The fourth step presents the algorithms to be used for efficient point additions. In the fifth and final step, optimized software implementations of the proposed algorithms are presented in order to show that theoretical speedups of step four can be practically obtained. In each of the five steps, this thesis focuses on five forms of elliptic curves over finite fields of large characteristic. A list of these forms and their defining equations are given as follows: (a) Short Weierstrass form, y2 = x3 + ax + b, (b) Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1, (c) Twisted Hessian form, ax3 + y3 + 1 = dxy, (d) Twisted Edwards form, ax2 + y2 = 1 + dx2y2, (e) Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1, These forms are the most promising candidates for efficient computations and thus considered in this work. Nevertheless, the methods employed in this thesis are capable of handling arbitrary elliptic curves. From a high level point of view, the following outcomes are achieved in this thesis. - Related literature results are brought together and further revisited. For most of the cases several missed formulae, algorithms, and efficient point representations are discovered. - Analogies are made among all studied forms. For instance, it is shown that two sets of affine addition formulae are sufficient to cover all possible affine inputs as long as the output is also an affine point in any of these forms. In the literature, many special cases, especially interactions with points at infinity were omitted from discussion. This thesis handles all of the possibilities. - Several new point doubling/addition formulae and algorithms are introduced, which are more efficient than the existing alternatives in the literature. Most notably, the speed of extended Jacobi quartic, twisted Edwards, and Jacobi intersection forms are improved. New unified addition formulae are proposed for short Weierstrass form. New coordinate systems are studied for the first time. - An optimized implementation is developed using a combination of generic x86-64 assembly instructions and the plain C language. The practical advantages of the proposed algorithms are supported by computer experiments. - All formulae, presented in the body of this thesis, are checked for correctness using computer algebra scripts together with details on register allocations.

Faster pairing computations on curves with high-degree twists

Research on efficient pairing implementation has focussed on reducing the loop length and on using high-degree twists. Existence of twists of degree larger than 2 is a very restrictive criterion but luckily constructions for pairing-friendly elliptic curves with such twists exist. In fact, Freeman, Scott and Teske showed in their overview paper that often the best known methods of constructing pairing-friendly elliptic curves over fields of large prime characteristic produce curves that admit twists of degree 3, 4 or 6. A few papers have presented explicit formulas for the doubling and the addition step in Miller’s algorithm, but the optimizations were all done for the Tate pairing with degree-2 twists, so the main usage of the high- degree twists remained incompatible with more efficient formulas. In this paper we present efficient formulas for curves with twists of degree 2, 3, 4 or 6. These formulas are significantly faster than their predecessors. We show how these faster formulas can be applied to Tate and ate pairing variants, thereby speeding up all practical suggestions for efficient pairing implementations over fields of large characteristic.

Strengthening of circular hollow steel tubular sections using high modulus CFRP sheets

This paper describes the behaviour of very high strength (VHS) circular steel tubes strengthened by carbon fibre reinforced polymer (CFRP) and subjected to axial tension. A series of tests were conducted with different bond lengths and number of layers. The distribution of strain through the thickness of CFRP layers and along CFRP bond length was studied. The strain was found to generally decrease along the CFRP bond length far from the joint. The strain through the thickness of the CFRP layers was also found to decrease from bottom to top layer. The effective bond length for high modulus CFRP was established. Finally empirical models were developed to estimate the maximum load for a given CFRP arrangement.

Effects of dry density and grain size distribution on soil-water characteristic curves of sandy soils

The unsaturated soil mechanics is receiving increasing attention from researchers and as well as from practicing engineers. However, the requirement of sophisticated devices to measure unsaturated soil properties and time consumption have made the geotechnical engineers keep away from implication of the unsaturated soil mechanics for solving practical geotechnical problems. The application of the conventional laboratory devices with some modifications to measure unsaturated soil properties can promote the application of unsaturated soil mechanics into engineering practice. Therefore, in the present study, a conventional direct shear device was modified to measure unsaturated shear strength parameters at low suction. Specially, for the analysis of rain-induced slope failures, it is important to measure unsaturated shear strength parameters at low suction where slopes become unstable. The modified device was used to measure unsaturated shear strength of two silty soils at low suction values (0 ~ 50 kPa) that were achieved by following drying path and wetting path of soil-water characteristic curves (SWCCs) of soils. The results revealed that the internal friction angle of soil was not significantly affected by the suction and as well as the drying-wetting SWCCs of soils. The apparent cohesion of soil increased with a decreasing rate as the suction increased. Further, the apparent cohesion obtained from soil in wetting was greater than that obtained from soil in drying. Shear stress-shear displacement curves obtained from soil specimens subjected to the same net normal stress and different suction values showed a higher initial stiffness and a greater peak stress as the suction increased. In addition, it was observed that soil became more dilative with the increase of suction. A soil in wetting exhibited slightly higher peak shear stress and more contractive volume change behaviour than that of in drying at the same net normal stress and the suction.

Path planning, guidance and control for a UAV forced landing

A forced landing is an unscheduled event in flight requiring an emergency landing, and is most commonly attributed to engine failure, failure of avionics or adverse weather. Since the ability to conduct a successful forced landing is the primary indicator for safety in the aviation industry, automating this capability for unmanned aerial vehicles (UAVs) will help facilitate their integration into, and subsequent routine operations over civilian airspace. Currently, there is no commercial system available to perform this task; however, a team at the Australian Research Centre for Aerospace Automation (ARCAA) is working towards developing such an automated forced landing system. This system, codenamed Flight Guardian, will operate onboard the aircraft and use machine vision for site identification, artificial intelligence for data assessment and evaluation, and path planning, guidance and control techniques to actualize the landing. This thesis focuses on research specific to the third category, and presents the design, testing and evaluation of a Trajectory Generation and Guidance System (TGGS) that navigates the aircraft to land at a chosen site, following an engine failure. Firstly, two algorithms are developed that adapts manned aircraft forced landing techniques to suit the UAV planning problem. Algorithm 1 allows the UAV to select a route (from a library) based on a fixed glide range and the ambient wind conditions, while Algorithm 2 uses a series of adjustable waypoints to cater for changing winds. A comparison of both algorithms in over 200 simulated forced landings found that using Algorithm 2, twice as many landings were within the designated area, with an average lateral miss distance of 200 m at the aimpoint. These results present a baseline for further refinements to the planning algorithms. A significant contribution is seen in the design of the 3-D Dubins Curves planning algorithm, which extends the elementary concepts underlying 2-D Dubins paths to account for powerless flight in three dimensions. This has also resulted in the development of new methods in testing for path traversability, in losing excess altitude, and in the actual path formation to ensure aircraft stability. Simulations using this algorithm have demonstrated lateral and vertical miss distances of under 20 m at the approach point, in wind speeds of up to 9 m/s. This is greater than a tenfold improvement on Algorithm 2 and emulates the performance of manned, powered aircraft. The lateral guidance algorithm originally developed by Park, Deyst, and How (2007) is enhanced to include wind information in the guidance logic. A simple assumption is also made that reduces the complexity of the algorithm in following a circular path, yet without sacrificing performance. Finally, a specific method of supplying the correct turning direction is also used. Simulations have shown that this new algorithm, named the Enhanced Nonlinear Guidance (ENG) algorithm, performs much better in changing winds, with cross-track errors at the approach point within 2 m, compared to over 10 m using Park's algorithm. A fourth contribution is made in designing the Flight Path Following Guidance (FPFG) algorithm, which uses path angle calculations and the MacCready theory to determine the optimal speed to fly in winds. This algorithm also uses proportional integral- derivative (PID) gain schedules to finely tune the tracking accuracies, and has demonstrated in simulation vertical miss distances of under 2 m in changing winds. A fifth contribution is made in designing the Modified Proportional Navigation (MPN) algorithm, which uses principles from proportional navigation and the ENG algorithm, as well as methods specifically its own, to calculate the required pitch to fly. This algorithm is robust to wind changes, and is easily adaptable to any aircraft type. Tracking accuracies obtained with this algorithm are also comparable to those obtained using the FPFG algorithm. For all three preceding guidance algorithms, a novel method utilising the geometric and time relationship between aircraft and path is also employed to ensure that the aircraft is still able to track the desired path to completion in strong winds, while remaining stabilised. Finally, a derived contribution is made in modifying the 3-D Dubins Curves algorithm to suit helicopter flight dynamics. This modification allows a helicopter to autonomously track both stationary and moving targets in flight, and is highly advantageous for applications such as traffic surveillance, police pursuit, security or payload delivery. Each of these achievements serves to enhance the on-board autonomy and safety of a UAV, which in turn will help facilitate the integration of UAVs into civilian airspace for a wider appreciation of the good that they can provide. The automated UAV forced landing planning and guidance strategies presented in this thesis will allow the progression of this technology from the design and developmental stages, through to a prototype system that can demonstrate its effectiveness to the UAV research and operations community.

Radiation effects on natural convection laminar flow from a horizontal circular cylinder

The effect of radiation on natural convection flow from an isothermal circular cylinder has been investigated numerically in this study. The governing boundary layer equations of motion are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are reduced to convenient boundary layer equations, which are then solved numerically by two distinct efficient methods namely: (i) implicit finite differencemethod or the Keller-Box Method (KBM) and (ii) Straight Forward Finite Difference Method (SFFD). Numerical results are presented by velocity and temperature distribution of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin-friction coefficient and the local Nusselt number for a wide range of surface heating parameter and radiation-conduction parameter. Due to the effects of the radiation the skin-friction coefficients as well as the rate of heat transfer increased and consequently the momentum and thermal boundary layer thickness enhanced.

Attractive subfamilies of BLS curves for implementing high-security pairings

Barreto-Lynn-Scott (BLS) curves are a stand-out candidate for implementing high-security pairings. This paper shows that particular choices of the pairing-friendly search parameter give rise to four subfami- lies of BLS curves, all of which offer highly efficient and implementation- friendly pairing instantiations. Curves from these particular subfamilies are defined over prime fields that support very efficient towering options for the full extension field. The coefficients for a specific curve and its correct twist are automat-ically determined without any computational effort. The choice of an extremely sparse search parameter is immediately reflected by a highly efficient optimal ate Miller loop and final exponentiation. As a resource for implementors, we give a list with examples of implementation-friendly BLS curves through several high-security levels.

MHD natural convection flow from an isothermal horizontal circular cylinder under consideration of temperature dependent viscosity

Magnetohydrodynamic (MHD) natural convection laminar flow from an iso-thermal horizontal circular cylinder immersed in a fluid with viscosity proportional to a linear function of temperature will be discussed with numerical simulations. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equa-tions are reduced to convenient form, which are solved numerically by two very efficient methods, namely, (i) Implicit finite difference method together with Keller box scheme and (ii) Direct numerical scheme. Numerical results are presented by velocity and temperature distributions of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin-friction coefficient and the local Nusselt number for a wide range of magnetohydrodynamic parameter, viscosity-variation parameter and viscous dissipation parameter. MHD flow in this geometry with temperature dependent viscosity is absent in the literature. The results obtained from the numerical simulations have been veri-fied by two methodologies.

Group law computations on Jacobians of hyperelliptic Curves

We derive an explicit method of computing the composition step in Cantor’s algorithm for group operations on Jacobians of hyperelliptic curves. Our technique is inspired by the geometric description of the group law and applies to hyperelliptic curves of arbitrary genus. While Cantor’s general composition involves arithmetic in the polynomial ring F_q[x], the algorithm we propose solves a linear system over the base field which can be written down directly from the Mumford coordinates of the group elements. We apply this method to give more efficient formulas for group operations in both affine and projective coordinates for cryptographic systems based on Jacobians of genus 2 hyperelliptic curves in general form.

An exploration of affine group laws for elliptic curves

Several forms of elliptic curves are suggested for an efficient implementation of Elliptic Curve Cryptography. However, a complete description of the group law has not appeared in the literature for most popular forms. This paper presents group law in affine coordinates for three forms of elliptic curves. With the existence of the proposed affine group laws, stating the projective group law for each form becomes trivial. This work also describes an automated framework for studying elliptic curve group law, which is applied internally when preparing this work.

Role of kilometer-scale weak circular heterogeneities on upper crustal deformation patterns: Evidence from scaled analogue modeling and the Sudbury Basin, Canada

The Sudbury Basin is a non-cylindrical fold basin occupying the central portion of the Sudbury Impact Structure. The impact structure lends itself excellently to explore the structural evolution of continental crust containing a circular region of long-term weakness. In a series of scaled analogue experiments various model crustal configurations were shortened horizontally at a constant rate. In mechanically weakened crust, model basins formed that mimic several first-order structural characteristics of the Sudbury Basin: (1) asymmetric, non-cylindrical folding of the Basin, (2) structures indicating concentric shortening around lateral basin termini and (3) the presence of a zone of strain concentration near the hinge zones of model basins. Geometrically and kinematically this zone corresponds to the South Range Shear Zone of the Sudbury Basin. According to our experiments, this shear zone is a direct mechanical consequence of basin formation, rather than the result of thrusting following folding. Overall, the models highlight the structurally anomalous character of the Sudbury Basin within the Paleoproterozoic Eastern Penokean Orogen. In particular, our models suggest that the Basin formed by pure shear thickening of crust, whereas transpressive deformation prevailed elsewhere in the orogen. The model basin is deformed by thickening and non-cylindrical synformal buckling, while conjugate transpressive shear zones propagated away from its lateral tips. This is consistent with pure shear deformation of a weak circular inclusion in a strong matrix. The models suggest that the Sudbury Basin formed as a consequence of long-term weakening of the upper crust by meteorite impact.