Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focused recently on the development of numerical methods with good stability and order properties. These numerical implementations have been made with fixed stepsize, but there are many situations when a fixed stepsize is not appropriate. In the numerical solution of ordinary differential equations, much work has been carried out on developing robust implementation techniques using variable stepsize. It has been necessary, in the deterministic case, to consider the "best" choice for an initial stepsize, as well as developing effective strategies for stepsize control-the same, of course, must be carried out in the stochastic case. In this paper, proportional integral (PI) control is applied to a variable stepsize implementation of an embedded pair of stochastic Runge-Kutta methods used to obtain numerical solutions of nonstiff SDEs. For stiff SDEs, the embedded pair of the balanced Milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change. The extension of these stepsize controllers from a digital filter theory point of view via PI with derivative (PID) control will also be implemented. The implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy.

Approaches to access control under uncertainty

The ultimate goal of an access control system is to allocate each user the precise level of access they need to complete their job - no more and no less. This proves to be challenging in an organisational setting. On one hand employees need enough access to the organisation’s resources in order to perform their jobs and on the other hand more access will bring about an increasing risk of misuse - either intentionally, where an employee uses the access for personal benefit, or unintentionally, through carelessness or being socially engineered to give access to an adversary. This thesis investigates issues of existing approaches to access control in allocating optimal level of access to users and proposes solutions in the form of new access control models. These issues are most evident when uncertainty surrounding users’ access needs, incentive to misuse and accountability are considered, hence the title of the thesis. We first analyse access control in environments where the administrator is unable to identify the users who may need access to resources. To resolve this uncertainty an administrative model with delegation support is proposed. Further, a detailed technical enforcement mechanism is introduced to ensure delegated resources cannot be misused. Then we explicitly consider that users are self-interested and capable of misusing resources if they choose to. We propose a novel game theoretic access control model to reason about and influence the factors that may affect users’ incentive to misuse. Next we study access control in environments where neither users’ access needs can be predicted nor they can be held accountable for misuse. It is shown that by allocating budget to users, a virtual currency through which they can pay for the resources they deem necessary, the need for a precise pre-allocation of permissions can be relaxed. The budget also imposes an upper-bound on users’ ability to misuse. A generalised budget allocation function is proposed and it is shown that given the context information the optimal level of budget for users can always be numerically determined. Finally, Role Based Access Control (RBAC) model is analysed under the explicit assumption of administrators’ uncertainty about self-interested users’ access needs and their incentives to misuse. A novel Budget-oriented Role Based Access Control (B-RBAC) model is proposed. The new model introduces the notion of users’ behaviour into RBAC and provides means to influence users’ incentives. It is shown how RBAC policy can be used to individualise the cost of access to resources and also to determine users’ budget. The implementation overheads of B-RBAC is examined and several low-cost sub-models are proposed.

Critical discourse analysis and political economy of communication : understanding the new corporate order

This article uses critical discourse analysis to analyse material shifts in the political economy of communications. It examines texts of major corporations to describe four key changes in political economy: (1) the separation of ownership from control; (2) the separation of business from industry; (3) the separation of accountability from responsibility; and (4) the subjugation of ‘going concerns’ by overriding concerns. The authors argue that this amounts to a political economic shift from traditional concepts of ‘capitalism’ to a new ‘corporatism’ in which the relationships between public and private, state and individual interests have become redefined and obscured through new discourse strategies. They conclude that the present financial and regulatory ‘crisis’ cannot be adequately resolved without a new analytic framework for examining the relationships between corporation, discourse and political economy.

Compaction control of topography and fault network structure along strike-slip faults in sedimentary basins

Strike-slip faults commonly display structurally complex areas of positive or negative topography. Understanding the development of such areas has important implications for earthquake studies and hydrocarbon exploration. Previous workers identified the key factors controlling the occurrence of both topographic modes and the related structural styles. Kinematic and stress boundary conditions are of first-order relevance. Surface mass transport and material properties affect fault network structure. Experiments demonstrate that dilatancy can generate positive topography even under simple-shear boundary conditions. Here, we use physical models with sand to show that the degree of compaction of the deformed rocks alone can determine the type of topography and related surface fault network structure in simple-shear settings. In our experiments, volume changes of ∼5% are sufficient to generate localized uplift or subsidence. We discuss scalability of model volume changes and fault network structure and show that our model fault zones satisfy geometrical similarity with natural flower structures. Our results imply that compaction may be an important factor in the development of topography and fault network structure along strike-slip faults in sedimentary basins.

A novel numerical approximation for the space fractional advection-dispersion equation

In this paper, we consider a space fractional advection–dispersion equation. The equation is obtained from the standard advection–diffusion equation by replacing the first- and second-order space derivatives by the Riesz fractional derivatives of order β1 ∈ (0, 1) and β2 ∈ (1, 2], respectively. The fractional advection and dispersion terms are approximated by using two fractional centred difference schemes. A new weighted Riesz fractional finite-difference approximation scheme is proposed. When the weighting factor θ equals 12, a second-order accuracy scheme is obtained. The stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

The use of a Riesz fractional differential-based approach for texture enhancement in image processing

Abstract: Texture enhancement is an important component of image processing, with extensive application in science and engineering. The quality of medical images, quantified using the texture of the images, plays a significant role in the routine diagnosis performed by medical practitioners. Previously, image texture enhancement was performed using classical integral order differential mask operators. Recently, first order fractional differential operators were implemented to enhance images. Experiments conclude that the use of the fractional differential not only maintains the low frequency contour features in the smooth areas of the image, but also nonlinearly enhances edges and textures corresponding to high-frequency image components. However, whilst these methods perform well in particular cases, they are not routinely useful across all applications. To this end, we applied the second order Riesz fractional differential operator to improve upon existing approaches of texture enhancement. Compared with the classical integral order differential mask operators and other fractional differential operators, our new algorithms provide higher signal to noise values, which leads to superior image quality.

Numerical approximation for a variable-order nonlinear reaction–subdiffusion equation

Fractional reaction–subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction–subdiffusion equation. A numerical approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved numerical approximation. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.

Excursion guidance criteria to guide control of peak emission and exposure to airborne engineered particles

The overall aim of our research was to characterize airborne particles from selected nanotechnology processes and to utilize the data to develop and test quantitative particle concentration-based criteria that can be used to trigger an assessment of particle emission controls. We investigated particle number concentration (PNC), particle mass (PM) concentration, count median diameter (CMD), alveolar deposited surface area, elemental composition, and morphology from sampling of aerosols arising from six nanotechnology processes. These included fibrous and non-fibrous particles, including carbon nanotubes (CNTs). We adopted standard occupational hygiene principles in relation to controlling peak emission and exposures, as outlined by both Safe Work Australia, (1) and the American Conference of Governmental Industrial Hygienists (ACGIH®). (2) The results from the study were used to analyses peak and 30-minute averaged particle number and mass concentration values measured during the operation of the nanotechnology processes. Analysis of peak (highest value recorded) and 30-minute averaged particle number and mass concentration values revealed: Peak PNC20–1000 nm emitted from the nanotechnology processes were up to three orders of magnitude greater than the local background particle concentration (LBPC). Peak PNC300–3000 nm was up to an order of magnitude greater, and PM2.5 concentrations up to four orders of magnitude greater. For three of these nanotechnology processes, the 30-minute average particle number and mass concentrations were also significantly different from the LBPC (p-value < 0.001). We propose emission or exposure controls may need to be implemented or modified, or further assessment of the controls be undertaken, if concentrations exceed three times the LBPC, which is also used as the local particle reference value, for more than a total of 30 minutes during a workday, and/or if a single short-term measurement exceeds five times the local particle reference value. The use of these quantitative criteria, which we are terming the universal excursion guidance criteria, will account for the typical variation in LBPC and inaccuracy of instruments, while precautionary enough to highlight peaks in particle concentration likely to be associated with particle emission from the nanotechnology process. Recommendations on when to utilize local excursion guidance criteria are also provided.

Privacy oriented access control for electronic health records

Information privacy is a critical success/failure factor in information technology supported healthcare (eHealth). eHealth systems utilise electronic health records (EHR) as the main source of information, thus, implementing appropriate privacy preserving methods for EHRs is vital for the proliferation of eHealth. Whilst information privacy may be a fundamental requirement for eHealth consumers, healthcare professionals demand non-restricted access to patient information for improved healthcare delivery, thus, creating an environment where stakeholder requirements are contradictory. Therefore, there is a need to achieve an appropriate balance of requirements in order to build successful eHealth systems. Towards achieving this balance, a new genre of eHealth systems called Accountable-eHealth (AeH) systems has been proposed. In this paper, an access control model for EHRs is presented that can be utilised by AeH systems to create information usage policies that fulfil both stakeholders’ requirements. These policies are used to accomplish the aforementioned balance of requirements creating a satisfactory eHealth environment for all stakeholders. The access control model is validated using a Web based prototype as a proof of concept.

The velocity synchronous discrete Fourier transform for order tracking in the field of rotating machinery

Diagnostics of rotating machinery has developed significantly in the last decades, and industrial applications are spreading in different sectors. Most applications are characterized by varying velocities of the shaft and in many cases transients are the most critical to monitor. In these variable speed conditions, fault symptoms are clearer in the angular/order domains than in the common time/frequency ones. In the past, this issue was often solved by synchronously sampling data by means of phase locked circuits governing the acquisition; however, thanks to the spread of cheap and powerful microprocessors, this procedure is nowadays rarer; sampling is usually performed at constant time intervals, and the conversion to the order domain is made by means of digital signal processing techniques. In the last decades different algorithms have been proposed for the extraction of an order spectrum from a signal sampled asynchronously with respect to the shaft rotational velocity; many of them (the so called computed order tracking family) use interpolation techniques to resample the signal at constant angular increments, followed by a common discrete Fourier transform to shift from the angular domain to the order domain. A less exploited family of techniques shifts directly from the time domain to the order spectrum, by means of modified Fourier transforms. This paper proposes a new transform, named velocity synchronous discrete Fourier transform, which takes advantage of the instantaneous velocity to improve the quality of its result, reaching performances that can challenge the computed order tracking.

Testing second order cyclostationarity in the squared envelope spectrum of non-white vibration signals

Cyclostationary models for the diagnostic signals measured on faulty rotating machineries have proved to be successful in many laboratory tests and industrial applications. The squared envelope spectrum has been pointed out as the most efficient indicator for the assessment of second order cyclostationary symptoms of damages, which are typical, for instance, of rolling element bearing faults. In an attempt to foster the spread of rotating machinery diagnostics, the current trend in the field is to reach higher levels of automation of the condition monitoring systems. For this purpose, statistical tests for the presence of cyclostationarity have been proposed during the last years. The statistical thresholds proposed in the past for the identification of cyclostationary components have been obtained under the hypothesis of having a white noise signal when the component is healthy. This need, coupled with the non-white nature of the real signals implies the necessity of pre-whitening or filtering the signal in optimal narrow-bands, increasing the complexity of the algorithm and the risk of losing diagnostic information or introducing biases on the result. In this paper, the authors introduce an original analytical derivation of the statistical tests for cyclostationarity in the squared envelope spectrum, dropping the hypothesis of white noise from the beginning. The effect of first order and second order cyclostationary components on the distribution of the squared envelope spectrum will be quantified and the effectiveness of the newly proposed threshold verified, providing a sound theoretical basis and a practical starting point for efficient automated diagnostics of machine components such as rolling element bearings. The analytical results will be verified by means of numerical simulations and by using experimental vibration data of rolling element bearings.

Order tracking for discrete-random separation in variable speed conditions

The transmission path from the excitation to the measured vibration on the surface of a mechanical system introduces a distortion both in amplitude and in phase. Moreover, in variable speed conditions, the amplification/attenuation and the phase shift, due to the transfer function of the mechanical system, varies in time. This phenomenon reduces the effectiveness of the traditionally tachometer based order tracking, compromising the results of a discrete-random separation performed by a synchronous averaging. In this paper, for the first time, the extent of the distortion is identified both in the time domain and in the order spectrum of the signal, highlighting the consequences for the diagnostics of rotating machinery. A particular focus is given to gears, providing some indications on how to take advantage of the quantification of the disturbance to better tune the techniques developed for the compensation of the distortion. The full theoretical analysis is presented and the results are applied to an experimental case.

Second-order elastic finite element analysis of steel structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included. The accuracy and efficiency of the technique is verified by comparisons with a number of plane and spatial structures, whose structural response has been reported in independent studies.

Motion planning and stochastic control with experimental validation on a planetary rover

Motion planning for planetary rovers must consider control uncertainty in order to maintain the safety of the platform during navigation. Modelling such control uncertainty is difficult due to the complex interaction between the platform and its environment. In this paper, we propose a motion planning approach whereby the outcome of control actions is learned from experience and represented statistically using a Gaussian process regression model. This model is used to construct a control policy for navigation to a goal region in a terrain map built using an on-board RGB-D camera. The terrain includes flat ground, small rocks, and non-traversable rocks. We report the results of 200 simulated and 35 experimental trials that validate the approach and demonstrate the value of considering control uncertainty in maintaining platform safety.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.